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PREFACE.
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~ THE present work aims at embracing a full course of Logie,
both Formal and Inductive.
In an introductory chapter, are set forth such doctrines
of psychology as have a bearing on Logic, the nature of
knowledge in general, and the classification of the sciences ;
the intention being to avoid doctrinal digressions in the
course of the work. Although preparatory to the under-
standing of what follows, this chapter may be passed over
lightly on a first perusal of the work.
The part on Deduction contains the usual doctrines of
the Syllogism, with the additions of Hamilton, and a full
abstract of the novel and elaborate schemes of De Morgan
and Boole.
The Inductive portion comprises the methods of induc-
tive research, and all those collateral topics brought for-
ward by Mr. Mill, as part of the problem of Induction ;
various modifications being made in the manner of state-
ment, the order of topics, and the proportion of the hand-
ling. The greatest innovation is the rendering of Cause
by the new doctrine called the Conservation, Persistence,
or Correlation of Force.
Mr. Mill’s view of the relation of Deduction and Indue-
tion is fully adopted, as being the solution of the otherwise
inextricable puzzle of the syllogism, and the means of
giving unity and comprehensiveness to Logic.
iv PREFACE,
A separate division is appropriated to the Logie of the
Sciences, with the view of still further exemplifying the
logical methods, and of throwing light upon various points
in the sciences themselves. The review comprises all the
theoretical or fundamental sciences—Mathematies, Physics,
Chemistry, Biology, and Psychology ; the sciences of Classi-
fication, or Natural History ; and two leading Practical
sciences—Politics and Medicine.
The department of Definition is, for the first time,
brought, under, a methodical scheme, and rendered of co-
ordinate value with Deduction and Induction, as a branch
of logical method. The modes of defining, as a generalizing
process, are given under two canons, a positive and a
negative ; and attention is called to the chief obstacles—
uncertainty in the denotation of words, and the gradual
transition of qualities into their opposites,
In discussing Fallacies, I have canvassed the grounds
for the usual practice of detaching the violations of logical
rules from, the exposition of the rules themselves; and
have endeavoured to show that the only portions of the
subject proper to reserve for separate handling, are the
Fallacious tendencies of the Mind, and Fallacies of Con-
fusion, As these are subjects of great moment, and admit
of wide illustration, both are considered with some minute-
ness.
None of the controversies in the subject are overlooked ;
but it has been deemed advisable to separate them from
the main body of the work. In an Appendix, are em-
braced the various Classifications of the Sciences, the Pro-
vince of Logic, the Classification of Nameable Things, the
Universal Postulate, the meanings of Analysis and Syn-
thesis, the Theories of Induction, the Art of Discovery,
and the maxims of Historical Evidence.
‘T'o adapt the work to an elementary course of Logic,
PREFACE, Vv
the parts to be omitted are the Additions to the Syllogism,
the Logic of the Sciences, and the chapters in the Appen-
dix. The junior student, or the candidate for a pass
examination, without attempting to master or commit these
reserved portions, might yet find their perusal of service
in understanding the rest.
There is a general conviction that the utility of the
purely Formal Logic is but small; and that the rules of
Induction should be exemplified even in the most limited
. course of logical discipline. I would suggest that an in-
creased attention should be bestowed on Definition and
Classification, with reference both to scientific study and
to matters not ordinarily called scientific.
As I may be open to the charge of presumption in
appearing as a rival to Mr. Mill, I will venture the remark,
that an attempt to carry out still more thoroughly the
enlarged scheme of logical method, seems the one thing
hitherto wanting to the success of his great work.
ABERDEEN, March, 1870
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INTRODUCTION . : ; ‘ : ‘ y G ‘ ‘
BOOK 1.
NAMES, NOTIONS, AND PROPOSITIONS.
P.
a Names or Terms i ; : : ¥
IL. Classes, Notions, or Concepts
IIL. Propositions . ° 7
BOOK II.
DEDUCTION.
I. The Syllogism .
IL. Recent Additions to the Syllogism — 3
Ill. Functions and Value of the Syllogism
IV. Trains of Reasoning and Deductive Sciences ,
V. Demonstration—Axioms—Necessary Truth : :
BOOK III.
INDUOTION.
‘Meaning and Scope of Induction
. The Ground of pe aay of N ature—Laws of Na-
ture ‘
III. Induction of Coexistence
V. Law of Causation
. Elimination of Cause and Effect—Observation and Experiment
VL The Experimental Methods ‘ d j :
VU. Examples of the Methods
VIII. Frustration of the Methods
IX. Chance, and its Elimination ‘ ‘
X. Induction aided by Deduction .
XI. Secondary Laws—Empirical and Derivative
. Explanation of Nature . ;
XIfl. Hypotheses
XIV. Approximate Generalizations and Probable "Evidence :
XV. Analogy : ‘ : °
XVI. Credibility and Incredibility ; ; ; ‘
PAGE
42
43
133
178
207
214
219
231
238
241
245
271
279
297
306
814
825
332
346
358
365
370
378
Vili CONTENTS.
BOOK IV.
DEFINITION.
CHAP.
I. Canons of Definition . :
II. General Names > :
III Classification ; . °
BOOK V.
LOGIC OF THE SCIENCES.
I, Logic of Mathematics . ;
II. Logic of Physics. : °
Ill. Logic of Chemistry
IV. Logic of Biology .
V. Logic of Psychology
VI. Sciences of Classification .
VII. Logic of Practice
VIII. Logic of Politics
IX. Logic of Medicine
BOOK VI.
FALLACIES.
I. Mill’s Classification of Fallacies
II. The Position of Fallacies .
Ill. Fallacious Tendencies of the Mind .
IV. Fallacies of Confusion . :
V. Logical Fallacies. ‘ .
APPENDIX.
A.—Classifications of the Sciences
B.—The Province of Logic
C.—Enumeration of Things
D.—The Universal Postulate .
EK —Aristotelian and Scholastic Fallacies
F.—Analysis and Synthesis
G.—Growth of the Logic of Induction
H.—Art of Discovery x : ‘
I.—Historical Evidence : :
K.—Explanation of Some Logical Terms .
PaGE
384
401
414 .
429
451
472
488
505
522
545
547
575
599
608
606
616
625
627
689
652
664
673
687
697
707
715
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INTRODUCTION.
1. Loaic may be briefly described as a body of doctrines
and rules having reference to Truth.
The functions of Logic will be afterwards given with par-
ticularity and precision. For the present we remark that it
concerns the Truth of things, no matter what the subject be.
While in one aspect it is theoretical, in the prevailing aim it is
practical.
In this introductory chapter we are to consider the following
topics.
_ (1) The Psychological data or groundwork of Logic.
(2) The First Principles of Logic.
(3) The Classification of the Sciences.
(4) The different views of the Province of Logie.
(5) The Divisions of Logic.
PSYCHOLOGICAL DATA OF LOGIC.
2. Logic, under every view, involves frequent references
to the laws and workings of the mind; and the more so
the more we extend its province.
In the common Logic of the Schools, the Syllogistic or
Deductive Logic, explanations are usually given of the intel-
lectual processes named Perception or Simple Apprehension,
Abstraction or the formation of concepts or notions, Judgment
or the laying down of propositions, and Reasoning or the
drawing of inferences or conclusions from premises.
In the Inductive Logic, an enquiry is instituted into our
2 PSYCHOLOGICAL DATA OF LOGIC.
idea of Cause; in connection with which, notice is taken of
the controversy respecting the Origin of our Knowledge in
the Mind, namely, as to whether it be wholly derived from
experience, or whether any portion of it (as Cause, the Axioms
of Mathematics, &c.) be intuitive, instinctive, or innate.
It is considered a part of Logic to set forth the theory and
the limits of the Explanation of phenomena; for which pur-
pose a reference must be made to the structure of the mental
powers. This was the avowed aim of Locke, in his Essay on
the Understanding, one of the greatest contributions to the
science of mind.
Under such circumstances, the most satisfactory course ap-
pears to be to bring forward and expound, once for all, at the
commencement, whatever portions of Psychology are in any
way implicated with the rules and methods of Logic. Butthe
exposition must necessarily be brief. |
Discrimination or Relativity.
3. In order to make us feel, there must be a change of
impression ; whence all feeling is two-sided. This is the
law of Discrimination or Relativity. ,
Observation shows that unbroken continuance of the same
impression is attended with unconsciousness; and that the
greater the change or transition, the greater ths consciousness.
An unvarying touch, or a monotonous sound ceases to be felt ;
in an even temperature, we lose all consciousness of heat or
cold. Still more convincing are the instances showing that
changes affect us in proportion to their greatness and sudden-
ness. Abrupt transitions are stimulating and exciting ; the
first exposure to sun-light after being in the dark, the first
mouthful of water when we are thirsty, the moment of transi-
tion from poverty to wealth—are accompanied with the highest
degree of feeling ; after which there is a gradual subsidence of
the excitement. |
Hence the fact of our being under some agency of sense or
feeling does not of itself attest our mode of feeling; there
must farther be given the condition immediately, and for
some time previous. That a man is the possessor of a thou-
sand pounds to-day is not a sufficient criterion of his feel-
ings as regards worldly abundance. If a year ago, the same
man possessed nothing, he feels in a way totally different from
bim that has fallen to that amount from a fortune of ten thou-
sand pounds.
DISCRIMINATION OR RELATIVITY. 3
_ 4. As regards Knowledge, there must likewise be a tran-
sition, or change ; and the act of knowing includes always
two things.
When we consider our mental states as Ae: the
same law holds. We know heat by a transition from cold;
light, by passing out of the dark; up, by contrast to down.
There is no such thing as an absolute knowledge of any one
property ; we could not know ‘motion,’ if we were debarred
from knowing ‘rest.’ Noonecould understand the meaning
ofa straight line, without being shown a line not straight, a
bent or crooked line,
We may attend more to one member of the couple than to
the other. In this way only can we think of an individual
property. We may be thinking more of the heat than of the
cold, of the straight than of the crooked; the one may be the
explicit, the other the implicit subject of our thoughts. As our
transitions may be in two directions—from heat to cold, and
from cold to heat—we have a difference of feeling in the two
cases. We are more conscious of heat, when passing to a
higher temperature, and of cold when passing toa lower. The
state we have passed to is our explicit consciousness, the state
we have passed from is our implicit consciousness.
The principle of Relativity has wide andimportant bearings
in Logic. It will appear in Naming; in Definition; in Pro-
positions or Affirmation. It will be appealed to in rectifying
a large class of Fallacies—the fallacies of the suppressed rela-
tive, or of the Absolute.
Agreement or Sinvilarity.
5, When an impression is repeated, after an interval, we
are affected with a new and peculiar consciousness, the
shock or consciousness of Agreement in difference.
We see a candle flame; it is withdrawn; after a time, it is
brought back. We have now, in addition to the luminous
effect of the presentation, a shock or feeling of agreement,
identity, repetition ; a state no less concerned in our intellec-
tual operations than the shock of difference or discrimination.
We are constantly experiencing the repetition of former im-
pressions, in circumstances more or less altered, and we are
affected with a greater shock according to the greatness of
the alteration. The degree or intensity of the consciousness
of Agreement may vary through a wide range, from the slight
4 PSYCHOLOGICAL DATA OF LOGIC.
recognition of a new day to the flash of a great discovery of
identification, like Newton’s assimilating the fall of a stone to
the deflection of the moon towards the earth,
Knowledge as conjoining Difference and Agreement.
6. Our knowledge of a fact is the Discrimination of it
from differing facts, and the Agreement or identification of
it with agreeing facts.
The only other element in knowledge is the Retentive
power of the mind, or memory, which is implied in these
two powers.
Our knowledge of heat is (1) a series of shocks of Difference
or discrimination between heat and cold, and (2) the Agree-
ments or repetitions of the same shocks under change of
circumstances. z
Besides the transition heat-cold, which is the primary cog-
nition of heat, we make other transitions into other sensations. -
We have occasion to pass from a sensation of warmth toa
sensation of light, and the difference of the two brings out a
new discriminative consciousness, and gives a new meaning to
warmth, and also to light; heat is no longer simply the con-
trast of cold, it is also the contrast of the feeling of luminosity.
So, every new sensation that we pass to from heat, with con- —
sciousness of difference, gives a new negative meaning to heat;
it isnot taste, nor smell, nor hardness, nor sound,
Again, our mental impression, knowledge, or idea of a
shilling, is the sum of all its differences from the things that
we have contrasted it with, and of all its agreements with the
things that we have compared it to. We call it round; sig-
nifying that it differs from things called square, oblong, oval,
&c.; that it agrees with other things called round—that we
have been frequently struck with the identity of this figure in
many different combinations,
So with the weight of the shilling. We know weight by
difference, and by agreement ; we recognise a shilling as heavier
than some things, lighter than others; which is difference; and
as identical with a third class, which is agreement.
The knowledge, idea, or recollection of any concrete
object, is thus the aggregate of those mental exercises of
Discrimination and Agreement, fixed and retained in the
mind by the power called retentiveness, or memory ; by which
power of retention we are able to discriminate and compare
VARIETIES OF KNOWLEDGE. 5
present impressions with past, and to accumulate a vast stock
of mental effects or deposits, called ideas, knowledge, thought.
Knowledge is of two kinds, called Object and Subject.
7. The knowledge ofa shilling, of a house, of a mountain, of
a star, is said to be objective; it relates to the object, or the
outer, world. The knowledge of a pleasure or a pain, or of
the succession of ideas in the mind, relates to the subject, or
the internal, world. We have a great accumulation of both
kinds of knowledge ; some minds abounding more in one, some
more in the other.
Knowledge as (1) Individual and Conerete, or (2) General
and Abstract.
8. The knowledge of a table in a room, at a particular time, is
in the highest degree individual or concrete. The knowledge
relating to any table, at any time, is said to be general and
abstract. By the mental power of Agreement or Similarity,
we bring to mind different individual tables, attending to their
points of community, in spite of many diversities. We affirm
properties common to them all, This is the generalising
power of the mind. It is one of the most signal functions of
our intelligence, and is purely an outgoing of the fundamental
power named Agreement, or Similarity.
Dispute as to the Character of General Knowledge, called
also Abstract Ideas,
9. In General Knowledge, strictly so called, there is
nothing but the fact of agreement among a number of
separate particulars; which agreement is signified by the
use of a common name.
A general name, as ‘circle,’ ‘round,’ ‘animal,’ ‘ wise,’ is
applied to things agreeing in a certain respect, while differing
in other respects, to signify their agreement.
It has been supposed that the points of community of
agreeing things exist apart from the things. This view is
called Realism.
It was believed by a certain school of philosophers, deriving
from Plato, that there exists, in the universe of being, a Circle
in general, or circular Form without substance, size, or colour;
that in like manner, there are archetypal Forms of Man, of
6 PSYCHOLOGICAL DATA OF LOGIC.
Just, of Good, &c. After a severe controversy, which raged
in the scholastic period, this view was abandoned.
Realism is still exemplified, however, in the doctrine of an
Independent External World, and also in the doctrine of the
separate existence of Mind or Soul. In strictness, the External
World is known only as perceived by our senses; Mind is
known only as conjoined with body. |
Another mode of regarding the fact of community in
diversity, is to suppose that the mind can represent to it-
self in a notion, the points of agreement by themselves,
and can leave entirely out of sight the points of differ-
ence. Thisis Conceptualism. |
Although there is no pure circle in existence, we are sup-
posed able to think of the round figure to the exclusion of the
other properties of the individual circles—material, colour, size.
This too is incorrect. It exaggerates the mind’s power of
giving a preference of attention to some of the attributes of a
concrete object, as a wheel, or a shilling. We may think
much of the roundness, and little of the size; but we cannot
think of the roundness, without thinking of some size or
colour.
The usual mode of thinking an abstraction, or of concen-
trating the mind upon one property, is to think alternately of
the different objects possessing the property. We can best —
think of roundness, by having in view various round things,
differing in material, size, colour, &c. The effect of the mind’s
passing and repassing between the individuals, is that the
roundness starts into great prominence, and the other proper-
ties fall into the background, without, however, being extin-
guished. The great fact constantly underlying Abstraction,
is the mustering of individuals agreeing in the midst of differ-
ence.
We are in the habit of using single individuals to typify a
multitude; as in the diagrams of Euclid. We do not, in
geometrical reasoning, think of a great number of circular
things ; we can study the circle upon one figure, provided we
take care to affirm nothing as to size, colour, or material,
which facts are inseparable even from the barest diagram.
When the logician speaks of a Notion, Concept, or Abstract
Idea, he must not be understood as implying anything be-
yond the agreement of a certain number of things in a given
manner.
THE INDIVIDUAL AND THE GENERAL. 7
Our idea of an Individual a conflux of Generalities.
10. What we term the Perception of an individual, as a
given tree, is not simply a sense impression of the moment,
it is an aggregation of many generalized impressions.
When we look at a tree, we are affected by a great number
of different influences—colours, shape, size, &c. Now, every
distinguishable impression recalls the previous stamps of the
same, by Agreement or Similarity ; and the idea of the tree is
not an original sense presentation, but a compound of this
with old presentations. Every feature of the tree suggests a
classification upon that point; the green and brown colours
are felt only as the collective impressions of those shades of
colour.
In our minds, therefore, the Concrete and the Abstract are
inextricably blended. Of a pure concrete, not also resolved
into classifications or abstractions, we have no experience.
Our knowledge proceeds in both ways at once; individuals
giving generals and generals re-acting upon individuals. If
there was one concrete thing in the world, having no property
in common with any other known concrete thing, we might,
by gazing upon that, and comparing it with ftself, possess an
idea of a concrete individuality, where no generality was im-
plicated ; but sucha concrete would be very different from any
concrete known to us. We are not in the position to imagine
such an idea.
11. The speciality of a concrete Individual is that itis a
definite aggregate not confounded with other individuals.
The number of general properties pointing to the individual
must be such as to give it a definite or special character,
instead of leaving it indefinite or common. The tree that I
now look at, is individualized by a concurrence of properties
never realized before ; or if not by such concurrence itself, by
its surroundings, and all the circumstances of time and place,
accompanying its perception. A _ shilling is individualized
by its adjuncts of place and time.
12. The distinction between Presentation and Represent-
ation, is the distinction between a definite conflux of
generalities, and an indefinite conflux.
A shilling in the hand is a Presentation. A shilling as a
general coin of the realm is Representative; it is common to
8 PSYCHOLOGICAL DATA OF LOGIC.
many places and times and circumstances, and not bound
down to one definite situation and one definite moment.
13. The names of Individuals usually correspond to their
character as a conflux of generals.
In a few instances, we have names that bear no reference to
generalities, as when a certain individual man is named—Coesar.
These are proper, or meaningless names; the bare symbols
for separating the thing from other things. But in the vast
majority of instances, the name follows the manner of conceiy-
ing the thing—that is, by specifying the concurring generalities.
A large gothic building; a stout man of forty; a cubical
crystal, with a certain hardness and specific gravity, found in
a certain formation :—are examples of designations in strict
accordance with the ideas of the things.
Philology confirms this. The primitive names of such con-
crete objects as sun, moon, father, mother, have all a gene-
ralized meaning; ‘moon ’ is the measurer, ‘father’ is the
feeder, and soon. There seems to be no possibility of con-
ceiving individuals without classifying and generalizing at the
same time ; and the one name means both an individual and
a general.
The intellectual function of Agreement, or Similarity, as the
basis of Reasoning.
14. Reasoning, in every form, supposes the operation of
Similarity—the assimilating of one thing to some other
thing. Mi
The most general type of Reasoning is to infer from one
particular fact to another particular fact of the same kind ;
the likeness being both the means of suggestion, and the jus-
tification of the transfer of properties. We throw a stone into
a pool; it makes a splashing noise, sinks to the bottom, and
diffuses a series of waves from the point where it fell. We
infer or reason, or presume, that another stone thrown into
the same pool will be followed by the same series of effects;
and we may extend the inference to another pool, or to any
mass of liquid. ‘This is to infer, to reason, to transcend our
actual experience, to make an affirmation respecting the un-
known. Now, the mind is prompted by the likeness of the
cases to take this step in advance, to anticipate what is to
happen. One would not infer that a handful of dried leaves
KINDS OF REASONING. 9
would produce all the consequences of throwing the stone;
we never expect either through our instinctive belief, or
through our experience of the world, that the same effects
will arise under different circumstances.
This mode of Reasoning is in constant use, and extends to the
animal intelligence. An animal accustomed to find a shelter
under a bush, reasons from one bush to another bush, being
moved solely by the resemblance of the second to the first. A
dog is deterred by the menacing movement of a strange per-
son wielding a strange stick: the partial resemblance to
former experiences is enough to rouse its fears.
A second mode of Reasoning is when by the help of general
language, we infer from one or a few cases, to all cases of the
kind; as when we conclude, after a certain number of trials,
that all stones sink in water, that all matter of vegetable origin
is combustible, that all animals are generated from other
animals. This is Induction, in the more technical sense—the
inferring not from particulars to other particulars, but from
particulars to universals. The mental process is still Simi-
larity, or the process whereby one thing suggests other
resembling things. Itis by similarity that we assemble in
the mind all kindred facts that have ever come under our
knowledge; we then are able to compare the points of agree-
ment, with a view to an accurate general statement, in other
words, an Inductive proposition.
The third kind of Reasoning, called Deductive, is also based
on the tracing of resemblance. When we infer that, because
all stones sink in water, a certain body will sink (which is
Deduction), it is because that body resembles the rest, or has
the points of community indicated by the general word
‘stone.’ When we have mastered a general principle, it is
by similarity that we discover cases to apply it to, and so ex-
tend our knowledge deductively.
Origin. of owr Knowledge in Haperience.
15. Our knowledge of the world, both of matter and of
mind, is the result of our conscious Experience.
As regards the Material, outer, or object world, we gain
_ our knowledge through the ordinary Senses, coupled with
our Movements, under the three laws of our INTELLIGENCE—
viz., Difference, Agreement, and Retentiveness. We see, hear,
touch, taste, smell; we have our active energies aroused by
things resisting, by movements, and by things extended; we
10 PSYCHOLOGICAL DATA OF LOGIC.
discriminate and identify impressions ; we acquire permanent
recollections, and associate things presented in combination ;
and, by all these processes (exemplified at full length in Mental
Science, or Psychology) we lay up our stock of imagery,
ideas, or thoughts, of the world of sensible experience,
As regards the Mind, or the knowledge of our inner life
the senses do not avail us. We are directly and immediately
conscious of our feelings, thoughts, and volitions, and acquire
a store of permanent recollections of these also. We remem-
ber our different pleasures and pains, and the order of their
occurrence; we learn not merely things, but our ideas of
things, und the laws of the rise and succession of these ideas.
Thus, it is a fact of our mental or subjective life, that we
easily recall to mind whatever strongly engaged our attention
in the reality.
16. It has been alleged that some parts of our knowledge,
instead of being the result of experience, like the greater
portion, are intuztive or inherent to the mind, apart from
the operation of the senses upon actual things, or the par-
ticular phenomena of the subjective consciousness. |
At different stages in the progress of Philosophy, there have
been given different lists of intuitive, or &@ priort elements of
knowledge. At the present day the controversy turns chiefly
on these four notions—Time, Space, Substance, Cause.
It is maintained that there is in these notions something
that experience could not give; so that some different origin
must be sought for them.
On the other side, the supporters of the Experience theory
hold that the Moving energies, with the Senses and Self-Con-
sciousness, aided by the intellectual functions, can account for
all these notions,
For example, True is an abstraction: and, like all other
abstractions, is, properly speaking, a certain mode of likeness
among individual things or feelings of the mind. All our
experiences, whether object or subject, are regarded by us as
more or less enduring ; the attribute of Time is the assimilation
or classification of enduring states, as enduring. Apart from
these actual experiences of differences and agreements of
enduring things, there can be no such thing as Time, unless
on the exploded doctrine of Realism, nor any self-subsisting
notion of Time, unless on the erroneous theory of Conceptual-
ism. In the absence of objects and states continuing or
enduring, an intuition of Time is a self-contradiction ; in the
ALLEGED INTUITIVE KNOWLEDGE. 11
presence of such experiences of enduring things, discriminated
and compared on the point of endurance, we cannot but have
an idea of Time.
Next as-to Spacr, or Extension, the fact common to all
Matter, and not pertaining to mind. Extension belongs both
to solid matter, and to the intervals between the masses of
solid matter, which intervals are measured by the same
sensibilities, namely, the muscular feelings of motion, sup-
ported by the passive sensations.
The @ priort philosophers allege that Space comes from no
experience, but is already inherent in the mind before any-
thing is perceived; being the condition of our perceiving
things external.
In opposition to this view, it is contended that Space in
the abstract is merely the community or similarity of extended
bodies, and of the intervals between them, commonly called
empty space. We compare all those things on this particular
point of agreement; we occasionally think of them under this
comparison ; aud in so doing we are thinking of Space. This
is the only view compatible with Nominalism. An innate
form of Space is a species of Conceptualism.
The pure intuition of Space is said to be the source of our
knowledge and belief of the Axioms of Geometry, this being
held to have a character that no experience can explain. In
the case of these Axioms, the a priori revelation takes the
form of Principles, and not of mere Notions; but the fact is
the same, although differently viewed. ‘That two straight
lines cannot enclose a space ;’ ‘that things equal to the same
thing are equal to one another:’ are held by those that
contend for an intuition of space, to be intuitive.
The idea of Cause is included among the alleged intuitions.
It may be expressed either as a mere Notion or as a
Principle, namely, ‘ that every effect must have a cause.’ An
equivalent proposition is, ‘that nature is uniform or that
what has been will be.’ The contention is, that while, by
experience, we might become aware that particular effects
follow the law of Cause, or of Uniformity, we could not from
experience know that every effect has and must have a cause,
that what has been will always be.
The idea of Supstance means that, underlying all the
phenomenon or appearances of Matter and of Mind, there is
an unknown or unknowable substratum, called Substance,
Noumenon, Permanent Existence. This idea we cannot pos-
sibly obtain from experience ; the very statement of it, shows
12 PSYCHOLUGICAL DATA OF LOGIC.
that it passes beyond experience; yet some philosophers con-
tend that we are obliged to assume and believe in it.
As applied to Mind, Substance is another name for Personal
Identity, or the supposed continuity of each one’s mental
existence—the canvass that receives and holds together all the
feelings, thoughts, volitions, that make up the stream of our
conscious life,
According to the counter doctrine on this head, the notion
of Substance is fictitious, incompetent, and unnecessary. The
real meaning of Substance, as applied to matter, is the point
of community of all material bodies, the most highly general-
ized fact respecting them ; otherwise expressed by Resistance,
Inertia, Momentum, the Mechanical property of matter. The
meaning of Substance as applied to Mind is the most highly
generalized property or properties of mind—the facts wherein
all minds agree on comparison, and which caused them to
receive the common designation Mind, as opposed to not-mind,
or matter. These generalized points of community are
Feeling, Volition, and Intellect, the three facts attaching in
various degrees to whatever is accounted Mind. |
The nature of Belief as applied to the controversy respect-
ing the origin of Knowledge.
17. There is a natural tendency to believe much more
than we have any experience of.
The primitive disposition of the mind as regards belief is"
to suppose that whatever is will continue, that what exists
here and now, exists everywhere and at all times. This in-
born credulity is checked and abridged by our experience ;
we soon discover that we have been assuming too much; and
by degrees we abate our confidence and adapt our views to
the reality of things.
The following are common examples of the tendency. Be-
fore experience, we believe that as we feel now, we shall
always feel; that other people feel as we do; that what hap-
pens to us happens to all; that whatever any one tells us is
true. By the natural impetuosity of the mind, we form these
assurances ; experience did not create them, but rather mode-
rates and checks them.
That we should treat any partial experience as universal,
being thus a consequence of blind .instinctive forwardness, is
no proof of what really happens in nature. As we are so liable
to extend our assertions beyond the facts, we should be par-
BELIEF PASSES BEYOND EXPERIENCE. 13
ticularly on our guard against universal declarations, This is
one of the weaknesses of human nature, and a leading source
of fallacy and error.
To make the application to the particular case of causation.
We are very ready to fall into statements as to the universality
of cause and effect; but so we do with many other things,
where we find ourselves utterly wrong. The real evidence of
the Law of Causation must be something different from our
being disposed to believe it.
Nothing can be affirmed as true, except on the warrant of
expervence.
18. As the natural disposition to believe carries us into
falsehood, we must, notwithstanding our instincts, cling to
experience as the only standard of truth.
This inevitably follows from the nature and sources of
Belief. Even the supporters of innate principles, at the pre-
sent day, admit that these principles cannot arise except along
with the actual things ; a qualification that subjects the innate
notions as completely to the measure of experience, as if there
was nothing innate about them. Our intuition of Cause is
supposed to show itself only when we have observed a number
of examples of cause and effect; it is, therefore, involved and
implicated with our experience to such a degree as to be
deprived of an independent standing. There is no means of
discovering what the intuitions would dictate of themselves.
For all purposes of logical certainty, therefore, they must be
put out of account; regard must be had solely to observation,
and experience.
Our Knowledge is Limited by our Sensibilities,
19. We are able to know what things affect our various
sensibilities, or what may be compounded of these; and
our knowledge extends no farther.
We have a certain number of sensibilities, namely, in the
Senses (Passive), and in the Muscles (Active); and when
any of these is affected we have knowledge or experience ;
we know sight, sounds, touches, tastes, smells, and various
organic affections; we know resistance and movement.
We know various emotional states, love, anger, fear, &e.
We have many experiences from the discrimination and
14 FIRST PRINCIPLES OF LOGIC.
the agreement of our various states. In these, we have
our alphabet of the knowable. We can then combine a num-
ber of primitive feelings into a constructive aggregate, as
when we attain to the idea of an orange, or of a man,
or of the entire globe. But we cannot by any effort pass
out of the compass of these primitive sensibilities. Supposing
the universe to contain powers and properties that do not im-
press one or other of our senses, as at present constituted, we
can never by any means be made cognisant of such properties.
On this ground the notion of a Substance distinct from all
attributes is a thing unknowable. We can know body by its
sensible properties, and mind by our conscious feelings,
thoughts, and volitions; and we can know nothing beyond.
FIRST PRINCIPLES OF LOGIC.
20. In Logic, there are certain general principles, consti-
tuting it a science properly so called, and lying at the
foundation of its practical rules and methods.
These principles are variously expressed. They are termed
Laws of Thought, and fundamental Axioms of Reasoning.
From embracing these highest of all generalities, which pene-
trate into every science, and from laying down rules on scien-
tific method, Logic has been designated ‘ scientia scientiarum’
—the science that comprehends all sciences.
The First Principles may be arranged thus :—
I. The Principlé of Consts'rency, or Necessary Truth.
II, The Principles of Depuction,
III. The Principle of Inpuction.
I.— Principle of Consistency—Necessary Truth.
21. It is a fundamental requisite of reasoning, as well as
of communication by speech, that what is affirmed in one
form of words shall be affirmed in another.
Language often contains equivalent expressions for the same
fact. There are synonymous names as ‘ round,’ ‘ circular;’ a
round thing is the same as acircular thing. ‘ Matter is heavy,’
‘matter gravitates’ are the same fact in different words; if the
one is true, so is the other, by virtue of mere consistency.
Again, there are forms that enable us to affirm many separate
facts in one sweeping statement ; instead of affirming in detail,
Mercury moves in an ellipse, Venus moves in an ellipse, &e.,
PRINCIPLE OF CONSISTENCY. 15
we can put forth the one condensed affirmation—all the planets
have elliptic orbits. Having advanced this general statement,
we are required by consistency to maintain each separate
particular, the orbit of Saturn is elliptical, and so on.
It is obvious that without this consistency, there could be
no intelligent communication between one human being and
another. Unless the affirmer adheres to his affirmation, how-
ever he may vary the language, no one can divine what he
means; there is no possibility of discussion or reasoning.
To these self-consistent, although variously worded, affirma-
tions is applied the descripion ‘ Necessary Truth.’ ‘ All matter
is heavy, therefore any one piece of matter is heavy’ is called
a necessary inference. A more exact designation would be
an equivalent, inplicated, or self-consistent assertion.
There is a vital contrast between passing from one form to
another form of expressing the same fact, and passing from
one fact to another distinct fact. When we say-—because both
A and B are mortal, therefore, A ismortal—we merely repeat
ourselves; when we say, because A is mortal, therefore B is
mortal—we make the affirmation of one fact, the ground of an
affirmation of a different fact. In order to the one leap, we
need only to know the meaning of language; in order to the
other, we must consult the facts of the world.
The supposition has been advanced that truths of implica-
tion or consistency, inappropriately called ‘ Necessary,’ are
drawn out from their equivalent statements by a peculiar
innate power of the mind, distinct from the powers of observing
the order of nature ; that without a special instinct they could
not be evolved, nor reposed in with the absolute credence that
we give tothem. There are no sufficient grounds for the sup-
position. We should be disposed to consistency of statement,
without any special instinct. The impossibiity of carrying on
intercourse by language, on any other footing, compels us to
be consistent in our statements ; at least up to a certain point,
for we are not always so. There is no instinct needed but the ©
broad instinct of self-preservation ; were it not for this we
should probably care very little about observing the conditions
of necessary truth. If we could go on as well by maintaining
an opinion in oue form of words, while denying it in another,
there appears to be nothing in our mental constitution that
would secure us against contradicting ourselves. Our facul-
ties as laid down by those philosophers that derive all our
knowledge from experience alone, taken together with our
practical necessities, seem quite sufficient to make us ad-
2
16 FIRST PRINCIPLES OF LOGIC.
here to our statements under all variety ot forms and expres-
sions.*
22. There are certain maxims of Consistency known by
the title ‘Laws of Thought’; they are the principles of
Identity, Contradiction, and HKacluded Middle. |
The principle of Identity is given in the form “Ais A”; a
thing is what it is; manis man. According to Plato, “The
Idea is equal to itself.” ‘
Properly speaking this is not the case contemplated under
the principle of Consistency ; it is not the same fact in other
language, but the same fact in the same language. That the
same meaning expressed by the same word or words, is the
same, would appear to be an utter superfluity of affirmation ;
what we want to be guarded against is mistaking the same
fact in a different form of language.
This obvious criticism is evaded by giving the law an inter-
pretation that supposes difference in the statement. The
meaning is said to be that the thing A, although differently
worded, is still A; whichis merely an awkward way of stating
the general maxim of Consistency. If A equals, or includes,
a, b, c, d, &c., then we may say, in slightly different words, A
is equal to the whole series of what it includes; a whole is the
sum of its parts; a complex attribute is the aggregate of the
component attributes.
The Principle of Contradiction. ‘The same thing cannot be
A and not-A ;’ this room cannot be both hot and not-hot, that
is, cold. Consistency requires that when we affirm a definite
fact, we do not at the same time deny it; having made an
assertion, we are to abide by that. The principle may be carried
one step farther. By the law of Relativity, every thing that
can be thought of, every affirmation that can be made, has an
opposite or counter notion or affirmation ; to the thing that
we call a ‘straight’ line, there corresponds a negative or oppo-
site called a ‘bent’ or crooked line. Now thorough-going
consistency requires that when we affirm a certain thing to be
* Only some of the a priori philosophers, as Leibnitz, contend for the
existence of an intuitive faculty in order to apprehend these judgments of
mere consistency. Kant, and others after him, confine the characteristics
of necessity, and of intuitive origin, to certain synthetic judgments, where
the two things given are distinct, and not mutually implicated facts. It was
the peculiarity of Kant to maintain that there are such synthetic eae
a priori transcending our actual experience: he instanced, in ee
the proposition that ‘two straight lines cannot enclose a space.’
CONTRADICTION AND EXCLUDED MIDDLE, 17
@ straight line, we must be prepared also to deny that it is a
bent line ; when we call this man wise, we must also deny that
he is foolish. This is an equivalent form that plays a great
part in Logic. Viewed thus, the Law of Contradiction has a
pregnant meaning, which can hardly be said of the Law of
Identity.
The Principle of Hacluded Middle. ‘A thing must either be or
not be ;’ ‘of contradictories one must be true, and the other false.’
This law grew out of the distinction of propositions into
those of total, or universal, and those of partial or particular
quantity—all men and some men.’ When a proposition of
universal quantity is opposed by one of particular quantity,
the opposition is not thorough-going; there is not a perfect
and entire contrariety. Perfect contrariety is between, ‘ all men
are mortal’ and ‘no men are mortal ;’ partial or incomplete con-
trariety is ‘all men are mortal,’ ‘some men are not mortal;’
and ‘no men are mortal,’ ‘some men are mortal.’ Between
this last species of opposition, there is no middle affirmation ;
if one is not true, if it is not true that all men are mortal, then
it must be true that some men are not mortal; we have no
third alternative. But in the thorough-going contrariety—
‘all diamonds are precious,’ ‘no diamonds are precious,’ there
is @ middle ground of compromise ; the fact may- be that some —
diamonds are precious and some not. Thus, the Law of
Excluded Middle is an incident of partial or incomplete con-
trariety. It was enunciated by Aristotle as following from the
classification of propositions according to quantity. It is too
much honoured by the dignity of a primary law of thought.
The Principle of Consistency, inadequately rendered by these
Laws of Thought, may be assigned as the basis of the logical
department entitled ‘Immediate Inference’ (as opposed to
Mediate Inference or Syllogism), ‘ Inferences improperly so
called,’ ‘Equivalent Propositional Forms.’ Whatever be the
general designation, the details are fully agreed upon; the
doctrine of the Conversion of Propositions is one of the leading
topics.
First Principles of Deduction.
23. In Deduction, there is the application of a general
proposition to a particular case coming under it.
The following is a deduction :—‘ All arsenic is poison ; now
this substance is arsenic; therefore, this substance is poison.’
This is something more than consistency, implication, or
18 FIRST PRINCIPLES OF LOGIC.
equivalence of phraseology. There would be equivalence of
affirmation in saying ‘all arsenic is poison; therefore, some
arsenic is poison.’ In the present case, however, we have
another step to take ; we need a second and distinct assertion,
‘ this substance is arsenic,’ before we can conclude, ‘ this sub-
stance is poison. Instead of deriving an affirmation from a
prior affirmation, by change of language, we derive an affirma-
tion from two prior affirmations ; and these have to be related
one to another in a proper form, in order that we may draw
the conclusion.
This process is called Mediate Inference; there being an —
intermediate link or stepping-stone between the primary pro-
position and the conclusion. We cannot, by mere Consistency,
resolve ‘ All arsenic is poison’ into ‘the substance in this
bottle is poison ;’ ‘no matter is destructible,’ mto ‘no ether
is destructible’; there is in both cases a missing link, Until
we show that the substance in the bottle is arsenic, and that
ether is matter, we cannot draw the special conclusions above
given.
24, The Axiom, or First Principle, at the basis of De-
duction, is expressed in a variety of forms, which are
‘reducible substantially to two :—
(1.) Whatever is true of a whole class is true of what can
be brought under the class.
(2.) Things co-existing with the same thing co-exist with
one another.
There are corresponding forms for negative reasoning.
The first form is the one suitable to the exposition of the
syllogism. It sets forth the deductive type of reasoning, as
consisting of a general principle brought to bear upon a case
or cases, fonnd to come under it,
The second form can be shown to be equivalent to the first.
It has the advantage of making prominent the mediate charac-
ter of deductive inference, so as to contrast it with immediate
inference, or mere identical propositions under the Law of
Consistency. Two things not known in themselves to co-
exist, are shown to co-exist by each co-existing with some third
thing. Mere consistency will not include this case. The
principle is admitted as soon as it is understood ; but solely
because each one’s experience bears it out.
The obverse forms, for negative reasoning, are—(1) What
is denied of a whole class is denied of whatever can be
AXIOMS OF DEDUCTION. 19
brought under the class; (2) One thing co-existing with a
second thing, with which second thing a third thing does not
co-exist, is not co-existent with that third thing.
25. The Axioms of Deduction suppose the Uniformity
of Nature.
This is obvious, if the axioms are based on experience. We
have observed, in a large number of instances, that things con-
ciding with the same thing coincide with one another; but
we have not observed it in all instances; we have not observed
it in what took place before we were born, in what is beyond
our reach, or in what is still to happen. Yet, from the cases
we have observed, we do not hesitate to extend the principle
to the unobserved cases. We thus assume that ‘nature is
uniform ;’ that what we find to-day, all circumstances being
the same, we shall find to-morrow.
Again, we may deny that the axioms are experimental, and
call them intuitive. The case is not altered. The intuition
still supposes nature’s uniformity ; the thing intuitively con-
ceived and believed is not true, unless nature be uniform.
Thus, on either supposition as to our knowledge of the Logical
_ (and Mathematical) Axioms, the truth, still deeper, and more
comprehensive, is that nature is uniform. The so-called
axioms, therefore, are not ultimate principles; they are only
secondary, proximate, or derivative; they proceed from a stem
bearing other branches besides them. If they are true, more is
true. The wider principle will next be stated, for the sake of
its other consequences.
First Principle of I: nduetion.
26. When we infer from a fact known, to another un-
known, we make a real inference, for which there must be
some guarantee.
The sole guarantee is the Uniformity of Nature.
Putting a piece of wood into the fire and seeing it consumed,
we infer that another piece will be consumed in like manner.
This is to take for granted that what has happened will, in the
same circumstances, happen again; in other words, that
Nature is Uniform.
The Uniformities of Nature fall under (1) Uniformities of
Co-existence, and (2) Uniformity of Succession. It is a uni-
formity of Co-existence that ‘inert matter gravitates,’ that
the distinctive property of matter called ‘ Inertness’ is asso-
20 FIRST PRINCIPLES OF LOGIO.
ciated, through all nature at all times, with the property of
weight or Gravitation.
The evidence for Uniformities of Co-existence is special
observation of each separate uniformity. From seeing two
things coupled together in a few instances, we canndt presume
that they are always coupled together; we must observe the
coupling in various times, places, and circumstances. If, after
a sufficient search, we find no single contradictory instance,
we affirm the union to prevail through all nature.
27. In Uniformities of Succession, there has been dis-
covered a daw of Uniformity that shortens the labour on
enquiry in this department. It is called the Law of Cause
and Kffect, or Causation. We may express it thus :—
‘Every event is uniformly preceded by some other event :’
‘To every event there is some antecedent, which happening,
it will happen,’
To say that ‘ Every effect must have a cause,’ is begging the
question ; the word cause implies an effect, and the word
effect implies a cause. The correct mode of expression is, ‘ To
every event there corresponds a prior event, which happening,
it will happen ; and which failing, it will not happen.’ ‘ The
antecedent may be, and often is, a whole assemblage of circum-
stances; as in the case of Health, an effect depending on
many conditions.
Since there are effects produced by a plurality of Causes, the
principle of Uniformity is limited and qualified by that circum-
stance. Thus, Death may be caused by starvation, by a
violent blow, by poison, &c. It is therefore proper to say
that given any of these conditions in sufficient amount, death
will follow ; but the occurrence of death does not prove that
there has been starvation; it proves only that one of the
producing agencies has been present. In the Inductive
enquiry into nature, all the causes that may produce each
effect are sought out.
From the Law of Causation, we deduce consequences such
as these :—‘ If the cause be absent, the effect will be absent’—-
‘cessante causa, cessat et effectus,’ ‘If the cause be present
the effect will be present,” ‘Whatever agent cannot be
removed without the cessation of the effect, must be the cause
or part of the cause,’ ‘Whatever agent can be removed
without the cessation of the effect is not the cause,’ ‘The
cause and effect vary proportionately.’
LAW OF CAUSATION. 21
These various aspects or implications of the Law of Causa-
tion are the maxims serving to eliminate and to prove cause
and effect in the phenomena of nature.
28. The Law of Uniform Causation appears in a form
still more pregnant with consequences, namely, the Law of
the Persistence, Conservation, Correlation, or Equivalence
of Force.
This is a generalization only recently effected.
Galileo and Newton may be considered as having established
the Law of the Persistence or Conservation of Mechanical
Force, that is, force applied to matter in masses. If one ball
strikes another and puts it in motion, the force imparted to
the second is exactly what is lost to the first.
Lavoisier established the persistence of ponderable matter,
showing that no atom of matter could be destroyed, and none
created. In burning and in evaporation, the particles merely
change their positions; they do not abandon their material
properties of inertia and gravity.
In the present day, evidence has been obtained to show that
other forces besides mechanical force, namely, Heat, Chemical
Force, Electricity, Nerve Force, have the same numerical
persistence; they can neither be created nor destroyed ;
They can, however, be mutually converted, at a definite rate.
Heat can give birth to Mechanical Force ; Chemical Force can
evolve Heat; Electricity is convertible into all the other
modes. In this conversion, nothing is lost, and nothing is
created ; when heat becomes a mechanical prime mover in the
steam engine, it disappears as heat. When mechanical force
is seemingly destroyed, as when a cannon ball spends itself on
an unyielding mass of stone, the whole momentum of the ball
is transformed into heat; at the place of encounter, both the
ball and the stone are raised in temperature, exactly in propor-
tion to the momentum arrested.
This great law of the quantitative persistence of Force, or
Momentum, deserves an eminent place in the Inductive Logic.
It encompasses and pervades all the natural sciences, each
one of which is but a partial development of it.
NATURE AND CLASSIFICATION OF KNOWLEDGE.
29. Knowledge is made up of affirmations respecting
the order of the world. These affirmations are the subject
of Belief, of which the ultimate criterion is Action.
22 NATURE AND CLASSIFICATION OF KNOWLEDGE.
Twice two is four; the sun rises and sets; unsupported
bodies fall to the ground; heat causes water to boil; animal
bodies are nourished by food and air; harmony is agreeable
to the mind :—are affirmations, or Knowledge, respecting the
universe. We believe them, and show our belief by acting on
them. When we desire water to boil, we apply heat; which
is our belief of the affirmation.
30. The first requisite of Knowledge is that it shall be
brue.
An Affirmation is true when, on actual trial, it corresponds
to the fact. This is the direct proof. Indirectly, we may
test the truth of affirmations by comparing one with another.
Wherever there is contradiction, there must be falsehood.
31. Knowledge is either Particular or General.
An Affirmation respecting a certain individual thing, as
‘this house is stable,’ ‘ Cesar was brave,’ ‘a certain patient
will not recover ’—is a particular or individual affirmation ;
it is limited to one subject. An affirmation respecting a whole
class or species of things—as ‘an erection is stable when the
line of the centre of gravity falls within the base’; ‘all great —
generals are brave’; ‘the stiffening of the limbs is a sign of
death ’;—are general: affirmations; they extend to instances
beyond number.
32. Owing to the frequent recurrence of the same things
and the same processes, we can attain to numerous genera-
lities.
If every individual thing in nature were throughout unique,
resembling no other thing, each would need a law to itself.
If, instead of a common substance ‘water’ in all seas, rivers,
and fountains, there were a thousand different substances, we
should have to multiply affirmations accordingly. If, instead
of the sixty-three elementary bodies known to us at present,
the globe were made up of six thousand elements with their
compounds, there would be a great increase in the bulk of our
knowledge. If instead of sixty-three, there had been six, we
should have been able to comprehend all physical knowledge
in comparatively few affirmations.
33. It is desirable to attain knowledge in the highest
possible degree of generality.
TRUTH AND GENERALITY. 23
The reason is obvious, A general affirmation is a great
many particular affirmations in one. It is a vast economy of
the human understanding. a
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BOOK Il.
DEDUCTION.
CHAPTER L
THE SYLLOGISM.
1. The Sytioaism is the fully expressed form of a De-
ductive Inference, that is, an inference from the General to
the Particular. “
When a step of reasoning or argumentation consists in as-
signing, as the proof of an affirmation (or denial), some more
general affirmation, it admits of being stated in a peculiar
form, in which there is sometimes greater facility in judging
of its soundness. The peculiarity of the form of statement
consists mainly in this, that everything belonging to the rea-
soning is set forth explicitly. Thus, when any one maintains
that Mathematics is useful as a mental discipline, and assigns
as the proof, that all the exact sciences are useful as mental
discipline, the reasoning, which is Deductive, and not Induc-
tive, contains these two assertions :—(1) All the exact sciences
are useful as mental discipline; (2) Mathematics is an exact
science. Both these are indispensable to the conclusion
* Mathematics is a mental discipline.’ The first is the general
principle, the second an intermediate proposition for applying
the general principle to the casein hand. Very often, one of
the two propositions is left unexpressed. In the example:
‘this man is a rogue, therefore he is not to be trusted,’ there
is an ellipsis of the general principle—‘ rogues are not to be
trusted.’ In the form ‘you cannot trust rogues, therefore you
cannot trust this man,’ the omission is in the second or apply-
ing proposition-—‘ this man is a rogue.’
Say
RRS SEL CU Te ERT
134 THE SYLLOGISM.
A Deductive reasoning fully and formally expressed is a
Syllogism.
The following arrangement—
(1) All men are fallible,
(2) John is a man,
(8) John is fallible— :
is a regular deductive reasoning, or an argumentation in th
syllogistic or complete form. The two first propositions
combine to make the proof of the third; they are called the
Premises of the reasoning or syllogism ; the third is the point
to be proved, and is called the Conclusion.
We shall see hereafter that, in the departures made from the
regular form of the syllogism, the order of the propositions
may be reversed ; the applying proposition coming first, and the
grounding proposition second. But whatever form the syllo-
gism may assume, one feature can never be absent—a general
proposition. This is indispensable. Unless one of the premises
be more general than the conclusion, the argument is not
deductive.
2. A Syllogism is said to contain three, and only three
Terms; the Subject and the Predicate of the Conelusion,
and another Term, occurring in both Premises; the Sub-
ject of the Conclusion is the Minor Term; the Predicate
of the Conclusion, the Major Term ; the term occurring in
both Premises, is the Middle Term.
By ‘ Terms’ are meant the expressed notions entering into
the subjects and predicates of the propositions, A proposition
couples or unites two Terms. ‘ X is Y’ contains the two terms
X and Y affirmatively conjoined. ‘ Men are not gods’ contains
the two terms ‘men’ and ‘gods’ under a negative copula, —
In seeking out the Terms, we begin with the proposition to
be proved, that is, the conclusion. The sudject of the conclusion
is the Minor or smaller term, the predicate the Major or greater
term. The propriety of these designations is grounded on
the circumstance, formerly adverted to, that in propositions
generally, the predicate covers the subject, and other subjects
besides; ‘kings are fallible,’ and many other beings besides
kings are fallible ; hence ‘kings’ are a smaller group forming
part of a larger group ‘fallible ;’ in compass or extent, there-
fore, ‘kings’ are a Minor term, ‘ fallible’ a Major term.’*
*Sir W. Hamilton complains that these designations are false and
erroueous becanse they do not apply to the terms as considered in Com-
prehension, There are more men than kings, and so the designations are
—
THE THREE TERMS. 135
The Middle Term must be sought not in the conclusion, but
in the Premises, or proving propositions, and must appear in
both. Thus, in the syllogism—
‘Men are fallible,
Kings are men,
Kings are fallible.
The term, absent from the conclusion, and present in both
premises, is ‘ men,’ the subject of the first and the predicate of
the second. It is called ‘ middle’ because it is the medium or
instrumentality for bringing together in the conclusion, the
major and minor terms; they being separated in the premises.
Also, as regards extent, compass, or denotation, it is inter-
mediate thus :—The minor * kings’ is less in extent than ‘ men;’
men are more numerous than kings. Again, ‘men’ is less in
extent than ‘fallible beings;’ there being many fallible beings
besides men. So ‘men’ being more extensive than the minor
term ‘ kings,’ and less extensive than the major term ‘ fallible
beings,’ is properly a middle or intermediate term. The grada-
tion is represented in a diagram thus :—
Fallible, 3 ‘ 3 major,
Men, . B : é middle,
Kings, : ; j minor.
Although the syllogism contains three propositions, each
with two terms, making six terms in all; yet, in virtue of
the double occurence of each, there are in reality only three
terms, ‘The example shows :—
The Middle term in both premises.
The Minor term in the conclusion and in one premise.
The Major term in the conclusion and in one premise.
__ 3. In the Syllogism, there are Three, and only three,
Propositions, namely, the two Premises and the Conclusion.
The Premise containing the Major Term and the Middle
Term, is called the Major Premise ; the Premise contain-
ing the Middle Term and the Minor Term, is called the
Minor Premise.
In the foregoing example, the Premise first in order contains
applicable to the extension of the terms; but, he argues, more attributes
are connoted by the term ‘kings’ than by the term men, and so major
and minor are inapplicable to the comprehension. In criticism of this
view, it may be said that confessedly the designations major and minor
are applicable to the terms viewed in their compass or extension, that these
terms are used in that sense, that they cannot be used without confusion
in both senses, and that Hamilton has shown no good reason for invert-
ing the common usige.
eis
136 THE SYLLOGISM.
the Major term ‘fallible,’ together with the Middle term,
‘men, —‘ men are fallible;’ this is the Major Premise. The
Premise second in order contains the Middle term, ‘ men,’ and
the Minor term, ‘ kings,’—‘ kings are men ’—and is the Mior
Premise.
We find it convenient to represent the forms of the syllogism
by letters or symbols, thus :—Let X be the minor term, Y, the
middle term, Z, the major term; then—
All Y is Z
All X is Y
All X is Z }
is a syllogistic form on the basis of affirmation ; that is to say,
the universal proposition in the first premise is affirmative, and
the conclusion is affirmative.
An example on the basis of negation is—
No Y is Z
All X is Y
No X is Z,
or, by Hamilton’s still more expressive symbols,—
S (subject of conclusion, mimor term),
M (middle term),
P (predicate of conclusion, major term) ;
All M is P No Mis P
All S is M All § is M
All S is P No S is P.
4, Syllogisms, or Syllogistic forms, are divided into
FIGURES, according to the position of the Middle Term.
There are, in all, Four Figures, | |
The First Figure is exemplified in the forms hitherto em-
ployed. In it, the Middle Term is Subject in the Major Pre-
mise, Predicate in the Minor Premise. .
Yis Z M is P M —
Wi =) Sane, —M
X is Z Sis P ; |
The idea implied under ‘ Figure’ is borrowed from. the
Figures of Rhetoric, which are departures, for effect, from the —
the plain and ordinary forms of speech. On this analogy,
however, as remarked by Hamilton, there ought to be some
one regular or stundurd form, from which all other forms are
deviations or departures, thence properly called ‘ Figures.’
Such standard form is what is mis-named the ‘First Figure,’
which is the pure type of a deductive argument The Major
or First Premise is the universal proposition indispensable in
pee
THE FIGURES. 137
deduction, the Minor or Second Premise is an affirmative pro-
position, whatever may be its quantity. As to order, the Uni-
versal is placed first, as being of the two premises the funda-
mental or chief; the use of the second premise, the minor,
being to apply the first to a particular case. ‘ All thieves are
deserving of punishment,’ is applied to a particular instance,
by means of an affirmation bringing the instance within the
sweep of the rule, that is, declaring such a one to be a thief.
This is the function of the minor.
In the Second Figure, or the first departure from the normal
syllogism, the middie term is predicate in both premises
“is Y PisM —M
XisY SisM —M
Here there is an obvious inversion of the. natural order of
things. In the major premise, Z is Y, P is M, the largest term
is made the subject, and the middle term the predicate, of the
proposition. Ifthe proposition be affirmative, this change is not
compatible with universality, and therefore the proposition can-
uot be the major in the same sense as in the standard syllogism.
If the proposition be negative, there is only a harmless con-
version ; we may, for ‘ no Y is Z,’ substitute ‘no Z is Y ;’ ‘no
men are gods,’ ‘no gods are men.’ This is an insignificant
and, for the most part, useless alteration of the negative form
of the standard syllogism. Two of the four forms of the
Figure (called Moods) are fashioned out of this trivial altera-
tion. The two other forms containing affirmative majors in-
volve still greater changes of the standard furm. In one, the
major is not the universal proposition required as the basis of
the deduction, but the applying proposition, which in the first
figure is the second or minor premise. In the conciuding
form, there is a much greater distortion, consequent on present-
ing the normal premises in obverted forms,
In the Third Figure, the middle term is subject in both
premises.
WA, 2 M is P M—
Y is X Mis§ M—
Here the major stands as in the first, or normal figure. The
minor has ity terms transposed; the middle term is subject,
and the minor term predicate. As before, this is a harmless
change, if the proposition be a universal negative ; in which case,
however, the minor prémise must be the universal or ground-
img proposition, and not the applying proposition ; so that, as
compared with the standard form, there is an inversion of the
order of the premises. Ifthe minor be affirmative, either it
ae
> _—
138 THE SYLLOGISM.
must be particular, or there is some distortion, rendering the
terms different in fact from what they are in appearance.
In the Fourth figure, the position of the middle term is the
first figure reversed ; ; it is predicate in major, and subject in
minor.
ZLisY PisM —M
Yis X Mis§S M —
This double inversion of the order of the terms implies still
greater deviations from the primary form. The inversion is
possible by such devices as above described for the smaller
inversions in the second and third figures.
d. Each Figure has a certain number of distinct fhe
called the Moods, or modes of the figure. The variation of
mood is determined by the variety of the propositions con-
tained, as regards Quantity, and Quality.
The order of the terms is fixed for each Figure; but the
propositions constituting the premises and the conclusion may,
within certain limits, be of one or other of the four forms,
A, I, E, O.
The First Figure, the normal syllogism, has Four Moods,
The First Mood is composed of three universal affirmations.
All YisZ) A, A, A All men are fallible.
All Xis Y (Barbara) All kings are men.
All X is Z All kings are fallible.
In the Second Mood,
The Major is a universal negative —E,
The Minor
The Conclusion a universal negative _k.
No Y isZ) H, A. E No men are gods,
All X is Y (Cedurent) All kings are men,
No X is Z No kings are gods.
The Third Mood is the first, with a particular minor, and
particular conclusion :—
All Y is Z Ae toed All men are fallible.
Some X is Y ' (Dari) Some beings are men.
Some X is Z Some beings are fallible.
The Fourth Mood is a similar variation on the second; par-
ticular minor and particular conclusion {—
No Y is Z HK, I, O No men are gods.
Some X is Y (Ferio) Some beings are men.
Some X is not Z Some beings are not gods.
FIRST FIGURE. 139
These four moods are obviously reducible to two; the third
and fourth being mere unessential varieties of the first and
second. The two comprehensive forms may be stated thus :—
All Y is Z No Y is Z
Allor some Xis Y All or some X is Y
All or some XisZ§ No Xis Z.
. Some X is not Z.
_ The first form is the normal type of all deduction for an
affirmative conclusion ; the second, the type for a negative
conclusion. They present the deductive process in its regular
order :—
First, a universal proposition, as the ground proposition of
the reasoning (Major premise) ;
Secondly, an afiirmative and applying proposition (Minor
premise) ;
Lastly, the universal truth applied to the particular case
(the Conclusion).
We desire to prove that kings are fallible, by applying to them
the principle of the fallibility of all men. The major states
the principle, the minor applies it. And so for a negative con-
clusion,
There cannot be any valid deduction whatsoever but must
conform to the foregoing type; whatever variation may be
made, this is at the bottom.
The Seconp Figure has likewise four Moods.
In the First Mood,
The Major is a universal negative —H.
The Minor a universal affirmative—A.
The Conclusion a universal negative —EH.
All X is Y > (Cesare) All kings are men.
No X is Z No kings are gods. |
This is a case where advantage is taken of the simple con-
version of the universal negative to make a trivial departure
from the standard (negative) syllogism. Only a slight change
is necessary to reconvert the present mood to the second mood
of the First Figure ; for ‘No Yis Z’ ‘No menare gods,’ we are
at liberty to substitute ‘No Z is Y,’ ‘No gods are men,’ which
is the whole difference.
No Zis Y H, A, EK, No gods are men.
In the Second Mood,
The Major _ is a universal affirmative—A,
The Minor @ universal negative—H,
140 THE SYLLOGISM.
The conclusion a universal negative—H.
All Zis Y ) A, E, E, All kings are men.
No X is Y > (Camestres) No gods are men.
No X is Z No gods are kings.
A much greater variation from the standard (negative) is
observable here. The grounding proposition, which must be
universal, is the minor premise: so that there is an inversion
of the normal order of the premises. Moreover, the same pro-
position has been converted simply, from the form ‘ No men
are gods ;” and the conclusion is likewise the converse of the
conclusion in the regular syllogism. By first restoring the order
of the premises, and next re-converting two universal negations,
we have the normal negative syllogism (Celarent).
No men are gods.
All kings are men.
No kings are gods.
The grounding universal is the negative proposition, ‘ no
men are gods’—the applying proposition is ‘all kings are men.’
In the Third Mood,
The Major is a universal negative —H,
The Minor a particular affirmative—I,
The Conclusion a particular negative —O,
Some X is Y (Festino) Some beings are men.
Some Xis not Z Some beings are not gods.
Here we remark the same trivial departure from one of the
standard forms, as in the first mood. The universal negative—
the major in the fourth mood of the first figure (Ferio)—is
simply converted (No Y is Z, into No Z is Y; no men are
gods, into no gods are men),
No Gis Y bi I,QO Nogods are men.
In the Fourth and last Mood, there is a more serious dis-
tortion.
The Major is a universal affirmative—A,
The Minor a particular negative —O,
The Conclusion a particular negative —O,
All Z is Y A,O,O All gods are men.
Some X is not Y >(Baroko) Some beings are not men.
Some X is not Z Some beings are not gods.
A glance at the premises shows us that they are not at
bottom what they appear on the surface. There is indeed a
universal proposition in the major premise, which might
auswer for the ground proposition ; but then the other pre-
SECOND FIGURE. 14]
mise, in that case the applying proposition, is negative, which
is not allowable. The real fact is that the affirmative major,
is a negative (universal) in disguise, and the negative minor,
E an affirmative in disguise. The disguises may be laid open,
thus—
All Z is Y No not-Y is Z
Some X isnot Y Some X is not-Y
Some X isnot Z Some X is not Z
The true middle term instead of being Y, is the negative of
_Y; or not-Y (U—Y) This is the key to the distortion. The
remedy consists in (1) obverting and converting the major—All
Z is Y, which becomes No not-Y is Z; and (2) in obverting
the minor—Some X is not Y, Some X i is not-Y. There thus
emerges a form of the third mood of the first figure (Ferio),
with not-Y, as the middle term.
This mood cannot be reduced to a mood of the First Figure
without Obversion. The older logicians sought to establish its
validity by a cumbrous process technically known as Reductio
ad impossibile. They showed that the conclusion cannot be
supposed false, without leading to a contradiction of one of
the premises, which are given as unimpeachable. Thus :—
AllZ is Y
Some X is not Y
Some X is not Z
If ‘Some X is not Z’ be declared false, the universal ‘ All X
is Z,’— which is its contradictory,—must be admitted as true.
Taking this new proposition, ‘All Xis Z’ along with the major
of the original syllogism, ‘ All Z is Y,’ we reach the conclusion
that ‘All X is Y.’ Thus :—
All Z is Y
AllX is Z
All X is Y
is a syllogism in Barbara, But we know from the original
premises that ‘Some X is not Y ;’ it cannot therefore be true
that ‘All X is Y.’ One of the premises of the above Burbara
must be unsound. The major ‘ All Z is Y,’ is one of the origi-
nal premises, granted as true; the error must lie on the minor,
‘All X is Z.’ Now this is the proposition taken on trial; and
its truth being shown to be incompatible with the truth of the
original premises, its contradictory, ‘Some X is not Z’ must
be true. And ‘Some X is not Z’ is the conclusion in question;
which is thus shown to be valid.
The Tuirp Ficure has six Moods.
142 THE SYLLOGISM.
In the First Mood,
The Maju is a universal affirmative—A.
The Minor a universal affirmative—A.
The Conclusion a particular affirmative—lI.
All Y is Z A, A, I All men are fallible.
AllY is X }+(Darapti) All men are living beings.
Some X is Z Some living beings are fallible.
The only departure, in this instance, from the standard
syllogism (with a particular minor, Dariv) is the universality .
of the minor, All Y is X. By simple conversion, this premise
becomes Some X is Y, and the syllogism is then the same as
the third mood of the regular syllogism.
This figure is quoted as a useful form. Certain reason-
ings are considered to fall more readily into the above ar-
rangement, than into the corresponding mood of the First
Figure.
The Second Mood contains an inversion of the order of the
Premises. This distortion is altogether gratuitous; it serves
no purpose but to seem a variety.
Some Y is Z)I, A, I Some men are kings.
All Yis X }+(Disamis) All men are fallible beings.
Some X is Z Some fallible beings are kings.
Here, if we redress the order of the premises, and simply
convert the new minor—Some Y is Z, into Some Z is Y,—
there arises a regular affirmative syllogism, with a particular
minor (Daviz) ; there being only the speciality that the minor
and the major terms have changed places, thus :—
All Y is X All men are fallible beings.
Some Zis Y Some kings are men.
From this the conclusion would be ‘Some Z is X,’ ‘some
kings are fallible beings,’ which, however, by simple con-
version, gives ‘Some X is Z,’ ‘some fallible beings are men.’
: The Third Mood is one of the trival variations of syllogistic
orm.
All Y is Z A, I, I, All men are fallible.
Some Y is X }(Datisi), Some men are kings.
Some X is Z Some kings are fallible beings.
There is no departure here, from the regular syllogism
(affirmative, with particular minor Darii), but in the minor
premise, which is Some Y is X, instead of its equivalent, Some
A198.) ;
THIRD FIGURE. 143
The Fourth Mood is exactly the counterpart of the previous
mood, with a negative major.
No Y is Z K, A,O. No men are gods.
All Y is X (Felapton) All men are living beings.
Some X isnot Z Some living beings are not gods,
This differs from the negative mood of the first figure, with
a particular minor (Ferzo), only in having a universal minor,
which, by conversion, becomes particular, Some X is Y ; the
syllogism is then exactly the fourth mood of the standard
syllogism.
The Fifth Mood is, in point of distortion, the parallel of the
last mood of the Second Figure (Baroko). Both the premises
appear different from what they are in reality.
Some Y is not Z) O, A, O, Some men are not kings.
All Y is X (Bokardo) All men are fallible.
Some X is not Z Some fallible beings are not kings.
If we look for a universal premise, to supply the ground
proposition, we seem to find it in the minor; but then the
other premise is negative, and therefore is not the applying
proposition. As in Baroko, we must transfigure both pre-
mises. ‘The present major is made affirmative, by obversion,—
‘Some Y is not-Z,’ and is then converted, ‘Some not-Z is Y.’
This is taken as the minor premise, the other being the major,
thus :—
All Y is X All men are fallible.
Some not-Z is Y Some not-kings are men.
which are the premises of the regular syllogism (affirmative,
with particular minor, Darii):and would give as a conclusion,
Some not-Zis X, Some not-kings are fallible,
or, by conversion and obversion,
Some X is not Z, Some fallible beings are kings.
As in the case of Barvko, the older logicians could not refer
this mood to the First Figure, and applied as a test of its validity
the Reductio ad impossibile. The process need not be repeated
at length. We assume the universal contrary to the conclu-
sion, and taking it along with the given minor, evolve a pro-
position that contradicts the given major: and argue, as under
Baroko, that the universal contrary of the conclusion must be
false, and therefore the conclusion itself valid.
The Sizth and last Mood is the negative counterpart of the
third, and should have been placed after the fourth; it is an
equally trivial departure from the regular syllogism (negative,
with particular premise, erio).
144 THE SYLLOGISM.
No Y is Z HK, I, O, No men are gods.
Some Y is X (Ferison) Some men are living beings.
Some X is not Z Some living beings are not gods,
The simple conversion of the minor ‘Some Y is X,’ into ‘Some
Xis Y,’ ‘some living beings are men,’ —reproduces Ferio, in the
standard figure. .
The Fourrn Ficure has five Moods. In this figure, there is
an inversion of both premises as compared with the regular
syllogism. This, of course, produces apparently a great degree
of distortion ; but there is very little in reality. In three of
the moods, the inversion is caused by the transposition cf the —
premises ; this rectified, they need only the simple conversion
of one or more of the propositions to make them standard
syllogisms.
Thus, to take the Furst Mood, which has universal affirmative
premises, and particular conclusion :—
All Zis Y | Aetievd All kings are men.
All Yis X }(Bramantip) All men are fallible.
Some X is Z j Some fallible beings are kings.
Transpose the premises, and there emerges a standard syllo-
gism (affirmative, with universal minor, Barbara)—
All Y is X All men are fallible.
All Zis Y All kings are men.
The conclusion from these premises is—
All Z is X All kings are fallible.
This conclusion, converted by limitation, gives—
Some X is Z Some fallible beings are kings.
The Second Mood is, if possible, still closer to a regular
syllogism, when the order of the premises is changed.
All Z is Y ) A, H, EH, All kings are men.
No Y isX (Camenes) No men are gods.
No X is Z No gods are kings.
Restore the order of the Premises :—
No Y is X No men are gods.
All Zis Y All kings are men.
These are the premises of the regular syllogism (negative, with
universal minor, Celarent), and the conclusion is
No Zis X No kings are gods,
Whence No X is Z No gods are kings.
The Third Mood is constructed on a similar plan; the devia
tion from regularity being caused by transposed premises :—
+ a
ae
FOURTH FIGURE. 145
Some Zis Y)I, A,I Some living beings are men.
All Yis X }+(Dimaris) All men are fallible.
Some X is Z Some fallible objects are living beings
With re-transposed premises,—
All Y is X All men are fallible.
Some Zis Y Some living beings are men.
Whence by Darii, in the standard Figure, the conclusion is,—
Some Z is X Some living beings are fallible.
- Or Some X is Z Some fallible objects are living beings.
The fourth and fifth Moods attain their peculiar form, not
through the inverted order, but through the conversion, of the
Premises. The Fourth runs thus .—
No Zis Y ) E, A,O No gods are men.
All Y isX (Fesapo) All men are living beings.
Some X is not Z Some living beings are not gods.
Convert both premises, the major simply, the minor by limita-
tion :—
No Y is Z No men are gods.
Some Xis Y Some living beings are men.
These are the premises of the negative form in the first figure,
with particular minor (Ferio), whence
Some X is not Z Some living beings are not gods,
The Fifth and last Mood differs from the fourth only in
having a particular minor; the universality of the minor in
the fourth being superfluous, as leading to no stronger conclu-
sion than the present form, The process of assimilation to
Ferio is precisely the same—
No Zis Y EH, I, O, No gods are men.
Some Y is X (Fresison) Some men are living beings.
Some X is not Z J- Some living beings are not gods.
Convert both premises simply :—
No Y is Z No men are gods.
Some X is Y Some living beings are men.
The premises are now in Ferto, whence,
Some X is not Z Some living beings are not gods.
The modes of the Fourth Figure, are thus, with the appear-
ance of great inversion, mere varieties of the primary Figure.
The transposition of the order of the premises is the most
insignificant of all the alterations made on a syllogism. It
signifies nothing to the reasoning, in what order the premises
are stated. The three first moods depart from the standard
moods in very little besides. The two last moods, as has
146 THE SYLLOGISM.
been seen, present both premises converted ; and the first of
the two is superfluous, even as a form.
The prime importance of the Syllogism attaches to its
standard forms, that is, to the First Figure. In it we learn
the essential structure of each valid deduction—a universal
ground proposition, affirmative or negative, and an applying
proposition, which must be affirmative. These appear, in the
standard syllogism, in the order stated—first, the ground
proposition (the major premise), secondly, the applying propo-
sition (the minor premise). In the subsequent figures, these
are sometimes transposed; and, in two forms, Baroko and
Bokardo, they are greatly disguised. The ground proposition
is called by Hamilton the sumption, the applying proposition,
the subsumption (more strictly, the subsunwng proposition).
It is not easy at first sight to point out any of the forms of
the 2nd, 3rd, or 4th Figures that are of special importance in
the conduct of reasoning or argumentation. The Fourth Figure
is the least important of all; next, perhaps, the second, which,
with the exception of Baroko, scarcely disguises the standard
forms. The Third Figure is useful in overthrowing universal
oppositions, by exceptions or contradictory particulars.
It was pointed out by Aristotle, that in the First Figure only
have we conclusions in all the forms, A, E, I, O. The Second
_ Figure is restricted to negative conclusions; the Third Figure,
to particulars, The Fourth Figure, which Aristotle did not re-
cognize, does not admit of a universally affirmative conclusion.
In explanation of the possible uses of the Figures after the
first, two circumstances may be remarked that lead to depart-
ures from the typical form. In the first place, the order of
subject and predicate in either premise, and consequently the
figure wherein the syllogism naturally falls, may vary with the
idea uppermost in the mind of the reasoner. ‘ The best form of
Government is Government by a plurality of persons,” and
“Government by a plurality of persons is the best form of
Government,” are variations of the same statement that would
cause a variation of Figure. In the second place, the extent
of the middle term relatively to the extent of the major and
minor, gives rise to variations. When the middle term is larger
than either major or minor, it naturally forms the predicate
both of the major and of the minor premise, producing a syllo-
gism of the Second Figure. When, again, the middle term is
smaller than either, it naturally forms the subject of both pre-
mises, producing a syllogism of the Third Figure, _ .
THE MNEMONIC LINES, 147
Tt has been shown in the detailed explanation above given,
that the fifteen moods of the three last Figures are strict
equivalents of the Moods of the First Figure, and therefcre
have the same validity as these standard moods. The demon-
stration of this equivalence is technically called the Repucrioy
of the syllogisms, or their revocation to the primitive forms of
affirmative and negative predication. The necessity of Reduc-
tion depends upon the nature of the proximate canons adopted
for the syllogism. If those canons are applicable only to
the First Figure, then, before we can test the validity of
irregular moods, we must reduce them to moods of the First
Figure. Ifthe proximate canons are applicable directly to all
syllogistic moods, reduction is unnecessary.
Order of the Premises. Many logicians have inverted the
order of the premises, commencing with the minor. Thus—
All X is Y
All Y is Z
All X is Z.
This is the form that seems most convenient and convincing,
in a chain of reasoning, as in the Sorites. It suits the particu-
lar form of the syllogistic axiom, expressed by ‘the mark of a
mark is a mark of the thing;’ X is a mark of Y, Y is
a mark of Z; hence X isa mark of Z. It, however, disguises
the gennine type of Deductive Reasoning, which ought to be
exhibited in the standard syllogism, even, if we depart from it
in the other figures. The universal proposition is rightly put
forward as the foundation of the reasoning, to which should
follow the applying premise, or the minor. In the moods of
the 2nd, 3rd, and 4th Figures, inversion of premises occurs as
one form of departure from the First or regular figure.
Aristotle’s mode of writing Barbara is—
A is predicated of all B
B is predicated of all C
A is predicated of all C—
where the minor is given first, and the propositions inverted
in the wording; ‘A is predicated of all B,’ is the same as All
Bis A.
6. The Mnemonic Lines of the Syllogism contain the
statement of the different moods, with the manner of reduc-
ing to the First Figure, those of the three last Figures.
To each of the moods, as described, a technical name has
been appended, Barbara, Celarent, &c. These words have
148 THE SYLLOGISM.
been constructed for showing the constituent propositions of
each mood, and how the moods of the 2nd, 8rd, and 4th
Figures may be transmuted into moods of the lst Figure; as
in the process actually gone through in the foregoing explana-
tion.
The names are made up in lines of Latin hexameter verse.
Among artificial aids to memory, they stand unrivalled ;:—
Fig. 1. bArbArA, cE]ArEnt, dArII, fErlOgue, prioris.
Fig. 2. cHsArk, cAmEstrHs, fEstInO, bArOkO, secundae.
Vig. 8. tertia, dArAptl, dIsAmIs, dAtIsI, fHlAptOn,
bOkArdO, fErIsO, habet: quarta insuper addit.
Fig. 4. brAmAntIp, cAmEnKs, dImArIs, fEsApO, frEsIsOn,
Hach of these names represents a mood; the three capital
letters in each standing for the three propositions, as symbo-
iized in their Quantity and Quality by the forms A, H, I, O.
Of the smaller letters, or consonants, 7, ”, t, are meaningless
or dumb letters. The consonants that commence each name
—b, c, d, f—indicate the moods in the First Figure that the
several moods in the other Figures are reduced to; Bramantip
is reduced to Barbara, Cesare to Celarent, and so on. The
consonants m, s, p, and k, which signify the processes of Reduc-
tion: m indicating that the premises have to be transposed ;
s indicating simple conversion ; p conversion by limitation, or
per accidens; while k is the symbol of reductio ad impossibile.
The application of eack is to the vowel immediately preceding.
hus, in Bramantip :—
All Z is Y
All Y is X
Some X is Z—
we learn from m that to obtain the form of Barbara, the first
mood of the First Figure, we must transpose the premises.
And as we should then see ourselves entitled to conclude ‘ All
Z is X,’ it has further to be signified by p, that to obtain the
conclusion ‘Some X is Z,’ we must make a limited conver-
sion. So in Fesapo to obtain Ferio of the First Figure, we
must convert E simply, and A by limitation. Although the
method of reduction ad impossibile may be applied to any of
the irregular moods, the letter / occurs only in two, Baroko
and Bokardo, these being the only two that the logicians found
irreducible by the processes of transposition and conversion.
7. The rules or Canons of valid reasoning are variously
stated. They are proximate rules, being derived from the
fundamental axioms of all Deduction,
CANONS OF THE SYLLOGISM. 149
Common Canons.—These are six in number.*
(1) Every Syllogism has Three, and only three, Terms.
(2) There must be T'hree, and only three, Propositions.
(3) The Middle Term must be distributed once, at least, in the
premises.
That is to say, the Middle Term must be a universal in one
or other of the premises. It must be the subject of a univer-
sal proposition (4/1 Y is Z, No Y is Z), or else the predicate of
a negative proposition No X is Y, Some X is not Y. As the
subject of a particular proposition (Some Y is Z, Some Y is
not-Z), and as the predicate of an affirmative proposition (All
X is Y, Some X is Y), the middle term Y is particular, or un-
distributed.
By a reference to the nineteen valid syllogisms, it will be
seen that in each of them the middle term is distributed once
in the premises. Thus, in the First Figure throughout, it
is the subject of the major, which is a universal (All Y is Z,
No Y is Z). This is as it ought to be in the standard syl-
logism. In the Second Figure, it is distributed three times
in the major, and once in the minor (Some X is not-Y). In
the Ist, 2nd, 4th, and 5th moods of the Third Figure, it is
distributed in the minor; being also distributed in the major,
in the Ist and 4th. In the Fourth Figure, it is distributed in
the minor, in all the moods but the last.
In the following couples, there is no distribution of the
middle term (Y), and consequently none of the couples could
stand as premises in a valid deduction,
All Z is Y Some Z is Y All Z is Y
All X is Y Some X is Y Some Zis ¥
Some Y is Z, Some Y is not Z All Zis Y
All X is Y, All X is Y Some Y is not X.
A pretended syllogism, in such forms as these, or any form
where the rule does not hold, is said to exemplify the fallacy
of undistributed middle.
Such are the following :—
Some Y is Z Some men are kings.
All X is Y All cooking animals are men.
All X is Z All cooking animals are kings.
Other examples will occur afterwards.
(4) No term undistributed in the premises must be distributed in
the conclusion. In other words, there must not be a greater
* After Whately, who gives them as a condensation of the twelve
canons of Aldrich.
150 THE SYLLOGISM.
quantity attaching to any term in the conclusion, than is
attached to the same term in the premises. If X be particular
in the premises, so must it be in the conclusion ; the same with
“ This condition, likewise, is fulfilled in the valid syllogisms.
hus :—
All Y is Z No Y is Z.
All X is Y Some X is Y.
All X is Z Some X is not Z.
In the first of the two, the subject of the conclusion is
universal in the minor premise, and may therefore be universal
in the conclusion ; in the second, it is particular in the minor,
and must be particular in the conclusion. Iu both, the predi-
cate of the conclusion is particular in the premises, and must
be particular in the conclusion. So if, in Dart, a universal
conclusion were drawn, it would be invalid.
All Y is Z All men are mortal.
Some X is Y Some extended things are men.
All X is Z All extended things are mortal.
We may have premises, free from the last-named vice of
undistributed middle, yet made to yield a false conclusion by
overstepping the present rule, or raising a term of particular
quantity, in the premises, to the rank of universal quantity
in the conclusion. To this error is given the name, Illicit
process ; and according as the unduly extended term occurs ir
the major or in the minor premise, the error is called illicit
process of the major or illicit process of the minor.
In the foregoing instance, the illicit process is in the minor.
We give an instance of illicit process of the major.
All Y is Z All men are fallible.
Some X is not Y Some beings are not men.
No X is Z No beings are fallible.
The major term ‘fallible,’ being the predicate of an affir-
mative proposition, is particular or undistributed ; in the con-
clusion, it is the predicate of a negative proposition, and is
therefore distributed.
(5.) There can be no conclusion drawn from negative premises.
No Y is Z No men are gods
NoXis Y No trees are men °
do not supply the materials for a deductive inference. The
reason of this is already apparent from what has been said as
to the applying proposition, which must always ajirm. To
know only that two things are each excluded from a third
thing is to know nothing concerning their mutual relation.
(6.) If one premise be negative, the ‘conclusion must be negatine,
HAMILTON’S CANONS. 151
This is illustrated throughout the series of valid syllogisms.
If one premise be negative, all that is predicated concerning
one of the terms is its exclusion in whole or in part from the
middle term: we cannot, therefore, conclude through the
medium of the middle term anything about its total or partial
co-extension with the other term.
_ In order to facilitate the detection of unsound syllogisms,
the two following rules, directly deducible from these canons,
are also enounced.
A. There is no inference from particular premises.
Some Y is Z Some Y is Z
Some X is Y Some X is not-Y
give no conclusion. The first example contains an undistri-
buted middle; and the weakest inference drawn from the
second (Some X is not Z) would contain an illicit process of
the major.
B. If one premise is particular, the conclusion must be par-
ticular.
As in Darit, Ferio, &c.
Any attempt to extract a universal conclusion where both
premises are not universal would incur either undistributed
middle or illicit process.
This last canon, and also the Sixth, are embraced in one
statement—‘ The conclusion always follows the weaker part.’
8. Hamilton’s Canons. These are three in number, The
first contains the 1st and 2nd of the foregoing list (Three
Terms and Three Propositions). The two others are as
follows :—
II. Of the Premises, the Sumption must in Quantity be
defimite (i.e. universal or singular); the Subsumptioa in
Quality affirmative.
As Hamilton means by the Sumption the universal or
ground proposition, and by the Subsumption, the applying or
subsuming proposition, this is declaring the characters of the
standard syllogism. It appears that, through all the mutations
of syllogistic moods, there must always be one universal
proposition (or else a definite singular), and one affirmative
proposition. (The meaning of the alternative, a singular propo-
sition will appear afterwards).
III. The conclusion must correspond in quality with the
Sumption, and in guantity with the Subsumption.
Whatever be the quality of the Universal or ground propo-
sition, that must be the quality of the conclusion; the one
152 THE SYLLOGISM.
being affirmative the other is affirmative; the one negative,
the other is negative.
Again, the quantit y of the Applying proposition is the true
quantity of the conclusion; universal giving universal, and
particular giving particular.
These two rules of Hamilton’s are given as the equivalent
for Whately’s four last. They have the advantage of placing
ina due prominence the fundamental structure of deductive
reasoning, which is altogether invisible in the foregoing canons; -
but they are uot readily applicable to the more distorted
figures. Before using them, we must first discover which term
contains the sumption, and which the subsumption; and for
this, we must refer to the directions given respecting the
irregular moods. In short, we must first redress the inver-
sions and distortions of the irregular moods, which is substan-
tially to go through the process of reducing each to the first
figure.
9. The rules of the syllogism given in the form of separate
canons for each figure. For the First or standard Figure,
the canons of Hamilton are the most suitable expression.
For each of the other Figures, special canons may be
framed according to the nature of the F igure.
. Thus, in the second Figure, it can be shown that,
(1) One premise ts neg gate.
(2) The major premise is wniversal,
The proof is easy. (1) If both premises were affirmative,
the middle term being the predicate of both premises, it would
be undistributed.
Again, (2) ifthe major were particular, the weakest conclusion
that could be drawn, Some X is not Z, involves illicit process
of the major.
It follows from the first of the two rules (One premise must
be negative) that, in this Figure, it is possible to prove negative
conclusions only.
In the Third Figure, the canons are,
(1) The minor premise is affirmative.
(2) The conclusion is particular.
If the minor premise were negative, the conclusion must be
negative, and the major term affirmative, which would involve
an illicit process of the major.
Again, the conclusion must be particular, whether the
syllogisms be affirmative or negative.
The minor premise being affirmative, there cannot be @ uni-
SPECIAL CANONS OF THE FIGURES. 153
versal affirmative conclusion without illicit minor. In a uni-
versal negative conclusion both terms are distributed: and
they cannot both be distributed in the premises, unless both
premises were negative, which could not be.
In the fourth Figure,
(1) Ln the negative moods, the major is universal.
Some Z is not Y, Some Z is Y
All Y is X, No Y is X
- could not yield even particular conclusions, without illicit
process of the major. We should have to infer—Some X is not
Z: and Z is undistributed in the premises in consequence of
the particularity of the major.
(2) Uf the major is affirmative, the minor is universal.
A particular minor to an affirmative major would give
All Z is Y, All Zis Y
Some Y is X, Some Y is not X
both forms containing undistributed middle.
(3) If the minor is negative, both premises are universal. Try
' All Zis Y, Some Z is Y,
Some Y is not X, No Y is X.
There is, in the first form, undistributed middle; and in the
second, the weakest conclusion, Some X is not Z, contains
illicit process of the major.
This rule is implied in the two preceding. By the First
rule, the Major is universal, because the mood is negative. By
the Second rule, the Minor is universal, because the major is
affirmative.
(4) Ifthe minor is affirmative, the conclusion is particular.
With minor affirmative, we have—
. All Z is Y, NoZis Y
All Y is X, All Y is X,
In both cases, a universal conclusion would be attended with
illicit process of the minor.
10. That the valid moods are those above given, and no
more, is shown by testing all the other possil.e moods ac-
cording to the syllogistic canons.
The possible moods may be arrived at by computing the
possible groups of threes that can be made out of the four pro-
positional forms—A, I, E, O. Now, taking the premises alone,
there are sixteen different couples that can be made from these
four letters.
A,A I, A HE, A O, A
AI (41) EI (6,1
154 THE SYLLOGISM.
A,E I, E (E,E) (0,5)
A,O (1,0) (8,0) (0,0).
Of these sixteen forms, we can reject at once, as inad-
missible, first, those that have both propositions particular—
II, 10, OI, OO. Wecan farther reject those that have
both negative—E H, E O, O E (O O is rejected on the pre-
vious ground). After these seven rejections, there are nine
forms remaining.
For a farther sifting, two methods are open to us. First,
let us try whether every one of the nine couples may stand as
premises to conclusions of all the forms, A, I, H, O.
A, A, A (A, I, A) (A, B, A) to AnQ,A)
A, Ayddovos aaj ©) ody eal
(A, A, EH) (A,I, B) A, E, H (A, O, B) -
(A, A, O) (A, I, O) A, E, O A, O, O
and so on through the remaining five forms.
Now, by applying the canon that requires a particular con-
clusion when one of the premises is particular, we exclude two
in the second column—A I A, A I H, and two in the fourth—
AOA, AOE. By applying the canon that requires a nega-
tive conclusion when one of the premises is negative, we ex~
clude, in the third column, A E A, A E 1; in the fourth
column, A O J (also A O A excluded on the previous ground),
Although no express canon is laid down requiring an aflirma-
tive conclusion from affirmative premises, such canon could be
proved to be valid ; and by means of it, two exclusions would
be made in the first column—A A H, A A O, and one farther
exclusion in the second. Hence, of the sixteen forms, six only
survive these successive purgations By a similar operation,
extended to the remaining twenty forms, it would appear that
there are in all twelve forms admissible ;—
AAA, AAI AEH, AEO, All, AOQ
HAH, EAO, EIO, IAD, LEO 40a
If these twelve forms were each admissible in all the Figures,
there would still be forty-eight valid syllogisms. But, by
stating them under the successive figures, their ranks are
thinned still farther. Thus, in the First Figure, A A I and>
A EO are superfluous because they infer a smaller conclu-
sion when a larger could be drawn; with the premises A A,
we can infer A (Barbara); with A E, we infer EH (Celarent).
Of the remaining ten, six would involve violations of funda-
mental canons, as may be seen by expressing them in full,
Two examples are enough. Thus, A E E gives—
All Y is Z All men are mortal
SIFTING OF THE VALID MOODS. 155
No X is Y No molluscs are men
No X is Z No molluscs are mortal
which contains illicit process of the major. The same would hap-
pen under a particular conclusion, as in A, H, O. Again, 1,A, 1—
Some Y is Z Some fishes are sharks
All X is Y All salmons are fishes
* Some X is Z Some salmon are sharks—
has the middle term undistributed.
By operating in this manner, we reduce the valid moods of
the First Figure to the four formerly given—A A A, E A H,
AITEIO. :
The same process repeated for the remaining figures has
the result of reducing the admissible forms to those actually
given in the scheme of the syllogism. !
The other method of elimination is to apply the special
canons of the figures to the nine forms of unobjectionable
premises, A A, Al, &c. By the canons of the standard syllo-
gism, the major is universal and the minor affirmative ; whence
the forms, A E, A O,J A, O A, are rejected at once ; and there
remain only the four, A A, AI, HK A, EI, corresponding to the
four moods of the First Figure. For the Second Figure, the
canons (One premise is negative; the major is universal)
exclude A A, AI, I A,I H, OA; leaving A E (Camestres), AO
(Baroko), E A (Cesare), EK I (Festino). For the Third Figure,
the first canon (The minor is affirmative) excludes A E, A O,
IE; and there remain A A (Darapti), A I { Datisi), I A (Disa-
mis), EH A (Felapton), EH I (Lerison), O A (Bokardo).
For the Fourth Figure, the first canon (In the negative
moods, the major is universal) excludes I H,O A. The second
canon (If the major is affirmative, the minor is universal)
excludes AI, AO. The remainder are A A (Bramantip), AB
(Camenes), I A (Dimaris), EH A (fesapo), EK I (Fresison).
AXIOM OF THE SYLLOGISM.
11. Logicians have aimed at reducing the whole of the
special canons or rules of the Syllogism to one comprehen-
sive Law or Principle.
The oldest form of this principle is that named the
Dictnm de omni et nullo. ‘ Whatever is affirmed or denied
of a class, is affirmed or denied of any patt of that class,’
As stated, this maxim seems merely one of the forms of Im-
mediate Inference :—‘all men are mortal,’ hence ‘this man,
ten men, some men, are mortal.’ ‘his, however, is not the
156 AXIOM OF THE SYLLOGISM.
form actually assumed by the syllogism. We have to prove
that some object is mortal, not expressly named a man, but
designated by some other title, as ‘king.’ We cannot say
‘men are mortal,’ therefore ‘ kings are mortal ;’ such an infer-
ence can be made only through an intermediate assertion,
‘kings are men.’ |
Another defect has been pointed out in the diclwm: namely
that it proceeds upon the old erroneous view of a proposition,
the reference of a thing to qa class. This, however, might be
got over by understanding ‘ class’ to mean the class indefindte,
marked by the connotation of the class name. Practically,
such must be the case; we have no means of pointing out the
class ‘men,’ except as the possessors of human attributes. _
Considering the dictwm as the basis of all Deductive Reason-
ing, we might amend it thus :—‘ whatever is true of a whole
class (ciass indefinite, fixed by connotation), is true of whatever
thing can be affirmed to come under or belong to the class (as
ascertained by connotation).’ This supposes the need of a
second affirmation, the minor proposition, and is no longer an
immediate inference.
12. The defects of the dictum are supposed to be remedied
by this form :—
Attributes, or Things, co-existing with the same Attri-
butes or ‘l'hings, co-exist with one another (Affirmative).
If the attributes of a king co-exist with those of a man, and
the attributes of a man co-exist with the attribute ‘ fallibility,’
the attributes of a king co-exist, or co-inhere with the attribute
fallibility. |
There is a close resemblance between the present form and
the mathematical axiom—Things equal to the same thing, are |
equal, The two are alike axioms of mediation; they connect
two things by a common third. |
The negative form is stated thus :—‘ One thing co-existing
with a second thing, with which second thing a third thing —
does not co-exist, is not co-existent with that third thing;
which resembles the axiom—Things unequal to the same thing, —
are unequal,
This mode of stating the axiom has often been adopted by
logicians :—.Vota note est nota rei ipsius ; Things that agree in
the same third, agree among themselves. For the negative
form —repugnans note, repugnat rei ipsi; Things whereof the
one agrees, the other does not agree, with the same third, do
not agree among themselves.
¥
NOTA NOTA. 157
The advantages of the form are indicated by the remarks
already made. It gives very great prominence to the fact of
mediation in Deductive Inference, and thus draws a broad line
between it, and Immediate or Apparent Inference. It also
accommodates itself to such a case as Darapti, with a singular
subject, thus,
7 Socrates was wise.
Socrates was poor.
Some wise men have been poor.
Now, the treating of a Singular proposition as a universal,
which is necessary to make the above a regular syllogistic
form, has always seemed a great anomaly in the syllogism.
Indeed, it is asubversion of the theory of Deductive Reasoning,
as supposed to consist in the application of a general or uni-
versal principle to a case coming under it. But, if we accept
the present form of the axiom, the above syllogism is rendered
with apparent ease. ‘Wise’ co-exists with ‘Socrates ;’ ‘Poor’
co-exists with Socrates; therefore ‘ Wise’ and ‘ Poor’ co-exists
with one another ; that is, ‘ Some wise persons are poor.’
A farther advantage of the same form consists in following
out the the ‘ Connotation’ theory of Propositions. The exten-
sion of the several propositions is completely banished from it,
and nothing but Connotation or Comprehension left. It is no
longer ‘all A is B,’ but the attribute A co-exists with the
attribute B,’andsoon. From the same cause, a seeming facility
is given in chains of reasoning, which can be rendered thus:
—A is a mark of B, B of C, C of D; wherefore A is a mark
of D.
Notwithstanding so many advantages, this form of the axiom
now described is unworkable as a basis of the syllogism. The
fatal defect consists in this, that it is ill adapted to bring out
the difference between total and partial coincidence of terms, the
observation of which is the essential precaution in syllogizing
correctly. If all terms were co-extensive, the axiom would flow
on admirably; A carries B, all B and none but B; B carries
C in the same manner; whence A carries B, without limita-
tion or reserve. But, in point of fact, we know that while A
carries B, other things carry B also, whence a process of limita-
tion is required, in transferring A to C through B :—A (in com-
mon with otber things) carries B; B (in common with other
things) carries C; whence A (in common with other things)
carries C. The axiom provides no means of making this limi-
tation ; if we were to follow A literally, we should be led to
suppose A and C co-extensive: for such is the only obvious
158 AXIOM OF THE SYLLOGISM.
meaning of ‘the attribute A coincides with the attribute
is
Unless the predicate is quantified, as Hamilton recommends,
the propositional form in Extension—‘ all men are mortal,’
does not explicitly suggest that ‘men are buta part of mortals ;’
yet we can readily conceive the fact when reminded of it ; the
extent of ‘mortal beings’ is greater than the extent of ‘ men.’
But the proposition stated in pure connotation or comprelhen-
sion, as the present axiom requires,—‘ the attributes of men co-
exist with the attribute mortality’—is difficult to adapt to the
fact that mortals are more numerous than man. We should
have to make a still greater circumlocution :—the attributes
of men co-exist, but are not the only attributes that co-exist,
with the attribute ‘mortality.’ So, the attributes of a king
co-exist, but are not the only attributes that co-exist, with the
attributes of men. The conclusion would then be—The
attributes of a king co-exist, but are not the only attributes
that co-exist, with the attribute ‘ mortality.’ Now, as the
axiom ‘attributes co-existing with the same: attribute co-exist
with one another’ does not suggest these necessary limita-
tions, it is not, as worded, an explicit basis for the syllogism,
_ It is only the same objection, otherwise put, that the axiom
does not accomniodate itself to the type of Deductive Reason-
ing, as contrasted with Induction—the application of a general
principle to a special case. Anything, that fails to make pro-
minent this circumstance is not adapted as a foundation for the
syllogism.
The scientific processes of Induction and Deduction are
habitually conceived on the basis of Extension; it is only thus
that we readily appreciate the greater or less generality of
propositions. Hence the proper view of the syllogism, as of
the notion and the proposition, is to base it on Extension, but
to determine the extension by Connotation or Comprehension.
‘ All men are mortal’ is best understood as the conerete
population of human beings, defined and determined by the
class attributes of humanity. This double point of view com-
plies with all the exigencies of reasoning, and is not advan-
tageously surrendered in favour of the statement of propositions
in pure comprehension.
The result of the comparison of the two axiomatic state-
ments is, that the Dictwm de omni et nullo, properly guarded,
is the most suitable and exact repr esentation of the cepeintind
feature of Deductive Reasoning or Syllogism.
The case of Singular Propositions, held for the nonce to be
. ai
SINGULAR PROPOSITIONS. 159
universal, is a grave exception to the Deductive process as we have
uniformly described it. On-examining such cases, however, we
may see good reason for banishing them from the syllogism. Let
us take the example already quoted :—
Socrates is poor
Socrates is wise
Some poor men are wise.
Properly, the conclusion is, ‘one poor man is wise.’ Now, if
‘ wise,’ ‘poor,’ and ‘a man,’ are attributes belonging to the mean-
ing of the word Socrates; there is then no march of reasoning at
all, We have given, in Socrates, inter alia, the facts ‘wise,’ ‘ poor,’
and ‘a man, and we merely repeat the concurrence, which is
selected from the whole aggregate of properties making up the
whole, ‘Socrates.’ The case is one under the head ‘ Greater and
Less Connotation,’ in Equivalent Propositional Forms, or Immedi-
ate Inference.
But the example in this form does not do justice to the syllogism
of singulars. We must suppose both propositions to be real, the
predicates being in no way involved in the subject. Thus :—
Socrates was the master of Plato
Socrates fought at Delium
The master of Plato fought at Delium.
It may fairly be doubted whether the transitions, in this
instance, are anything more than equivalent forms. For the
proposition, ‘Socrates was the master of Plato, and fought at
Delium,’ compounded out of the two premises, is obviously nothing
more than a grammatical abbreviation. No one can say that there
is here any change of meaning, or anything beyond a verbal
modification of the original form. The next step is, ‘the master
of Plato fought at Delium,’ which is the previous statement cut
down by the omission of ‘Socrates.’ It contents itself with
reproducing a part of the meaning, or saying less than had been
previously said. The full equivalent of the affirmation is ‘the
master of Plato fought at Delium, and the master of Plato was
Socrates ;’ the new form omits the last piece of information, and
gives only the first. Now, we never consider that we have made
a real inference,.a step in advance, when we repeat /ess than we
are entitled to say, or drop from a complex statement some portion
not desired at the moment. Such an operation keeps strictly
within the domain of Equivalence or Immediate Inference. In no
way, therefore, can a syllogism with two singular premises be
viewed as a genuine syllogistic or deductive inference.
13. The Proof of the Axiom is uncontradicted experi-
ence.
The Dictum is not a mere rule of consistency, exacting the
admission, in equivalent forms, of all that has been conceded
in one form. It is a mediate process, and the mediation has
to be justified by an appeal to the facts. As far as proof goes,
8
160 AXIOM OF THE SYLLOGISM.
it resembles in character the second form above given— Things
co-existing with the same thing, co-exist,’ and the mathema-
tical axiom ‘ Things equal to the same thing are equal.’ All
the three principles stand upon the same foundation ; some
philosophers refer them to intuition, others to experience ; but
the mode of proof for one is the mode for all.. The dictum
seems to approach nearest to a mere rule of consistency ; yet
the fact of mediation makes all the difference; ‘ the identical
of an identical is identical ’ is a new step and needs a new jus-—
tification. Nobody would accept even so obvious an inference
—as ‘men are mortal, kings are men, kings are mortal,’ with-
out first verifying upon examples the peculiar kind of transi-
tion involved. Weare so alive to the snares lurking in the
most obvious and plausible forms of language, that we do not
trust any of them without the check of actual trials. Nothing
could seem more satisfactory than ‘ A co-exists with B, B with
C, therefore A co-exists with C wholly and unconditionally,’ yet
until we have elaborately fenced the operation against the
simple conversion of a universal, the conclusion is unwarranted.
Viewing together the Mathematical axiom of Equality and the
axiom of the Syllogism, Mr. de Morgan remarks :—‘ In both there
is a law of thought appealed to on primary subjective testimony of
consciousness ;’ ‘ equal of equal is equal’ in the one; ‘ identical of
identical is identical’ in the other. The two laws are equally
necessary, equally self-evident, equally incapable of being resolved
into simpler elements.
14. There are other modes of stating the Axiom. Hamil-
ton has two forms. The first is for what he calls Informal
Reasoning :—In so far as two notions (notions proper or
individuals) either both agree, or one agreeing the other
does not, with a common third notion; in so far, these
notions do or do not agree with one another. .
_ This is simply one way of wording the Nota note, and is
liable to the objections urged against that form. There is no
provision for distinguishing total from partial agreement, and
therefore no basis for the working of the syllogism. The
words ‘agreement’ and ‘ disagreement’ are less apt than ‘co-
existence’ and ‘non-coexistence’ for expressing the axiom;
they have the defects inherent in the ‘judgment’ theory of
Propositions.
15. For the Figured Sylogism, where the terms are re-
lated as subject and predicate of propositions in a given
: os
OI ae 2 T
HAMILTON’S FORMS, 16]
order, Hamilton enounces this form:—What worse re-
lation of subject and predicate subsists between either of
two terms and a common third term, with which one, at
least, is positively related; that relation subsists between
the terms themselves.
The peculiar phraseology ‘ What worse relation’ is a man-
ner of saying that the conclusion must carry the weakest re-
lationship signified by the premises. If there be a negative in
the premises, there must be a negative in the conclusion ; if
there be particularity in the premises, there must be particu-
larity in the conclusion. The same thing is otherwise ex-
pressed—‘ The conclusion must follow the weaker part.’
This is the Axiom given in Extension, and is in accordance
with the Dictwm, although not stated with the same generality.
It more resembles one of the canons for working out the syllo-
gistic details, itself resting on the Dictum.
16. The first of Hamilton’s two forms is expressed
otherwise thus (Thomson) :—The agreement or disagree-
ment of one conception with another, is ascertained by a
third conception, inasmuch as this, wholly or by the same
part, agrees with both, or with only one of the conceptions
to be compared.
This form appears to be based upon Comprehension, or the
Nota note, but endeavours to introduce the limitations requisite
for discriminating total and partial quantity. The phraseology,
however,—‘ conception, &c.’—is ambiguous; it may express
either extension or comprehension—‘ men’ or the attributes
‘human.’ If, taken in extension (which is most probable), is
closely reproduces Hamilton’s second form, and puts stress
upon the difference between total and partial coincidence.
Nevertheless, it does not rise to the sweep of the Dictuin,
in declaring the paramount circumstance of deductive reason-
ing,—the carrying out of a general law to particular cases.
lf ‘conception’ means attributes, comprehension, or conno-
tation, the phraseology would indicate Hamilton’s syllogism of
Comprehension, and would not suggest the common syllogism.
The attributes * king’ and the attribute ‘mortal’ agree (better
‘ coincide’) by agreeing (coinciding) with the same part of the
attributes ‘human.’ Hamilton’s syllogism is more explicit ;
thu:—The attributes ‘king’ contain the attributes ‘man;’
the attributes ‘man’ contain the attribute ‘mortal ;’ the
att:ibutes ‘king’ contain the attribute ‘ mortal.’
.- Oe eee
ree el a
Pl
162 AXIOM OF THE SYLLOGISM.
17. In the comprehensive scheme of De Morgan, the
axiom is a generalization of many special axioms. The
syllogism is treated as the composition of two relations
into one ; the axiom is ‘ the relation of a relation is a rela
tion compounded of the two,’ or
The truth of this is seen, and its application controlled, by
the special instances of relationship. One of these instances is
the axiom of the common syliogism. Others are the mathe-
matical axioms, ‘ Equal of equal is equal,’ and ‘greater of
greater is still greater’ (a fortiori). Among more special in-
stances are ‘ antecedent and consequent,’ ‘ancestor and
descendant. | Ss
18. It has been supposed by some that the common
axiom, as expressed by the ‘dictum de omni et nullo,’ is
a consequence of the Laws of Thought (Identity, Contradic-.
tion and Excluded Middle).
Hamilton maintains that categorical syllogisms are regulated
by the fundamental laws of Identity and Contradiction. He
interprets the law of Identity as the identity of a whole and
the sum of its parts, whence he considers it right to infer
that what belongs to a whole belongs to its part. Mr. Mansel
agrees with Hamilton in referring the syllogistic laws to the
same principles. .
The effect of this doctrine is to abolish the difference be-
tween Immediate and Mediate Inference, by bringing mediate
inference under Immediate, or under the law of Consisteney.
On the face of it, the supposition is unlikely ; and accordingly
it has been denied by other logicians. Thus, Mr. de Morgan
(Syllabus, p. 47) remarks of the attempts to reduce the syllog-
ism to the three so-called Laws of Thought, ‘When any one
attempts to show how, I shall be able to judge of the process;
as it is, I find that others do not go beyond the simple asser-
tion, and that I myself can detect the petitio principit in every |
one of my own attempts.’ a
The law of Consistency requires us to concede that what is
true of a class is true of every individual in the class; ‘all men
are fallible,’ ‘ the half of men are fallible, this man is fallible’? ;
here there is no transition, it is the same fact, repeated only to
a less extent. But when we say ‘kings are men,’ ‘ kings are
fallible,’ there is a transition to a different subject, a subject
not present to the mind as a part of the original whole, but 4
brought under it by a second assertion, Now a distinct axiom, |
7
DERIVATION OF SPECIAL CANONS. 163
is needed to transfer the attribute under this new case. The
axiom may be in its nature self-evident, but the conclusions
regulated by it are not identical with either of the premises, as
an immediate inference, properly so called, is identical with the
original form.
19. The special canons of the Syllogism are derivable
from the Axiom.
(1) It easily follows from the Dictum, as explained, that
there are three terms, and no more. There is a Universal Pro-
position containing a subject and a predicate, an applying or
Interpreting proposition, adding a third term, and repeating
one of the terms of the universal:—All or no Y is Z, All X
is Y. The conclusion contains no new term-—All X is Z.
Whence there are three terms in all.
(2) The same examination shows that there are three and
no more than three propositions ;—the Universal, the Inter-
preting Proposition, and the Conclusion.
(3) The third special canon is—‘ The middle term must be
distributed once in the premises.’ Distribution or Universal
Quantity in the middle term is essential to the total coincidence
or non-coincidence of at least one of the other terms with the
middle term ; without which the two extreme terms could not
be shown either to coincide, or not to coincide, in whole or in
part. ‘Some men are fallible,’ ‘kings are some men,’—would
not bring about a coincidence between ‘ fallibility’ and ‘ kings ;’
one portion of men might be fallible, and a different portion
might be kings. This is obviated if fallibility adheres to all
men ; it must then adhere to whatever objects are found to be
men.
(4) The fourth special canon is—-‘ No term undistributed
in the premises must. be distributed in the conclusion.’ It may
be brought under the Dictum thus:—The distribution of a
term in the conclusion means universal or total coincidence
with the other term of the conclusion ;—* All X is Z’ means
that X is wholly coincident with, wholly included in Z. Now
X and Z are brought together by a middle term Y; and if X
did not wholly coincide with Y in the first instance, it could not
be transferred, in total coincidence, to Z. If we had only some
X is Y, even although all Y is Z, we could not declare all X to
be Z. There is carried over to Z ouiy so much of X as goes
with Y ; if that be the whole, the whole is carried ; if a part,
part iscarried. If ‘all men are fallible,’ and ‘some beings are
men,’ only some beings are fallible, namely, as many as are men,
164 AXIOM OF THE SYLLOGISM,
(5) ‘ From negative premises, there is no inference.” Nega-
tive premises do not comply with the essential fact of the in-
terpreting proposition, which is to declare that a given case
comes under the sweep of the rule. -Whether the universal
be affirmative or negative, the applying proposition must, from
its nature, be affirmative. No Y is Z,no X is Y, could not be
the means of bringing X under Z, or of bringing these two
terms together in a conclusion ; we could not, from such pre-
mises, infer even No X is Z. ‘No matter is destructible’ re-
quires to be followed up with ‘ether is matter’ to prove that
‘no ether is indestructible.’
(6) ‘If one premise be negative, the conclusion is negative,’ ex-
presses exactly what happens in the negative form of the axiom.
In the enlarged scheme of De Morgan, some of these rules
are violated in appearance, but only in appearance. Thus
from ‘two negative premises’ he draws a conclusion in the
affirmative. This, however, arises from the elasticity of ex-
pression allowed by the use of contrary forms. Every affirma-
tive proposition may be given as a negative; and there may
be the semblance of negation, with the reality of affirmation
in conformity with the axiom. Thus—
AllYisZ =z No/Yisnot%
All XisY = No X is not Y.
All X is Z All X is Z.
20. The axioms—‘ Equals added to equals, give equal
sums, and the argumentum a fortiori, if received as axioms
in Logic, are distinct from the axiom of the Syllogism, and
must be independently proved. |
The argumentum a fortiort is represented thus:—If A is
greater than B, and B greater than C, still greater is A than
C. This, and the other axiom stated, are purely mathematical
in their character; they serve for the comparing of quautitics
as equal or unequal. They rest on their own special evidence
of fact. |
It will be seen that Boole draws the Syllogism under the
axiom that suffices for the reduction of equations. He assumes
that the analogy of the logical method and the algebraical is
sufficiently close to allow of the substitution.
The conflicting opinions as to the evidence of axioms gener-
ally, whether of logic, of mathematics, or of other sciences, will
be discussed in a succeeding chapter.
~ TESTING OF ARGUMENTS, 165
EXAMPLES OF THE SYLLOGISM.
21. The chief application of the theory and the forms of
the syllogism is to detect fallacies in deductive reasonings.
There are certain forms of deductive reasoning or argument,
that are specious to appearance, and fallacious in reality ; and
the analysis of the syllogism is useful in disclosing the fallaci-
ousness.
22. The course of procedure, in dealing with an argu-
ment in any way uncertain or perplexed, is as follows :—
I. Ascertain what is the conclusion, or the point to be
proved. State this distinctly in a proposition so as to dis-
tinguish the Subject (minor term of the syllogism) and the
Predicate (major term).
Il. Find out the middée term of the argument. In a valid
syllogism there must be a middle term, and only one: and it
must be something not occurring in the conclusion.
IIf. Find out some proposition connecting the middle term
with the major term; this is the major premise of the syllogism.
Also some proposition connecting the middle term with the
minor term; giving the mimor premise of the syllogism.
IV. The two premises and the conclusion being stated in
form and order, the validity may be judged according to the
laws of.the syllogism.
(1) If the deduction coincides with any of the valid moods,
it is valid; if not, not.
(2) It being seen what Figure the argument comes under, it
may be tested by the special canons of that figure.
(3) The general canons of the syllogism may be applied to
discover errors, if there be any such.
Any one of these three modes may be adopted at choice ;
inasmuch as each of them singly is conclusive.
The easiest remembered mode of testing a syllogism, when
once in form, is by the six general canons of the syllogism.
Of these, the two that are most usually violated in sophistical
reasonings are the 3rd (Distribution of the Middle Term) and
the 4th (‘The quantity of the terms in the conclusion not greater
than in the Premises). An argument with negative premises
(5) would deceive no one. It would also be obvious, without
much Logic, that one premise being negative, the conclusion
must be negative (6).
23. As an alternative, we may discard the consideration
166 EXAMPLES OF THE SYLLOGISM.
of the separate Figures, and reduce every argument at once
to the standard form of Deduction.
From the very nature of deductive reasoning, the conclusion
is a special application of some more general proposition.
This more general proposition must be found in the premises 3
itis the ground proposition ; in Hamilton’s phraseology, the
Sumption. There must also be found another proposition
declaring its applicability to a particular case, namely, the
case given inthe conclusion. ‘These two indispensable proposi-
tions may occur under distorted forms, which we must be able
to redress by the methods already pointed out, that is, by
obversion and conversion, as the case may be. Also, the
eonclusion may require to be obverted or converted, or both.
By such methods, we may evade all the variations of figure,
and come at once to the regular type of deduction.
EXAMPLES.
All men are mortal All Y is Z7.—(A)
No dogs are men No X is Y.—(E) 7; 1st Fig.
No dogs are mortal No X is Z.—(E)
(1) This syllogism is in the First Figure, but there is no
mood in that Figure containing the propositions A, EH, E.
(2) Otherwise: The major term, mortal, is distributed in
the conclusion, and not in the premises ; there is illicit process
of the major.
(3) Or lastly : It contradicts the canon of the normal syllo-
gism, whereby the minor is declared to be affirmative.
All planets are round All Z is Y.—A
A wheel is round All X is Y.—A }2nd Fig,
A wheel is a planet All X is Z.—A
(1) There is no such mood in the Second Figure,
(2) The middle term, ‘ round,’ is undistributed.
(3) There is a violation of the special canon of the Second
Figure—One premise must be negative.
‘Every honest man attends to his business; this person
attends to his business ; this person is an honest man.’ This
is the exact counterpart of the foregoing. The conclusion
being ‘this person is an honest man ;’ the minor term is ‘ this
person,’ the major, ‘an honest man.’ The middle term is
‘attends to his business.’ The major premise (major and
middle), ‘Every honest man attends to his business,’ A; the
minor premise, ‘this man attends to his business,’ A (a definite
7) ?.?
i eee a
FALLACY OF CONVERSION. 167
individual may be considered as either A or I). Onany one of
the three grounds given in the foregoing example, the reason-
ing is fallacious.
These. two examples are regarded by logicians as‘of a type
calculated to mislead, and therefore exemplifying the use of
the laws of the syllogism. It is interesting to enquire what
circumstance gives them their fallacious plausibility. With
this view, we may proceed by the alternative method above
pointed out, namely, by ascertaining whether these be the
regular premises of deduction.
To prove that a wheel is a planet, we must have a more
general proposition, of which this shall be a particular case.
Such a proposition would be ‘all round bodies are planets:’
We should then require an applying or subsuming proposition,
namely, ‘wheels are round bodies.’ With these two proposi-
tions, the conclusion would be legitimate, that wheels are
planets. Looking at the premises given, however, we do not
find a proposition corresponding to the first, or the general
proposition. It is stated, not that ‘all round bodies are
planets,’ but only that ‘all planets are round,’ a different
proposition. The confounding of the two is effected by the
simple conversion of a universal affirmative; by arguing from
‘all planets are round,’ that ‘all round bodies are planets,’
which we can do only if there are no round things but planets.
In short, the fallacy, traced to its root, isa fallacy of conversion ;
and if we are liable to be deceived by such syllogisms as the pre-
sent, it is because we are liable to slip into this fallacy. There is
something in the form of the universal affirmative that throws
us off our guard; from the expression All X is Y, we are apt
to assume the co-extension of X and Y, unless cautioned and
educated to the contrary. In cases where the co-extension
exists, and only in such cases, could the argument in question
give a sound conclusion. Thus—
All matter gravitates.
Air gravitates.
Air is matter.
Now, by the same process as before, it is shown that the
general proposition needed for this conclusion is ‘ All gravi-
tating things are matter,’ which happens to be true, but is not
justified by the assertion in the major, ‘all matter gravitates ;’
for there might be other gravitating things.
So in the second example ‘ Every honest man attends to his
business,’ &c., we should require the terms ‘ honest man’ and
‘attention to business’ to be co-extensive, which they are not.
dy cy. ee .
7 . A +.
: .
168 EXAMPLES OF THE SYLLOGISM.
Whatever tendency we have to be deceived by such reasonings
depends solely upon the intellectual weakness of presuming
co-extension of terms, in universal affirmations.
Hume says:—‘ We have no perfect idea of anything but a
perception. A substance is entirely different from a perception.
We have therefore no idea of substance. ’
The first step is to resolve the conclusion into its two terms.
As often happens, in Logic, these terms are not the grammati-
cal subject and grammatical predicate ; a transformation must
be given to suit the tenor of the premises. Comparing the
first proposition with the last, we see that the mor term, or
subject of the conclusion, must be ‘having an idea;’ the
major term is ‘substance. The affirmation is negative ;
literally, our ‘ having an idea’ is not true of substance. It is
denied that substance is one of the things included under
having an idea. The next point is to single out the middle
term, namely, ‘ perception.’ Joined with the major and minor
terms respectively, this yields as premises—
No ‘having an idea’ is not perception.
All substance is not perception.
No ‘having an idea’ is true of substance.
In the present form, the reasoning is wholly inadmissible ; the
premises are both negative. We might, however, obvert the
middle term ‘perception,’ and regard not-perception as the
true middle (like changing ‘ not wise’ into not-wise, or foolish).
We have thus—
No ‘ having an idea’ is poP neta ae E
All substance is not-perception A | 2nd Fig. (Cesare).
No ‘having an idea’ is substance. H;
In this form the argument is sound.
It is often desirable to express arguments of great subtlety,
such as the present, in the standard form of deduction. The
requisite transmutation would have to be effected thus. The
conclusion, ‘ “‘ having an idea” is not true of substance,’ is to
- be converted ‘No substance is included in our having an
idea,’ For this, the universal proposition would be a proposi-
tion of denial more comprehensive than substance :—No
not- perception is included in our having an idea, The minor
is then, All substance is not-perception ; whence we conelude
according to the regular form for the negative deduction.
From the middle term being a negation, however, this, can
never be an easy form of argument; and more especially so in
3
1
4 * =
eee et ie
a 2
oe Lee el
wc ro
EXAMPLES OF THE SYLLOGISM. 169
the present argument, where perception is as wide as exist-
ence, and has only a formal, and not a real obverse.
Thus, then, we have, in the First Figure, as Ceiwrent—
Nothing that is not a perception (no not-perccption) can
be perfectly conceived, :
Substance is not a perception (a not-perception), A.
Substance cannot be perfectly conceived. E.
‘None but Whites are civilized; the Hindoos are not
Whites ; therefore they are not civilized.’
~ Ina syllogism thus :—
. No not-Whites are civilized E
The Hindoos are not Whites A > (Celarent),
The Hindoos are not civilized E
A correct argument, the middle term being ‘ not- Whites,’ for
which the positive equivalent would be the remaining members
of the Universe, ‘races of men ’ (Black, brown, yellow, &c.)
This would give a more intelligible form :—
No communities of the black, browu, or yellow races are
civilized ;
The Hindoos are of the black or brown races,
The Hindoos are not civilized.
* Abstinence from the eating of blood had reference to the
divine institution of sacrifices; one of the precepts delivered
to Noah was abstinence from the eating of blood; therefore,
one of the precepts delivered to Noah contained the divine
institution of sacrifices ’ (Whately).
Although prolix in the wording, there is little distortion in
this example. The minor term is obviously ‘one of the
precepts delivered to Noah,’ the major, ‘contained or had
reference to the divine institution of sacrifices.’ The middle
term is ‘ abstinence from the eating of blood ;’ and the arrange-
ment is exactly as in the standard syllogism.
‘Few treatises of science convey important truths, without
any intermixture of error, in a perspicuous and interesting
form; and therefore, though a treatise would deserve much
attention which should possess such excellence, it is plain that
few treatises of science deserve much attention.’ (Whately).
The conclusion gives as minor term ‘few treatises of
science,’ as major ‘ deserve much attention.” The middle term
is ‘convey important truths, &c.’ The major premise, there-
fore, is—
170 EXAMPLES OF THE SYLLOGISM,
All treatises of science that convey &c., deserve attention:
The minor premise— .
Few treatises of science are works conveying important, &.
The conclusion—
Few treatises of science deserve attention (Dari).
It was formerly remarked (p. 82) that for Some, in the minor
term, we may have—Few, most, many, one, two,—provided
that the same quantity is used in the premises and in the
conclusion, .
‘Enoch (according to the testimony of Scripture) pleased
God ; but without faith it is impossible to please Him ; there-
fore Enoch had faith’ (Whately).
The minor and major terms are obyious. The middle is
‘pleasing God.’ The major premise is—‘ pleasing God is im-
possible without faith,’ which is a circumlocution by way of
expressing emphatically the proposition ‘pleasing God is
having faith ’—‘ all persons that please God have faith.’ The
minor premise being ‘noch pleased God,’ the conclusion fol-
lows from the regular type of deduction:
It was said by some one during the Reform discussions of
1867 :—‘ Every reasonable man wishes the Reform Bill to
pass. Idon’t.’ There was but one inference. The speaker
was not a reasonable man (Camestres). This is a good example
to show that an effective argument may be given out of the
First Figure.
If we follow the ordinary method of reduction in this case,
we find ourselves in a difficulty. Camestres is usually reduced
to the First Figure by transposing the premises and simply
converting the original minor: if we do so in this case, we
find a singular proposition in the major premise, which cannot
be converted without doing great violence to the ordinary
forms of language, and cannot stand as the grounding pro-
position conceived as a general rule. The general rule in this
case is obviously the existing major—‘ Every reasonable man
wishes the Reform Bill to pass.’ But if we view this as the
general rule, then we appear to have a negative applying pro-
position—‘ I don’t.’ Looking more closely at the premises, we
see that the true nature of the predication is disguised. The
major proposition is really negative, and the minor really affir-
mative. The remedy for the distortion is to obvert the major
into—' No reasonable man wishes the Reform Bill to fail ;’ or
‘No man that wishes the Reform Bill to fail is reasonable.’
EXAMPLES OF THE SYLLOGISM. 171
The minor when altered to correspond becomes—‘ I do ;’ and
we have a syllogism in Celarent,
Another example of this same mood, Camestres, illustrates
the occurrence in ordinary reasoning of other syllogistic forms
than the moods of the standard figure. We are presented with
the assertion that ‘No despotism is a good form of govern-
ment,’ and on asking the ground of such an assertion, are
told—‘ Hvery good form of government promotes the intelli-
gence of its subjects, and no despotism does that.’ This is an
argument in Camestres.
Every good form of government promotes Af ee
the intelligence of its subjects.
Es
No despotism promotes, &c.
No despotism is a good form of govern- \ om
ment.
The above statement of the Major is the natural statement of
the proposition ; the order of subject and predicate is such as
a reasoner would naturally observe. ‘That it promotes the in-
telligence of its subject: is affirmed of every good form of
government; the order of the terms conforms to the usual
arrangement of having the largest term in the predicate ;
other agencies than good government promote the intelligence
of the people.
As in the former Camestres, this syllogism cannot be reduced
to the First Figure by the process indicated in the Mnemonic
letters without putting the real Major, or grounding proposi-
tion, in the Minor place. We may retain the present order
without violating the rule that the applying proposition must
be affirmative. For the present major, affirmative in form, is
obviously negative in its bearing; while the minor, negative
in form, is really of an affirmative nature, asserting that a
despotic form of government possesses the character contem-
plated in the ground proposition as precluding the title of
good. By obverting the predicate of the major, the middle
term, we manifest the real character of the premises :—
No form of government that fails to promote the intelli-
gence of its subjects is a good from of government. :
A despotism fails to promote the intelligence of its subjects.
No despotism is a good form of government.
In speaking of the general uses of the Figures, we remarked
that the Third Figure is sometimes useful in making good an
unobtrusive and timid contradictory. The three first moods
172 EXAMPLES OF THE SYLLOGISM.
supply mild contraries to a universal negative; the two last
mild contraries to a universal affirmative. We give an ex-
ample of each.
Suppose a speaker to maintain absolutely and without
reservation that speculation is of no value. His position in
logical fourm is—‘ No speculation is valuable.’ We subvert this
and extort from the speaker a concession that his position is
too extreme, when we obtain his assent to the two proposi-
tions—‘ Some truths affecting human conduct are speculations’,
and ‘ All truths affecting human conduct are valuable.’ These
two propositions involve the sub-contrary of the extreme
negative ;—namely, Some speculations are valuable. They are
given in the order of subject and predicate natural to the
occasion, and they fall into the Third Figure. They serve as
premises either for Disamis, or Datisi, according to the order
we observe in enouncing them. Thus :—
Some truths affecting human conduct } 47,
are speculations
All truths affecting human conduct ree
are valuable
Some speculations are valuable Is
This is a syllogism in Disamis. But it is to be observed that
we invert the normal order of the major and minor terms in
the conclusion. The most natural form is Datisi—thus:— |
All truths affecting human conduct
are valuable ‘ Laat
Some truths affecting human conduct
are speculations
Some speculations are valuable I
If our opponent should concede that all truths affecting
human conduct are speculations, we should have a syllogism
in Darapti. In that case, our partial contradiction would
seem peculiarly bland, because our premises would then be
superfluously strong, and we should have the appearance of
remitting something in the conclusion.
Our next example illustrates the partial subversion of a
universal affirmative by making good its sub-contrary, a
particular negative. It is maintained that no attention should
be given to what isnot practical. This may assume the logical
form of a universal aflirmation,—‘ Everything that is unprac-
tical should be neglected.’ Desiring to Contradict this in
mild form, we may use the following argument :—
i
eae perms a
, ae.
ARNAULD’S UNIVERSAL TEST. 173
No truth applicable to practice should be fF]
neglected.
Every truth applicable to practice may %
seem unpractical. P
Some seemingly unpractical truths should) ,5
not be neglected. 33
This isa syllogism in Felapton. The major—‘ Some truths
applicable to practice should not be neglected,’ would equally
suit our purpose, and with the above minor wonld give a
Bokardo. In such cases as the above, itis difficult to say
which is the grounding proposition. There is no violation of
the essential nature of Deduction in regarding a particular
proposition, or approximate generalization, as the ground of
the argument. To make the reasoning a genuine deduction, it
is required only that the grounding proposition be more
general than the conclusion.
Arnauld’s Universal Test.
It may be worth while to give an example of Arnauld’s
mode of testing a deductive argument without reference to its
logical form.
He directs the pupil simply to observe whether the conclusion
is contained in the premises. He gives the following example
of his method : —
*T am in doubt whether this reasoning be good :—
The duty of a Christian is not to praise those that conmit criminal
actions.
Now those that engage ina duel commit a criminal action.
Therefore it is the duty of a Christian not to praise those that
engage in duels.
* Now I need not trouble myself as to the figure or mood to
which this may be reduced. It is sufficient for me to
consider whether the conclusion be contained in one of the two
first propositions, and if the other show this. And I find at
once that the first proposition, since it differs in nothing from
the conclusion, except that there is in the one, those that com-
mit criminal actions, and in the other those that engage in duels,
—that in which there is commit criminal actions, will contain
that in which there is engage in duels, provided that conumitting
criminal actions contains engaging in duels.
‘ Now it is clear by the sense that the term those that commit
criminal actions is taken universally, and that it extends to all
those that commit any such actions whatever; and thus the
174 EXAMPLES OF THE SYLLOGISM.
minor, Those that engage in a duel commit a criminal action,
showing that to engage in a duel is contained under this term,
commit criminal actions, shows also that the first proposition
contains the conclusion.’
This test of Arnauld’s is the simplest of application to premises
not couched in syliogistic terms. It is easily applied in any
case: the only change of form that could aid in the scrutiny,
would be to make the containing proposition of the same form
with the conclusion.
To the following arguments, the student may supply such
grounding propositions as would give them validity :—
A true philosopher is independent of the caprices of fortune,
for he places his chief happiness in moral and intellectual ex-
cellence.
A slave is a human being, therefore he should not be held in
bondage.
Not being thirsty, he cannot be suffering from fever.
The Reformation was accompanied and followed by many
disturbances, and is therefore to be condemned.
Solon must be considered a wise legislator, seeing that he
adapted his laws to the temper of the Athenians.
He was too impulsive a man not to have committed many
errors.
Educated among savages, he could not be expected to know
the customs of polite society.
Not every advice is prudent, for many advices are not safe.
Many assertions that are open to doubt are nevertheless
worthy of attention, for many assertions that are open to doubt
may be true.
‘Napoleon never cared for anybody but himself.” In modi-
fied opposition to this, it may be urged that, after all, ‘he
was human.’ Supposing this rejoinder is intended to establish
that Napoleon had some disinterested affections, what ground-
ing proposition does it require ?
In like manner, subvert the assertion, ‘ Napoleon never
knew fear,’
Volcanic eruptions, earthquakes, and plagues cannot be
interpreted as a warning to evil-doers, for they involve alike
the innocent and the guilty.
Some dogs are useful animals, for is not the retriever useful ?
All zeal is not virtuous, there being a zeal that has no dis-
cretion,
‘Table-turning,’ (you may say,) ‘is a thiny I don’t under
MISCELLANEOUS EXERCISES, 175
stand.’ Admitting this, I ask you to construct in an affirma-
tive form, an argument which would entitle you, logically, yet
not convincingly, to deny the existence of table-turning.
_ (Spalding).
Miscellaneous Syllogisms.
‘Suppose a man says, ‘I dislike all foreigners;’ find a
premise which, with his own assertion, would entitle him to
say also, ‘ No foreigner deserves to be liked.’ (Spalding).
All cold is to be expelled by heat: this person’s disorder is
a cold; and must therefore be expelled by heat.
No carnivorous animals have four stomachs: all ruminants
have four stomachs: no ruminants are carnivorous,
Some men of inferior ability are legislators. All peers are
legislators, and some peers are men of inferior ability.
‘No war is long popular: for every war increases taxation ;
and the popularity of anything that touches our pockets is very
short-lived.’ (Spalding).
He that will not learn cannot become learned. This being
so, there are many clever young men that we cannot expect
to become learned.
There is some anger that is not blameworthy. What pre-
mise do you need for the conclusion,—‘ Some passions are not
blamewortby.’
‘No truth is without result; yet many truths are misunder-
stood.’ What is the conclusion P
Some deserve to be imitated that are nevertheless fools.
Whoever speaks the truth deserves to be imitated.
Humanity is a moral virtue: the study of polite letters is
humanity ; the study of polite letters is a moral virtue.
White is a good fellow : if, therefore, linen is white, it is a
ood fellow.
‘ He that says you are an animal speaks truly : he that says
you are a goose, says you are an animal; he that says you are
a goose speaks truly.” (Arnauld),
‘You are not what I am: I am aman: therefore yon are
not a man.’ (Arnauld).
One symptom of the plague is fever; this man has fever;
therefore he has the plague.
Some objects of great beauty answer no other perceptible
purpose, but to gratify the sight: many flowers have great
beauty ; and many of them accordingly answer no other pur-
pose but to gratify tl.e sight. .
Every good statesman is favourable to progress. Some
© * a
176 EXAMPLES OF THE SYLLOGISM.
members of Parliament, not being favourable to progress, are
not good statesmen.
‘ Unpleasant things are not always injurious ; afflictions are
often salutary.’ Sup ply the missing premise.
John is taller va Williain ; William is taller than Charles ;
John is taller than Charles.
‘Of two evils the less is to be preferred ; occasional turbu-
lence, therefore being a less evil than rigid despotism, is to be
_ preferred to it.’ (Whatley).
All fixed stars twinkle ; yonder star twinkles ; therefore it
is fixed.
All that do not act foolishly are respectable; all fools act
foolishly ; no fools are respectable.
‘Most men that make a parade of honesty are dishonest ;
this man makes a parade of honesty.’ Can we conclude that
he is dishonest ?
Ill doers are ill dreaders. This man dreads evil, and is,
therefore, a scoundrel.
All aristocracies are self-willed ; some self-willed people are
not cruel; some aristocracies are not cruel.
Some democracies are not persistent in their designs; the
Government of the United States is a democracy ; the Govern-
ment of the United States is not persistent in its designs.
All plants contain cellular tissue ; no animals are plants; no
animals contain cellular tissue.
‘I snatch at the conclusion that every eager desire is an
evil thing; since I know that the desire of evil is evil, and
that not a few eager desires have evil objects.’ (Spalding).
A good marksman must have a steady hand; George has a
steady hand ; therefore, George is a good marksman.
Flotation is possible only in liquids, and so not possible in
this water, which is frozen.
Poetry is not Science. The characteristics of Science are
truth and generality, and Poetry possesses neither.
Nothing that is not possible for man to do has ever been
done by man. Raising the dead is not possible for man, and,
consequently, has never been done by man.
‘If I know that Messieurs A. B. and C. are not only learned,
men but also silly ones, will you allow me to draw any infer-
ence ?’ (Spalding).
Irrational prejudice is symptomatic of a weak mind, and we
sometimes see it in very learned men. State this in syllogistic
form, and draw the legitimate conclusion.
One who misapplies riches deserves poverty ; which one who
a
EXAMPLES OF CHAINS OF REASONING. 177
is benevolent does not deserve. Is the legitimate conclusion
consonant with fact?
‘If a rule never is, and a principle always is, a law admitting
no exception, judge that a rule must be something different
from a principle.” (Spalding).
No branch of science can be made absolutely perfect, yet
all branches of science are worthy of diligent culture. What
inference do you draw from this ?
‘What was it that first gained him the public ear? It cer
tainly was not the pure Saxon-English in which his sentences
are clothed, for, alas! we find that many writers who neglect
their grammar even, secure an immence audience, to the de-
light of their publishers, and their own gratification.’
_ ‘It has been supposed by some philosophers, that electricity is
the real agent by which the nerves act upon the muscles. But
there are many objections to such a view; and this very im-
portant one among the rest,—that electricity may be trans-
mitted along a nervous trunk which has been compressed by
a string tied tightly round it, whilst the passage of ordinary
nervous power is as completely checked by this process as if
the nerve had been divided.’
The following are examples of chains of reasoning, resolvable
into consecutive syllogisms.
‘The concept ‘ horse’ cannot, if it remain a concept, that is,
@ universal attribution, be represented in imagination ; but ex-
cept it be represented in imagination, it cannot be applied to
any object; and except it be so applied, it cannot be realized
in thought.’ (Hamilton).
‘But, to prove that moral sentiments are instinctive or
inscrutable, it is boldly asserted, by the advocates of the
hypothesis in question, that the moral sentiments of all men
are precisely alike.
‘The argument, in favour of the hypothesis, which is raised
on this hardy assertion, may be stated briefly in the following
manner ;— No opinion or sentiment which is a result of observa-
tion and induction is held or felt by all mankind. Observation
and induction, as applied to the same subject, lead different
men to different conclusions. But the judgments which are
passed internally upon the rectitude or pravity of actions, or
the moral sentiments or feelings which actions excite, are
precisely alike with all men. Consequently, our moral
sentiments or feelings were not gotten by our inductions from
178 RECENT ADDITIONS TO THE SYLLOGISM.
the tendencies of the actions which excite them: nor were
these sentiments or feelings gotten by inductions of others, and
then impressed upon our minds by human authority and ex-
ample. Consequently, our moral sentiments are instinctive, or
are ultimate or inscrutable facts.’ (Austin.)
‘The general object which all laws have, or ought to have,
in common, is to augment the total happiness of the commun-
ity ; and therefore, in the first place, to exclude, as far as may
be, every thing that tends to subtract from that happiness:
in other words, to exclude mischief. But all punishment is
mischief: all punishment in itself is evil. Upon the principle
of utility, if it ought at all to be admitted, it ought only to be
admitted in as far as it promises to exclude some greater evil.’
(Bentham),
‘If our intellectual part is common, the reason also, in respect
of which we are rational beings, is common: if this is so, com-
mon also is the reason which commands us what to do, and
what not to do; if this is so, there is a common law also; if
this is so, we are fellow-citizens ; if this is so, we are members
of some political community; if this is so, the world is in a
manner a state.’ (Marcus Antoninus). It is not to be sup-
posed that all these transitions make distinct syllogisms ; some
are at best but immediate or equivalent transitions.
CHAPTER II.
RECENT ADDITIONS TO THE SYLLOGISM.
HAMILTON’S ADDITIONS.
Sir Witt1am Hamiton’s extensions of the theory and the
forms of the syllogism are chiefly based on the Quantification
of the Predicate, and on the full development of the two
modes of Quantity—LHxtension and Comprehension. He has
also much criticism in detail on many parts of the syllogistice
theory,
It has been seen (p. 86) that the thorough quantification of the
predicate yields four new propositional forms, making eight
in all. Two of these, the affirmative forms, ‘ All X is all Y,’
‘Some X is all Y,’ which are held by De Morgan and by Mill,
.
°
4
Rai i a Nia ae
QUANTIFICATION OF THE PREDICATE. 179
to be compound propositions, have been adopted by some other
logicians, as Thomson (‘Laws of Thought’) and Spalding.
The remaining two forms—the negative ‘ All X is not some Y,’
_ *Some X is not all Y’ have been set aside as not occurring in
actual instances.
_ The addition of two new forms greatly increases the number
of possible syllogistic moods. By trying all the combinations
of three propositions out of six, and by rejecting all that violate
laws of the syllogism, and all that repeat others, Dr. Thomson
makes out 22 moods in the First Figure, 20 moods in the
Second Figure, 20 moods in the Third Figure; so that apart
from the Fourth Figure, of which no account is taken, there
are 62 moods. We give, as examples, some of the new moods.
U U U contains three universal affirmatives with universal
predicates.
All Y is all Z
All X is all Y
All X is all Z
a syllogism, to which there is no counterpart in nature, unless
the terms are merely different names for the same thing; as
‘all water is all oxide of hydrogen.” We may find a proposi-
tion whose terms are of co-equal extent to constitute a major,
(all matter are all gravitating things); but we shall probably
never be able to couple with this a minor also co-extensive in
its terms, if these terms really mean different things.
U E Bis an example, constituting an exception to the canon
requiring the minor in the First Figure, or normal deductive
syllogism, to be affirmative.
All Y is all Z All matter is all gravitating things
NoX is Y No mind is matter
NoXis Z No mind gravitates
Here the quantification of Z (universal) avoids illicit process
of the major.
It is not pretended that any useful form grows out of these
additions to the syllogistic moods; and even as a formal
exercise, no one has thought it worth while to state them im
full; far less to provide examples of them in the concrete.
Only Hamilton himself (followed by Professor Spencer
Baynes) has endeavoured to enumerate the syllogistic moods
growing out of the eight quantified propositional forms. He
even gives the number variously. The earliest statement is
thirty-six valid moods, for each figure (excluding the Fourth),
that is, twelve affirmative, and twenty-four negative. Dr.
Thomson has tabulated the forms, agreeing with Hamilton so
“¢, eee es
180 HAMILTON'S ADDITIONS OF THE SYLLOGISM.
far, but deducting from Hamilton’s complete list as useless
though possible varieties, 14 moods in the first figure, 16 in
the second, and 16 in the third. He thus reduces Hamilton’s
108 moods to 62. In a later statement Hamilton gives 42
_ syllogisms, reducible to 21.
Syllogisms viewed either in Extension or in Comprehension. It
is a great point with Hamilton to show that the common syl-
logism is defective, from not being expressed both in Extension
and in Comprehension. He complains that all logicians, with
the doubtful exception of Aristotle, have limited their con-
sideration to reasoning as given in the quantity of Extension.
He exemplifies the difference of the two syllogisms thus .—
Hatenston. Comprehension.
Bis A Cis B
Cis B Bis A
Cis A Cis A
All men are mortal Caius is a man
Caius is a man All men are mortal
Caius is mortal Caius is mortal
In the first example the class ‘mortal’ contains under it
the class man; in the second example, the attributes of ‘man’
contain in them the attribute ‘ mortal.’
The following is an example in Celarent,
Hatension. Comprehension.
No men are gods Kings are men
All kings are men Men are not gods
No kings are gods Kings are not gods
The second form (Comprehension) may be read thus :—
The attributes of a king contain the attributes of a man.
The attributes of a man do not contain the attributes of a god.
The attributes of a king do not contain the attributes charac-
teristic of a god.
It is to be remarked, with reference to this scheme of double
syllogisms, according as the terms are taken in extent, or in
intent—breadth or depth—that the two modes express one
and the same meaning; and that the really fundamental.
meaning is Intent, or the Connotation of the Terms employed.
The real meaning of the last example is, first, that the
attributes connoted by the term, man, fail to accompany, or
are incompatible with, the attributes connoted by the term,
‘god’ (major); that the attributes connoted by ‘king’ are
accompanied with the attributes connoted by ‘man.’ The
other form, however, falls readiest into common language,
the form of Extension, that is, of inclusion or exclusion of
i ee ae een eee ii ae ale
SYLLOGISMS IN COMPREHENSION, _ 181
classes; men are out of the class of gods; kings are
in the class men; therefore, kings are out of the class
gods. This is a more concrete and intelligible form; still, it
is not the contrast or the opposite of the other. We do not
_ think of this form justly, correctly, unless we conceive the
terms as determined by their connotation. The extent is
bounded solely by the intent. lt is not as if we had a com-
plete list of men, and a complete list of kings, and saw the
kings inserted among the men, while the list of men had
nothing in common with the list of gods. This is the full and
literal rendering of the reasoning in extension ; and the very
statement of it is enough to show that we do ‘not reason so.
When we speak of a class, we do so in a figurative manner ;
we suppose an actual array of individuals when there is no
such array; there being only the defining mark, the connota-
tion of them, to define them whenever they appear. The
extent of ‘man’ is the imaginary aggregate of all objects
agreeing in the marks connoted by the term, the defining
characteristics of man; if we lose sight of this condition for a
moment, we have nothing fixed in our grasp. Accordingly,
comprehension is inseparable from extension in every case; it
is an ever present fact, without our topsy-turvying the
syllogism, or constituting a parallel array of moods to match
the moods in extension.
Hamilton’s forms in comprehension depend solely on his in-
troducing the idea of ‘ containing and contained’ into the
sroups of attributes signified by the terms of the proposition.
A king has more attributes than a man; the individual person
‘Frederick the Second’ has more attributes thana king. Thus,
Frederick is the largest term, in point of number of attributes,
man is the smallest. Hence we may, by straining a metaphor,
apply the relation of whole and part, containing and contained,
to this circumstance, as well as tothe groups (in extension)
men, kings, Frederick; and may carry the analogy so far as
to construct syllogisms to match. But no new or distinct
meaning is conveyed ; and there is not even a more intelligible ,
rendering of an old meaning.
Hamilton, in discussing the conditions of the Distinctness of
Notions, remarks justly that the highest degree of distinctness
cannot be attained without fixing the Comprehension, in other
words, the meaning, definition, or connotation of the term.
(Lectures on Logic 1.168). He remarks also that the quantity
of Extension is a creation of the mind itself, and only created
through, as abstracted from, the quantity of comprehension ;
wn
182 DE MORGAN’S ADDITIONS TO THE SYLLOGISM.
whereas the quantity of comprehension is at once given in the
nature of things (p. 218). All which tends to the conclusion
that the comprehension is what we think of in a notion; and
consequently the comprehension cannot be left out of the ac-
count in any syllogistic form. It is the power behind the
throne, even when extension is the ostensible reigning circum-
stance.
In objecting to the Fourth Figure, Hamilton grounds his
dislike on the circumstance, that the premises proceed in the
whole of comprehension, while the conclusion is drawn in the
counter whole of extension. He explains the matter thus.
The scheme of the Figure is—
Pis M
Mis§S
Sis P
Now in the premises P is contained under M; and M con-
tained under S; whence in the conclusion we should expect P
to be contained under 8. In this, however, we are disappointed ;
for the reasoning suddenly turns round in the conclusion, and
affirms S as a part of P. [Not strictly correct; for Sis qualified
by “some,’ which may still leave it the larger term; ‘Some 8
is P.’] If we had an affirmative syllogism in the form
All P is M All kings are men
All Mis § All men are fallible
All S$ is P All fallible beings are kings
we should have an illegitimate inference; which might no
doubt be evaded if the conclusion could be read thus—
All the attributes of fallible beings are contained in the at
tributes of Kings.
But no one ever reads the figure in this way,
DE MORGANS ADDITIONS.
We have seen Mr. De Morgan’s views as to Terms, and his
enumeration of Fundamental Propositions. Before proceeding
to view his enlargements of the Oy Opiate we shall advert’ to
his remarks on the CopuLa.
He complains that the ‘is’ of logicians is not confined to
one strict meaning. It professes to be a word of the highest
abstraction, a formal mode of joining two terms, carrying no
meaning, and obeying no law, except such as is barely neces-
sary to make the forms of inference hold good. ‘ X is Y* com-
mits us to nothing specific. Yet, at times, logicians employ it
in the sense of identity, The best description of its employ-
COPULAR RELATIONS. 183
ment, he considers to be—‘ agreement in some understood, and,
for the occasion, unvarying particular.’
He supposes that a copular symbol had been used, instead
_ of ‘is;’ the effect of which would have been to stamp upvn
the copula the character of an abstraction, as is done by the
use of symbols, X, Y, Z, for terms. Had such a symbol been
used, the copwlar conditions would have been stated. These
are twoin number. The first is transitiveness ; meaning that
if X stands in a certain relation to Y, and Y in the same re-
lation to Z, X stands in the given relation to Z. Very many
copule show this transitive relation ;—is,—rules,— lifts,—
draws,—leads to,—is superior to, —is ancestor to,—is brother
of,—.joins,—depends on,—is greater than,—is equal to,—is
less than,—agrees with (in a given particular), &.
The second condition is convertibility, in which the relation
is its own correlation; whatever X is to Y, Yisto X. Ina
certain number of the foregoing examples, there occur con-
vertible relations; is,—is brother of,—joins (if a middle
verb),—is equal to,—agrees with. There are cases of con-
vertibility without the transitive character ; converses with,—
is in the habit of meeting,—is cousin of,—is in controversy
with, &c.
Again, there are copula not convertible, but correlative; A
gives to B; B receives from A. These forms also are duly
reasoned upon; and syllogisms might be constructed aecord-
ingly. Hvery X gives toa Y; Some Xs give to no Ys; No
X gives to a Y; Every X receives froma Y ; Some Xs receive
from no Ys,—are examples of the propositional forms. They
are all capable of conversion, by substituting the correlative
copula.
The admission of Relation in general, Mr. De Morgan con-
tends, and of the composition of relation, makes logic more
in alliance with ordinary thinking. ‘The reduction of all
relations by ‘is’—‘mind acts on matter, mind is a thing
acting on matter,’—is a systematic evasion, hostile to the pro-
gress of the science.
Logicians are aware that the form ‘ A equals B, B equals C,
therefore A equals C’ is not reducible to the syllogism. So
with the relation of ‘ greater than,’ in the argument a fortiori.
Yet, to the ordinary mind, these inferences are as natural, as
forcible, and as prompt, as the syllogistic inference. Mr. De
Morgan, therefore, would propose to include all such forms in
one sweep by a generalized copula of relation, which would be
formally embodied and symbolized in propositions. Thus—
9
184 DE MORGAN’S ADDITIONS TO THE SYLLOGISM.
Every X has a relation to some Y
Kvery Y has a relation to some Z
from which the inference would be that ‘very X has a com-
pound relation to some Z;’ the compound of the relations X ~
to Y,and Y to Z Under this form, we reason, John can
coutrol Thomas; Thomas can control William; John can
control William. Under the general and comprehensive
copular relation, specific modes might be developed for specific
purposes. The Logical copula in common use is the equival-
ent of ‘ fastened to,’ ‘connected with,’ ‘co-exists with,’ and
may be considered for logical purposes the most important.
The copula of equality and inequality is developed in Mathe-
matics, and an inference according to it would probably be
called a mathematical inference.
The converse copular relation, ‘ causes,’ would be singled
out on account of its great importance :—A causes B, B is
caused by A. We practically construct syllogisms from these
propositions, without passing through our minds the formal
transformation to—A is the cause of C. |
These remarks of Mr. De Morgan’s are undoubtedly just
and cogent; and they are highly valuable in the way of eman-
cipating the student trom the Aristotelian limits, as well as
for pointing out the vagueness and vacillation of the ordinary
copula. Still, we could hardly afford the labour of following
out the technical developments of half-a-dozen distinct forms
of copula. It is well to see that such developments are not
merely competent in themselves, but needed to formulate the
whole compass of our habitual thinking and reasoning. Being,
however, aware of this fact, we must be content with con-
structing one scheme adapted to the most useful and most
frequently recurring relationship ; which scheme we should
then regard as an example of the rest, one out of many, Any
one having Mr. De Morgan’s genius for the construction of
forms might do well to develop a variety of copular relations ;
from these such selections might be made as would extend
the inferential grasp of the ordinary student.
Mr. De Morgan’s Extensions of the Syllogistic forms are
avowedly based upon the full recognition of contraries, as laid
out in his scheme of eight fundamental propositions. Also,
by providing symbols for contraries he can exhibit all denials
as assertions; No X is Y, is All X is y (U—Y). Hence, the
unit syllogism may be represented in an affirmative form— If
an X be a Y, if that same Y be a Z, then the X is a Z.’
mee ee a nary? a.
SYLLOGISTIC FORMS. 185
All syllogisms are derivable from the following combinations
of Premises :—
(1) All Xs are Ys, and all Ys are Zs. Tho conclusion is
All Xs are Zs; the unit syllogism. This is the inversion of
the Aristotelian order of premises, but it is in the author’s
view the proper and the natural order.
(2) Some Xs are Ys, all Ys are Zs; some Xs are Zs. The
unit syllogism is here, as it were, cut down to the form,—‘ as
often as there are Xs in the first premise, there are in the con-
clusion.’
(3) Some Xsare all Ys, some Ys are Zs ; conclusion—some
Xs are Zs. In point of form, this is the previous case inverted.
The universal middle term (all Ys) is transferred from the
second premise to the first.
(4) Some Xs are all Ys, All Ys are Zs; Some Xs are Zs.
Here, although there is an additional universal middle, all
Ys, occurring in both premises, there is no stronger conclusion
than in the two preceding cases, where the middle term is
universal (or distributed) only once.
These are all the possible couples of affirmative premises
apart from any cognisance of contrary terms. Now, all
negations may be rendered as affirmations about contraries ;
and therefore the application of these cases to all combinations
of propositions, direct or contrary, will give all possible valid
syllogisms.
Taking X, Y, Z, and their contraries x, y, z, there are eight
combinations of threes:—X Y Z,x Y Z,x y Z, xyz, XY 4z,
XyZ,Xyz,xYz. Toeach of these the four modes of inference
ean be applied; and when x, y, z, are read as the contraries of
X, Y, Z, we obtain the proper expression of the syllogism.
Thus, the first or unit syllogism, applied to x y Z, gives Hvery
x is y, Hvery y is Z; therefore, Every x is Z This unfolded,
by giving the equivalents of the contrary terms x, y, in the
forms X, Y, the whole syllogism may be read thus :—
Kivery x is y (All not-X is not-Y) is the same as No Y is
not X, or Every Y is X, or Some Xs are all Ys.
livery y is Z (Every not-Y is Z) is the same as Everything
is either Y or Z(one of De Morgan’s new propositional forms).
In like manner, the conclusion Every x is Z, (Every not-X
is Z) is Everything is either X or Z. The syllogism then is :—
Some Xs are all Ys (Every Y is X).
Everything is either Y or Z.
Everything is either X or Z.
A syllogism not in the Aristotelian figures. From the very
SM UPN Srey et
186 DE MORGAN’S ADDITIONS TO THE SYLLOGISM,
wide compass of the form, Everything is either Y or Z, there
can be few applications of such a syllogism.
Some extended things are all material things.
Everything is either material or pertaining to mind.
Everything is either extended or pertaining to mind.
The remaining seven forms being expressed and unfolded in
like manner, there would arise the eight forms. of wniversal
syllogism, that is wniversal premises with universal conclu-
sion.
Again, apply case second to the same eight forms—Some
Xs are Ys, all Ys are Zs; some Xs are Zs ; and there emerge
eight minor-particular syllogisms, particular conclusion with the
minor (or first) premise particular.
Apply case third—Some Xs are all Ys, some Ys are Zs;
some Xs are Zs—and we have eight major-particular syllogisms,
particular conclusion with the major (or second) premise par-
ticular.
Apply case fourth—Some Xs are all Ys, All Ys are Zs,
Some Xs are Zs—and we have eight strengthened particular
syllogisms, wniversal premises with particular conclusion By a
strengthened syllogism, the author means one whose premises
are stronger than they need be to bear out the conclusion.
The above 32 forms are those that give inference, out of 64
possible combinations of the premises. The remaining 32
forms could be drawn out by representing the eight proposi-
tional arrangements, X Y Z, x Y Z, &c., in four varieties of
premises, which the author states. Thus: (1) Some Xs are
some Ys, Some Xs are all Ys; (2) All Xs are some Ys, Some
Xs aresome Ys; (8) Some Xs are some Ys, Some things are
neither Xs nor Ys; (4) Some Xs are Ys; All Xs are not some
Ys. From none of these combinations of premises could any
inference be drawn.
The test of validity, and the rule of inference, the author
expresses thus :— '
There is inference (1) When both the premises are uni-
versal. (2) When, one premise only being particular, the
middle term has different quantities in the two premises.
Hither of these cases happening, the conclusion is found by
erasing the middle term and its quantities. Premises of like
quality give an ajirmative conclusion; of different quality, a
negative. A universal conclusion follows only from universals
with the middle term differently quantified in the two. From
two particular premises nothing follows.
A particular premise having the concluding term strengthened
i
RULES OF INFERENCE. 187
(that is, made universal), the conclusion is also strengthencd,
und the syllogism becomes universal; for example, Darii, by
this process, would become Barbara. With the middle term
strengthened, the conclusion is not strengthened, and there
being, therefore, a surplus of affirmation in the premises, the
syllogism forms what the author calls a strengthened particular
syllogism, Thus, Darapti, in the third figure—
All Y is Z
All Y is X
Some X is Z—
has the middle term universal in both premises, when once is
enough , there would be inference with ‘Some Y is X’ in the
minor. Felapton and fesapo are other examples.
A different case is exemplified in Bramantip. The two
universals—‘ All Z is Y, All Y is X,’ yield the universal ‘all
Z is X,’ which, for the sake of a different order of the terms
in the concl usion, is converted and weakened into the particular
‘Some X is Z.’ This is termed by the author a weakened
universal.
Hach form of proposition has corresponding to it certain
opponent forms. ‘Thus, if the propositions A, B, gives C, they
cannot give ¢ (the contrary of C). Hence A and C being true,
B is false or B true; that is A, c, give B, that is to say, either
premise joined with the contrary of the conclusion gives the con-
trary of the other premise. Thus, there are two opponent forms
to every syllogism. And the syllogisms may be so grouped in
threes, that each one of any three may have the two others
for opponents. Barbara has, for opponent forms, Baroko and
Bokardo.
Mr. De Morgan considers it of importance to remark that
the adjective for expressing universal quantity—‘ All’ means
two things, which should be kept distinct. It may be ‘ All’
collectively, the entire collection or aggregate of individuals;
this he calls the cwmular form ; and it may be ‘all’ distribu-
tively, in the sense of ‘every one,’ or ‘any one,’ however
taken, which he calls the exemplar mode. He holds that the
language of Aristotle, and of his immediate followers, was
exemplar and not cumular; zas dv6pwrros, he contends, is each
or every man, not all man. ‘ All man,’ as a comprehensive
genus, has parts,—for example, the sevoral species or varieties
of men ; ‘every man’ has no parts, but makes assertions about
every individual of the genus man.
The exemplar mode is that used in geometrical proof. A
proposition in Euclid assumes some one case, and the demon-
188 DE MORGAN’S ADDITIONS TO THE SYLLOGISM.
stration is such that nothing prevents the one chosen from
being any one. It would be useful in geometry, to admit the
form ‘any one X is any one Y.’
In negation, the exemplar form is needed. ‘ All men are
not fishes,’ does not deny the proposition, ‘ All men are fishes.’
The denial would, however, be given in ‘Every man is not
any fish.’* |
Properly speaking, the cumular proposition can be found
proved only through exemplars; hence the exemplar precedes
in the order of thought; a circumstance justifying its adoption
as the basis of a logical system. According to it, quantily 1s
mode of selection by example; universal is replaced by wholly
indefinite; particular by not wholly indefinite. The forms of
the propositions would be modified thus :—
Any one X is any one Y. X and Y singular and identical.
Some one X is not some one Y. KHither X not singular, or
Y not singular ; or if both singular, not identical.
Any one X is 8ome one Y. All Xs are some Ys.
Some one X is not any one Y. Some Xs are not (all) Ys.
Some one X is any one Y. Some Xs are all Ys.
Any one X is not some one Y. All Xs are not some Ys.
Any one X is notany one Y. All Xs are not (all) Ys.
Some one X is not some one Y. Some Xs are some Ys.
The ‘ Numerically Definite Syllogism ’ is a scheme of infer-
ence which supposes exact numbers to be given.
If in 100 instances of any thing, 70 are Xs, and 30, Ys,
then at least 20 Xs must be Ys. The author develops at great
length a symbolical scheme founded on this assumption.
Syllogisms with numerically definite quantity occur rarely,
if ever, in common thought. But it is not unfrequent to find
forms where the number of instances of one term is the whole
number of instances of the other term ;—‘ For every Z there
* Mr. Mill, in a controversial note to his chapter on the Functions
of the Syllogism, makes the following remark:—The language of
ratiocination would, I think, be brought into closer agreement with
the real nature of the process, if the general propositions employed
in reasonittg, instead of being in the form All men are mortal, or
Every man is mortal, were expressed in the form Any man is mortal.
This mode of expression, exhibiting as the type of all reasoning from
experience “ The men A, B, C, &c. are so and so, therefore amy man is 80
and so,” would much better manifest the true idea— that inductive reason-
ing is always, at the bottom, inference from particulars to particulars, and
that the whole function of general propositions in reasoning, is to vonch
for the legitimacy of such inferences.
THE ARISTOTELIAN SYSTEM COMPARED, 189
is an X that is Y; some Zs are not Ys;’ ‘For every man in
the house there is a person that is aged ; some of the men are
not aged ;’ from which it follows, but not by any common form
of syllogism, that ‘some persons in the house are not men.’
To this case the author applies the designation ‘syllogism
of transposed quantity.’ Of terms in common use the only
one that gives syllogisms of this character is ‘ most :-—‘ Most
Ys are Xs; most Ys are Zs; th refore some Xs are Zs,’
Adverting to the distinction of Figure, he styles the First
the figure of direct transition; the Fourth, which is nothing
but the first with a converted conclusion, the figure of inverted
transition; the Second, the figure of veference to (the middle
term); the Third, the figure of reference form (the middle
term). Apart from the conversion of the conclusion, the
Fourth Figure is the most natural order, as it takes up what
was left off with—‘ X is in Y, Y is in Z, therefore X is in Z;’ this
is the first figure, according to the simplest arrangement of
the premises.
In the author’s system, however, Figure attains importance
only through a wider view of the copular relation.
Mr. De Morgan compares his system with the Aristotelian,
of which he regards it as an extension, through the single de-
vice of adding contraries to the matters of predication. (Hamil-
ton also claims to extend Aristotle, but on a different principle).
Accordingly the Aristotelian syllogisms may be all collected
from the preceding system, by the following modifications.
1. The exclusion of all idea of a limited universe, of contrary
names, and of the propositions, ‘ Every thing is either X or Y,’ —
‘Some things are neither Xsnor Ys.’ 2. The exclusion of the
form of conversion, ‘Some Xs areall Ys.’ 3. The exclusion of
every copula except the transitive and convertible copula. 4.
The regardivg of the identical pairs—No X is Y, No Y is X,
and Some X is Y, Some Y is X—as distinct propositions of
themselves determining distinction of figure and mood; as
Celarent and Cesare, Ferio and Ferison, &c. 5. The-introduc-
ing of the distinction of figure. 6. The writing of the major
and minor propositions first and second, instead of second and
first.
Farther, in the Aristotelian scheme, there are four funda-
mental syllogisms in the first figure, each of which has an
opponent in the second, and ‘an opponent in the third. The
opponents of Barbara are Buroko and Bokardo, There are
three fundamental syllogisms in the fourth figure (Dimaris,
190 BOOLE’S ADDITIONS TO THE SYLLOGISM.
Camenes, Fresison), each of which has the two others for op-
ponents. Altogether there are fifteen fundamental! syllogisms.
The remaining four are—three strengthened particular syllo-
gisms, Darapti (III), Felapton (III), Fesapo (IV), and one
weakened universal; Bramantip (IV).
The Aristotelian rule that the middle term must be distri-
buted once fails with the introduction of contraries. The rule
to be substituted is—All pairs of universals are conclusive,
but a universal and a particular require that the middle term
should also be a universal and a particular,—universal in one
premise and particular in the other.
The rule that when both premises are negative, there is no
syllogism, also fails. In the system completed by contraries,
there are eight such syllogisms ; as many, in fact, as with pre-
mises both affirmative. But in these cases, as before re-
marked, the premises are not both negative in reality.
Again, on the rule ‘that two particular premises can give
no conclusion,’ the author brings forward as a legitimate
inference, ‘Most Ys are Xs, most Ys are Zs, therefore some
Xs are Zs; most men wear coats, most men wear waistcoats,
therefore some men wear both coats and waistcoats,’ He
develops this form at length into a symbolical scheme, under
the name of ‘ The numerically definite syllogism.’
Mr. De Morgan’s system, on the whole, is characterized by
an immense multiplication, not only of symbolical forms, but
of verbal designations for the relationships growing out of the
syllogism.
BOOLE’S ADDITIONS.
The late Professor Boole, of Cork, published two works
on Formal Logic. The first and smaller, entitled—‘ The
Mathematical Analysis of Logic,’ comprised an Algebraic
rendering of the syllogism, showing how all the moods might
be symbolically deduced. The second and larger work, en-
titled—* An Investigation of the Laws of Thought, on which
are founded the Mathematical Theories of Logic and Proba-
bilities,’ takes a much wider sweep, and is an entirely new
application of the symbolical methods of Algebra, to Inference,
both Immediate and Mediate ; the largest share of attention
being given to the first, or the so- called Immediate Inference
The author also extends the same nomenclature and handling
to Probabilities.
Besides the novel employment of symbolical processes of the
Algebraic kind, the work is intended to bear fruit in other
Cr Tee
CONNEXION OF LOOIC AND MATHEMATICS. 191
ways. In using the title ‘ Laws of Thought,’ tho author in-
dicates that one purpose of his theory of Reasoning is to throw
light upon the workings of the Intellect. He considers that
our views of the Science of Logic must materially influence,
perhaps mainly determine, our opinions upon the nature of the
intellectual faculties. For example, whether reasoning con-
sists merely in the application of certain first or necessary
truths, originally imprinted on the mind, whether the mind is
itself a seat of law [whatever that may mean], or whether all
reasoning is of particulars, concerns not Logic merely, but also
the theory of the intellectual faculties. It cannot be said, how-
ever, that the author has been able to decide which alternative
is the correct one.
He farther proposes to elucidate the subtle connexion be-
tween Logic and Mathematics; how far a common theory is
applicable to both kinds of reasoning, and how far the likeness
fails. He hoids that the ultimate laws of Logic are mathe-
matical in their form, that they are, except in a single point,
identical with the general laws of Number. The exhibition
of Logic in the form of a Calculus is not arbitrary: the ultimate
Jaws of thought render that mode possible, and forbid the
perfect manifestation of the science in any other form. It is
not of the essence of Mathematics to be conversant with the
ideas of number and quantity. The author does not design to
supersede, by symbolic processes, the common forms of reason-
ing; nevertheless, cases may arise where the value of scientific
procedure, even in things confessedly within the scope of
ordinary reasoning, may be felt aud acknowledged.
The author’s scheme starts with the consideration of Lan-
guage as an instrument, not of communication merely, but of
Reasoning; it being his intention to substitute, for ordinary
language, a set of symbols adapted to perform this function in
a more effective manner.
The signs composing Language, with a view to Reasoning
especially, are characterized in the following definition :—‘ A
sign is an arbitrary mark, having a fixed interpretation, and
susceptible of combination with other signs in subjection to
fixed laws dependent upon their mutual interpretation.’ The
first part is obvious; a sign, in its primary invention is purely
arbitrary ; ‘house’ and ‘domus’ are equally good for the
purposes of language. It is also obvious that each sign should
possess a fixed interpretation, that there should never be any
ambiguity of meauing. Ordinary language is greatly liable to
192 BOOLE’S ADDITIONS TO THE SYLLOGISM.
this infirmity; hence, one of its defects as an instrument of
reasoning. Lastly, signs must be susceptible of combination
with other signs, which combinations must have fixed laws
depending upon their mutual interpretation.
The author proceeds to explain his artificial symbols for
superseding, by a higher mechanism, the vocables of our ordi-
nary speech. The symbols, and their connecting signs of
operation, are borrowed from Algebra, and are manipulated by
the algebraic processes, after allowances are made for the
difference between the material of Logic, and the material of
Mathematics (Number and Quantity).
All the operations of Language, as an instrument of Reason-
ing, may be conducted by a system of signs composed of the
following elements :—
First, Literal symbols, as a, y, 2, &c., representing things as
subjects of our conceptions. For the object ‘man’ we may use
x, for a ‘ brute,’ y, for the quality ‘ living,’ z, and so on.
Second. Signs of operation, as +, —, X, standing for the
operations whereby conceptions are combined, or, when com-
bined are resolved into their elements ; ‘men and brutes’ may
be represented by « + y.
Third. The sign of identity =.
These symbols of Logic are used according to definite laws,
partly agreeing with, and partly differing from, the laws of
the corresponding symbols in the science of Algebra.
The first class of symbols above given are the appellative or
descriptive signs, expressing either concrete things, or the
qualities of things; that is to say, they are the equivalents of
the two appellative parts of speech, the Noun and the Adjec-
tive. Thus, let a denote ‘men,’ or all men; and let y denote
the adjective good ; then all good men would be expressed by
some suitable combination of « and y, Now the suitable com-
bination, for the case of a thing qualified by an attribute, or of
{wo or more co-inhering attributes is a product @ X y, or
ay. Why this, and not the sum a + y, is the proper symbol,
the author does not specifically explain; the means, as in
other symbolical sciences, are left to be justified by the end,
namely, arriving at true results. Soif # stands for ‘ white’
or ‘white things,’ y for sheep, x y stands for ‘ white sheep ;’
and if z stands for ‘horned,’ z « y will represent ‘horned
white sheep.’ In this symbolism, the order of the symbols is
unimportant, just as the order of the adjective and the sub-
stantive is indifferent as regards the meaning; ‘good man,’
‘vir bonus’ are equally accepted by the mind to suggest that
oe
. lo
SYMBOLS FUR PARTS AND WHOLE. 193
the conception ‘man’ is to be limited by the conception
*good.’’ Hence we may use at pleasure x y, andy a; « y 2,
and zy a, &c.
It is a law of speech that an appellative gains nothing (ex-
cept perHaps rhetorically) by repetition or duplication ; ‘ good,
good, is the same as good; ‘horse, horse,’ is the same as horse.
To adapt this to symbols, « ¢ would amount to no more than
w; that is, using = (as in Algebra) for equivalence, or iden-
tity, « “= 2 Here Logic and Algebra are at variance, and
the methods of manipulating logical symbols must vary ac-
cordiugly. The author shows that the form « = », or # =
#, has still deeper meanings.
Next as to signs for collecting parts into a whole (quantity in
extension) or for separating a whole into parts. These cor-
respond to the conjunctions ‘and,’ ‘ or,’ in common speech—
‘trees and minerals;’ ‘barren mountains, or fertile vales.’
The sign of addition is now used; let x be ‘trees’ and y
‘minerals ;’ the conjoined expression is + y. This employ-
ment of the sign is so closely allied to addition in arithmetic,
that it may be worked upon the same principle. Again, let
« stand for men, y for women, and z for European; then
‘Huropean men and (European) women’ would be represented
by z(@ + y) = 4a+ zy.
Addition implies subtraction. ‘ All men except Europeans’
will be expressed by a—y. ‘ White men except white Asiatics’
(% men, y Asiatics, z white),
2(w—y) = em—a2y
With a view to Propositions, it is necessary to consider the
rendering of the copula. For this purpose all propositions have
to be reduced to the form ‘is’ or ‘are ;’ ‘ Cesar conquered the
Gauls,’ must be resolyed into ‘ Cesar is he that conquered the
Gauls.’ This is the copula of identity, the most generalized
form of relationship of subject and predicate. It may be ex-
pressed by the symbol =; and the meaning so far coincides
with the Algebraic meaning, that the Logical equation is little
different from the Algebraic equation.
Take the Proposition, ‘The stars are the suns and the
planets.’ Let stars be represented by 2, suns, by y, and
planets, by z; then,
: = z
Whence we can deduce,
«—y=—=z2z(The stars, except the suns, are planets),
or, «© — z = y (The stars, except the planets, are suns).
Thus, in the Logical equation, we may apply the mathe-
194 BOOLE’S ADDITIONS TO THE SYLILOGISM.
matical axioms ‘equals added to equals give equal sums;
‘equals taken from equals give equal differences.’
If two classes of things, * and y, be identical, that is, if
all members of the one are members of the other, then such
members of the one class as possess a given property, z, will
be identical with the members of the other that possess the
same property. Hence, if we have the equation
oe Yy:
then, whatever class or property 2 may represent, we have also
oe =Sz Yy.
In point of form, this coincides with the algebraic law—if
both members of an equation be multiplied by the same
quantity, the products are equal. %
The analogy, however, does not extend to division, For,
supposing the members of a class ~, possessing the property
z, are identical with the members of a class y, possessing the
same property, it does not follow that the members of the class
x universally are identical with the members of the class y.
Hence, it cannot be inferred from the equation
42% =2Y,
that the equation
==
is also true. Thus, the process of division, as applied to
equations in Algebra, has no formal equivalent in Logic.
Multiplication sufficiently represents the combination or com-
position of conceptions, but division does not appear to repre-
sent their decomposition or abstraction. The want of analogy
on this point, however, is not total. Even in Algebra, the
rule of division does not hold throughout ; for example, it does
not apply when the divisor is z=0O. Through this one
loophole, the author is able to restore the consistency of the
algebraical and the logical processes.
Reverting to the equation
x = & ‘
he remarks that only two values of 2 will comply with it;
namely, 0 and 1. For 0? = 0, and 1*=—1; and of no other
numbers is the relation true. Hence, in an Algebra, whose
symbols a, y, z, &c., never knew any values but 0 and 1, the
laws of operation would coincide with the laws of operation in
Logic. The two sciences are divided by no other difference
than the manner of interpretation. ,
In chapter III., Boole professes to derive the laws of the
symbols of Logic, above assumed, from the laws of the opera-
SYMBOLS FOR COMPLEX SUBJECTS. 195
tion of the mind. He proceeds thus :—In every discourse,
there is a limit to the subjects considered ; in other words,
_ a unwerse. [He is here at one with De Morgan]. Thus the
term ‘men’ is used with. reference to a certain implied exten-
sion, on the part of the speaker ; it may be all men whatsoever ;
or it may be a more limited universe, as civilized men, men in
the vigour of life, and so on. The term ‘ men’ raises in the
mind of the hearer the beings so intended to be comprised.
Let us next consider the employment of an adjective in addition.
Suppose ‘men’ to be spoken of in the widest sense, the uni-
verse ‘all men;’ then the application of the adjective ‘ good’
prescribes the operation of selecting from the universe all
objects possessing the further quality ‘good ;’ such selection
corresponds to the combination—good men. Thus, the office of
an adjective is not to add the quality, ‘ good’ for instance, to
all the universe, men, but to select, from the universe, individuals
according to the idea prescribed in the word. The intellectual
faculties employed in these successive operations may be sup-
posed to be those denominated Conception or Imagination, and
Attention ; or perhaps the entire act may be summed up in
one function of Conception. Hach step in the process may be
characterized as a definite act of conception.
Now, the syllogism above adopted exactly corresponds to
this operation. The symbol z directs attention upon a certain
universe, men for example; the symbol y, good or white, di-
rects us to search that universe for individuals owning the pro-
perty named ; and the combination y x, or * y, expresses the
selection—good men or white men. This symbol will not fall
under the relations expressed by a sum ; its meaning is a group
qualified by the conjoined conceptions x and y, not an aggregate
made up by adding the universe x to the universe y. In this
way does Boole consider that he has established his positions: (1)
that the operations of the mind are subject to general laws, and
(2) that these laws are mathematical in their form; whence
the laws of the symbols of Logic are deducible from the opera-
tions of the mind in reasoning.
He then proceeds to determine the logical value and signifi-
cance of the symbols 0 and 1, to which quantities Algebra has
to be cut down, in order to become Formal Logic. The sym-
bol 0 corresponds to Nothing; the symbol 1 corresponds to
the universe of discourse. Nothing and Universe are the two
limits of extension—none and all. Whatever the class y may
be, the individuals common to it and to the class 0, or Nothing,
are Nothing or none. That is,
Ox ¥y=—0,or0y=0
ay a
a
196 BOOLE’S ADDITIONS TO THE SYLLOGISM.
Again, the symbol 1, satisfies the law of equation,
_xXy=yorly sy
whatever y may represent. ‘The class represented by 1, there-
fore must be ‘the Universe,’ the only class cuntaining all the
individuals that exist in any class, .
Now as tocontraries, If x represent any class of objects,
1—« will represent the contrary, or supplementary class, what
remains when z is withdrawn from the Universe of discourse
1. Ifa be ‘men’ in the universe ‘animals,’ 1 —~ is the not-
men, the remaining members, or the brutes. This coincides
with De Morgan’s symbolism, U—z« for the contrary of a.
The author next offers from his fundamental logical equa-
tion, 2”? = x, or x —«* = 0, a formal proof of the Law of Con-
tradiction, thus :—The equation admits of the form
z(1—z)—=0
which, being interpreted according to the meaning of the
symbols, is that a class determined at once by 2, and by its
contrary 1 — a, is the same as 0 or Nothing; that is, does not
exist.
Advancing farther into the consideration of Propositions
(chap. IV.), the author divides these into ‘ primary’ or
simple, and ‘secondary’ or complex; the one relating to
things, the other to propositions. Under the last named class
are included hypotheticals, &c. He begins by propounding a
general method for expressing any ‘term’ that may enter
into a primary proposition. The method is merely the appli-
cation of his symbols as already explained. Thus, let # repre-
sent opaque substances, y polished substances, z stones ; then
“xy z = opaque polished stones. .
Now as 1 — z represents substances that are the contrary of |
stones, or are not stones,
9 a y (1 — z) = opaque polished substances that are not stones ;
Oo
w« (1—y) (1 —2)= opaque substances, not polished, and
not stones,
Again, for the case of collections of things,—or objects con-
joined by ‘and,’ ‘or,’—the sign of addition must be added, as
above explained. The sign ‘or’ gives a disjunctive form; all
#’s are either y’s or z’s; and this has two meanings not dis-
criminated by the use of ‘or,’ but differently rendered in the
formula. It is a question whether x may, or may not be both
yandz. ‘ He is either a rogue or fool;’ he may or may not
be both, so far as this expression goes, although the more
Se ee
COMPLEX TERMS. 197
usual rendering would be ‘not both.’ The two ways of sym-
bolic expression are the following. (1) Things that are either
w’s or y’s, are things that if «’s are not y’s, and if y’s are not
ws; that is
x(1—y)+y(l—2).
(2) Things that are either «’s, or if not a’s, then y’s.
x+y (1—2).
This admits the supposition of being both « and y, a suppo-
sition more explicitly given in the enlarged equivalent form.
ey + 2«(l—y)+y (l—z),
where we have all three alternatives : zy expressing the concur.
rence of both#z andy. If heis not a rogue heisa fool, «
fool, y rogue, « (1—vy); if he is not a fool he is a rogue,
y (1 — 2); he is a fool and a rogue together, w y.
To take a more complex example, exhibiting the full power
of the method; let
* = hard, y = elastic, e = metals;
and we shall have the following results:
non-elastic metals = z (1 — y).
Elastic substances, together with non-elastic metals, y +z
1 — y).
Hard substances except metals, « — z.
Metallic substances, except those neither hard nor elastic,
een) (l—y) orz4 Pee ony
To take a still more complicated examples: ‘ Hard substance,
except such (hard substances) as are metallic and non-elastic,
and such (hard substances) as are elastic and non-metallic.’
Hard substances being represented by #; substances hard,
metallic, and non-elastic, are « z (1 — y); substances hard,
_ elastic, and non-metallic, are z y (1--z), and the whole expres-
sion is
z—fe a(l—y)+ay (1—z) or ~— «x z(1—y)—a# y (1—z).
Such is the expression of Terms. To form Propositions,
the sign = is used for the copula of identity. Thus, to ex-
press identity between ‘ Fixed Stars’ and ‘ Suns,’ or to express
that ‘ All fixed stars are suns,’ and ‘ All suns are fixed stars,’
{ Hamilton’s universal with universal predicate],
ime is
This is the form applicable to the verbal proposition or de-
finition ; and the author exemplifies it by such. For example,
Senior’s definition of wealth, as consisting in things trans-
ferable, limited in supply, and either productive of pleasure
198 BOOLE’S ADDITIONS TO THE SYLLOGISM.
or preventive of pain, is symbolized thus. Let w = wealth;
t = things transferable; s ~ limited in supply; p = pro-
ductive of pleasure; r = preventive of pain. Now it is to be
remarked that the conjunction ‘and’ is not necessary and
might be misleading; ‘and’ conjoining two adjectives ‘ great
and good men,’ is very different from ‘and’ coupling two
groups ‘great men and good men;’ the first is « y z the
second « zg + y z We farther remark that the disjunctive
‘or’ in ‘ productive of pleasure or preventive of pain,’ means
things that ‘if not productive of pleasure are preventive of
pain ;’ and that, ‘if not preventive of pain are productive of
pleasure ;’ and does not suppose any class of things to be both
at once. With these explanations, the definition is embodied —
in the formula,
w= st \p(1—7) + r (l—p) ;
Passing now to [teal Propositions, as—‘ men are mortal,’ we
need a mode of rendering particular terms; ‘ All men are
sone mortal beings.’ Let v represent an indefinite class, some
of whose members are mortal beings; and let « stand for the
the entire class ‘ mortal beings ;’ then v 2 will represent ‘some
mortal beings.’ Hence if y stand for men, the equation sought
is—
YT Us
The qualifying symbol v is thus the mark of particularity in
every case. In the proposition, ‘ the planets are either primary
or secondary’ (some primary bodies or else some secondary
bodies),
Let # represent planets (the subject) ;
y = primary bodies;
z = secondary bodies ;
then, assuming that the planets cannot be both primary and
secondary, the equation of the proposition is
=v fy (1 = 4) +2(1—y).}
A more simple form, stating the same proposition, is
xv (y +2).
For, the meaning obviously is, that the planets fall exhaust-
ively under the two heads, primary aud secondary; that is, are
made up of some primary and some secondary bodies,
Such is the symbolism applicable to affirmative real proposi-
tions, where the predicate, as a rule, must be sapposed to
surpass the subject. The author next shows how to express
negative propositions. .
ee. ee oa ee ee
EXPRESSION OF PROPOSITIONS. 199
Suppose the case, ‘No men are perfect beings,’ a universal
negative. Here, we make an assertion to the effect that ‘ all
men’ are ‘not perfect beings.’ The meaning may then be
expressed thus :—All men (subject) are (copula) not any part
of perfect (predicate). Let y represent ‘ men,’ and # *‘ perfect
beings.’ ‘ Not perfect beings’ are repr esented by she negative
form 1—z ; and ‘some not perfect beings,’ by this form, quali-
fied by the sign of particularity, v. Hence, the equation is
y =v (l—2).
Thus, to express the form No as are ys, we have to convert it
into ‘ All ws are not (any part of) ys.’
A particular negative proposition, ‘some men are not wise,’
is resolvable into ‘some men’ (subject) ‘are’ (copula) ‘ not
wise’ (predicate). Putting, then, y for ‘men,’ « for ‘ wise,’
and v for an indefinite containing some individuals of the class
qualified by it, we have for ‘some men, vy, for ‘not any
part of the wise,’ v (1 —-~), or the equation
vy =v(l— 2).
So much for the eattil odd expression of primary or simple
propositions. Itis next to be seen how these forms are turned
to account in furnishing immediate infereuces, or in exhaust-
ing all the equivalent propositional forms of each; in which
operation the eamigy principally expends the force of his
method.
With this view, permission must be given to work the several
equations after the algebraical model, with the restrictions
already stated. The reader must be satisfied from the ex-
planations afforded that the signs used have the same force in
Logic as in Algebra. The conditions of valid reasoning are
then those three :—First, that a fixed interpretation be as-
signed to the symbols; secondly, that the formal processes of
solution or demonstration be conducted in obedience to the
laws laid down as to the meanings of the signs of operation ;
thirdly, that the final result be interpreted in the same way as
the original data. Having once clothed the logical meaning
in the algebraic dress, the author claims to proceed exactly as
if he had to deal with an algebraic equation wherein the symbols
have only the two meanings and 1.
The exhaustive renderings of each proposition are to be
gained by a process of ‘development,’ which is explained at
length, and is strictly after the manner of Algebra, with the
conditions of value specified. The skeleton of the form of
_ development is furnished from these considerations :—Suppose
we are considering a class of things with refereuce to the point
200 BOOLE’S ADDITIONS TO THE SYLLOGISM.
whether its members possess or do not possess a property < ;
as avimals, with reference to, humanity. Suppose next that
the members possessing the property 2, possess also a property
wu; and that the members not possessing the property a are
subject to a condition v. On these suppositions the class in its
totality is represented by :
uetyv(1—2). ;
Any function of x, f (x), whereiu « is a logical symbol,
susceptible only of the values 0 and 1, is said to be developed,
when it is reduced to the form a x + b (1 — 2), a and b being
so determined as to make the result equivalent to the function
whence it is derived. The following out of this development
is purely algebraical, and occupies a good many pages of the
work. To a student versed in ordinary Algebraical equations,
the whole is sufliciently intelligible. We shall here indicate
merely the results and applications. The following is given
asan example. Itis a definition with two defining marks.
‘Clean beasts are such as both divide the hoof and chew the
cud.’
Let 2 = clean beasts,
y = beasts dividing the hoof,
% —= beasts chewing the cud,
The definition will then be represented by the equation
“= y 2,
which may be reduced to the form
xr—y2z2=—0,
Here a function of x, y, and z, namely « — y z has to be
developed according to the methods laid down. As a speci-
men, we may transcribe the development ;
Oxy + ay (1 —2)+a(1—y)2+x2(1—y) (1—2z) —(1—a) ya +
0 (1—2x) y (1 —z) + 0(1—ax) (l— y)z + 0 (1—z)(1— y) (1—a).
Now all those terms that are multiplied by 0 necessarily
vanish and the remaining terms are *
xy (1—z)=0,axz (1—y)=0, x2 (1 —y)(1—z) =0,(1— 2x) yz=0.
Which equations all express the denial, or nothingness, of
the combinations given in the left side of each. Thus 2 y
(1 — «) = 0 means that there cannot be beasts that are clean
(x) and that divide the hoof (y), and that do not chew the
cud (1 —z). So the last of the four, (1 — x) y e=0, indi-
cates that there are no beasts unclean (1 — #) and yet divid-
ing the hoof (y), and chewing the cud (2).
These equivalent forms are somewhat obvious in themselves
without the aid of analysis; but the author evolves more
complicated equivalents, such as these :—‘ Unclean beasts are
EQUIVALENT FORMS. 201
all that divide the hoof without chewing the cud, all that chew
the eud without dividing the hoof, and all that neitber divide
the hoof nor chew the cud.’ he reader may be curious to
_ see the corresponding equation :—
1—a#=y(l—2)+2(1—y) +(1—y) (l—a2).
It is obvious, from this instance, that, out of a definition
containing three or four defining marks (Senior’s definition of
wealth, for example), a great many equivalent forms are deriv-
able. Whether there be any important form that the unassisted
mind might not evolve, is not quite apparent. It is possible,
however, that cases might arise where the symbolical method
would yield equivalents too recondite for an intellect with
only the ordinary logical training.
The author extends his analysis so as to comprise a more
difficult order of examples, typified thus. Suppose the analysis
of a particular class of substances has conducted us to the
following general conclusions, namely :—
First. Wherever the properties A and B are combined,
either the property C or the property D is present also; but
they are not present jointly.
Secondly. Wherever B and C are combined, A and D are
either both present or both absent.
Thirdly. Wherever A and B are both absent, C and D are
both absent also; and vice versa, where C and D are both
absent, A and D are both absent also.
Let it then be required from these conditions to determine
what may be concluded in any particular instance from the
presence of the property A, with respect to the presence or
absence of the properties B and C, paying no regard to the
property D. ‘The working of the corresponding equations
leads to this answer :— Wherever A is present, there either C
is present and B absent, or C is absent. And, inversely,
wherever C is present and A is absent, there A is present.
Several other curious combinations might be quoted, still
growing out of the equivalence of simple propositions. We
are next led to the consideration of Secondary Propositions
(hypotheticals, &c.), which the author symbolizes by introduc-
ing the idea of Time as their peculiarity, A simple, unqualified
proposition (affirmative) holds through all time; a negative,
through no time; a qualified proposition holds only through
a certain limited time. The symbol 1 may represent an
unqualified truth, as being true through the whole universe of
time; (0 will stand for an unqualified negation, something true
for no time. Let X represent a certain proposition, and let
202 BOOLE’S ADDITONS TO THE SYLLOGISM.
represent the time of its being true. So, if Y represent
another proposition, y may be taken for the time of its being
true. Taking both propositions together, « +- y will denote the
aggregate of the times when both X and Y are respectively
true, those times being separated from each other. Again,
x — y may denote a remainder of time left when the time y is
taken from the time %, it being supposed that a includes y.
So, « = y will indicate that X and Y are true for identical
times. Further, « y indicates the portion of time when X and
Y are both true.
Now, as x denotes the time of X’s being true, 1 — # will
denote the time that X is false. So # (1 — y) will denote the
time when X is true and Y is false: and so on. The same
system is to be applied to any number of symbols.
To express the proposition ‘ X is true’ (there being no limit
or qualification), we have
e== di
To express the proposition ‘ X is false—?
® =-0.
To express—‘ Hither the proposition X is true or the propo-
sition Y is true (not both).’ First, ‘When X is true Y is
false,’ is signified by (1 —y); ‘when Y is true X is false,’ —
is signified by y (1 — 2): the equation then is
a(l1—y)+y(l—2)=1.
Next to express the conditional Proposition, ‘ If the proposi-
tion Y is true, the proposition X is true.’ This implies that
whenever Y is true, X is true; or that the time of the truth of
X covers the whole time of the truth of Y, and possibly more.
Hence X is at least equal to, if not larger than Y. Conse-
quently some form must be given, implying that Y is contained
in X: a form analogous to that required for a universal affir-
mative proposition. Let v represent an indefinite portion of .
time, such as to express the unknown part of a whole, ‘some,
it may be—all,’ and the equation required is
yY— ve.
It is unnecessary to exemplify the symbolism for the more
complicated cases. The author is so far carried away by the
success of his expedient for expressing compound or secondary
propositions by a reference to time, that he speculates on an
analogous mode of expressing the primary propositions by a
referesice to space; and thinks that he thus lends some coun-
tenanve to the doctrine that Space and Time are ‘ forms of the
human understanding.’
A chapter is devoted to the treatment of the secondary pro-
¥
_ENUMERATION OF PROPOSITIONS, — 203
positions, by way of exhausting their whole implication, in the
manner previously shewn for the primary propositions; the
effect being, however, merely to deduce the usual consequences
of disjunctive and of conditional assumptions. It is to be
remarked that the process is still one of immediate inference,
confirming the view that in hypothetical syllogisms so-called,
there is no real or mediate inference.
In order to exhibit the value of the symbolical evolution of
equivalent forms, Boole selects for analysis two specimens of
metaphysical argumentation, sufficiently perplexing to test the
powers of a logical method. They are (1) a portion of Samuel
Clarke’s ‘ Demonstration of the Being and Attributes of God,’
and (2) Spinoza’s argument to prove the identity of God and
the Universe. He confessed that one main difficulty in dealing
with those arguments is to extricate the real premises of the
authors; he might have added the farther difficulty of assign-
ing definite and consistent meanings to the very abstract terms
made use of by them—necessity, existence, eternity, cause, &c.
But the premises once obtained, it is possible to embody them
in symbols, and then to extract all their equivalents by solving
the corresponding equations. 'The method may be commended
as an interesting effort, varying and corroborating the method
followed by a logical and acute mind working upon the ipsa
corpora of the premises, without symbolism.
We have now reviewed the larger half of Boole’s work, and
as yet have seen no mention of the syllogism. A short chapter
is all that is bestowed upon mediate inference; which, how-
ever, is a mere carrying out of the algebraic method, with the
modifications demanded by the nature of the case.
He begins by accepting De Morgan’s additions to the four
types of propositions in the common Logic. He lays out the
eight forms, with his equations for them: expressing the four
new forms by supplying a contrary subject to each of the old
forms. The parallelism is shown thus
A — All Ys are Xs y= ve (1)
(A) All not-Ys are Xs l—y=ve (2)
E No Ys are Xs y = v(1—2) (3)
(E) No not-Ys are Xs 1l1—y=v(1—2) (4)
= { All Xs are Ys eCm=vy
I Some Ys are Xs vy = Ue (5)
(1) Some not-Ys are Xs v(l—y) = ve (6)
204 BOOLE’S ADDITIONS TO THE SYLLOGISM.
— J Some Xs are not Ys vy =o(1—y}
O Some Ys are not Xs vy =v(l— a) a
(O) Some not-Ys are not-Xs v(l—y)=v(l—a2) (8
The second form of E coincides with A by mere transposition
of letters. The second form of I is O, in like manner. The
second form of O (O) is the only new form—Some not-Ys are
not-Xs, some things are neither Ys nor Xs. This is one of
De Morgan’s two disjunctives; his other disjunctive—no
not-X is not Y, every thing is either X or Y—does not appear
in the above list.
The laws of Conversion follow from the symbolical forms.
The proposition ‘ All Ys are Xs’ being represented by
y = v x, we have only to read v x = y, Some Xs are Ys. To
convert the same proposition by negation (obversion and con-
version), we deduce, by eliminating »,
y(l—2)=0
which gives by solution with reference to 1 — 2,
0
1—2#=5 (1 —y);
whose interpretation is ‘ All not-Xs are not-Ys. [This opera-
tion contains methods and symbols not explained in the fore-
going abstract |.
So far as Conversion goes, the author merely continues his
former methods of reducing and interpreting equations ; as we
might expect from considering that conversion is merely one
variety of Immediate or Equivalent Inference. The sYLLOGiIsm
demands a step in advance. The two premises must be em-
bodied in two equations, with a common middle term, and that
term must be made to disappear in a third formed out of these
two. Thus,
All Xs are Ys e=vy
All Ys are Zs y = v's.
Whence, by substituting for y, in the first equation, its
value in the second, we have
All Xs are Zs 2 ues.
The form v v’z shows that # is a part of a part of 2. Sowith ©
all other cases ; it is requisite merely to eliminate the middle
term y. The method might be easily carried through the
whole of the ordinary syllogisms ; as well as applied to the un-
figured and fallacious forms. But the author proceeds to
deduce the general rules of the syllogism by an equation com-
prehending all the forms of valid reasoning. He gives as the
results of the analysis these rules: ‘when one middle term, at
a
ae
RULES OF THE SYLLOGISM. 205
least is universal, equate the extremes.’ ‘In case of unlike
middle terms (one positive and the other negative), with one
universal extreme, change the quantity and quality of that
extreme, and equate the result to the other extreme: and with
two universal middle terms, change the quantity and the
quality of either extreme, and equate the result to the other
extreme unchanged.’
Suppose the case—
All Ys are Xs
All Zs are Ys.
This belongs to the first rule. ‘All Ys’ is the universal
middle term; the extremes being equated give as the conclu-
sion,
All Zs are Xs.
Suppose next—
All Xs are Ys
No Zs are Ys.
The proper expression of these premises is—
All Xs are Ys
All Zs are not-Ys.
They belong to the case of unlike middle terms, and have
one universal extreme. Whence, by application of the rule,
we change the quality and the quantity of that extreme, and
equate it with the other extreme—
All Xs are not Zs, or No Xs are Zs.
Commencing from the other universal extreme, we obtain
the equivalent result—
No Zs are Xs,
A third case—
All Ys are Xs
All not-Ys are Zs.
Here the terms are of unlike quality. There are two uni-
versal middle terms, and, by the rule, we change the quantity
and the quality of either extreme (Some Xs into All not-Xs),
and equate with the other extreme (Some Zs).
All not-Xs are Zs.
The two last examples are selected by the author as present-
ing syllogisms that would not be regarded as valid in the
Scholastic Logic, which virtually requires that the subject of a
proposition should be positive. [As often remarked already,
the want of a thorough-going recognition of contraries is the
defect of the Aristotelian scheme]. The cases are, however,
perfectly legitimate in themselves, and the rules for determin-
ing them are undoubtedly the most general canons of syllogistie
206 BOOLE’S ADDITIONS TO THE SYLLOGISM.
inference. The analysis employed, the author contends, is not
properly of the syllogism, but of a much more general mode
of combining propositions to yield results; and he gives an
imaginary case to illustrate this wider import.
Without pursuing the syllogism farther, Boole now dis-
cusses the vexed question as to the fundamental type of de-
ductive reasoning, and takes issue with Whately and with
Mill, who agree in this that all valid ratiocination is ultimately
the inferring of propositions from others of a more generat
kind; the syllogism being a full and adequate formal repre-
sentation of the process. Now, as the Syllogism is a species
of elimination, the question resolves itself into these two deter-
minations, namely, first, whether all elimination is reducible
to Syllogism; and, secondly, whether deductive reasoning
consists only of elimination.
To the first question, he replies, that it is always theoreti-
cally possible so to resolve and to combine propositions that —
elimination may subsequently be effected by the syllogistic
canons, but that the process of reduction would, in many cases,
be constrained and unnatural, and would involve operations
that are not syllogistic.
To the second question, he replies that reasoning cannot, ex-
cept by arbitrary restriction, be confined to elimination. It
cannot be less than the ageregate of the methods founded on
the Laws of Thought, and the process of elimination, import-
ant as it is, is only one process among others.
He farther remarks that, of all the Laws of Thought, the
one of fundamental importance in Logic, is the Law of Con-
tradiction, to which Leibnitz also assigned the same position.
All persons that have attained a just notion of the Rela-
tivity of Knowledge, would agree with Boole in the prime im-
portance thus given to Contrariety or Contradiction; but this
merely goes the length of Equivalence or Immediate Inference.
It prepares the way for Syllogism, and is the main key to the
useful enlargements of the syllogism ; but it does not touch
what is essential to deduction. The axiom, or ‘law of thought,’
at the foundation of mediate inference must be something else.
and if it is not the axiom assigned in the previous chapter of
this work, itis an axiom yet to be sought Passing from Boole’s
somewhat vague generalities to his actual method, which con-
sists in combining two equations standing for the premises of
the syllogism, into a third standing for the conclusion ; and
adverting to the maxim that justifies the process of reduction,
ee os ae
_—
AXIOM OF THE SYLLOGISM. 207
we seem to see that it is the same maxim as enters into a pro-
blem of equations with two or more unknown quantities ; as
for example, given «+ y= a,x — y — 8, to find wand y.
Grant that the conditions of a logical syllogism are fairly ex-
pressed by Boole’s symbols, and that the algebraic reduction is
suitable and relevant to the case, then the logical axiom is the
algebraic axiom that permits the substituting for y in one
equation, of its equivalent in the other; as when we obtain from
&—y = b, y = x — J, and insert this value of y in the equa-
tion « + y=a. The axiom of direct application to the
case would be that, for any quantity, its equivalent may be
substituted in an equation; in other words, the substitution,
for any quantity, of its equivalent, does not change the value
of the equation. This is a various reading of the axiom of
mediate equality—things equal to the same thing are equal to
one another; an axiom to which Mr. Mill compares, in point
of form, the axiom of the syllogism. If one thing is equal to
a second, and the second equal to a third, the first is also equal
to the third. In a combination containing A and B, we may
introduce in room of B its equivalent C.
A large portion of the work is devoted to Probabilities, in
handling which, the author continues the symbolism employed
in the previous portion of the work. It is generally admitted
that he has made important additions to the theory of this
subject, the common ground of Mathematics and of Logie.
CHAPTER III.
FUNCTIONS AND VALUE OF THE SYLLOGISM.
1. It is the peculiarity of the Syllogism, that the conclu-
sion does not advance beyond the premises. This circum-
stance has been viewed in two lights.
On the one hand, it is regarded as the characteristic
excellence of the Syllogism.
On the other hand, it is represented as constituting a
pelitio principit.
In the syllogism ‘men are mortal, kings are men, kings are
mortal.’ the conclusion seems already affirmed in the premises.
10
SOLE ee
208 FUNCTIONS AND VALUE OF TH# SYLLOGISM.
By virtue of the universal major, coupled with the interpreting
minor, there is distinctly involved in the premises the fact that
, kings are mortal.’
(1) To this circumstance has been attributed ‘the peculiar
ee dignity, and certainty of syllogistic inference.
When the two premises are supplied, the conclusion cannot be
refused without self-contradiction. There is nothing precarious
in the leap from the premises to the conclusion.
The same circumstance has been represented in a more dis-
advantageous light. The allegation is made that mere repeti-
tion is not inference; that to reproduce in a new form what is
already given may be highly convenient (as in the various
kinds of Immediate Inference), but is no march, no progress
from the known to the unknown.
(2) There remains a far more serious charge, and one that
takes us direct to the root of Formal Reasoning. Supposing
there were any doubt as to the conclusion that kings are mortal,
by what right do we proclaim, in the major, that all men are
mortal, kings included ?P
It would be requisite, seemingly, to establish the onesie
before we can establish the major. Ina order to say, ‘ All men
are mortal,’ we must have found, in some other way, that all
kings, and all peoples are mortal. So that the conclusion first
contributes its quota to the major premise, and then takes it
back again.
This is the deadlock of the syllogism, the cirouri aia ad
has brought down upon it the charge of ‘ reasoning in a circle’
(petitio principit). In point of fact, we can hardly produce a
more glaring case of that fallacy.
The extrication from the puzzle is due to Mr. John Stuart
Mill, and the consequence has been a total revolution in Logie.
2. The major premise of a syllogism (in the regular
figure) may, so far as the evidence is concerned, be divided
into two parts; the one part containing the instances
observec, and the other part containing the instances not
observed, but inferred.
The major premise, ‘ All men are mortal,’ consists of two
very different statements. The first is, that a certain number
of men have actually died. The evidence for these is actual
observation, the highest of all evidence. The second statement
is, that the men now living. and the men yet to be born, will
die ; for which there is not the evidence of observation.
In the same manuer may we analyze any other general
REASONING IS FROM PARTICULARS TO PARTICULARS. 209
affirmation or negation. The proposition ‘transparent bodies
bend light’ is made up of the bodies that have been actually
experimented on, and of bodies that have not been experi-
mented on; in the one case, the predicate is affirmed on the
evidence of fact; in the other case, the predicate is affirmed by
virtue of the inductive leap from the known to the unknown.
Thus, the ordinary form of the general proposition confounds
together the observed with the unobserved; the indiscriminate
fusion of the two is what has perplexed the theory of the
syllogism.
3. In affirming a general proposition, real Inference is
exhausted.
When we have said ‘All men are mortal,’ we have made
the greatest possible stretch of inference. We have affirmed
mortality of all men, of every class, in every age, past and
future. We have incurred the utmost peril of the inductive
hazard. Whatever justification needs to be offered for the
inference in hand, must be advanced as a security for the
major premise. |
4. The type of reasoning that best discloses the real
process is reasoning from Particulars to Particulars.
The basis of fact in every argument may be stated\to be
the particulars actually known from experience; as the mor-
tality of the men that have died. The inference is usually to
some other particulars unobserved, as ‘the present inhabitants
of London will die.’ The real evidence for the mortality of
the men now living is the death of their predecessors. A, B,
and C, have died ; D, now living, will die.
The practice of reasoning at once from certain particulars
experienced, to some other particular as yet unexperienced,
(there being a similarity in the cases) is not only the usual,
but the most obvious and ready method. We feel that the
real force of every reasoning lies not in the general statement,
but in the actual facts; and we are as much moved by the
facts in their particularity, as when they are given in a gene-
rality. That boiling water will scald the hand, is sufficiently
proved by its having done so in innumerable past instances ;
the deterring force lies in these actual instances. We are in-
fluenced by individual precedents, as strongly as by rules.
This is seen extensively in all professions. The experience
of a professional man consists of the cases he has actually ob-
210 FUNCTIONS AND VALUE OF THE SYLLOGISM.
served ; these he remembers as particulars, and when a new
example i is presented, he at once assimilates that with the pre-
vious particulars, and infers accordingly. When Dr. Mead
was called in to the last illness of Queen Mary, he pronounced
the disease to be small pox; his knowledge of that ailment
was the remembrance of a series of patients previously wit-
nessed by him; the queen’s symptoms resembled those, and he
drew the inference.
5. Wherever we may infer from a certain number of
particulars given, to one other particular, we may infer to
a whole class, or make the inference general.
If we can infer, from the men that have died, that the pre-
sent Pope will die, it is by virtue of a sufficient amount of re-
semblance between them and him; and we must be prepared
to make the same inference in all other cases where the re-
semblance holds. We may, therefore, say once for all, whoever
resembles past generations of human beings, in the points
wherein the pope resembles them, will die. The justification —
of one is the justification of the whole. The inference to an
individual case must ‘not be arbitrary ; it must be grounded on
a resemblance, and be applicable wherever the resemblance i is
found.
In a general proposition, therefore, we state the points of
resemblance that entitle us to infer from past particulars to a
new particular; and in stating these points we render the in-
ference at once general, and formally exhaustive. We mingle
up in one statement the observed known, and the inferred
unknown, the evidence and the conclusions. The use of
general language enables us thus to rise beyond particular
inferences.
6. Deductive Inference may be described as a BIA of
Interpretation.
Although the major premise covers the conclusion, it does
nos point to it by name, but only by character. The premise
‘men are mortal’ does not specify kings, nor the living pope ;
it indicates certain marks by which we are to judge whether
kings and popes are to be pronounced mortal, namely, the
marks of ‘men or humanity.’ Something, therafobera is want-
ing in addition to the major premise, in order to the conclu-
sion, the pope is mortal; we have to be assured that he is a
man, that he conforms to the defining marks of human beings,
To supply this requisite is the purpose of the minor premise,
at Mae Pah. a. YS
ae : oun r
DEDUCTIVE INFERENCE IS INTERPRETATION 211
which declares that the pope possesses the attributes of men,
or identifies him with the subject of the major premise. The
necessity for such an affirmation rescues the syllogism from
Immediate Inference or tautology. ‘ All men are mortal’ in-
eludes ‘the pope is mortal,’ on the supposition that the pope is
aman; and if this supposition is explicitly given in a distinct
proposition, the pope is then brought within the sweep of the
major premise : and the conclusion is established.
After affirming a general proposition (or making a general
denial) connecting or disconnecting a certain subject with a
certain predicate—men and mortality— we have still to hunt
out the particular cases of the subject, the things that possess
its attributes. This is the real deduction, and it is a material
and nota formal process. Itis an operation of comparing the
actual individuals already pointed out by the generalized subject
—actual and known men—with all future individuals as they
occur, and of pronouncing agreement of the new with the old.
The deductive inference that ‘ the pope is mortal,’ presupposes
an examination (direct or indirect) of the pope’s personality.
If this resembles the usual type of humanity, judged from the
instances actually known to us, we identify him with the
subject, ‘men,’ in our general proposition. The identity being
considered satisfactory, we complete the syllogistic formula,
and declare him to be mortal.
The proposition ‘men are mortal,’ by its form of universality,
imposes upon us, and leads us to suppose that we have in our
grasp the whole human race. The correcter view is to regard
it as an allegation respecting a certain number, with a power
of including others as they come on the stage. The proposition
assigns marks for the future identification of the beings that
are to be declared mortal; and, as the identification proceeds,
the minor premise is replenished with appropriate cases, and
so brings forth the conclusion.
The interpretation of a law or a command illustrates the
purely deductive part of the operation of reasoning—the sup-
plying of the minor. The law is given in general terms; cer-
tain characters are assigned as belonging to the subject of the
proposition. The administrator or judge ascertains whether
any particular case has or has not the characters specified. If
it has, a minor proposition is afforded, and a conclusion is
drawn.
This case also shows that the syllogism is the mere formal
completing of an operation, not at all formal, but in the strict
‘sense material. The operation consists in comparing one par-
212 FUNCTIONS AND VALUE OF THE SYLLOGISM.
ticular fact with other particular facts, through the medium of
a general description. The wording of a law, however gene-
ral be the terms, must be such as to suggest definite individual
eases. When the law mentions heritable property, or person-
alty, it must either state or suggest the particular things in-
tended; and the question of the application to a given case
turns upon the comparison of the case with the cases cited
or suggested by the general term or definition. Hence, the
business of the reasoner, in actual practice, 1s concrete com-
parison, from which, in the last resort, he can never be ex-
empted. This is riateriél deduction, which: in its essence, is the
same as material induction, being the carrying out of the in-
ductive operation, or the in-gathering of the details shadowed
forth, but not actually seen, in the general proposition.
Legal decisions are founded sometimes on statutes, some-
times on precedents or previous decisions. There is no generic
distincticn between the two modes. A statute has no meaning
except the particular cases specified or suggested ; and a pre-
cedent must involve a principle or rule. In both, the judge
refers back to concrete particulars, which are viewed under a
certain point of likeness or community.
Another case is the application of general theorems furnished
by the observations of others, such as the principles of science
established by foregone researches. We may have had no
share in arriving at the induction known as the atomic theory ;
we have not even seen the facts, we receive them embodied
and registered in the general statement of the law. We must
understand the meaning of that statement; we must realize
the kind of facts intended by it. When a case is started, a
given compound of two substances, we must say, by concrete
comparison, whether this compound has the characters of the
compounds expressed as chemical compounds. For example,
is the atmosphere a chemical compound? Does it agree with
the general characters of chemical compounds, or with those
typical instances that the general characters can do nothing
but refer us to. This is a truly material deduction; it is that
process of comparing instances that is the essence of the
generalizing operation, as seen in induction. It exactly
resembles generalization with a view to definition.
7. Although the deductive stage of induction is still an
inference from particulars to particulars, which nothing
can supersede, there are certain advantages in embodying
the possible inferences in a formal generality.
Powe. wae)
UTILITY OF THE SYLLOGISM. 213
Mr. Mill remarks that the syllogistic form of inference, from
generals to particulars, which supposes that each induction
is made general, is ‘a collateral security for the correctness of
the generalization itself.’ It is so in two ways.
First. It increases the sense of responsibility on the part of
the reasoner, by letting him know that his inference to one
individual must equally apply to a large host of individuals.
A common device for checking a rash inference is to point out
the extent of the consequences involved. The legal decision
against John Hampden, in the matter of thirty shillings of
ship money, was portentous as affirming the king’s power to
tax the nation without a parliament.
Secondly. If an induction is unsound, the making it
general is likely to. suggest contradictory instances. This is
merely a modification of the same consequence. Any person
attempting to justify a particular despotism must be prepared
to say that, in all similar circumstances, despotism would be
desirable. The remark is sometimes made, in the controversy
as to the inspiration of the Bible, that even Milton was
inspired; but, if so, then all great poets—Homer, Virgil,
Dante, Chaucer, Shakespeare, Dryden, Byron, Shelley—must
also own the gift of inspiration.
Mr. Grote, in defending the received canon of the Platonic
writings from the critics that would reject many of the Dia-
logues, on the ground of their style being unworthy of Plato,
points out the numerous Dialogues that would have to be
sacrificed to this criterion, if each critic were allowed to reject
for himself, and all rejections were admitted.
8. One great use of the syllogistic form is to analyze,
bring to light, and present for separate consideration, the
parts of a step or a chain of reasoning.
This has been already exemplified in the applications of the
syllogism to confused reasonings. It is advantageous to know
that the truth of a conclusion by inference supposes the truth
of two separate allegations, both alike necessary to the conclu-
sion. To prove that A is C, by a mediate inference (B is C,
A is B), two propositions have to be verified ; and the mind is
aided in disentangling a perplexed argumentation, by knowing
what to look out for.
In stating the distinction between the two modes of reasoning,
used both in Law and in Politics—reasoning from Precedents or
Examples, and reasoning from Rules or Principles—Sir G. C,
Lewis adverts to the great superiority of the last, the reasoning
214 TRAINS OF REASONING AND DEDUCTIVE SCIENCES.
from Rules. The reason of the comparative obscurity of the
argument from example or precedent, is that the principle involved
is usually suppressed. ‘The reasoning is much more perspicuous
when the general principle is stated first, the particular case is
placed under it, and the conclusion is then drawn. In order to
argue from one case to another, it is necessary to reject from each
the circumstances immaterial to the matter in hand, and to
compare those in which they agree. In complex cases, this process
is often extremely difficult. Much sagacity and knowledge of the
subject are required, in order to discriminate between material
and immaterial facts—to reject enough, but not more than
enough. For if immaterial facts are retained, the comparison
becomes obscure and uncertain; if material facts are rejected, it
becomes fallacious. This process, which, in the argument from
precedent, must often be performed mentally, though it may be
easy and sure to the experienced practician, perplexes the tiro.
Hence, students of the law have great difficulty in collecting legal
rules from cases, though they are soon able to apply a rule of law,
laid down in general terms, to a particular case of practice.’
CHAPTER IV.
TRAINS OF REASONING AND DEDUCTIVE SCIENCES.
1. A series of syllogisms may be connected in a chain.
Logicians have always recognized compound reasonings.
The Sorites is a connected chain of syllogisms. The conclusion
of one syllogism may be the major premise to a second, and so on.
The Sorites is usually stated in this form :—
A is B, Bis C, Cis D, &c., therefore A is D.
The regular form of proof (by the First Figure of the Syllo-
gism is—
B is C, A is B, therefore A is C.
C is D, A is ©, therefore A is D, &e.
It can scarcely ever happen that a proper deduction in this
simple form can be protracted over two or three syllogisms.
The application of a universal proposition to a particular case
seldom needs to descend by three or more distinct steps:
indeed, in by far the greater number of instances, the descent
is made at once.
No new logical principle, or modification of principle, is
involved in these consecutive reasonings. Their lucid state.
EXAMPLE OF A CHAIN. 215
ment is a matter of consideration for the expositor, but they
present no speciality to the logician. Still, they are usually
discussed in treatises on logic; and we may, following the
example of Mr. Mill, take occasion from them to discuss two
themes—the compatibility of the foregoing theory of the syllo-
gism with such trains, and the nature of the Deductive
Sciences.
2. A chain of Reasoning is reducible to a series of syllo-
gisms, the major in each being an induction from par-
ticulars, or a truth ultimately based in particulars.
Thus, if we were to prove that intelligent beings, although
they may be interrogated, are not to be experimented on like
brute matter, we should have the following chain :—wherever
there is intelligence, there is sensibility, in other words, suscepti-
bility to pleasure and pain ; we are not at liberty to inflict pain ;
now, most experiments that could be tried upon sentient crea-
tures would be painful ; hence, intelligent beings are not fit
subjects for experimental enquiry. Three syllogisms are con-
cerned in this chain of reasoning. The majors are—
(1) Society prohibits the infliction of pain.
(2) All intelligent beings have sensibility to pain.
(3) Experiments for ascertaining function in sentient beings
lead to pain.
Hach of these majors may be resolved, according to the
method of the previous chapter, into particulars observed and
particulars inferred, or left to be inferred, by virtue of identity.
The first major (Society prohibits) is in the form of a command,
the case where we may be supposed to be least concerned with
the particulars, and most concerned with the general descrip-
tion serving to identify the particulars. Still it must not be
forgotten that the real force even of a command is embodied
in the instances where it is enforced; the general state-
ment means nothing, is nothing, except as referring us to
these; the application of the rule is an inductive extension
of these instances. The second major (intelligent beings have
sensibility) takes in the observed coincidences of intelligence
and sensibility, together with the future extensions of these by
identification with the presence of intelligence—the first term
of the couple. The third major is likewise an inductive gene-
ralization, containing the observed particulars where experi-
menting has ended in pain, together with the resembling
inferred particulars.
We may arrange the train of reasoning in syllogisms. Thus,
--taking a different order—
216 TRAINS OF REASONING AND DEDUCTIVE SCIENCES.
First Syllogism.
Experiments for ascertaining function in sentient creatures
lead to pain.
The present proposal is an experiment for saver taney
function.
The present proposal will lead to pain (Barbara).
Second Syllogism.
Society prohibits the infliction of pain.
The present proposal will lead to pain,
Society prohibits the proposal to experiment on sentient
beings (Cesare).
Third Syllogism.
Society prohibits experiments on sentient beings.
All intelligent beings are sentient beings.
Society prohibits experiments on intelligent beings, (Cesare).
The form (Society prohibits, &c.), has the force of a nega-
tive ; were it not so, the last syllogism would not be valid.
The language of inference from particulars to particulars
might be used in each of these syllogisms. Thus in the first :
Experiments for ascertaining function in sensitive beings have
been observed to lead to pain; the present case is an experi-
ment for ascertaining function: the present case will lead to
pain (as the observed cases have done). Similarly for the
others. .
The Deductive Sciences.
3. The Deductive Sciences are those where the labour
mainly lies in applying or carrying out ascertained induc-
tions, that is, in the discovery of minors to given majors.
From the foregoing theory of the syllogism, it is apparent
that every deduction supposes a previous induction. The
Deductive Sciences, therefore, do not dispense with induction.
Whereas, in the Inductive Sciences, such as Chemistry and
Physiology, the chief labour consists in arriving at inductions ;
in the Deductive Sciences, as Mathematics, the inductions are
few and easily gained (being in fact sometimes called intui-
tions) and the labour consists in carrying them out into their
various applications, by bringing cases under them. We soon
arrive at the inductions ‘things equal to the same thing are
equal,’ or ‘the sums of equals are equal ;’ ‘ the differences of
ae.
wa
a
GEOMETRICAL DEDUCTION. 217
equals are equal : ’ but it was not easy to bring under the sweep
of these inductions the proposition ‘a sphere is equal to two-
thirds of the circumscribed cylinder.’ This is arrived at only
after a long and circuitous process of successive deductions,
based upon the invention of numerous diagrams.
- If we take a comparatively simple case of geometric deduc-
tion, the 47th of the First Book of Huclid, ‘the square des-
cribed on the hypothenuse of a right-angled triangle is equal to
the sum of the squares described on the two sides,’ we shall find
that the proof can be accomplished by two main leaps—two
syllogisms having axiomatic majors, and a preparatory syllo-
gism having as its major a previously established derivative
proposition. The rest of the process is not syllogistic. We
first, by an ingeniously devised construction, establish two
minors under the proposition—‘ A parallelogram and a triangle
being on the same base and between the same parallels, the
parallelogram is double of the triangle ;’ and then proceed to
the main steps, the application of the axioms. We first apply
the axiom—‘ The doubles of equals are equal,’ (a derivative
from the axiom—‘The sums of equals are equal,’) to prove
that the square described on one of the sides is equal to a part
of the hypothenuse square, and that the square described on
the other side is equal to the remaining part of the hypothen-
use square. This being done, it needs but an easy application
of the axiom—‘ The sums of equals are equal,’ to complete the
proof.
The deductive sciences circumvent their problems; they
accomplish indirectly what there is no means of accomplishing
directly. The science of mathematics instead of resting satis-
fied with announcing its axioms and definitions, and leaving
people to apply them at once, evolves a vast scheme of deductive
properties, to any one of which we may repair in an emergency,
instead of making a connexion at once with the fountain head.
We measure a height by bringing the case under some theorem
of Plane Trigonometry that chances to be adapted to the
means at our command.
The length and the complicacy of mathematical or other
reasonings may be ascribed to these two circumstances.
(1) There are many steps of mere Immediate Inference, as
in applying Definitions. Thus, when Euclid shows that two
figures coincide, he makes a formal appeal to the Definition of
Equality (namely, Coincidence), and, by virtue of tliat declares
them to be equal. This is seemingly a step in the reasoning ;
it involves a distinct act of attention on the part of the stu-
* «™ sv 6,37" “a
218 TRAINS OF REASONING AND DEDUCTIVE SCIENCES.
dent, but it is not a deduction or syllogism. So, there may be
steps involving other transitions to Equivalent Forms, as Ob-
version, Conversion, &c.
(2) Not only is a great deal of preparatory construction or
scaffolding often required in order to bring the case under the
sweep of a previous generality, but, when the construction is
made, there jut out from every part of it separate inferences,
and all these have to be made convergent to the purpose in
hand. Moreover, many propositions start at once with a com-
plicated hypothesis—‘ If a point be taken without a cirele (1),
and straight lines be drawn from it to the circumference (2),
whereof one passes through the centre (3),’ &c.; the proof in
these cases is a convergent series of steps, each starting from
a distinct member of the hypothesis.
The process of Identification to supply a minor is difficult
according to the complicacy of the subject of the major; as in
Diseases, in Law, in Politics, &c.
+
sem of 4nd * a gl ail
asl-s
PUSHING OF DEDUCTIONS. 219
forees. A process of computation is substituted for a process
_ of observation; the consequence is, in most instances, a great
economy.
The pushing of truths of induction to all their deductive
applications is one great department of scientific research.
The aptitude for the operation is almost purely intellectual.
When a great law, such as Gravitation, has been established,
_the following out of all its deductive consequences supplies
work to several generations of men. The generalization of
the present day, called the Persistence of Force, will give pro-
bably an equal amount of occupation to the more purely de-
ductive or speculative aptitudes of the scientific mind. The
inductive laws that connect Mind with Body, when ascertained
with precision, will admit of being deductively pushed in
numerous ways, and will yield many facts at present discover-
able only by separate observations. The doctrine of the
Relativity of all Feeling and Thought hag not as yet been
completely followed out to its consequences.
CHAPTER V.
DEMONSTRATION.—AXIOMS.—NECESSARY TRUTH.
1. The kind of evidence named ‘ Demonstration’ has its
sources in Induction.
Demonstrative proof is only another name for Deductive
proof, which, in the last resort,is Induction. The propositions
of Euclid are said to be demonstrated ; and, as above seen, this
means that the conclusions are proved by bringing each case
under the sweep of the fundamental principles of the science.
To make out Mathematical Demonstration inductive, it is
requisite to show—(1) that the foundations of the Science
(the axioms) are inductive; and (2) that the axiom of the
Syllogism is inductive. The axioms of mathematics supply
the principles, and the axiom of the syllogism justifies their
application.
In the question respecting the ultimate foundations of the
so-called axioms, these are the chief examples in dispute. It
is maintained, on one side, that the axioms of Mathematics,
Ieee
220 DEMONSTRATION.—AXIOMS.—NECESSARY TRUTH.
the axiom of the Syllogism, together with the axiom of Causn-
tion, —are inductions from particular facts of experience; and
on the other side, that they are of intuitive origin, and, in this
origin, possess a higher certainty than can be given by experi-
ence. *
2. The chief argument against the Inductive origin of
these principles is that they are necessary, and no experi-
ence can give the character of necessity. |
The idea of ‘ necessity,’ as attaching to such truths as the
mathematical axioms, dates from Leibnitz; it was re-stated,
in a qualified form, by Kant, and persists in the minds of many
to the present day. The term, however, is ambiguous,
Meanings of Necessity.
3. I. In common speech, ‘ necessity * is a synonym of
certainty ; and would apply to inductive truths. - |
When speaking of anything that is certain to happen, we use
among other words, the term ‘necessary.’ We should call the
freezing of water, at 32°, a necessity, meaning that we are
perfectly sure of its happening. We even say that vice isa
necessary consequence of bad training.
The necessity in such cases has admittedly nothing to do
with intuitive perception. Experience is competent, in every
instance, to give the strong assurance that the word signifies.
So, we have only experience to rely upon in believing that the |
sun must rise to-morrow.
There could be nothing incompatible with this usage in
terming all the inductive laws of nature ‘ necessary ’—the law
of gravity, the laws of motion, the fundamental laws of organi-
zation, and so on. But metaphysicians are accustomed to call
these principles ‘contingent,’ as opposed to necessary; for al-
though they are true, as the universe is now constituted, they
might have been otherwise. The law of gravity might have
been wanting ; the laws of organized beings might have been
different. But, in no circumstance (it is said) could ‘two
straight lines enclose a space ;’ this, therefore, is necessary in
a more peculiar sense of the word, as will be next stated,
* On the subject of Mathematical Evidence, other questions have been
raised, namely, the place of the Definitions in the Science, and the su
posed hypothetical character of definitions, These questions will be ad:
verted to afterwards (Loatc or THE SCIEs crs, Mathematics), (quae
NECESSITY AS IMPLICATION, Del
4, II. ‘Necessity’ more properly means implication ;
‘necessary truths’ in this sense are the truths demanded
by Consistency. Their denial is a contradiction in terms.
These truths have already been fully exemplified. (See
InrrRopUCTION, and also EquivaLent PropositionaL Forms). That
the less cannot contain the greater, is necessary ; it follows
from the very meaning of less and greater ; it could not be
contradicted without declaring the greater not to be the .
greater. ‘The same thing cannot be in two places at once’
is necessary ; the meaning of a ‘place’ is some definite spot
the negative of all other places; to say that a thing is ina
particular place is to deny that it is in a second, or a third,
or any other place. ‘Time isan eternal now!’ must be set
down as self-contradictory.
‘Some of the axioms of Huclid are necessary in this sense.
‘A whole is greater than its part’ is implicated in the defini-
tion of whole and part; it could not be contradicted without
contradicting the definition, A whole is summed up by its
parts; omit any of these, and the whole is not made up; the
result is something less than the whole.
‘Things that coincide are equal’ is not an axiom but a de-
finition ; it is the mark or test of equality, the only mark that
ean be propounded in the last resort.
Of all the alleged necessary truths, the one most frequently
cited in the present controversy is—‘ Two straight lines can-
not enclose a space.’ This was held by Kant to be a real pro-
position, a synthetic judgment; in other words, the subject is
not implied in the predicate; to it the criterion of ‘implica-
tion’ wonld, therefore, not apply. |
On the other hand, mathematicians are now probably unani-
mous in regarding this as a corollary from the definition of
the straight line, or as implicated in the very essence of
straightness ; so that to deuy it would be a contradiction in
terms. They would characterize it, in Kant’s own language,
as an ‘analytic’ judgment. A very little reflection on the
case proves that the mathematicians are right. Starting from
the definition of the straight line—‘ when two lines are such
that they cannot coincide in two points without coinciding alto-
gether, they are called straight lines,’ we see that the very
terms forbid the enclosing of a space; what meaning can we
attach to ‘coinciding altogether,’ but the exclusion of non-
coincidence, or of an intermediate space? Total coincidence,
and an intervening space, are wholly incompatible ; if the one
922 DEMONSTRATION.—AXIOMS.—NECESSARY TRUTH.
is true the other is false. The proposition is therefore neces-
sary in the sense of implication, as much so as a ‘ straight
line is not a bent line,’ ‘a whole is greater than its part.’
The axiom ‘Things eqnal to the same thing are equal to
one another’ is not a truth of implication, and therefore is not
a necessary truth in the present sense. The subject and the
predicate express distinct properties, and the one does not in-
volve the other. The axiom declares that mediate coincidence
is to be held as carrying with it, or as making, mmediate
coincidence ; but the two modes of coincidence are not iden-
tical. It is immediate coincidence that makes equality, accord-
ing to the definition of eqn: lity; the axiom extends this very
uarrow, and often inapplicable test, and declares that coin-
cidence through some third thing, a go-between, will be found
in the end to be the same as actual coincidence, and is conse-
quently to be accepted in all cases as a test of equality. If,
therefore, this axiom is to be held as a necessary truth, some
other meaning than the present must be assigned to necessity.
5. Necessary truths, in the foregoing signification, are so
far independent of experience, that they are perceived to be
true when the language is understood. They do not, how-
ever, require any powers of intuitive perception. |
As soon as we fully comprehend the notion of whole and
part, we perceive that the whole is greater than the part ;
we do not nced to make observations and experiments to prove
it. We required concrete experience, in the first instance, to
attain to the notion of whole and part; but the nution once
arrived at implies that the whole is greater. In fact, we could
not have the notion without an experience tantamount to this
conclusion. When we know a fact, we know it, even when
called by another name, which is all that is meant, at present,
by necessary truth. When we have mastered the notion of _
straightness, we have also mastered that aspect of it expressed
by the affirmation, ‘two straight lines cannot enclose a
space,’
No intuitive or innate powers or perceptions are needed for
such cases. Our ordinary intellectual powers enable us to
pronounce, in more than one form, that an object is everything
or anything that we have found it to be. We cannot have the
full meaning of ‘ straightness’ without going throagh a com
parison of straight objects among themselves, and with their
opposites, bent or crooked objects. The result of this com-
parison is, iter alia, that straightness in two lines is seen to
INCONCEIVABILITY OF THE OPPOSITE. 223
be incompatible with enclosing a space ; the enclosure of space
iuvolyes crookedness in at least one of the lines.
6. Ill. A third meaning and criterion of Necessity, is
enconcewability of the opposite.
It is maintained that ‘things equal to the same thing are
equal to one another,’ because the mind is unable to conceive
things agreeing with a common standard, and yet not agree-
ing when directly compared. It is also maintained that we
are unable to conceive ‘effects arising without a cause ;’ whence
such propositions are declared to be true necessarily. The
test of inconceivability of the opposite (stroagly urged by
Whewell, and held with modifications by Spencer), is liable to
serious objections. What we can, or cannot conceive, is mani-
festly dependent, in a very large measure, on our education :
the proof of which is that many truths inconceivable in one
age and country are not only conceivable under a different
state of education, but are so thoroughly engrained that their
opposites are inconceivable. The Greeks held matter to be
eternal and self-existent; many moderns hold that the self-
existence of matter is inconceivable. Some maintain that
mind is the only conceivable source of moving power or force ;
others, regarding the action of mind upon matter as incon-
ceivable, have contrived special hypotheses to get over the
difficulty,—we may instance Malebranche’s doctrine of Divine
Interference, and Leibnitz’s Pre-established Harmony. New-
ton could not conceive gravity without a medium.
With regard to truths of Implication, the difficulty of con-
ceiving the opposite must be at its maximum. Yet self-con-
tradiction is not an impossible operation, for it is often done.
In Theology, people have even boasted of holding contradic-
tory propositions. But where the subject does not imply the
predicate, there is no self-contradiction, and the opposite of
any such proposition may be conceived. That things medi-
ately coinciding, should not immediately coincide, is conceiv-
able ; for the facts are different; the difficulty that we feel is
in contradicting our habitual experience on a matter so very
familiar and tangible.
Propositions of avowedly inductive origin may be so strongly
associated that their opposites are all but impossible to con-
ceive. It is scarcely in our power to conceive colour without
extension; and yet the two are united solely by our experi-
ence; they strike the mind through different avenues, and their
incessant conjunction constitutes a practically indissoluble
224 DEMONSTRATION.—AXIOMS.—NECESSARY TRUTH.
bond. We should have some difficulty in conceiving soot
flakes, particles of dust, and small pieces of paper, falling to
the ground plumb and swift like a stone. The Greek proverb
for the impossible was water flowing back to its source.
The Nature of Axioms,
7. The fundamental principles of the Deductive Sciences
are called Axioms.
Every Deductive Science must begin with certain funda-—
mental assumptions. In Mathematics, andin Logic, these are
deemed so self-evident, that no express effort is made to
establish them. In Mechanics, the statement of the Laws of
Motion is accompanied with a few examples to make them at
once intelligible and evident. In Chemistry, the Atomic
Theory is somewhat too far removed from ordinary compre-
hension to be called a self-evident axiom, albeit the most fun-
damental assumption contained in the science.
The requisites of an axiom are, first, that it should be a real
proposition, and not a definition ; and, secondly, that it should
be independent of any other principle within the science.
On the first of these two requirements, we should have to
reject Euclid’s axioms—‘ Magnitudes that coincide are equal,’
and ‘ The whole is greater than its part.’
On the second requirement, we must reject,—
The differences of equals are equal ;
If equals be added to unequals, the wholes are unequal ;
If equals be taken from aia the remainders are
unequal ;
Doubles of equals or of the same are equal ;
Halves of equals or of the same are equal ;
Two straight lines cannot be drawn through the same point,
and parallel to the same straight line, without coinciding.
It may be useful to give an explicit statement of these
truths, but as they are all derivable from other axioms
(together with Definitions), they should be appended to these
others, as corollaries or inferences. If, in any instance, we set
up a derwative proposition as an axiom, we break down the
sole boundary between axioms and the propositions or theorems
constituting the body of a science.
8. The only two Axioms of Mathematics, properly so
called, are, the axiom of ‘ mediate coincidence,’ and the
axiom of the ‘ equality of the sums of equals.’ These are
Inductive truths. reeontnael
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AXIOMS OF MATHEMATICS. 225
The excision of Definitions with their corollaries, and of
Derivative Propositions, leaves only the two axioms now men-
tioned—‘ Things equal to the same thing are equal,’ and ‘ The
sums of equals are equal.’ These are real, and not essential or
analytic, propositions: and they are ultimate within the
science. They are two distinct tests of equality, over and
above the defining test, immediate coincidence. From them,
together with the definition, all other tests of equality are
deducible.
To say that they are Inductive truths, generalizations from
our experience of the particular facts, is to say that they have
the same origin as the great mass of our knowledge (not
deductive). That day and night alternate, that water flows
downward, that smoke ascends, that plants grow from seed,
that animals die, that men seek pleasure and eschew pain,—are
all obtained by a comparison of observed facts ; and this is the
regular, the usual source of scientific generalities. The burden
of proof lies upon those that would assign any other source to
the two axioms named; some reasons must be given to show
that they are exceptions to the prevailing rule.
The chief reasons actually assigned are those already ex-
amined, their Necessity, and the Inconceivability of their Op-
posites. As corroborating these, or rather as putting in a
different shape the supposed difficulty of referring the axioms
to experience, it is said that the intensity of owr conviction that
‘things equal to the same thing are equal’ is greater than could
arise from the accwmulated comparisons that we have instituted
on actual things. The considerations that serve to obviate
what force there is in this objection are the following.
First, by the law of Belief already explained, every uncon-
tradicted experience has, on its side, all the force of our primi-
tive credulity. The initial believing impetus of the mind errs
on the side of excess; and if nothing has happened to check
it in a particular case, it will be found strong enough for
anything.
Secondly, our opportunities of comparing magnitudes are
numerous and incessant ; they require only the very simplest
and most accessible instruments. The child, having at com-
mand, three equal chips of wood, cannot avoid making, in the
course of an hour, scores of comparisons that exemplify the
axiom of mediate equality.
Thirdly, it is usual to remark, on the mathematical axioms
generally, that the subjects of them—namely, magnitudes and
forms—are with the greatest possible ease represented in ima-
226 DEMONSTRATION,—AXIOMS.—NECESSARY TRUTH.
gination, so that we can make numerous ideal experiments, in
addition to our comparison of actual things in the concrete
9. The Axioms of the Syllogism repose upon experience.
In the form—‘ Attributes co-existing with the same attri-
bute, co-exist,’ we have a principle closely resembling Euclid’s
first axiom of Equality ; the character of the evidence for both
must be the same. Now, so far is this axiom from being an
absolute and intuitive certainty, that it is erroneous. Wemay
illustrate it by a parallel form, ‘Things in contact with the
same thing are in contact with one another ;’ which is plausible
but fallacious.
The dictum de omni et nullo cannot be exempted from the
criterion of experience. It is not intelligible without much
familiarity with examples of the generalizing process ; and, as,
in the case of all other first principles, the same knowledge
that makes it understood, suffices to verify it.
However expressed, the Axioms of the Syllogism are, in the
first place, Real Propositions, and not identical statements under
the so-called Law of Identity, or Self-Consistency. And, in
the second place, as Real Propositions, they are not intuitively
suggested tothe mind; they grow up with our experience, and
if our belief in them seems to outrun experience, the same
thing happens to all our beliefs,
10. As regards the Law of Causation, usually ineluded
among the so-called a prior elernents of ourknowledge, there
is a strong primitive tendency to believe it in a crude form,
while experience must adapt this belief to the actual facts.
We have already seen that the primitive tendency of the
mind is to believe, until checked, that what is now will continue,
that what is here is the same everywhere. Neither experience
nor any intellectual faculty creates this impetus; but experi-
ence arrests and modifies it, till by degrees it adapts itself to
the real occurrences. The headlong impulse is curbed in such
matters as the surrounding temperature, luminosity, and visi-
ble appearances ; it is left in possession of other matters, as the
force of gravity. The instinct is important as giving the active
element of belief; it is perfectly worthless as a guide to the
things proper to be believed. So far as concerns the authority
or evidence, for causation, experience is paramount over
instinct ; apart from experience, the infant would for life be-
lieve that all the water of the globe is of the temperature of its
first bath.
THE UNIFORMITY OF NATURE, T77
The crude impulse to believe that what is will continue,
after the shock of many contradictions, is transformed into a
belief in the uniformity of nature, as represented by the law of
Causation.
11. The axiom underlying the axioms of Mathematics,
and the axiom of the syllogism, is the axiom of the Uni-
formity of Nature.
The consideration of cause and effect brings us face to face
with the most fundamental assumption of all human know-
ledge, expressed by such language as ‘Nature is Uniform’
‘the Future will resemble the Past’, ‘ Nature has fixed Laws.’
This axiom is the common ground of all inference, wh>ther
avowedly inductive, or induction disguised under the forms of
deduction. Without this assumption, experience can prove
nothing. We may have found, in ten thousand instances, that
magnitudes coinciding with the same magnitude also coincide
when applied to one another; so far as these instances go, the
fact is not to be disputed ; the evidence of actual trial is the
highest we have. But they do not prove that it will happen
in any untried instance. This must be received without proof ;
it can repose on nothing more fundamental than itself. If we
see n to offer any proof for it, we merely beg it in another
shape. (See Apprenpix D.)
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INDUCTION.
CHAPTER I.
MEANING AND SCOPE OF INDUCTION.
1. Induction is the arriving at General Propositions, by
means of Observation or Fact.
In an Induction, there are three essentials: —(1) the result
must be a proposition—an affirmation of concurrence or non-
concurrence—as opposed to a Notion: (2) the Proposition
must be general, or applicable to all cases of a given kind: (3)
the method must be an appeal to observation or Fact.
(1) By Induction, we arrive at Propositions,—Affirmations
of coincidence or non-coincidence of distinct properties ; we
have to do, not with verbal, but with Real Predication. That
‘The boiling temperature destroys animal life,’ is an induction
so far as being a proposition, affirmation, or real predication ;
there are two distinct facts—boiling heat, and destruction of
animal life—and these two facts are coupled in an affirmation
of coincidence.
To this essential of Induction, are opposed the cases where
what we arrive at isa Notion or Definition. Sometimes we
are liable to confound the two. This happens when we are
attending too exclusively to the second characteristic of Induc-
tion— generality. In the process of defining, we generalize a
number of individuals, so as to obtain and express their point
or points of community, which expressed community is a De-
finition or Notion; as Heat, Knowledge, Justice. If such
definitions, or expressed general notions, are absolutely limited
to one indivisible fact or attribute, they are by that circum-
stance decisively contrasted with inductions, which always join
11
232 MEANING AND SCOPE OF INDUCTION.
at least two facts or attributes. Thus, the generalized notions
of length, resistance, whiteness, heat, could not be confounded
with inductions; there is clearly absent from these the con-
joining or coupling of distinct properties. But we have seen
many instances where a definition expresses a plurality of
attributes concurring in the same subject, as in all the natural
kinds—minerals, plants, animals—and in various other things.
There is no small delicacy in placing the boundary between
those generalities ending in plural notions, or definitions, and
proper inductive generalizations. We have to ask whether or
not the stress is laid on the circumstance of conjunction,
whether it is made a question—are the properties conjoined
or not, In definition, the conjunction is tacitly assumed; in
induction, it is laid open to question; it has to be proved or
disproved. (See p. 292),
(2) The Propositions established by Induction are general.
A single individual concurrence, as ‘ the wind is shaking the
tree,’ is in its statement a proposition, but not an induction.
On such individual statements, we base inductions, but one is
not enough. If the coincidence recurs, we mark the recur-
rence ; we are affected by the shock or flash of identity, a very
important step in our knowledge. If, pursuing the sugges-
tion, we remark that as often as the wind is high, the trees:
are shaken; that the two things have concurred within the
whole course of our observation; that the same concurrence
has been uniform in the observation of all other persons
whose experience we have been informed of,—we are then
entitled to take a still wider sweep, and to say, ‘every time
that a high wind has been observed, a waving of the trees has’
also been observed.’ . sat 4
Still, with all this multitude and uniformity of observations,
there is no proper Induction. What then remains? The
answer is, the extension of the concurrence from the observed
to the unobserved cases—to the futwre which has not yet
come within observation, to the pas/ before observation began, __
to the remote where there has been no access to observe. This —
is the leap, the hazard of Induction, which is necessary to
complete the process. Without this leap, our facts are
barren ; they teach us what has been, after the event; whereas, —
we want knowledge that shall instruct us before the event, —
that shall impart what we have no means of observing. A
complete induction, then, is a generalization that shall express
what is conjoined everywhere, and at all times, superseding
for ever the labour of fresh observation. it GORE
IMPROPER INDUCTIONS. 933
We thus contrast Induction with that species of ‘ Induc-
tions improperly so called,’ where a general statement merely
sums up the observed particulars.
If, after observing that each one of the planets shines by the
sun’s light, we affirm that ‘all the planets shine by the sun’s
light,’ we make a general proposition to appearance, but it
falls short of an induction in the full sense of the term. The
general statement is merely another way of expressing the par-
ticulars ; it does not advance beyond them. But without such
an advance there is no real inference, no march of information,
no addition to our knowledge. Induction is the instrument of
multiplying and extending knowledge; it teaches us how,
from a few facts observed, to affirm a great many that have
not been observed. If, from the observation of the planets
now discovered, we make an assertion respecting all that have
yet to be discovered, we make the leap implied in real or
inductive inference. If the assertion had been made when
only six planets were known, actual observation would have
been the guarantee for those six, induction for the remaining
bundred or upwards.
Sc the proposition ‘all animals have a nervous system’ is
an induction only when affirmed on the observation of a part
of the animal species. If the representatives of every species
had been examined before the statement was made, the pro-
position would be proved by observation, and not by induction;
the generality would be merely a literal repetition or summary
of the particulars.
This kind of improper induction is assumed in the attempt, made
first by Aristotle and repeated by others, to bring Induction under
the syllogism. Induction ‘is defined by Aristotle, “ proving the
major term of the middle by means of the minor;” in which
definition, the expressions major, middle, and minor, are used
relatively to their extension, to designate respectively the attribute
proved, the constituted species of which it is proved, and the
aggregate of individuals by which the species is constituted.’
(Mansel’s Aldrich, Note G.), Thus—
X, Y, Z, (minor) are B (major),
X, Y, Z, are all A (middle),
All A is B.
This has the appearance, but only the appearance of a syllogism
in thé Third Figure. It is liable to the criticism already made
upon syllogisms with two singular premises. It is nota syllogism -
at all, in any correct sense, but a mere process of equivalence. The
two premises can be summed in one, by verbal or grammatical
condensation ; and when that has been done, the conclusion is a
mere repetition of part of the meaning of the combined statement.
234 MEANING AND SCOPE OF INDUCTION.
A more ambitious form of the Inductive Syllogism is given by
Aldrich and Whately, which trenches on Induction proper.
The magnets that I have observed, together with those that I
have not observed, attract iron,
These magnets are all magnets,
All magnets attract iron. |
The major here obviously assumes the very point to be estab-
lished, and makes the inductive leap. No formal logician is entitled
to lay down a premise of this nature. The process altogether
transcends syllogism or formal logic.
In no sense is the Inductive Syllogism an admissible logical
form,
A truly inductive Proposition may be but a narrow genera-
lity. That ‘the breeze always spreads the royal flag hoisted
at Windsor Castle’ is a proper induction ; it covers the unseen,
and the future as well as the seen. The still wider induction,
‘the breeze spreads all the flags of all nations,’ is not more
essentially inductive, although of more value as knowledge.
(3) An Inductive Proposition is based on the observation
of facts. Many true propositions, instead of being based on
a direct appeal to observation, are derived from other propo-
sitions ; such are, with a few exceptions, the propositions of
Mathematics, and many truths in all the other sciences. In
this view, Induction is contrasted with Deduction. Induction
is necessarily the prior source of truths; the Deductive pro-
positions are obtained from Inductions, We must commence
with observation of fact, and thence rise to Inductive gene-
ralities, before we can proceed downwards in the way of
deduction. 2
By the use of our observing faculties for the object world,
and of self-consciousness for the mind, we not merely obtain
our notions of things—stars, mountains, trees, men, pleasures
—but also discern the conjunctions or connexions of things.
A single conjunction excites little notice, but an iterated con-
junction awakens our feeling of identity; we attend to the
circumstance, and watch for the recurrence. If, in the midst of
fluctuation, some one couple of things is found always associ-
ated, we state the fact to ourselves as a natural conjunction, a
_ law of nature; and the statement is an inductive proposition.
A meteor flashing along the sky is an isolated circumstance ;
we term it casual or accidental. The recurrence of a stream
of meteors year after year, in the same month, is a coincidence,
which we elevate into an induction, affirming it for the future
as wellas for the past. oe
The semblance of Induction is put on by certain operations
,
INDUCTION AND DEDUCTION CONFOUNDED. 235
purely Deductive. Of these Inductions improperly so called,
two forms may be mentioned.
First. There is a certain likeness to Induction in the demon-
strations of Huclid; which are each made upon an exemplary
diagram, and thence extended to all similar instances, by what —
is termed parity of reasoning.
When Euclid proves that the angles at the base of an isos-
celes triangle are equal, he proves it upon a single diagram,
and rests the general proposition upon the circumstance that
the same result would be arrived at in every other case of the
same sort. The resemblance to Induction les in extending
what is found in one instance to all other instances. Yet the
resemblance fails on vital points.
In reality, such truths are not established by measuring the
particular diagram, and recording that measure as an observed
fact, to be taken with other facts similarly observed, in mak-
ing up a general rule; as if we were, by means of an induction
from the pyramids, to lay down a general law of pyramidical
structure. The only use made of the figure is to provide a
concrete reference in applying the general language of the
demonstration. One triangle is as good as another for the
purpose. We expressly omit from the reasoning all reference
to the size of the triangle, to its material, to the size of the
angle included by the two equal sides; consequently, our
proof is independent of any one of these elements, and holds
under all variations of each. The demonstration is to the
effect that, guoad isosceles triangle, the affirmation is true; it
is a perfectly general truth. The expression, ‘ the same might
be proved of any other isosceles triangle,’ would be idle and
superfluous; the fact is already proved of every such triangle.
Secondly. The term Induction has been improperly applied
to discoveries of identification to establish a minor—a purely
deductive operation.
When Kepler, after comparing a great many positions of
Mars, came to the conclusion that all these places lay in an
ellipse of certain dimensions, he made an advance from the
known to the unknown, which is one criterion of induction.
Without any farther observations, it was possible to assign .
the place of the planet at any moment of time throughout
the entire circuit. Yet, notwithstanding this remarkable
peculiarity, the case is not an induction. It is, in fact, a
deduction. We might term it a discoyery of identification to
establish a minor. :
Supposing that, in the time of Kepler, the geometrical pro-
236 MEANING AND SCOPF OF INDUCTION.
positions of the ellipse had been still undiscovered, he cou!d
not have established his law, nor applied it to fill in the inter-
mediate places of the planet. What he really discovered was
an identity between the series of observed positions of Mars
and the path of an ellipse with the sun in the focus. It was
by the help of the known properties of the ellipse that he made
this identity. The identity once established, any or all of tne
propositions of the ellipse could be applied to the orbit of
Mars, and by these the orbit could be as it were drawn, so as
to show the successive positions of Mars as he described his
circuit. There could have been no inference from places
observed, to places unobserved, except through the application
of those laws respecting the ellipse, which had been dis-
covered by the Greek geometers. The propositions of the
ellipse supplied the major premise of the reasoning. Kepler’s
observations supplied the minor premise; they showed that
the places of Mars coincided with the places in an ellipse ;
whereupon whatever was true of the ellipse was true of the
orbit of Mars. 1
Similar instances of discoveries of Deduction could be cited.
When after the inductive establishment of the laws of
magnetism upon Iron, other substances were discovered to
be magnetic as Nickel, Cobalt, Manganese, Chromium, &c.,
the magnetic laws were forthwith transferred deductively to
these bodies. Franklin’s great discovery of the identity of
lightning and electricity, enabled all the previously ascertained
facts regarding electricity to be applied to the atmospheric
charge.
In contrast to the law of the elliptic orbits, we may quote
Kepler’s third law—the relation of the periodic times to the
mean distances, an induction in the proper sense of the word,
There is still a mathematical element present, but that element
is not the major proposition, to which Kepler supplied a minor.
The numerical ratio merely expresses the point of concurrence
of the particulars observed, it being the nature of that con-
currence to be numerical. The basis of the induction was the
agreement of the six planets in the numerical ratio; and the
induction was brought out in its real character when new
planets were discovered and the law applied to them at once,
and before there was time to observe the fact in each indiyi-
dual case.
Of a similar nature to Kepler’s third law ‘s the law of the
refraction of light, a proper induction set in mathematical lan-
guage. From a number of positions of the incident and re-
FUNDAMENTAL INDUCTIVE METHOD. IT
fracted rays of light in various substances, Snell found that
the relation of the two could be expressed by a definite
numerical proportion of the sines of the angles, the proportion
being constant for the same transparent medium. JHe had
_ observed the relation in anumber of cases, and he inductively
affirmed it in all.
In like manner the establishment of the law of gravitation
was an induction numerically expressed.
2. The sole method of attaining Inductive truths being
the observation and the comparison of particulars, the sole
evidence for such truths is Universal Agreement.
A permanent or uniform concurrence can be established, in
the last resort, only by the observation of its uniformity. That
unsupported bodies fall to the ground, is a conjunction sug-
gested by the observation of mankind, and proved by the
unanimity of all observers in all times and places. “What is
found true, wherever we have been able to carry our observa-
tions, is to be accepted as universally true, until exceptions are
discovered: This is to apply the Universal Postulate, the
primary assumption at the root of all knowledge beyond the
present—that what has never been contradicted (after sufficient
search) is to be received as true.
Through this method alone—of Universal Agreement in de-
tail—can our most general and fundamental truths be dis-
covered and proved. It is the only proper Inductive Method.
By it are established the Axioms of Mathematics, the Axioms
of the Syllogism, the Law of Gravity, the Law of Causation or
of Conservation. Likewise on it we depend for the proof of
all uniformities that, although not ultimate, are for the time
unresolved into higher uniformities ; or what are termed Kmpi-
rical Laws.
CHAPTER IL
THE GROUND OF INDUCTION—UNIFORMITY OF
NATURE—LAWS OF NATURE.
1. As Induction proper infers from the known to the
unknown ; it assumes that, under certain circumstances
(to be specified), what has been will be. The same thing
is otherwise expressed by affirming that Nature is Uni-
form; that there are Laws of Nature.
This great foundation of all possible inference is stated in
many forms of language. ‘ Nature repeats itself,’ ‘the future
will resemble the past,’ ‘the absent is like the present,’ ‘ the
Universe is governed by Laws.’ In one great department, it
is named Causation, or the Law of Cause and Hffect. :
The principle is put in another light by the remark of Mr.
Mill that the Uniformity of Nature is the ultimate major premise
of every inductive inference. To prove that the present
generation of men will die, we may construct a syllogism
thus :—major—what has been in the past will continue
(under given circumstances); minor—men have died in the
past ; conclusion—men will continue to die.
Nature is not uniform in all things. One day agrees with
another in part, and differs in part. Human beings are
born with a certain amount of uniformity, and also with
a certain amount of difference. The law of uniformity, there- —
fore, needs to be limited and qualified.
2. The course of the world is not a Uniformity, but
Uniformities. ‘There are departments of uniformity, which —
are radically distinct.
The most pointed illustration of this statement is the
Classification of the Sciences. Although, in early ages, men’s
minds were strongly prepossessed with a supposed Unity of
Nature, we now recognize a plurality of distinct kinds of
phenomena, each kind having its own separate principles or
laws. Thus, the facts and principles of Number are studied
apart from the facts and principles of Life.
LAWS OF NATURE. 239
The phrase ‘ Laws of Nature’ may be understood to imply
(1) that Nature is uniform, and (2) that this uniformity is a
plurality and not a unity. There are separate departments,
each with its own uniformities or laws. That unsupported
bodies fall to the ground, that fire is quenched by water, that
men pursue pleasure—are said to be laws of nature; they are,
however, generically different laws, and are distributed under
distinct branches or departments of Science or Knowledge.
The word ‘ Law’ is a metaphor taken from human society,
where it supposes the relationship named authority and obedi-
ence. Seeing that in all well-constituted societies, the decrees
emanating from the sovereign authority are alike binding upou
all citizens, in all times and places, they have the characteristic
of uniformity ; and it is on this characteristic alone, that ‘law’
can be employed to signify the order of the natural world.
The full definition of a law is inapplicable to physical sequences.
The likeness fails in the essential point. In human authority,
a certain beneficial result is aimed at by rules of conduct on
the part of the subjects of the state ; which conduct is enforced
by a penalty or punishment; and the penalty is directed with
precision upon the wrong doer. In the order of the world,
on the contrary, a man conforming to the physical sequences
is safe, whatever be the extent of his violations of moral law.
Night exposure may be more injurious to the policeman than
to the thief; immunity is purchased not by virtuous conduct
as regards others, but by prudential care as regards self.
8. The term ‘ Law of Nature’ is sometimes used in a
more restricted sense, to express the highest generalities,
or ultimate uniformities of nature.
There being a constant wish to discover, not merely laws
that shall be true, but laws of the highest and most command-
ing generality, such laws are more emphatically termed
‘The Laws of Nature’—the most centralized and all-compre-
hending expressions of the order of nature. This more
imposing character appears to belong to the law of Gravity,
and to the principle named ‘ The Conservation of Force.’
4, As regards Logical Method, the general Uniformity
of nature may be distributed under three branches, already
expressed in the ultimate classification of Propositions—
CO-EXISTENCE (as Co-inherence of Attributes), CAUSATION,
and KqQuaLiry.
The three great relationships found capable of embracing
240 THE GROUND OF INDUCTION.
all propositions were stated to be (1) Co-existence, (2)
Sequence, (8) Equality and Inequality (Number and Quan-
tity). Under Co-existence was included Order in Plaee, and
Co-INHERING ATTRIBUTES; the first—Order in Place, being
resolvable into laws of Quantity. Under Sequeuce or Succes-
sion was included Order in Time and Causation; the first-named
being also a purely numerical relationship. The third rela
tionship, Equality and Inequality, is the basis of Mathematics,
the science of Quantity and Number.
Thus the three distinct heads of scientific investigation,
comprising all the uniformities or laws of nature, are Unifor-
mities of Co-existence, Uniformities of Succession (Causation),
Uniformities of Hquality and Inequality. These are the thiee
cases that Induction has to deal with. é
In the actual working of Induction, we find it to be almost
entirely absorbed with the second head—CausaTIon. —
Besides that there are very few general laws of pure Co-
existence, Causation is singular in providing a comprehensive
Uniformity, which may be appealed to deductively, for all
cases. The uniformities of Co-existence (independent of
Causation) can be proved only piece-meal; each stands on its
own evidence of observation in the detail; no one assists us
to prove another. There is thus a blankness of resources
in regard to the proper laws of Co-existence ; their Logic is
speedily exhausted.
The same defect, strange as it may sound, attaches to the
uniformities of Quantity—based on the relations of Kquality
and Inequality. The certainty of the mathematical axioms is
a certainty due to their easy and thorough verification one by
one; not to their falling under any uniformity more compre-
hensive than themselves. It is by ‘ Agreement through all
Nature’ that we prove that ‘ Things equal to the same “thing
are equal ;’ having found this fact always true, never false,
we extend it, by the Inductive hazard, to all cases whatsoever.
We repeat the operation upon the other. great axiom—‘ The
sums of equals are equal.’ We must proceed, in the same
method of detail, to all other axioms—as the dictum of the
syllogism, the axiom a fortiori, &e.
The extended machinery of Inductive research, constituting
the Logic or Method of Induction, is thus nearly confined to
Causation. The greatest resources for eliminating accidental
accompaniments and for seizing the real concomitances of
facts—the so-called ‘ Experimental Methods’—have their full
application only to Cause and Effect.
CHAPTER III.
INDUCTION OF CO-EXISTENCE.
1. Of Uniformities of Co-existence, a very large num-
ber may be traced to Causation. It remains to be seen
whether there be any not so traceable.
The numerous Co-existences of Order in Place, or the dis-
tribution and arrangements of material objects throughout the
Universe, are all the results of causation, starting from some
prior arrangements. The distribution of sea and land, the
stratification of the earth’s crust, the existence of an atmos-
phere, the distribution of the materials of the globe generally,
—are the result of natural agencies or forces, operating upon
prior arrangements. Salt is found in the ocean, because the
water has dissolved all accessible portions of it. The heavy
metals are found in deep rocks in consequence of their weight ;
the corrosible and combining metals occur in combination ;
and those that are reluctant to combine, occur nearly pure, as
Platinum and Gold.
There are thus no independent laws of co-existence to be
found among uniformities of Order in Place. We must seek
for them, if there be any such, among Co-INHERING ATTRIBUTES.
It is possible that attributes or properties not connected as cause
and effect, may yet be conjoined uniformly through all nature,
If so, they are likely to. be found among the natural kinds—
Minerals, Plants, Animals. The conjunction of body and
mind in man, and in the animals, is to all appearance such a
case as we are in quest of.
2. It is the special peculiarity of the Natural Kinds to
combine many attributes in unity of subject. In them we
have the chief exemplification of co-inhering attributes ;
and they seem to furnish uniformities of co-existence.
Thus Gold unites a certain specific gravity (19.3), crystal-
lization (cubical), tenacity, fusibility (melting point, 1200° C),
colour and lustre (yellow), electrical conduction, atomic weight
(196), combining properties (acted on by aqua regia). These
are eight leading attributes that concur in every piece of gold;
242, INDUCTION OF CO-EXISTENCE.
and unless we see our way to deriving some of them from
others, we must pronounce them essentic, essential or defining
attributes of gold. There is a co-existence, or co-inherence of
these eight facts, with others, in the object named gold.
To appearance there is here a uniformity of co-existence.
No specimen of gold is devoid of any one of the eight proper-
ties. Properly speaking, however, this is merely affirming an
identical proposition. Should there occur a specimen wanting
in one, two, or three of the eight, we should say not that a law
of co-existence was infringed, but that a different substance
was produced. If these be the essential attributes of gold—the
meaning or connotation of the name, then, on the failure of any
one or more, the name would cease to be applied, the substance
would not be ranked as gold, it would be classed as a new and ~
distinct substance. Gold with the specific gravity of 9, or
with a silvery colour, or with a lability to corrode, would not
be gold, it would be treated as a different material, a distinct
grouping or aggregate of powers and properties. If there be
any one of the now enumerated properties of gold that we
could see changed and yet keep up the designation gold, that
property is declared not to be the essence, but a concomitant
of gold. A proper inductive enquiry would hold in sucha case,
3. For a Law or Uniformity of Co-existence, properly
so called, we must refer to examples, if such there be,
where two or more independent properties are conjoined
through all nature, or in all substances where one of them
occurs.
We must search among the properties of kinds—mineral,
vegetable, and animal, for some that are coupled throughout
every species, and under every variety of aggregation. For
example, could we find a certain crystalline form regularly
conjoined with certain chemical characters, not in one sub-
stance only, but in all substances possessing that erystal-
lization,—this would be a proper law or uniformity of co-exist-
ence. There would still remain a question, often difficult to
settle—whether, on the one hand, the two are mutually im-
plicated properties, or, on the other hand, whether they are
connected by cause and effect.
To detect such uniformities of general co-existence, among
the essential properties of mineral bodies, whether simple or
compound, is a proper object of scientific enquiry. Nor has
it been neglected by physical enquirers. The following are
the leading examples obtained up to the present time,
LAWS OF CO-EXISTENCE. 243
(1) A law has been discovered connecting Atomic Weight
and Specific Heat by an inverse proportion. For equal
weights of the simple bodies, the atomic weight, multiplied by
a number expressing the specific heat, gives a nearly uniform
product. Thus, for sulphur, the atomic weight (32), multi-
plied by the specific heat (0.1776), gives 5.68; the atomic
weight of platinum (197), multiplied by its specific heat,
(0.0824), gives 6,88. The products for all the elements are
near the constant number 6.
(2) A law obtains between the Specific Gravity of substances
in the gaseous state and the Atomic Weights. Thus, the specific
gravity of oxygen is 16, its atomic weight 16; hydrogen,
specific gravity 1, atomic weight 1; phosphorus, specific
gravity 62, atomic weight 31 (the relation here is 2 to 1);
steam, specific gravity 9, atomic weight 18 (relation of 1 to 2).
The relationship of the two numbers is thus, in some instances,
equality ; in other instances, the one is a multiple of the
other. The law is one of importance in ascertaining atomic
weights.
With an exception to be noticed presently, these are perhaps
the two most widely-operating laws, as yet discovered, whereby
two distinct properties are conjoined throughout substances
generally. There are various laws of narrower range, as, for
example, Andrews’s laws of the heat of combination of the
metals.
4, A peculiar importance belongs to the law of universal
co-existence uniting the two properties — Inertia and
Gravity. These properties are co-existent through all
matter and proportionate in their amount.
Inertia, the defining attribute of matter, means both resist-
ance to moyement, and force when moyed. It is totally dis-
tinct from gravity. A body rolled on a level surface shows its
inertia; so also do two weights equipoised, as in the beautiful
experiments of Attwood. Now, all inert matter gravitates ;
and the force of gravitation is proportional to the inertia.
Kqual weights, (which are the estimate of gravity), are equally
resisting to a horizontal impulse (the measure of inertia) or to
a vertical impulse in the balanced condition.
It cannot be maintained that these properties are mutually
implicated. We can easily suppose matter (considered as
inert) without the property of distant mutual attraction, or
gravitation ; this last property may be fairly viewed as added
to, or superinduced upon mere inertia, Nor can we call the
aS? ree
244 INDUCTION OF CO-EXISTENCE,
two either cause and effect, or effects of a common cause ; our
knowledge does not entitle us to make either supposition. We
can prove cause and effect only by exhibiting first a cause,
and then an effect flowing from it. Here the two facts or
properties are inseparable.
There is no other equally unambiguous instance of a law of
universal co-existence. The examples above quoted with
reference to three properties—specific gravity in the gaseous
state, atomic weight, and specific heat—may, for anything we
know, be mutually implicated, or related as cause and effect.
If we understood more thoroughly the ultimate arrangement
of the atoms of bodies, and their intestine motions, we might
not improbably find that some one fundamental property was
at the foundation of all the three ;—a real essence, of which
these are but propria. As regards many of the minor laws,
the existence of either implication or causation is more than a
mere surmise.
Under such circumstances we are entitled to conclude that
uniformities of general co-existence are very rare. The pre-
sumption or probability (although not the certainty) in every
new case of uniformity is that it is a case of causation and not
of co-existence. Thus, the conjunction of Mind and Body may
be a co-existence independent of causation, like inertia and
gravity ; but it may also follow the more prevailing type, and
be a case of cause and effect. Which is cause and which
effect, or whether they are effects of a common cause, a | be
open to dispute.
5. The only proof of Uniformities of Co-existence not
known to depend on causation, is uncontradicted Agree-
ment through all nature.
This is the proof of the Law of Causation itself. Now any
uniformity not coming under causation must stand on its
own independent evidence ; and this evidence is uniform
agreement throughout the whole compass of observation.
We must find it true in all times, all places, and all circum:
stances ; and provided our search has been so extensive, that if
there were any exceptions we should light upon them, and no
exceptions have been found, we are entitled to declare it a law
of all nature.
The coincidence of gravity with inertia has been proved over
the entire globe ; it applies undoubtedly to the solar system ;
and by very strong analogy to the distant stars. This, there-
fore, may be held to be an established uniformity of co-existence.
CONCOMITANT PROPERTIES OF KINDS. 9A5
The alliance of mind with a bodily mechanism extends
throughout the whole of animal life, past and present.
The co-existences above mentioned regarding the properties
of gaseous specific gravity, atomic weight, and specific heat,
have to be verified by the method of Agreement throughout all
bodies. We cannot, as in cause and effect, presume from a
small number to all the rest.
6. The special coincidences making up the Natural
Kinds must also be verified by Agreement over the whole
field of instances.
We have already remarked that an exception to a kind,
arising from the failure of an essential property, would not be
the infringement of a uniformity, but the setting up of a new
kind. The only case for proving a co-existence would be the
case of conconutant properties, or those not adopted into the
essence or connotation of the kind. Of such a character is the
blackness of the crow, the whiteness of the swan, and varia-.
tions of colour generally ; a point seldom treated as essential,
whether in minerals, plants, or animals. Now the sole proof
that ‘every crow is black,’ is observation through all Nature ;
so long as no other colour is seen, we affirm the general pro-
position ; the occurrence of various albinos has disproved the
generality, and reduced it to an approximate generalization, of
a very high order of probability.
CHAPTER IV.
LAW OF CAUSATION.
1. The Uniformities of Succession presented in nature
are subject to one great uniformity—the law of Causation.
The law may be expressed thus :—In every change, there
is a uniformity of connexion between the antecedents and the
consequents.
No single expression sums up all that is implied in Cause
and Effect. When it is said, ‘Every effect has a cause, and
every cause an effect, and that the sequence is regular, the
same causes being always followed by the same effects,’ the
— AY
eo
246 LAW OF CAUSATION.
proposition is an identical statement; the word ‘ Cause’ means
what brings about an effect; and the word ‘ Effect,’ what
follows from a cause. To avoid this objection, we may state
the law as follows :—‘ Every event that happens is definitely
and uniformly connected with some prior event, or events,
which happening, it happens; and which failing, it fails’
The kindling of a fire follows regularly on the prior events of
making a heap of combustibles and applying a light.
A law is more sharply stated by help of its denials. Causa-
tion denies two things. First, it denies pure spontaneity of
commencement. If the law is true, no cuange arises out of
vacuity or stillness ; there must be some prior event, change,
or movement, as a sine gud non of the occurrence of any new
event. A fire never bursts out without some commencing
circumstance, in the shape of movement, change, or activity,
Secondly. The law denies that events follow one another
irregularly, indiscriminately, or capriciously. The same cir-
cumstances that make a fire burst out to-day, will, if repeated,
‘make it burst out to-morrow, or at any future time. The
same pain, in the same circumstances, does not at one time
repel, and at another, attract and allure us. In short, the
law is the statement of wnzformity in the Succession of events.
2. In Causation, the same cause always produces the
same effect; but the converse does not hold; the same
effect is not always produced by the same cause. There
may be Plurality of Causes. .
A severe blow on a man’s head will always cause death:
but death is not always caused by a blow on the head. There
are many causes of motion; and the presence of any one in —
the proper circumstances, will always be followed by motion. —
This is an important limitation of the law, and has to be
kept in view in the investigation of causes. lH a change has
occurred, there must have been a previous change, or ante-
cedent fact, but not necessarily one particular antecedent.
3. The Plurality of Causes is subject to uniformity in
two respects: (1) the number of causes is fixed ; (2) the
character of each is as definite as if it were the sole cause.
The causes of death may be numerous, but they are all
fixed and knowable; and, when known, may be counted on
with certainty and precision. The fact of plurality renders
the causation of an event ambiguous; there may be several
alternative antecalents. Yet, these antecedents being, once
satel +
PRACTICAL ASPECT OF CAUSATION, 247
for all, exhaustively known, we are sure that one of them is
the operative circumstance in the case before us.
It will be pointed out afterwards that plurality of causes is
more an incident of our imperfect knowledge than a fact in
the nature of things. As knowledge extends, we find less of
plurality. The numerous apparent causes of motion are differ-
ent only in superficial appearance ; they are all oue at bottom.
4, Causation may be viewed under three different aspects.
(1) The first may be called the practical and popular aspect
—a partial view suited to the ordinary emergencies of life.
Under this aspect, the cause is some one circumstance or
condition demanding our solicitude, as being precarious.
Thus, when the soldier, on the eve of an engagement, is urged
to keep his powder dry, this is not the whole cause of his
hitting the enemy; itis the circumstance that happens to be
an peril at the time.
(2) The second aspect is the Scientific or complete view of
Causation. Under this view, all the conditions or antecedent
circumstances are fully enumerated.
(3) A third aspect is Causation viewed as embracing the
modern generalization, entitled the Conservation or Correlation
of Force.
CAUSATION PRACTICALLY VIEWED.
5. In common language, the Cause of an event is some
one circumstance selected from the assemblage of condi-
tions, as being practically the turning point at the moment.
A man slips his foot on a ladder, falls, and is killed. The
cause of the fatality is said to be the slipping ; for if this one
circumstance had been prevented, the effect would not have
happened. Yet, in order to the result, many other conditions
were necessary :—the weight of the body (gravity), the height
of the position (a certain collocation), the fragility of the human
frame. Yet, for practical purposes, we leave out of sight at
the moment all the elements that are independent of us and
secure, taking notice only of what is in our power and needs our
attention. By a common ellipsis, all arrangements that are
fixed and settled, are passed over in silence. We presume
on the forces of heat and gravity, and devote our care to the
choice and shaping of the materials whereby these forces may
be made to work out our ends.
~ When we speak of food as the cause of animal strength, we
Fae sO ae ee ae
MiG ets eo ‘
' .
948 LAW OF CAUSATION.
suppose a healthy constitution, able to digest and assimi-
late it. But, in this particular case, mankind long erred in
ignorantly suppressing a condition no less essential than
food, namely, the oxygen of the atmosphere — the aerial
element of our food.*
Language is adapted principally to this mode of viewing
causation. In the distinction of agent and thing acted on,
which pervades the whole of grammar, and gives the character
to the active verb, there is an arbitrary selection of one circum-
stance as cause, other equally indispensable circumstances being
overlooked. A prize ox is reared in a breed of cattle; the
breeder is by courtesy styled the cause or agent; but his activity
is only a single, although indispensable circumstance. A teacher
instructs a pupil, and is credited as the cause or author of the
pupil’s knowledge A still more glaring ellipsis is practised
in attributing the issue of a war to the commander-in-chief ;
as when we speak of the conquests of Alexander or Caesar.
‘The monk that shook the world’ is rhetoric for the agency of
Luther. us
The first attempt at a precise analysis of Causation was made by
Aristotle. He enumerates four kinds of Causes, —the material, the
formal, the efficient, and the final. The material cause is literally
the matter used in any construction; marble or bronze is the
material of a statue. The formal cause is the form, type, or
pattern in the mind of the workman; as, the idea or design con-
ceived by the statuary. The formal cause of a building is the
architect’s plan. The efficient cause is the power acting to produce
the work, the manual energy and skill of the workman, or the
mechanical prime mover, whether human power, wind, water, or
steam. The final cause is the end, or motive on whose account the
work is produced —the subsistence, profit, or pleasure of the
artificer. Pt
Aristotle gives the instance of a physician curing himself, as
combining all the four causes in one subject.
* Whenever the existence or safety of anything depends upon a swum or
system of contrivances adapted to a common end—which, together, are
conditions necessary for its preservation —then the destruction, disturbance,
or removal of one of these contrivances—the failure of any part of this
composite system of safeguards—is considered as the cause of the ruin of
the whole. For example, if the action of any one of the functions or organs
necessary to human life is stopped, life is extinguished, and the circum.
stance producing that effect is said to be the cause of death. So, if a ship
springs a leak and sinks, or if an army is surprised through the absence of
a sentinel from his post— the springing of the leak, and the absence of the
sentinel, is said to be the cause of the loss of the ship and the surprise of
the army. The language by which such an effect is commonly ascribed to
a merely negative cause is elliptical. (G. C. Liuwis).
t
a
7
TEAR Fo
SCIENTIFIC CAUSATION. DAD
This analysis is obviously taken from humar industry, which
contains the several circumstances mentioned. It throws no light
upon causation in the order of nature; while the attempts to
express natural phenomena according to such a scheme, have led
to distortions and unmeaning conceptions,
The first and second causes give the celebrated distinction of
Matter and Form, which pervades the whole of Aristotle’s philo-
sophy. The third, the Efficient, has continued in the language of
science; a better designation for the meaning is Prime Mover, or
Moving Power. The fourth, the Final cause, is more perspicu-
ously expressed by Motive, End, Intention, Purpose, Object or
Design ; it applies to nature only as personified, or as the work of
@ personality.
SCIENTIFIC CAUSATION,
6. In scientific investigations, the Cause must be regarded
as the entire aggregate of conditions or circumstances re-
quisite to the ettect.
All the conditions suppressed by the practical man are
brought back by the scientific man in a full statement of the
cause. If any are omitted, it is because they are so obvious
that no person could overlook them. There is a legitimate
ellipsis of expression, even in the scientific enumeration of con-
ditions.
The cause of the inundations of the Nile would be described
as (1) the fall of moisture as snow on the lofty mountains of
Africa where the Nile has its source; (2) the melting of this
snow by the summer heat. Gravity, the laws of heat, the con-
stitution of water, are all a part of the cause, and if not men-
tioned, are supposed to be fully present to the mind of the
hearer.
The growth of plants is a complicated causation. There
must concur, the properties of the germ, the contact with the
soil, air, water, saline bodies in the soil, heat, light, &e.
The agriculturist thinks only of a select number of these—the
seed, the quality of the soil, moisture, and heat; the vegetable
physiologist brings into view the physical, chemical, and vital
agencies, which are the causes of the phenomenon in the final
analysis.
The cause of vision is summarily given as light entering the
lenses of the eye. The full enumeration of the circumstances
would include the optical action of the lenses, the physiology
of the coats of the eye, and of the nerves and brain; and
finally, the link associating a certain activity of the brain with
a feeling in the mind.
250 LAW OF CAUSATION.
The cause of the Reformation was Luther’s preaching against
the sale of indulgences, concurring with the administration of
the church, and the state of men’s minds at the time.
In speaking of antecedents of the French Revolution, it is
customary to use the plural—Causes; signifying that a union
of many circumstances or conditions was involved. In the
enumeration of Alison, no less than stwfeen causes are given.
Gibbon attributes the rapid growth of Christianity to one
primary cause, namely, the convincing evidence of the doctrine,
and of the ruling providence of its author; and to five aiding
secondary causes, ‘ which assisted in prolucing the effect, viz.:
1, the inflexible zeal of the early Christians; 2, the doctrine
of a future life, as held by the Christian Church; 3, the mira-
culous powers ascribed to the primitive church; 4, the pure
and austere morals of the Christians; 5, the union and
discipline of the Christian republic.’ ;
The conditions of phenomena include negative as well as
positive circumstances; the absence of hindrances to the
operation of the agents concerned. The sun is the cause of
vision, provided he is not screened, provided the subject is not
asleep or blind. It is usual to suppress the mention of all
such hindrances, if they are really absent.
7. The suppressing of essential conditions is a common
fallacy of Causation.
When, in the statement of a cause, there is not merely an
ellipsis of understood circumstances, but an omission of some ~
essential fact, the consequence is positive error.
When the healthy effect of residence at a medicinal spa is
attributed exclusively to the operation of the waters, there is
a fallacy of causation; the whole circumstances and situation
being the cause.
This is a common form of Inductive fallacy, and prevails in
all the complicated sciences, as Politics and Medicine.
CAUSATION AS CONSERVATION OF FORCE OR ENERGY.
8. A great advance, in the mode of viewing Causation,
is made by the modern discovery of the law named ‘ Cor-
relation of Force,’ or ‘ Conservation of Energy.’
The great generalization of recent times, variously designated
the Conservation, Persistence, Correlation, Convertibility,
Equivalence, Indestructibility of Huergy, is the highest expres-
sion of Cause and Effect. In every instance of causation, there
LAW OF CONSERVATION. 951
is a putting forth of force in given circumstances, and the law
in question states exactly what becomes of the force, and is
often the sufficing explanation of the special phenomena, as
well as the embodiment of nature’s uniformity in successions.
Statement of the Law of Conservation.
9. Force, Energy, Moving Power, or Work Power, is
embodied in various forms, all mutually convertible at a
definite (fixed) rate. The extinction of energy in one form
is accompanied by the creation of energy in another form:
in the transmutation work is said to be done, and no force
is absolutely lost.
(1) Matter in motion is Force manifested as actual, apparent,
or kmetic energy; but the modes of motion may be very
various. We are most familiar with that of mechanical
energy, as in the case of a flying-ball, a water stream, or the
wind. There is, however, reason to believe that the forces
named heat, light, and electricity, consist in minute move-
ments of material particles.
Matter in position corresponds to a possible production of
power; or the configuration of a material system corresponds,
in virtue of the mutual action of its parts, to a definite amount
of possible or potential eneryy. A head of water represents a
certain amount of moving power by is very position. This
energy may not be evoked, and may exist for ever only as
potential. Yet it is as really existing as when it is employed
to turn a wheel.
(2) The different forms of energy may, under certain ar-
rangements, be transmuted one into the other. Mechanical
force may pass into heat, and heat into mechanical force: an
energy of motion may be exchanged for an energy of position
and conversly. The rate of exchange is invariable.
(3) In the interchange of energies nothing is lust. In every
case where energy disappears by resistance, and is seemingly
lost, a definite equivalent of heat is generated.
If we suppose a portion of the universe isolated so that it
neither gives nor receives energy from without, then the
principle of the Conservation of Knergy asserts that the sum
of the kinetic and potential energies within this material system
is constant and unalterable. The actions and reactions of its
parts can only vary the relative proportions of kinetic and
potential energies, but not their amount.
Of these three circumstances the first matter im motion or in
position, is the definition or generalisation of force or energy ;
MP
952 CAUSATION AS CONSERVATION OF FORCE,
the second, transmutation of one form of power into another ;
and the third, conservation of the sum of the energies of
motion and position of any self-contained system, under all
changes, are the properties or predicates, constituting the Law
of Correlation or the Conservation of Energy.
10. In explaining the principle of Conservation as
applied to the different forms of actual energy, we may
rank them in two divisions, Moar and MoLecuLaR,—
motion in mass and motion in molecule.
The Molar Forces are the same as those termed
Mechanical.
The molar or mechanical forces are the motions of sensible
masses, as a hammer, a waterfall, a locomotive, a planet. The
science of Mechanics, or Molar Physics, is occupied with the
computation of these forces, in their transfer and re-distribu-
tion under all varieties of circumstances.
The Persistence or Conservation of Force was first distinctly
conceived with reference to these palpable motions. Newton’s
First Law of Motion expresses the fact that a.massonce in ~
motion will, if unobstructed, always continue in motion at the
same rate; which is the same as saying that force never
decays. In free space, beyond the reach of molestation from —
without, a moving body would preserve its motion for ever.
This is the simplest aspect of Conservation.
A moving body encountering a second body, whether at rest
or already in motion—(1) if we suppose both bodies to be per-—
fectly elastic—imparts its own motion, in whole or in part, to
the body struck. This is a new situation. There is a loss of
power on one side, and a gain on the other ; a redistribution
of the movements of the two masses. Now, in this state of
things, the Law of Conservation declares that in the inter-
change nothing is wasted; whatever the striking body loses,
the struck body gains.
If the two masses are equal, there will be simply an in-—
terchange of velocities, and of momenta ; and if they are not
equal, still the impact will not alter either the total no
or the moving energy of the whole.
(2) When the bodies are inelastic, then the visible energy :
will disappear in whole or in part. If a contemporary of
Newton had been asked what becomes of the force of cannon
shot arrested by a dead wall, he would probably have answered
that an infinitesimally small movement was imparted to the
me
CONSERVATION OF MECHANICAL FORCE, 9538
mass of rock and its contiguous material. This would have ~
been regarded as a consistent following out of the theory of
conservation in communicated momentum. The lost energy
of the quick-moving ball would exist as energy in a huge
mass very slowly moving.
Had the farther question been asked—what becomes of the
force of two opposing movements destroying one another—
the above answer would not have served the purpose. No
motion is created in any form; there is nothing to appearance
but sheer waste on both sides.
The new difficulty would in all likelihood have been met by
a very plausible assumptiom. It might have been said that
the conservation of force was to be interpreted as force operat-
ing in the same direction ; all forces in the opposite direction
being held as negative quantities, like debt to credit. It would
be a sufficient account of any force that it had neutralized an
equal and opposing motive force; as when a payment of a
hundred pounds to any one’s credit extinguishes a hundred
pounds of debt.
Yet this explanation is fallacious as a principle, and in
opposition to the facts of the case. Two bodies moving in
opposing directions are not to be compared to positive and
negative; each has a positive value, for any purpose whatso-
ever. Two streams running in opposite directions, are as
good for mill-power as two streams moving in the same
direction. Hasy mechanical contrivances can, without loss,
divert a moving power into any direction, The two opposing
forces that by collision extinguish one another, could by a
suitable arrangement, unite their power in the same course.
The destruction, therefore, that ensues in a hostile collision,
is (on the present assumption) pure destruction, unredeemed
waste, annihilation. It is at variance with the Law of Con-
servation, which would have to be restricted and qualified to
moving bodies always following the same course.
The principle of Conservation has been rescued from this
perplexity by the discoveries of recent times. If two in-
elastic bodies encounter and arrest one another’s movements,
the mechanical or molar energy is indeed sunk ; but re-appears
in an equivalent energy communicated to the molecules, and
manifested as Heat. The molecular motion excited in the
encountering masses is exactly equal to the molar energy
consumed. This is an entirely new view of Force; and
saves the principle of Conservation, by giving it an
enlarged scope. It teaches us to take account of all the
254 CAUSATION AS CONSERVATION OF FORCE,
protean transformations of energy, and prevents us from
rashly declaring that force is destroyed when it has ceased to
appear in the original shape. Mechanical force in some cir-
cumstances, well understood, yields mechanical force ; in other
circumstances, for example, hostile collision, it yields a mole-
cular force, namely, Heat.
Going back upon the first query propounded to a contem-
porary of Newton,—the account to be given of a ball’s
impinging on a dead rock,—we should now answer the ques-
tion not by mechanical transference—a slow motion imparted
to the rock—but by molecular transformation. The ball and
the place where it struck would both be found to rise in tem-
perature, and the more as the moving force of the ball was
greater. All the energy would be accounted for in this way.
Tn every case of collision, and even of impact without opposi-
tion, something is lost by conversion into heat. The loss of
power by friction is a generation of heat.
11. The MotecuLar Forces may be provisionally enu-
merated as follows :—(1) Heat, (2) Chemical Force, (3)
Electricity, (4) Nerve Force, (5) Light.
This enumeration is to be held as provisional; it may not
include all the species ; and it may represent, as distinct kinds,
what are only slight modifications of one kind.
(1) Heat.—Probably the best example for showing the mole-
cular forces, in their contrast to the molar, or mechanical, is
Heat. Our experience of this influence is abundant and
various. Yet, only of late years have we been led to call it a
form of moving matter, a species of molecular motion or
vibration, which bursts forth on the shock tHat extinguishes a
mechanical impetus.
Such shocks of mechanical collision are the usual mode
of transmuting mechanical energy into heat. Friction is
only a more gradual and protracted collision. A familiar
illustration is seen in hammering a piece of cold iron till it
becomes red hot. The high temperature of the sun is hypo-
thetically accounted for by collisions of enormous swift-moving
masses, brought together by gravity.
Such is the situation for converting mechanical motion
into Heat. The transmutation of heat into Mechanical
force, is effected through the expansion of bulk caused by
raising the temperature of bodies. In solids, and in liquids,
this expansion is small in range, but great in force; and is
adapted only to special cases, as the splitting of rocks, where
MOLECULAR FORCES. 255
there is need for a great power moving only a very little way.
Through the medium of gases, the expansion can be converted
into mechanical energy, in any form we please, as in the
diversified performances of steam power.
In generating mechanical power by heat, as in the steam
engine, the source of heat must be of a higher temperature
than the medium; the fire must be hotter than the water and
the steam. The power is given forth by the descent of the
heating body toa lower temperature. Between bodies equally
hot, there is no development of mechanical power, no forcible
expansion of any one body.
There is a peculiar incontinence attaching to the Heat
force. We usually find that some body possesses it in such
superior degree as leads to radiation upon other bodies, with
loss to the radiating body. This is the moment for obtaining
a mechanical or other equivalent. It is also the moment of
dissipation of energy without equivalent, if the opportunity is
not turned to account. The solar heat falling on the planets
gives an equivalent in raising their temperature, and in pro-
_ ducing other forces; what is not intercepted is at once dissi-
pated into empty space, without farther result than to elevate
by a slight addition the general temperature of space; a real
but unavailable equivalent of the heat lost to the sun.
It is as regards Heat that the rate of exchange with
mechanical force has been settled with the highest numerical
precision. The assumed unit of mechanical energy is the
foot-pound of England (and the metre-kilogramme of the
Continent), meaning the force expended in raising one pound
weight one foot. The unit of heat is defined as the
amount that must pass to one pound of water in order to
raise its temperature (or sensible heat motion) by one
degree of the thermometer. The rate of exchange or
equivalence 1s 772 foot-pounds to one pound of water
raised 1° Fahrenheit; or 1390 foot-pounds to 1° Centigrade.
In the Continental scale of weights and measures, the
expression is 425 metre-kilogrammes to one kilogramme of
water raised 1° Centigrade. By a perfect machinery of
conversion of heat into mechanical power, the heat requisite
to boil a gallon (ten pounds) of freezing water would lift
1889600 pounds one foot. i
(2) Chemical Force.—Energy, in a form adapted to separate
chemical compounds, and as it appears when bodies combine
chemically, is chemical force. When water is decomposed into its
Raman oxysen and hydrogen—a certain amount of force is
a4
956 CAUSATION AS CONSERVATION OF FORCE.
absorbed or used up in order to bring about the decomposi-
tion ; and the same force reappears when the elements are
re-combined.
This chemical force is a very slight modification of Heat.
In the case of combination, the force evolved appears as heat
in it8 common form. Indeed, our artificial heat of combus-
tion, is the chemical force liberated in the chemical combina- _
tion of oxygen and carbon (supposing coal or charcoal to be
the fuel). By peculiar arrangements, this force of combination
may be prevented from appearing as sensible heat, and may
take other forms ; it may decompose other compounds (as in
the double decomposition of salts); or it may pass into elec-
tricity or into magnetism.
Again, Heat may operate as a decomposing agent. Many
compounds are decomposed at once by the application of
heat, as the oxides of the noble metals. A familiar example is
the decomposition of chalk or carbonate of lime, in a lime
kiln; the heat drives off the carbonic acid, and what remains
is burnt lime. Other compounds are decomposed by heat,
when there is an arrangement for combining one of the de-
composed elements with a third substance; as when water is
decomposed in a red-hot iron tube, the oxygen combining with
the iron.
That heat, the result of combination, should be the means
of decomposition, is the proper, the natural consequence of
the Law of Conservation. Whatever is given out when ele-
ments combine, must be restored when they separate again. —
This is the exact relationship of heat to chemical action, which
is disguised and apparently reversed by the familiar empley-
ment of heat to make bodies combine, as in lighting a
fire. The application of heat in such a case, however, is a
mere incident; it seems to operate by disturbing the quies-
cence of the elements. It no more renders heat a combining
power, than the pailful of water thrown into a pump before
pumping is the cause of the subsequent flow.
The rate of commutation of Heat and Chemical Force, has
to be given in the detail, inasmuch as different compounds
give forth different quantities. I quote as examples a few
oxygen compounds. One pound of hydrogen burnt (that is,
combined with oxygen) would elevate, by 1° C., about thirty-
four thousand pounds of water. This is the most heating of —
all oxygen combinations ; we have long been familiar with the
intense heat of the oxy-hydrogen blow-pipe. Of simple
bodies burnt, or combined with oxygen, the next in rank, is —
HEAT.— ELECTRICITY. 257
carbon, the chief ingredient of ordinary combustion, and also
of animal combustion. The figure for carbon is less than one
fourth the figure for hydrogen; a pound of carbon burnt
elevates, by 1° C., about eight thousand pounds of water.
Phosphorus ranks next among the simple bodies examined
(5747 pounds); then sulphur (2307); the metals, zine, iron,
and tin, are nearly equal (zinc, 1301, iron, 1576, tin, 1233).
(3) Hlectricity—This variety of molecular force is distin-
guished by two main peculiarities. The first is polarity, or the
development of opposite forces at opposite points ; the magnet
is the most familiar example of the power, operating in masses
of matter. The second is named conduction, and means the
rapid transmission of the force from one part of a body to
another, along a wire, for example ; a process of conveyance
quite different from any of the modes of the transmission of
heat. An electrical charge passes almost instantaneously, and
with little diminution of force, through miles of copper wire.
The name ‘ Electricity’ now includes various phenomena
marked by characters widely different. Three types or species
may be indicated—Magnetism, Friction or Franklinic Elec-
tricity, and Voltaic Electricity: all these have a molar
as well as a purely molecular side; the last is in close
relation to chemical force. Magnetism, as a member of the
group of Correlated Forces, under the Law of Conservation,
is best studied in the form called Electro-magnetism, or mag-
netism generated from electricity ; for, while the magnetism,
which is a mechanical attraction, can be estimated by its
mechanical effects, the electricity can be estimated chemically
by the amount of acid and zinc combined in the cells of the
battery. Friction Hlectricity, in the common electrical machine,
is generated by mechanical force (sometimes by heat, as in
crystals); its discharge, being marked by vehemence, concentra-
tion, or wtensity, is not measurable with accuracy ; the effects
are seen in the rupture of atomic cohesions, in strong outbursts
of heat and light, and other indications of concentrated force.
Voltaic SLilectricity is the species most closely allied with
Chemical Force; which force is its source, its measure, and
one of its results. Through chemical force, as measured by
the amount of material chemically combined in the voltaic
cells, we can state the rate of exchange or commutation of
Voltaic Electricity with Mechanical force, and with Heat,
These three modes of Force—Heat, Chemical force, Elec-
tricity—are the well-defined species of molecular activity;
258 CAUSATION AS CONSERVATION OF FORCE
they can all be measured and put into strict equivalence with
Mechanical Energy. ‘There siill remain, however, Light,
and any modes of activity in living hodies, distinct from, and
superadded to the forces of the inorganic world; the Nerve
Force is one well-marked example. From the close analogies —
between this last-named force and Electricity, we may take it
next in order. R
(4) Merve Force.—The Nerve Force is the special activity o
the nerves and brain. Like Klectricity,itisacurrentforce. It
differs from Electricity in moving at a comparatively slow rate;
and also in depending for its maintenance upon chemical com-
binations in the material of the nerves ; hence, while electricity
decreases as it goes, the nerve force increases. Although this
foree cannot be subjected to accurate measurement, we con-
clude from analogy that there is an exact equivalence between
it and the chemical transformations that are its source; part
of the food of the body is expended in supplying it. It con-
tributes to muscular power, in which case it has a mechanical
equivalent; and to molecular changes, chemical or other, also
on a definite rate. As the physical concomitant of mental
states, we must still regard it as definitely related in quantity
to these; a double amount of feeling, other things being the
same, involves a double amount of nervous transformation.
(5) Light.—The divorcing of Light from Heat, in the enu-—
meration of the molecular forces, needs to be explicitly justified.
The divorce is at best provisional and temporary ; the reasons
ire such as the following. . Although Light is a distinct product
of the other forces, more especially Heat, and is instrumental
in causing at least one of them, Chemical force, yet hitherto
nothing has been done towards establishing the rate of com-
mutation or exchange between it and the others. Whena
body is heated till it becomes luminous, there ought to bea
definite loss of heat, equivalent, on a certain scale, to the
light produced; at present, however, we have made no ap-
proach to such an estimate. Moreover, although light is
the instigator of chemical change, we cannot say that it oper-
ates by supplying chemical power, as heat or as electricity
does; the effect may be similar to the action of heat in lighting
« fire, a mere disturbance sufficing to begin the chemical
union of elements ready to combine. Chlorine and hydrogen,
mixed together, will not combine chemically in the dark; the —
combination begins under the light. It is to be remarked, —
however, that decomposition is the direct test of chemical force.
Now, light will not cause decomposition unlags in the presence
’ POTENTIAL ENERGY, 259
of a body, like hydrogen or chlorine, having a powerful
tendency to combine; or, when, as in vegetation, light is
accompanied by heat. We are, therefore, led to regard light
chiefly as the prompter to a change otherwise maintained. And
in this view there is a numerical proportion between the amount
of light and the extent of the chemical action; as shown in
the researches of Bunsen and Roscoe (Phil. Trans., 1857).
When mechanical force operates against gravity, as when
a projectile is thrown upwards, the force is at last spent ; the
equivalent gained is a position of advantage, with respect to
gravity ; for, by the continued operation of the gravitating
energy, the whole of the impetus lost will be restored in the
downward direction (the resistance of the air being left out
of the account). We are familiar with this employment of
gravity in clocks propelled by weights regularly wound up to
a height. To this peculiar situation, Prof. Rankine has
applied the name ‘potential energy,’ to distinguish it from
the energy of a mass in actual motion. The placing asunder
of the celestial bodies, all which gravitate towards each other,
was the primeval situation of advantage, whence may have
arisen (by collisions) the heat of our suns and planets, and by
consequence all the other modes of force—mechanical, chemi-
cal, and electrical.
It is by this operation that the force of gravity is introduced
into the circle of forces, and is counted as a cause or productive
agent. Viewed in itself, it creates no force; what is gained
in visible force is lost in position; to restore the position
would require the power to be given back. It can, however,
divert power; it can also store up and re-distribute it, as a
banker does money.
A similar position of advantage may be found in the mole-
cular forces. Thus, the existence of two elementary bodies,
able to combine, is a potential chemical energy, which, on the
occurrence of the opportunity and the stimulus, is converted
into actual molecular energy. Such is the potential force of
our coal, and of all the uncombined and combinable elements
of the globe,— as native sulphur, the native metals, and the
lower compounds susceptible of entering into higher com-
pounds.
The molecular attractions of bodies (as cohesion) may oper:
ate exactly in the manner of gravity. A spring is an obvious:
example. The elasticity of compressed air may be turned to
the same account,
ca
260 CAUSATION AS CONSERVATION OF FORCE.
12. Causation, viewed as Conservation, is thus the trans-
ferring or re-embodying of a definite amount of Force.
When a ship is propelled by wind or by steam, the motion
is said to be caused by those agents ; which expend themselves
in producing the effect. The expansiveness of steam is due to
heat operating through the medium of water. The heat arises
from the combustion or chemical union of coal and oxygen.
The coal was the carbon of plants of former ages, whose
growth demanded an expenditure of solar heat.
So, again, in the human body, mechanical force is obtained
by mucsular exertion ; that exertion is owing to the oxidation
of the materials found in the blood; these materials are either
vegetable products, or the bodies of other animals fed on
vegetables ; and, thus we come round again to the agency of
the solar ray in vegetation.
Transferred energy is thus the final and sufficing explanation
of all change, and the only explanation in the highest sense of
the word. Any ‘fact of causation not carried up into this
supreme law, may be correctly stated, but it is not accounted
for. .
Whatever appearances militate against the principle of Con-
servation are to be held as fallacious. The ‘ perpetual motion’
has long been rejected as incompatible with the mere mechani-
cal phase of the principle. There still remain to be removed
various errors against the more comprehensive view. For
example, the incautious remark is frequently made that Light
is the operative cause of vegetative growth, meaning light
alone; but the large amount of chemical power required to
decompose water into its elements (the bodies of all others
most costly in their demands) could be furnished only by the
heating rays of the sun; however much light may co-operate
in giving stimulus or direction.
13. The Law of Conservation exhausts Causation, viewed
as the transfer of Force or Moving Power, but leaves many
complicated, and, as yet, unsolved questions of CoLLoca-
TION.
If we view causation as the transfer or re-distribution of a
certain definite amount of moving power, nothing can be
simpler than the statement of the principle; and, in many
instances, we find it easy to make the exact calculation. But
the circumstances attending the transfer, the situation or
collocation of the materials engaged, may have all degrees of
complexity. - + eaael
Py Ae
COLLOCATIONS, 261
The simplest situation is the transfer of mechanical power
by impact, as when a golf ball is impelled by the momentum of
'the club, At least, we usually suppose this to be a simple
case; we take no account of the internal agitations of the
particles of the body struck, being content to assume that the
momentum is transferred with inconsiderable loss. Here,
then, the collocation is the easiest possible; it is the sensible
contact of one moving body with another, either at rest or
already in motion. Even when one moving body strikes
another moving in a different direction, the difficulty of the
collocation is not much increased ; the mechanical theorems of
oblique forces will predict the new distribution, and assign the
directions after the impact.
When we pass from the interchange of mechanical forces, to
the mutual interchange of mechanical and molecular, we en-
counter situations or collocations of various degrees of com-
plexity. Least difficult is the relation of mechanical energy
to heat. When a moving body encounters a dead resistance,
the whole of the energy is resolved into molecular motion of
the encountering masses; if the body struck gives way in
part, and takes on motion, the actual energy generated is so
much deducted from the energy transformed into heat.
The transfer of heat into mechanical force, as in the steam
engine, is accomplished by the expansiveness of the heated
matter. Starting from the fact of forcible expansion, the con-
version is merely an instance of mechanical impact. The
difficulties are postponed to the next stage.
The interchange of Heat and Chemical Force, the production
of each from the other, at will, is effected by an arrangement
that can be expressed with considerable definiteness in the
gross, although leaving the ultimate links of transition in deep
obscurity. ‘The active combination of two combinable bodies,
as carbon and oxygen, evolves heat ; but the minute circum-
stances of the evolution can be only hypothetically surmised.
The intestine heat motions of carbon and of oxygen, in their
separation, when transferred to the joint carbonic acid mole-
cules, are in excess, and the surplus gives elevation of tem-
perature, or sensible heat, to the mass.
The re-conversion of Heat into Chemical Force (potential),
as in chemical decompositions, is somewhat more complicated,
but an account can be given of the situation in gross. In the
cases where decomposition is effected by heat alone, we have
the simple restoring of the surplus heat of the combination,
In the other cases, where a new combination must be formed,
262 CAUSATION AS CONSERVATION OF FORCE.
we have an additional circumstance, still perfectly Seana
and, in a rough manner, hypothetically conceivable.
The difficulties of Collocation grow thick upon us when we
grapple with the Electrical group of forces. The polarized
state of matter, whether in mass, as the magnet and the
Leyden jar, or in molecule, as in the decomposing cells of the
voltaic battery, is a new and unique phenomenon; and its
generation by mechanical force or by heat may be stated in
the extreme terms, but without intermediate explanation,
even by a plausible hypothesis. After many laborious tenta-
tives, Faraday discovered the arrangement for directly convert-
ing mechanical power into voltaic electricity (commonly called
the magneto-electric machine), but the links of the transition
or intermediate molecular changes are as yet unassignable.
Yet worse perplexities surround the collocations for trans-
ferring force in Living Bodies. Even the simplest case—the
production of Animal Heat from chemical combination or
combustion—is anomalous when compared with the same
phenomenon out of the body. The general fact is oxidation,
but the circumstances and arrangements are peculiar and
unknown. Again, the production of Muscular Force from the
process of oxidation is in accordance with the Law of Conserva-
tion, while the transition links are hitherto inscrutable. Like-
wise, the Nerve Force has the same common origin in chemical
transformations (or closely allied molecular transformations)
as the other forces, and follows a regular rule of exchange,
while the mode of derivation is involved in obscurity.
14. Seeing that, in Causation, there must be provided,
not merely a sufficient force, energy, or moving power, but
also the suitable arrangement for making the transfer as
required ; this completing arrangement, or collocation, is a
part of the Cause, and (by ellipsis) is frequently spoken of
and investigated as the Cause.
A running stream is the proper source of the energy that —
turns a mill. In order to the effect, however, the due colloca-
tion or connexion must be made for bringing the water to
bear upon the machinery. Hence, the stream being taken for
granted, the cause of the grinding of the corn is the providing
of machinery, and the regulation of the sluices ; which circum-
stances are of the character, not of force, but of collocation.
So, ina Voltaic Battery, intended to decompose water, or
to excite an electro-magnet, the prime mover is chemical
force arising in the cells of the battery; the completing
*
. °
_— EE .
>
ree i eB i eee
UNKNOWN COLLOCATIONS. 263
arrangements include the whole apparatus of the battery, and
the final act of closing the circuit.
The combination of the food materials with the oxygen of
the air, may be reckoned the source of all animal power;
but so numerous are the conditions to be secured in the
way of arrangement or due collocation, that we have often
to think far more of these than of the propelling agency de-
rived from the primal source of all moving power. We not
unfrequently assign as the cause of a man’s bodily strength, a
good digestion, healthy lungs, or a good constitution generally,
and say nothing of the real derivation of the strength; the
reason being that, without the complex group of arrangements
implied in these facts, the power would not be transferred from
the common fund and embodied in the man’s muscular and
vervous energies.
When a man properly supplied with food, goes through a
day’s work, we recognize a transfer of moving power, under
the Law of Conservation. When any, one prostrate with
weakness is restored to strength by a few drops of laudanum,
there is no proportion between the cause and the effect, con-
sidered as moving power giving birth to equal, although
different moving power. The salutary interference must be
regarded, not as a communication of moving energy corres-
‘ponding to the access of energy that follows, but as the restor-
ing of some arrangement or collocation, necessary to the
conversion of the body’s nourishment into the various forces
of animal life. |
As our knowledge of the Law of Conservation is such as to
account for the remote source of all power whatsoever, the
enquiry usually presented for scientific investigation is by
what arrangements a given effect has been secured, or through
what media the bank of Nature’s Force has been drawn upon
in the particular instance. Not many years ago the pheno-
menon of volcanoes was regarded as wholly mysterious ; since
the establishment of the Law of Conservation, all that part of
the mystery connected with the source of the upheaving power
has been removed. It is the internal heat of the earth con-
verted at certain points into mechanical energy. What re-
mains for scientificinvestigation is a pure question of collocation;
we are still ignorant of the arrangements for effecting the
transference of power in that particular manner.
In the same way, all the great cosmical changes, marking
the evolution of the solar system, and the geological history of
the earth, are referable to the primal sources of energy; the
264 CAUSATION AS CONSERVATION OF FORCE.
moving power at work is no longer a secret. Yet the circum-
stances, arrangements, or collocations, whereby the ‘power
operated to produce our existing mountain chains, the rise and
fall of continents, the fluctuations of climate, and all the other
phenomena revealed by a geological examination of the earth,
are as yet in uncertainty.
15. The importance of Collocation appears in another
aspect, as representing the modes of Potential Energy.
Potential Energy is energy of situation, arrangement, or
collocation. The Potential Energy, stored up when moving
bodies work against gravity, till their force is exhausted, is
described as a position of advantage, a collocation of power,
with reference to a gravitating mass. Here we have the re-
markable case of force embodied in absolute stillness or quies-
cence. A mountain tarn is absolutely quiescent while its
enclosure is perfect ; the immense impetus to be displayed in
its descent to the plains is not at present represented even by
molecular motion.
A similar energy of collocation is created when bodies are
distended in opposition tv their cohesive attractions, as in
springs.
Lastly, there is the energy of separation of Chemical ele-
ments, as in coal, sulphur, metals, and other combinable sub-.
stances, simple or compound. Gunpowder is a concentration
of potential chemical energies, or of combinable elements in a
situation of readiness to combine.
It is in the case of these potential energies that we seem to
create moving power, to bring forth force, without a prior
equivalent force, to make small causes yield great effects. The
apparent cause, or antecedent, of a great outburst of moving
power, is something altogether trivial, as if force were
evoked and absolutely created. Cause and Effect cannot, in
such instances, be stated as one moving power transmuted into
an equal moving power, molar or molecular.
Human Society, with limitations easily divinable by any
reflecting student. ,
In the situation of enquiring into the Cause of a given
Effect, Experiment is for a moment unavailing. We can try
the effect of a given cause, but we cannot try the cause of a
given effect. Assuming heat as an agent, we can make experi-
meats on its various powers or capabilities; but given the heat
of a fermenting mass, as an effect, we cannot, by experiment,
get out the cause. We must first conjecture a cause; experi-
ments may then be instituted to find out the effects of that
supposed cause; if these tally with the effect in question, —
we have made out our point.
The problem of Causation may thus be presented in both
aspects—given a cause to find the effect, given an effect to
find the cause—but the experimental solution is one; namely,
to watch the effect of an assumed cause. The course of the
phenomenon flows in one way; cause first, effect second.
When we seem to be working backward, we are in reality
working forward.
REVIEW OF THE COMPLICATIONS OF CAUSE AND EFFECT,
_ 4, The Inductive Elimination of Causes and Effects may
be illustrated by a review of the various complications
actually met with.
We have already adduced examples of the complications
that have to be unravelled, in order to assign the neat effects
of a cause, or the causes of an effect. We are able to present
a more comprehensive view of the actually occurring entangle-
ments,
COMPLICATIONS OF CAUSE AND EFFECT. 275
Those natural aggregates, termed Kinds by pre-eminence,
are marked by the concurrence, in a single object, of many
different properties. Oxygen, carbon, phosphorus, iron, mer-
eury, platinum—have each a great number of distinct powers
or activities ; hence, when the introduction of any one of them
is followed by some change in the things they are brought into
contact with, we are at first uncertain which of all the many
properties of the substance is the operative circumstance.
Carbon, for example, is found to absorb gases in large amount;
which suggests the enquiry, which of the properties of carbon
is this owing to:—its specific gravity, porosity, blackness,
amorphous structure, or any other? Again, mercury has
certain medicinal effects; and we desire to know which of its
many properties is the causative circumstance. Platinum, in
a finely divided or spongy state, brought into contact with a
bie of hydrogen, makes it ignite. What does this depend
upon
So then, in the elementary bodies of Chemistry, the simplest
substances known to us, there is a great concourse of anteced-
ents present whenever any one is brought into play. But, in
nature, these are usually found mixed together (I am not
alluding to Chemical combination, which yields new substances)
in great varieties of compounds. Thus, the Atmosphere is a
mixture of two simple bodies—nitrogen and oxygen; various
known chemical compounds—water, carbonic acid, and am-
monia; and a great many other gaseous effluvia, together
with solid particles, partly dust and partly ova of plants and
animals. Moreover, it possesses at each moment a certain
temperature, a certain electrical condition, and perhaps
other peculiarities. Thus, when the atmospheric air is pre-
sented to us as a cause or agency, the possible variety of
antecedents is very great. Many researches have been occu-
pied in eliminating the causal conditions in combustion, in
vegetable and in animal life, in putrefaction, in spontaneous
generation (so-called), &c.
Again, the sea is not pure water, but a solution of numerous
saline bodies.
Most minerals are mixed substances. A geological stratum
is highly compound; and when certain vegetables are found
to grow in a particular soil, elimination must be applied to
ascertain which are the needful constituents.
In Vegetable and in Animal Kinds, the complication is
still greater. The chemical constituents of plants and of ani-
mals have very complex atoms, whose disintegration may yield
276 , WEAPONS OF ELIMINATION.
a variety of different products. Hence, vegetable and animal —
substances used as food, as medicines, as dyes, &c., have many &
possible modes of operating. We must, however, ‘when living
bodies are agents, farther take into account the organic or living
structure; the poison of a living plant or animal has powers
of derangement quite different from the chemical action of ite
chemical constituents.
The complication in the world of Mind is very great. ar
human being is by nature many-sided, and by education still
more so. Hence, when one person exercises an influence upon
another, it is far from obvious, at first sight, by what peculiari- —
ties the effect arises. So again, in the explanation of motives,
a historian is often baffled to select the one that ates
swayed a given effect. »
The operations of Government are ramified in their conse- =
quences. A single enactment—the imposition of a tax on
windows or its removal, free-trade, or its opposite — Operates
variously according to cir cumstances.
te
WEAPONS OF ELIMINATION,
d 4
:aF
5. It is in the comprehensive Law of Causation itself, a
once established by Induction, that we have the instru-
ments for eliminating causes and effects in the detail, __
As already said, there is but one proper Inductive Method
—Universal Agreement; there is, in the first instance, no
shorter cut to an Inductive Generalization. We must go
through the labour of a full examination of instances, until we
feel assured that our search is complete, that if contrary cases —
existed, they must have been met with.
By such thorou oh-going examination, various inductive laws
have been established, including that momentous truth called
the Law of Causation. Now, in whichever of its two properly
scientific aspects, we view this law—whether in the less sug-
gestive but perfectly accurate form of Uniformity of Sequence, -
or in the new and better form of Conservation accompanied
with Collocation, we find in it a means of shortening the labour 4
of ascertaining specific causes and effects. By applying the —
general law, in either form, there is often a possibility of ae a
ing causation by a single instance.
Thus, to take the first form of Causation— Every event
uniformly followed by some other event; and every event is — i
aniformly preceded by one or other of a definite number of” 4
events ’:—given an antecedent, one consequent succeeds; given _
CAUSATION THE BASIS OF ELIMINATION. OT
a consequent, some one of a few definite antecedents has pre-
ceded. Now from this it follows, that whenever an agent is
introduced into a quiescent state of things, and when certain
changes follow at once on that fact, the sequence happening
once will happen always. Nothing springs out of nothing.
Nature in the matter of sequences is uniform; and a single
case, cleared of ambiguities, establishes a law. By the stroke
of an axe, a block is cleft; the same effect will always follow
the same cause. Hence, a single experiment in the laboratory
may establish for ever a casual property.
On the second or more precise form of Causation, there is
a definite transfer of motive power under some given arrange-
ment of things. We know, by this law, without any new
observation, that a blow with a hammer will realize its
equivalent, either in mechanical energy, or in some form
of molecular force. If in a certain situation, it splinters a
stone, it will always do the same thing, in the same situation.
In a different arrangement, it raises the temperature of a
surface ; and what it does once, it does always. All that we
have to settle empirically in this form of the law, is the
transfer attending each collocation, and the collocation attend-
ing each transfer. By induction proper (universal agree-
_ ment) we have already ascertained this to be uniform, and
accordingly pronounce upon a single clear instance.
There is thus only one Inductive Method at the foundation
(Agreement), but there are several Deductive Methods, or
methods depending upon the grand generalization of Cause.
For instance, the method known as the ‘ Method of Differ-
ence,’ is not an inductive but a deductive method; for, with-
out the law of Causation, the method would be incompetent.
Even the ‘ Method of Agreement’ as employed for the pur-
pose of elimination, supposes the Law of Causation, and is to
that extent a deductive method.
6. The Law of Causation involves the three following
affirmations, each of which is the groundwork of a process
of Elimination.
(1) Whatever antecedent can be left out, without preju-
dice to the effect, can be no part of the cause.
A cause is what produces an effect. As the presence of
the cause is the presence of the effect, so the absence of the
cause is the absence of the effect. The absence of the cause,
with the presence of the effect, would be a contradiction of
the law. Weare sure, therefore, that whatever can be omitted
278 WEAPONS OF ELIMINATION.
or withdrawn without making any difference to the effect in
question, is not the cause, or any part of the cause. If we
cut a string that we suppose to be the support of a weight,
and the weight continues to be supported, the string is not
the support.
Upon the Law of Causation, viewed on this side, reposes
Mr. Mill’s Method of elimination by Agreement. A certain
effect remains after the successive withdrawal of all the ante-
cedents except one; which leaves that one in sole and undis-
puted possession, and therefore the cause.
(2) When an antecedent cannot be left out without the
consequent disappearing, such antecedent must be the
cause or a part of the cause.
‘s+
This affirmation, likewise, is implied in the law. It presents
the other side of the same linking of cause and effect; absence
of the cause is absence of the effect. Whatever, by disappear-
ing, makes the effect to disappear, is by that very fact an
essential or causal condition. If the cutting of a string 7s the
falling of a weight; the string is the support of the weight.
This aspect of cause gives the decisive Method of Difference;
the method whereby a single instance may be incontrovertible
proof of a cause.
(3) An antecedent and a consequent rising and falling
together in numerical concomitance are to be held as Cause
and Effect.
This is Causation in the more special aspect of Conserva-
tion, and is directly implicated in that principle. In the
transfer of moving power, the quantity gained is the quantity
lost ; and the tracing of quantitative concomitance is our very
best clue to the force operative in a given effect. As the com-
bustion of a locomotive is increased, so is the steam power.
In those agencies that merely bring about a collocation, —
there is no numerical ratio between the agent and the result.
A slight touch is enough to complete the electric circuit, and
a double vehemence adds nothing to the energy of the cirenit,
The process now described is the Method of Concomitant
Variations.
These are the three chief methods of Eliminating the un-
concerned circumstances present in cause and effect. After
considerable progress has been made in the discovery of
causes, recourse may be had to a farther proceeding, namely,
to allow for the influence of all known causes, and to attribute
ELIMINATION FOUNDED ON CAUSATION. 279
what remains of the effect to what remains of the cause. This
also is a proper inference from the Law of Causation. It is
termed the Method of Residues.
The Method of Agreement may be employed negatively ;
that is, cases may be found where cause and effect are uni-
formly absent together. We may call it Agreement in Absence.
When this circumstance can be conjoined with the positive
_ method—Agreement in presence—an approach is made to the
decisive cogency of the Method of Difference. Mr. Mill has
given to this conjoint mode the designation—Joint-Method.
The following chapter will exemplify the employment of
these Five Methods of Inductive (or Deductive) Elimination
in investigating Cause and Effect.
It is not possible to separate from the thorough working of
these instruments of Elimination the process of generalizing,
or attaining to Inductive generalities. In carrying out the
Method of Agreement, for example, the collation of a large
number of instances where a cause or an effect. is present,
cannot fail to suggest laws of causation of a higher generality
than the enquirer sets out with. Nevertheless, it will not be
expedient to dwell upon this generalizing operation while we
are bent upon the eliminating process. Generalization belongs
to Discovery ; Elimination is Proof; and Proof, more than
‘Discovery, is the end of Logic. Still, we shall have to make
room for a consideration of the best modes of arriving at the
higher generalities.
CHAPTER VI.
THE EXPERIMENTAL METHODS.
1. There are three chief methods of eliminating the —
cause of a phenomenon from the neutral or indifferent
accompaniments—Agreement, Difference, and Concomitant
Variations.
METHOD OF AGREEMENT,
2. The Method of Agreement is expressed thus :—If
two or more instances of a phenomenon under investiga-
13 :
280 THE EXPERIMENTAL METHODS.
tion have only one circumstance in common, that eireum-
stance is the cause (or effect) of the phenomenon.
The instances are studiously varied so as to leave out in
turn all the circumstances attending the phenomenon. What-
ever is left out, in any one instance, without detriment to the
effect, cannot be the cause; the possibilities are gradually
reduced in number; and, if the means of elimination are com-
plete, the enquiry terminates in assigning one circumstance
that has never been wanting where the phenomenon appears. |
The method is illustrated symbolically thus :—Let A repre-
sent a cause and aan effect. In nature we seldom have A
followed by a alone; were such isolation the rule, the Experi-
mental Methods would be unnecessary. What we find is A.in
combination with other things as A B C, and a also in com-
bination, asinabec. But, now, if these conjunctions were
rigid and invariable, we should have no opening for the
methocs. The real fact is, however, that though a cause may
be always in combination with other agents, it is not always
in the same combination ; at one time the union is A B C, at
another time A B D, and again A C E; there being corres- _
ponding conjunctions in the effects—a b ¢,abd,ace, |
If we suppose, then, the instances—
ABC giving a be, ‘f ’
A BD giving a bd, Cee 4
ACE giving ace, pies
we reason thus. So far as the first instance is concerned—
ABC giving abc, the effect a may be produced by A, or
by B, or by ©. In the second instance—A B D giving a 6 d,
the cause C is absent, the effect a still remaining; hence C is
not a cause of a. In the third instance—A C E giving ace,
—B is absent, a remaining; hence B is not a cause of a. The
only antecedent persisting through all the instances is A;
when a is present as a consequent, A is always present as an
antecedent. If, then, we are sure that every other antecedent
circumstance has been removed in turn, the consequent a still
surviving, we have conclusive evidence that A is a cause,
condition, or invariable accompaniment of a.
It matters not which is the form of the enquiry,—given an
effect to find a cause, or given a cause to find an effect. The
first is supposed to be the more frequent occurrence. Science, .
from of old, was
rerum cognoscere causas.
If the problem be given in the first form, the proof is ali
given in the second; we try a cause to see what effect
—
eee
y
METHOD OF AGREEMENT, 281
will follow, which proves at once that the consequent is the
effect of the antecedent, and that the antecedent is the cause
of the consequent ; the two affirmations being identical.
Although our professed object now is to unfold the Induc-
tive elimination of Cause and Effect, having already disposed
of the case of Co-existence as Co-inhering Attributes, yet, in
expounding the Methods, we must receive instances indis-
criminately, as we do not at first know how they will turn ont.
There are many connexions of Cause and Effect that appear
as Co-existences, and there are instances that we must leave
undecided, being unable to assign the ultimate nature of the
union. The more obvious tests of Causation are these :—
(1) sequence in time, as when innoculation is followed by the
small-pox pustule; (2) expenditure of energy, as when a
cannon ball shatters a fort. Where these tests are wanting, as
in co-inhering powers of the same substance—for example,
gravity and inertia—we are left to presume co-existence,
there being, as alternative possibilities, mutual implication, and
the co-existing effects of a common cause.
This explanation is more especially called for in commenc-
ing the Method of Agreement—the universal or fundamental
mode of proof for all connexions whatever. Under this
method in particular, we must be ready to admit all kinds of
conjunctions; reducing them under Causation, when we are
able, and indicating pure Co-existence when the presumption
inclines to that mode.
As a simple example, we may take the case of the conver-
sion of solid bodies into liquids, and the farther conversion of
liquids into gases. The bodies so converted are of every
possible variety of properties ; the one circumstance common
to all the instances of such conversion is the application of
heat. ‘The elimination is complete as regards this antecedent,
which is therefore correctly assigned as the essential condition
or cause. We may apply in this example, the most decided
test of Causation, the expenditure of energy or force; we should
never regard the fact as a mere Co-existence.
The next example is of a different character.
The peculiar phenomenon known as the interference of
polarized light—consisting in the exhibition of rings of alter-
nating or ‘periodical’ colours, when a polarized beam of
light passes through certain transparent substances—may
be propounded for investigation. We may ask—is there any
other property or phenomenon always present in the bodies
that show this peculiar effect? Now, the bodies must, as a
men Pes oe
4.44
\ ne
, 7
Y82 THE EXPERIMENTAL METHODS.
matter of course, be transparent; but all transparent bodies
do not exhibit the polarized bands; hence, transparency is
eliminated. By farther comparison of instances, we find that
there is no constant mode of colour, of weight, of hardness,
of form (crystalline), of composition (physical or chemical) ; ;
so that no one of all these properties is concerned in ‘the
phenomenon. There is, however, one property common to
all the substances that furnish these coloured bands, they are —
all doubly refracting substances, that is, present two images of
things seen through them obliquely. By Agreement through
all known substances, there is proof of the concurrence of
these two properties,
It is not ascertained, however, and cannot be ascertained by
Agreement alone, whether the two facts are cause and effect,
or whether they are a case of co-existence without causation.
Agreement is the method of proof for all conjunctions what-
soever—whether Causation or Co-existence. The enquiry
belongs to a particular class—the conjoined Properties of
Kinds, where there may be laws of co-existence without cau-
sation. The decisive criteria of causation are wanting in the
case. KL mit
To take a third example. In flowers, there is a remark-
able concurrence between the scarlet colour and the absence
of fragrance. The following quotation gives a selection of
instances.
‘Among all the colours that blooms assume, none are less
associated with fragrance than scarlet. We cannot at present
recollect a bright scarlet blossom that is sweet-scented—yet
no other colour among flowers is more admired and sought ~
after. Scarlet prevails among Balsamina, Euphorbia, Pelar- —
gonium, Poppy, Salvia, Bouvardia, and Verbena, yet none of —
the scarlets are of sweet. perfumes. Some of the light-coloured i
Balsams and Verbenas are sweet-scented, but none of the —
scarlets are. The common Sage, with blue blooms, is odorifer-
ous both in flower and foliage; but the scarlet Salvias are —
devoid of smell. None of the sweet-scented-leaved Pelar-
goniums have scarlet blooms, and none of the scarlet. bloomers
have sweet scent of leaves nor of blooms. Some of the white-
margined Poppies have pleasant odours; but the British
scarlets are not sweet-scented. The British white-blooming —
Hawthorn is of the most delightful fragrance; the scarlet-
flowering has no smell. Some of the Honeysuckles _ are
sweetly perfumed, but the Scarlet Trumpet is scentless’ (ELDER,
American Gardener's Monthly). india cael
EXAMPLES OF AGREEMENT. 283
Fourth Example. The North-Hast wind is known to be
specially injurious to a great many persons. Let the enquiry
be—what circumstance or quality is this owing to? By a
mental analysis, we can distinguish various qualities in winds;
—the degree of violence, the temperature, the humidity or
dryness, the electricity, and the ozone. We then refer to
the actual instances to see if some one mode of any of these
qualities uniformly accompanies this particular wind. Now
we find, that as regards violence, easterly winds are generally
feeble and steady, but on particular occasions, they are stormy ;
hence, we cannot attribute their noxiousness to the intensity
of the current. Again, while often cold, they are sometimes
comparatively warm; and although they are more disagree-
able when cold, yet they do not lose their character by being
raised in temperature ; so that the bad feature is not coldness.
Neither is there one uniform degree of moisture; they are some-
times wet and sometimes dry. Again, as to electricity, there
is no constant electric charge connected with them, either
positive or negative, feeble or intense; the electric tension of
the atmosphere generally rises as the temperature falls.
Farther, as respects ozone, they have undoubtedly less of this
element than the South-West winds; yet an easterly wind at
the sea shore has more ozone than a westerly wind in the heart
of atown. It would thus appear that the depressing effect
cannot be assigned to any one of these five circumstances.
When, however, we investigate closely the conditions of the
north easterly current, we find that it blows from the pole
towards the equator, and is for several thousand miles close
upon the surface of the ground ; whereas the south-west wind
- coming from the equator descends upon us from a height.
Now, in the course of this long contact with the ground, a
great number of impure elements—gaseous effluvia, fine dust,
microscopic germs—may be caught up and may remain sus-
pended in the lower stratum breathed by us. On this point
alone, so far as we can at present discover, the agreement is
constant and uniform.
_ What is the conclusion? As Agreement by itself does not
decide that conjoined circumstances are cause and effect, we
must find some mode of excluding Co-existence, and rendering
the case one of succession. When the two circumstances are
plainly in succession, as when a fracture follows a blow, uni-
form agreement (with elimination) proves causation ; when
they are not demonstrably successive; the agreement fails in
this respect.
-284 THE EXPERIMENTAL METHODS,
Now, there is a general belief that the two events supposed
—the east wind and the uncomfortable sensations—are not
contemporaneous, but in succession; the wind first, the feel-
ings afterwards. This belief is supported by the circumstance
that a change of feelings, must have, according to the law of
causation, an antecedent condition; and if all antecedents,
besides the one above named, are eliminated, that one is the
cause, or an essential part of the cause. ‘
The phenomenon to be explained is not a permanent fact
or potentiality, like polarization or double refraction, it is a
temporary manifestation, and requires some causal circum-
stance to bring it forth. In this respect, it resembles the
actual display of one of these optical properties; it cannot
happen without a suitable agent and collocation, which is pro-
perly a cause of the appearance.
If then, the elimination be supposed complete, there is a
proof by Agreement that the deleterious influence of the east
wind is due to the circumstance named ; aud the case exempli-
fies the eliminating efficacy of the method. |
In the foregoing example, we cannot withhold from our
mind a certain presumption in favour of the result, grounded
on our knowledge of the deleterious tendency of atmosphere
impurities caught up from the surface of the ground. This
is a circumstance not properly belonging to the proof by —
Agreement; it is a confirmation from deductive sources. The
addition of such a presumption always operates strongly on
our belief; the total absence of it leaves a considerable shade
of uncertainty in all the methods, but most of all in Agree-
ment. ‘The third example shows this deficiency ; we are not
at present aware of any connexion of a causal kind between —
the scarlet colour of flowers and the absence of fragrant
odour; the proof of the law rests upon the Agreement alone.
That method of proof is final, only when the elimination has been
exhausted, by variation of circumstances, and when the coin-
cidence has been shown through all nature, so as to establish
a law of Universal Co-existence.
Fifth Example. Let the phenomenon given be Crystallization,
and let the thing sought be the antecedent circumstances,
positive and negative, of the formation of crystals. This is a
case of succession, and therefore of Causation. ‘
We must begin by collecting instances of the effect. In the
following series, the circumstances are purposely varied with —
@ view to elimination :— oad
1. Freezing of water. : ately
EXAMPLES OF AGREEMENT, 285
. Cooling and solidifying of molten metals and minerals.
Deposition cf salts from solutions.
. Volatilizing of solutions.
Deposition of solids from the gaseous state, as iodine.
Pressure.
. Slow internal change, as in rocks.
. The transformation of metals from the tough to the
brittle condition, by hammering, vibration, and re-
peated heatings and coolings.
Looking at the first and second instances—ice, and the
solidifying of molten metal—we discover two antecedent cir-
cumstances, namely, lowering of temperature, aud change
from the liquid to the solid state.
The third instance—deposition of salts from solution—
agrees in the same two circumstances, there is a lowering of
temperature, and also a change from liquid to solid.
The fourth instance—the volatilizing of solutions, as in
boiling down sea-water—appears to failin the matter of cool-
ing, but still contains the circumstance of prior liquidity ; the
prominent fact is that the solvent is driven off, and the dis-
solved substance thereby compelled to resume the solid state.
The fifth instance—the deposition of solids at once from
the gaseous state, as in the case of iodine—seems to eliminate
prior liquidity. We must then shift the ground, and, for
liquidity, substitute one of the two higher states of matter.
The sixth instance-is ‘ heavy and long continued pressure
upon an amorphous substance ;’ principally shown in geology.
This would eliminate the prior liquid or gaseous condition, and
bring to view the forced approximation of the constituent
particles of bodies. But the same circumstance accompanies
all the previous cases, being merely a different expression of
what is common to them. We know heat as forcibly enlarg-
ing the bulk of bodies—making their particles mutually re-
pellent ; the withdrawal of this force leaves the attractions of
the particles free to operate.
The seventh instance—slow geological transformation—
unless viewed by the light of the circumstance just named, is
difficult to interpret. It is not, however, incompatible with
the predominance of the molecular attractive forces by the
abatement of the repellent forces.
The eighth instance—change of metals from the toagh to
the brittle state—is a true case of crystallization ; brittle.
ness is accompanied with an imperfect crystalline arrangement.
The effect is produced by cooling after hammering ; by re-
CO NI Or 09 BD
286 THE EXPERIMENTAL METHODS,
peated heating and cooling; by long-continned vibration or
concussion :—all which influences tend to expel the structural
heat of the substance; the consequence being that the mole-
cular attraction is more preponderant.
We have thus eliminated Cooling, Deposition from Solution,
and Prior Liquidity ; and have found but one uniform antece-
dent—the increased scope and operation of the molecular or
solid-forming cohesion; to which point, however, these other
circumstances really tend ; they are all of them remoter ante-
cedents of the one constant antecedent. The examination of
the instances has enabled us to generalize the phenomenon, as
well as to establish the generality upon evidence, namely, the
evidence of Agreement.
As we have stated this enquiry, it is a clear case of Cause
and Hffect. We have sought the antecedent circumstances
whereby a body in an amorphous or unerystallized state be-
comes crystallized ; and we find that there is an expenditure
and re-distribution of power or energy. The result of the ex-
penditure is not an active manifestation, as when we produced
mechanical force, or heat; it is an arrangement, or structural
collocation ; a case already contemplated (p. 265) among the
results of expended force.
Sixth Example. Let us next apply the method to eliminate
the cause, or the antecedent conditions essential to the pro-
duction and maintenance, of Light.
Now, the most constant circumstance is a high temperature ;
solid bodies become luminous at a temperature of from 980°
to 1000° Fahrenheit. So far, there is a remarkable unanimity.
It is found, however, that gases do not always become lumin-
ous at this temperature, nor at a much higher; a current of —
gas may be raised to upwards of 2000° F. without being
luminous; whence we conclude that the state of the body is
also a condition. Again, the electric spark is a luminous
effect, which would give the disturbance of the electric
discharge as an antecedent. As there is a possibility, however,
ihat the great violence of the discharge may be accompanied
with sudden rise of temperature, this may be merely another
form of heat. We should need to show, by varying the
instances, that high temperature is not essential to the spark. _
In the next place, certain substances give light at common
temperatures, to which fact has been given the name phosphor-
escence. Some minerals, gently heated, emit a feeble light,
which soon ceases, and cannot be renewed until the body hag
been exposed to the sun or the electric spark. This.isstilla —
COGENCY OF AGREEMENT. 287
form of heat, but not of the intense degree of ordinary light.
More peculiar still is animal phosphorescence, as the glow-
worm, fire-fly, and certain sea animalcules. Here the accom-
paniment is a special mode of vitality hitherto uneliminated,
and excluding the circumstance of high temperature (Mr.
Herbert. Spencer suggests that it is an incident attending
oxidation). Once more, a faint flash of light occurs with
certain substances in the act of erystallizing.
_ We may thus collect from Agreement, that ignited solids at
the temperature of 1000° are luminous, and that an electric
discharge is luminous; but we cannot at present lay down
any wider generalization. Excepting the very general fact of
molecular disturbance of some kind or other, which we are
unable to qualify in the precise mode concerned in the effect,
our comparison of instances does not point to a constant
circumsta:ice. For the present, we regard Light as having
a plurality of causes.
As farther instances of Agreement, we may quote the proof
of the coincidence of Sleep with low nervous action, which
means a feeble cerebral circulation; also, the connexion of
Memory with the intensity of Present Consciousness. The
uniformity of these conjunctions under all varieties of other
conditions is the evidence afforded by Agreement. The Rela-
tivity of Knowledge is established partly by Agreement, partly
by the method of Concomitant Variations, as will be shown.
‘The cogency of Agreement is manifestly in proportion to
the thoroughness of the elimination. Whatever circumstance
has never been eliminated is a possible cause. There are not
a few instances, as in the action of drugs, where nature does
not provide the variety requisite for a thorough elimination.
The complicacy of the Natural Kinds passes our means of
extrication by Agreement alone.
METHOD OF DIFFERENCE,
3. Elimination by Difference is expressed in the follow-
ing canon :—If an instance where a phenomenon occurs,
and an instance where it does not occur, have every cir-
cumstance in commen except one, that one occurring only,
in the first ; the circumstance present in the first and
absent in the second, is the cause, or a part of the cause,
of the given phenomenon.
We are supposed to have two instances and only two. Hach
is a complex sequence, a group of antecedents followed by a
288 THE EXPERIMENTAL METHODS.
group of consequents. The two complex sequences differ by
only a single sequence, present in the one, and absent in the
other. Thus the sequence A BC D gives a bed, and BC D
gives bcd: the only difference being the presence of A in the
antecedent, and of a in the consequent, of one sequence, aud
the absence of these in the other sequence. Supposing A B C-D
changed into B C D, by the loss of A; while at the mom-
ent abcd is changed into b ¢ d by the loss of a; we have
a proof of the connexion of A witha. Indeed, the assertions
are identical; to say that the disappearance of one thing is
followed by the disappearance of another thing, there being no
other change, is merely a way of expressing causal connexion.
Difference plays a great part in our everyday inferences.
The usual form is the sudden introduction of some limited and —
definite agency or change, followed by an equally definite con-
sequence. When the drinking of water is followed at once by
the cessation of thirst, we do not hesitate to pronounce the one
fact the cause of the other. The human system is a great
complication, but the only difference made upon it in two
successive minutes is the sequence of drinking and the satisfy-
ing of thirst; there has been, we presume, no time for any
other change to manifest itself. So when we waken a sleeper
by a noise, or strike a light by the friction of a match, we
infer causation; the new agency being instantaneously fol- ~~
lowed by the new effect.
The first example given, under Agreement, is also proved by
Difference. That Heat is the cause of the melting of ice, of
wax, or of lead, is proved by making, upon these substances,
the one change of raising the temperature. Being quite sure
that in the conversion of ice into water, no change has been
made except this, we have a conclusive experiment of Differ-
ence to show that heat is the cause.
The same substance in two states, as solid and liquid, or as
amorphous and crystallized, enables us to ascertain what effects
are due to change of state. Thus charcoal, uncrystallized, is
black, opaque, and a conductor of electricity ; as crystallized,
in the Diamond, it is transparent and a non-conductor.
A large part of our knowledge of nature and of living beings
is gained by making experimental changes and watching the
consequences. Our proof is the immediate result. An im-
mediate response is satisfactory evidence in almost any de-
partment. Thus, in medicine, there is little doubt as to the
operative force of purgatives, emetics, sudorifics, diuretics,
narcotics, stimulants, irritants; the uncertainty attaches to
METHOD OF DIFFERENCE, 28%
alteratives, tonics, and the protracted treatment of chronic
cases. The effect of quinine, in ague, is established beyond
dispute.
_ Whether it be to add, or to withdraw, a definite agent, a
change instantly following is proved to be an effect. Hvenin
politics, we may have a proof from difference; as in the
accession or resignation of a minister, like Chatham. No
other circumstances arising in the ordinary course of a year
would make that total change in the course of politics that
followed on Chatham’s becoming minister. It could not be
denied that he was the cause (in the practical sense of cause)
of our successes in America, and on the continent of Europe.
The consequences of his retirement were equally decided as
proving, on the method of Difference, the vast superiority of
his powers as an administrator.
Wherever Difference can be resorted to, the knowledge of
causes is gained at once. In ordinary cases, the method is so
obvious in its application, so satisfactory and conclusive, as
scarcely to need a master to explain or enforce it. The special
discipline of Logic, so far as this method is concerned, lies in
showing the precautions requisite in the more complicated
cases.
In Physiology, the functions of the nerves were ascertained
by the experiment of, dividing each in turn, and watching the
effect. Whatever function is immediately arrested on the
division of a nerve, is shown to be due to that nerve, or to
require that nerve in order to its performance. Such experi-
ments, however, do not exhibit the entire circle of conditions
involved in the function in question. We know that the
integrity of the spinal cord is necessary to sensation and to
movement in the trunk and in the extremities of the body;
we do not exhaustively know what else is necessary. For this
more extensive knowledge we should have to multiply experi-
ments all through the brain. If the destruction of any part
interferes with these functions, that part enters into the
causal conditions; if otherwise, it does not enter into those
conditions.
The extension of this class of experiments to the brain
exemplifies one situation where the method of Difference may
be indecisive. Deep incisions in the brain, intended to affect
one single organ, as the cerebellum, may injure adjoining
organs; and may therefore be inconclusive as to the functions
of the special organ in view. It is on this ground that
Brown-Séquard objects to the views of Flourens regarding the
290 THE EXPERIMENTAL METHODS.
function of the cerebellum. The one certain inference in such
cases is, that whatever function survives, in its integrity, the
destruction of an organ, cannot be exclusively due to that
organ. The obverse inference is certain only on the supposi-
tion that the injary has been confined to the part affected:
With reference to the connexion of scarlet bloom with
absence of odour, we have a seerming case of Difference in
comparing such varieties as the white-flowering and the red-
flowering hawthorn: the one fragrant, the other not. In the
complicacy of Kinds, we can seldom be sure that a variation
is rigidly confined to the circumstances that are apparent,
Moreover, where there is not a clear case of Causation, Differ-
ence is insufficient to prove a coincidence.
Sir G. C. Lewis lays it down as essential to the validity of
a proof by Difference, that we should know, by a previous
induction, the general adequacy of the assigned cause to the
production of the effect. When we infer that a man, shot
through the heart, drops down dead, we need to know, he
thinks, that, as a general rule, a gunshot wound in the heart,
is a cause of death. ‘To this remark the reply is, that practi-
cally we do make use of such previous knowledge, but itis
not essential to the method of Difference. Provided we are
quite sure that the new agent is the only change that has
preceded the effect, the instance is conclusive, on the Law of
Causation solely. The use of a more specific induction. is to
supply the defect of certainty in the instance itself. There
may be other unseen agencies at work, as well as the one
supposed, and this is the only ground either for invoking a
general presumption, or for multiplying instances of the
phenomenon. In practice, we seek both for presumptions
(from prior inductions) and for repetition of instances; but
an ideally perfect instance of Difference, in a case of Causation,
is conclusive in itself.
Agreement and Difference can be easily compared as to their
respective advantages and disadvantages. Agreement needs
_a large number of instances, but their character is not re-
stricted. Any instance that omits a single antecedent contri-
butes to the result ; the repetition of the same instance is of use
only as giving means of selection. Difference requires only
one instance ; but that one is peculiar, and rarely to be found.
A great extension is given to the power of Agreement, by,
extending it to agreement im absence. When such cases are
JOINT METHOD. 291
conjoined with those where the agreement is in presence, there
is an approach to the conclusiveness of the method of Differ-
ence. ‘I’his double employment of the method of Agreement
is brought forward by Mr. Mill under the designations—the
* Joint Method of Agreement and Difference,’ and the ‘ Indirect
Method of Difference.’ It might also be called the ‘Method
of Double Agreement.’
JOINT METHOD.
4. The canon of this Method is:—If two or more in-
stances where the phenomenon occurs have only one cir-
cumstance in common, while two or more instances where
it does not ocenr have nothing in common save the absence
of that one circumstance; the circumstance wherein alone
the two-sets of: instances differ, is the effect, or the cause,
ora necessary part of the cause of the phenomenon.
If we require to ascertain, under this method, that A is
the cause of a, or a the effect of A, we add, to the instances of
uniform presence of A and a, other instances of uniform
absence, as B F G followed by b fg, C H I followed by c h i,
and so on. If we have never discovered A wanting as an
antecedent without having a absent as a consequent, there is
a strong additional presumption that A anda are united as
cause and effect—a presumption that may approach to the
certainty of the method of Difference.
_ It is a confirmation of the cause, suggested by Agreement,
of the noxiousness of the North-East wind, that the South-
West wind, the genial and wholesome current, is wanting in
the circumstance assigned. It descends upon us from the
eleyated regions of the atmosphere, where impurities are
highly diluted by dissemination.
Again, to revert to the example of Crystallization. Let us
review the non-crystallized solids, and note the mode of
their formation. The amorphous stones and rocks, as sand-
stone, chalk, &c., are known to be sedimentary deposits from
water. Before being solidified, they existed as solid particles ;
they were not dissolved in water, neither did they exist in a
molten condition. This Agreement in absence would confirm
the inference from Agreement in presence—that (so far as
certain instances went) crystals existed in a previous higher
condition. But the general inference, from the full compari-
son of examples, was the superior play given to the molecular
attraction by counterworking the molecular repulsion. Now,
992 THE EXPERIMENTAL METHODS,
this general fact is absent from all mere sedimentary deposits;
these bodies have no aid, in the shape of loss of heat or other
cause, to their molecular attractions. !
The comparison of the amorphous rocks yields another
circumstance, namely, the wregular mixture of different sub-
stances. For, although in a mud sediment silica or alumina
may prevail, neither is ever pure ; and the mixture of different
elements is a bar to crystallization, unless they are of the
kind called isomeric (from crystallizing alike). There is more
to be got over in crystallizing compounds of unlike elements,
and the crystals must be deficient in regularity.
Another uncrystallized class comprizes the vegetable and —
animal tissues. In their case, however, the antecedent circum-
stances are too complicated and obscure to furnish insight;
they rather stand in want of illustration by the parallel lights
of more obvious eases. Besides, there is in them a method
and order of aggregation more analogous to the crystallized,
than to the amorphous solids.
_ A third class includes the Colloids, or glue- bodies, of
Graham (represented by gum, starch, gelatin, albumen, tannin,
caramel). They are not confined to the viscid form of glue,
but include compact solids, as flint. The points of contrast
between these and crystallized bodies are numerous and ~
important. Their mode of formation is various; many of
them are the products of living bodies, and therefore share in
the complication of living growth. Flint is an aggregate of
particles of silica, which particles were originally the shells of
animals, and therefore also organic in their formation. In
this case, the molecular attraction of silica, in its progress
towards crystallization, is thwarted by the pre-existing forms
of the silicious particles.
It would require too long a discussion to show the bearing
of the colloid peculiarities on the question as to the antece-
dents of the crystalline formation, Enough has been given to
show the working of the method of Obverse Agreement. —
METHOD OF CONCOMITANT VARIATIONS,
5. Canon of the Method : — Whatever phenomenon
varies in any manner whenever another phenomenon
varies in some particular manner, is either a cause or an —
effect of that phenomenon, or is connected with it through —
some bond of concomitance.
The effects of Heat are known only through proportionate
CONCOMITANT VARIATIONS. 293
variation. We cannot deprive a body of all its heat; the
nature of the agency forbids us. But, by making changes in
the amount, we ascertain concomitant changes in the accom-
panyiug circumstances, and so can establish cause and effect.
it is thus that we arrive at the law of the expansion of bodies
by heat. In the same way, we prove the equivalence of Heat
and Mechanical Force asa branch of the great law of Con-
servation or Persistence of Force.
The proof of the First Law of Motion, as given by Newton,
assumed the form of Concomitant Variations. On the earth,
there is no instance of motion persisting indefinitely. In
proportion, however, as the known obstructions to motion—
friction and resistance of the air—are abated, the motion of a
body is prolonged. A wheel spinning in an exhausted receiver
upon a smooth axle runsa very long time. In Borda’s experi-
ment with the pendulum, the swing was prolonged to more
than thirty hours, by diminishing friction and exhausting the
air. Now, comparing the whole series of cases, from speedy
exhaustion of movement to prolonged continuance, we find
that there is a strict concomitance between the degree of
obstruction and the arrest; we hence infer that if obstruction
were entirely absent, motion would be-perpetual.
The celebrated experiment of carrying the barometer to the
top of Puy de Déme was a proof by variation of the connexion
between the pressure of the air and the rise of the mercury.
By Concomitant Variations, we derive one of the proofs of
the connexion between the brain and the mind. In the same
manner, we learn to associate health with the healthy agencies,
and diseases with noxious agencies.
The doctrine that change of impression is an essential con-
dition of consciousness, from which proceeds the theory of
Relativity as applied to feeling and to knowledge, is most
strikingly attested by Concomitant Variations. The intensity
of a mental impression notably varies according to the greatness
of the transition from one state to another: witness the in-
fluence of novelty, of all great changes of circumstances, of
suddenness and surprise.
The Statistics of Crime, reveal causes by the method of
Variations. When we find crimes diminishing according as
labour is abundant, according as habits of sobriety have in-
creased, according to the multiplication of the means of
detection, or according to the system of punishments, we may
presume a causal connexion, in circumstances not admitting
of the method of Difference.
994: : THE EXPERIMENTAL METHODS.
The Concomitance may be inverse. Thus we find that the
tendency to chemical action between two substances increases
as their cohesion is diminished, being much greater between
liquids than between solids. So, the greater the elevation of
the land; the less the temperature, and the more scanty the
vegetation.
Parallel. Variation is sometimes interrupted by critical
points, as in the expansion of bodies by heat, which suffers a
reverse near the poimt of freezing. Again, the energy of a solu-
tion does not always follow the strength ; very dilute solutions
occasionally exercise a specific power, not possessed in any
degree by stronger. So, in the animal body, food and stimu-
lants operate proportionally up to a certain point, at’ which
their farther operation is checked by the peculiarities in the
structure of the living organs.
The properties of highly rarefied gases do not exhibit an
exact continuity of the phenomena that vary with density. In
a perfect vacuum, there is no electrical discharge; but the
variations of the discharge, in highly rarefied air, do not pro-
ceed in exact accordance with the degree of rarefaction.
We cannot always reason from a few steps in a series to the
whole series, partly because of the occurrence of critical points,
and partly from the development at the extremes of new and
unsuspected powers. Sir John Herschel remarks, that until
very recently ‘the formule empirically deduced for the elas-
ticity of steam, those for the resistance of fluids, and on other
similar subjects, have almost invariably failed to support the
theoretical structures that have been erected upon them.’
The method of Concomitant Variations 1s powerful in
suggesting, as well as efficacious in proving, causal connexions.
The mind is apt to be aroused to the bond between two
circumstances by encountering several conjunctions of the
two in unequal degrees. Very often, we are not alive toa
connexion of cause and effect till an unusual manifestation of
the one is accompanied with an unusual manifestation of the
other. We may be using some hurtful article of food for a
length of time unknowingly ; the discovery is made by an
accidental increase of quantity occurring with an ageravation
of some painful sensation. This is one form of the efficacy of
an Extreme Case; an efficacy felt both in science and in
rhetoric. ?
A remarkable case of Concomitant Variations is fornighed by
the discovery of a connexion between the solar spots and the
positions of the planets. Thus, as regards Venus, ‘spots are
CONTINUOUS COMPARISON, 295
nearest to the solar equator when the heliographical latitude
of Venus is 0°,’ and obversely.
An important device for discovering, and also for proving,
laws of causation, consists in arranging things possessing a
common property in a serial order, according to the degree of
the property. Thus, we may arrange bodies according to
their Transparency or Opacity, according to Specific Gravity,
to Conduction of Heat and Electricity, and so on. We are
then in a position to detect any corresponding increase. in
some accompanying property, and thereby to establish a law of
concomitance or causation. This method is designated, by
Mr. Mill, Classification by Series, and by Sir G. C. Lewis,
the Method of Continuous Comparison. The progress of Life
in the animal scale; the progress of mental development in
human beings; the progress of civilized institutions, as
Government, Judicature, the Representative System,—may be
expressed in a series, so as to trace concomitant variations.
It is greatly to be desired that, in Physical Science, all the
substances in Nature should be set forth in distinct tabula-
tions, according to the degree of every important property.
It was when transparent bodies were arranged in the order of
their refracting power, that the connexion was discovered
between high refracting power and combustibility.
METHOD OF RESIDUES.
6. The canon of Residues is :— Subduct from any
phenomenon such part as previous induction has shown
to be the effect of certain antecedents, and the residue of
the phenomenon is the effect of the remaining antecedents.
After a certain progress is made in the inductive determina-
tion of Causes, new problems are greatly simplified by sub-
ducting from a complex sequence, the influence of known
causes. Sometimes this of itself may amount to a complete
elimination Such procedure is styled the Method of Residues.
It is an instrument of Discovery as well as of Proof.
The method is symbolically illustrated thus :—Suppose the
antecedents A B C followed by the consequents abc; and
that by previous inductions, we have ascertained, that B gives
b, and C givese. Then by subtraction, we find. A to be the
cause of a. The operation is substantially the method of Dif-
ference, and has all the decisiveness belonging to that method.
Sir John Herschel was the first to show the importance of
studying residual phenomena. His examples are very. strik-
296 THE EXPERIMENTAL METHODS. ;
ing (Introduction to Natural Philosophy, p. 156). Thus,
the retardation of the comet of Encke has been the means of
suggesting, and may ultimately suffice to prove, the existence
of a resisting medium diffused throughout space. Again, the
observation of Arago—that a magnetic needle, seta vibrating,
is sooner brought to rest when suspended over a plate of copper
—was the first clue to the discovery of Magneto-Hlectricity.
The anomalies in the motion of Uranus led Adams and Le
Verrier to the discovery of Neptune. 4
The study of the electrical odour was the first step to the
discovery of the remarkable substance—Ozone.
Sir G. C. Lewis remarks that ‘ the unforeseen effects of
changes in legislation, or of improvements in the useful arts,
may often be discerned by the Method of Residues. In
comparing statistical accounts, for example, or other registers
of facts, for a series of years, we perceive at a certain period
an altered state of circumstances, which is unexplained by the __
ordinary course of events, but which must have some cause. __
For this residuary phenomenon, we seek an explanation untilit
is furnished by the incidental operation of some collateral
cause. For example, on comparing the accounts of live cattle _ ;
and sheep annually sold in Smithfield market for some years
past, it appears that there is a large increase in cattle, while i
the sheep are nearly stationary. The consumption of meat in
London may be presumed to have increased, at least in pro-
portion to the increase of its population; and there is no
reason for supposing that the consumption of beef has increased
faster than that of mutton. There is, therefore, a residuary
phenomenon, viz., the stationary numbers of the sheep sold
in Smithfield—for which we have to find a cause. This cause
is the increased transport of dead meat to the metropolis,
owing to steam navigation and railways, and the greater
convenience of sending mutton than beef in a slaughtered
state.’ .
The question as to the existence of a special force of Vitality—
the vital force, or the vital principle—takes the form of an
enquiry into aresiduum. We have first to make allowance
for the operation of all the known forces of inorganic matter ;
and when these have been exhaustively computed, the re-
mainder may be set down to a special influence, or vital
principle. For anything we know at present, the inoryanic
forces, operating in the special collocations of organized bodies,
may be competent to produce all the observed effects.
The only proof of an exhaustive Analysis, whether in
PROOF OF AN ANALYSIS BY RESIDUES, 297
material actions or in mental processes, is there being nothing
left. Thus, in the Human Mind, it is disputed whether there
be a separate and unique faculty, called the Moral Faculty, or
the Moral Sense. Now, there can be no doubt as to the
presence of common elements of Feeling, Will, and Thought, in
our moral judgments and actions ; as, in the case of the vital
principle, the question is, what remains, when these are all
allowed for. ‘The same application of the Method of Residues
occurs in the controversy as to Instincts, and Innate Ideas;
does Experience, concurring with the usually admitted Intel-
lectual Powers, account for the whole of the facts ?
CHAPTER VII.
EXAMPLES OF THE METHODS.
The Experimental Methods have been regarded mainly as
instruments of Elimination and Proof, or of separating irrele-
vant accompaniments from causal accompaniments. In their
working, however, they unavoidably lead to inductive generali-
zations, in which aspect they are methods of Discovery. The
same search for instances, the same comparison of them when
found, both conduct us to new principles or laws, and prove
them when once attained. Still, it was not desirable to keep
up the double illustration throughout. In the miscellaneous
examples that are to follow, occasional allusion will be made
to the procedure suited to the discovery of generalities.
The proofs adduced to show that the mode of action, in
Smelling, is Oxidation, may be quoted in illustration of the
Methods. The phenomenon is one of great interest, and of
some perplexity. The following important facts were indicated
by Graham.
The sweet odours are due to hydro-carbons, as the ethers,
alcohol, and the aromatic perfumes. Now, all these substances
are highly oxidizable at common temperatures, being speedily
decomposed in the air. Again, sulphuretted hydrogen, the
most familiar of malodorous substances, is readily oxidized,
and is destroyed in that manner. ‘These are instances of
Agreement (in presence).
298 EXAMPLES OF THE EXPERIMENTAL METHODS.
A farther instance of Agreement is shown in the decomposi-
‘tion of hydrogen compounds, in the act of causing smell.
When a small quantity of seleniuretted hydrogen is inhaled
by the nose, the metallic selenium is found reduced upon the
lining membrane of the cavities. The sensation is an intensely
bad smell. |
_ A remarkable case of Agreement in Absence is furnished by
the marsh gas—carburetted hydrogen. This gas has no smell.
As the proof of the concurring absence of its oxidation at com-
mon temperatures, Graham obtained it from the deep mines
where it existed, for geological ages, in contact with oxygen.
Again, hydrogen itself, if obtained in purity, has no smell ; and
it does not combine with oxygen at the usual temperature of
the air.
An instance approaching to Difference is the following. If
oxygen is excluded from the cavities of the nose, there is no
smell. Also, a current of carbonic acid arrests the odour; an
influence which may (although not with absolute certainty)
be supposed hostile to oxidation.
To make the evidence complete, it is requisite that all the
instances of the effect should be of the same unvarying tenor, or
that there should be no exceptions. Until every apparent dis-
crepancy is reconciled, the facts are inconclusive. A seeming
exception is the pungency of ozone, which is looked upon as a
more active form of oxygen. Now wecan hardly suppose that
ozone combines with oxygen; a more likely supposition is
that, by its superior activity, it combines with the nasal mucus.
The research into the cause of Dew has been used by Sir
John Herschel, and again by Mr. Mill, as a happy example of
experimental elimination involving nearly the whole of the
methods. All the stages of this inductive determination are
highly instructive. !
The first point is to settle precisely the phenomenon'to be
explained. This is an exercise of Definition, and can never be
too rigidly attended to. There is some danger, in the present
case, of confounding the effect with certain other effects; and
hence the expediency of defining by an exhaustive contrast.
Well, Dew is moisture; but that moisture is not rain, and not
fog or mist; it is moisture spontaneously appearing on the
surface of bodies when there is no visible wetness in the air. —
In a perfectly clear and cloudless night, there may be a copious
moisture on the surface of the ground, and this moisture is the
thing to be accounted for. FON
RESEARCH ON DEW. 299
~ Now, the problem being given as an effect, with the cause
unknown, we cannot make experiments, until a cause is sug-
gested. This is a pure effort of Discovery, preparatory to the
application of the methods of inductive proof. On the various
occasions when dew appears, we must look out for the atten-
dant circumstances, with a view to their successive elimination.
We know, for example, that dew appears chiefly at night,
which would suggest some of the circumstances connected
with night-fall, as darkness, cold, and any of the concomitants
of these. That darkness is not the cause could be shown if
either dew appears before sunset, or if it ever fails to appear
at night. As the last alternative is very frequent, we must,
so far as the Experimental Methods are concerned, pronounce
ee darkness. There would then remain the agency of
old.
Farther, in this preliminary stage of looking out for a pos-
sible cause, we need not confine ourselves to the actual pheno-
menon. In the conduct of the research, as recorded, much
‘Stress was laid upon the reference to analogous effects, or to
other cases where moisture spontaneously appears on surfaces,
in the absence of visible wet. All such analogies are valuable
for suggestion or discovery, in the first instance, and for proof
afterwards. They are these :—(1) the moisture that gathers
on cold stone cr metal when breathed upon ; (2) the moisture
on the outside of a tumbler of spring water fresh from the
well in hot weather; (3) the moisture that often appears on
glasses when brought into a hot room full of people; (4)
what appears on the inside of windows when a room is
crowded, and during changes in the outside temperature ; (5)
what runs down our walls, especially outer passages, when a
warm moist thaw succeeds to frost. All these cases correspond
to the definition; and their comparison is likely to indicate
some circumstance to be subjected to experimental elimination.
To take the first instance—the breath upon a cold metallic sur-
face; the warmth of the air and the coldness of the surface
are obvious accompaniments. Some of the others would sug-
gest the same conjunction, while all are compatible with it.
Now, this is the situation already suggested by the original
phenomenon, the dew at night-fall. Consequently, we are in
@ position to proceed experimentally ; we can try the cooling
down of surfaces under variation of circumstances.
An easy experiment will tell us whether the cooling of the
surface be a uniform fact, in the production of dew. Lay a
thermometer on the dewed grass, hanging another in the air;
300 EXAMPLES OF THE EXPERIMENTAL METHODS.
and repeat this on many successive nights. The actual result
is that whenever a surface is dewed, it is colder than the air
around it. This is a proof from Agreement; but proofs from
Agreement, unless they can be multiplied through all nature,
in all climes, seasons, and situations, will not of themselves
decide either causation, or universal coincidence.
By varying the circumstances, we can bring to bear the
other methods. We may, for example, try Agreement in
Absence ; that is, make the same appeal to experiment in
nights where there is no dew anywhere. The phenomenon,
however, would be found to evade this test; there would be
cases of actual cooling of surfaces below the temperature of
the air, and yet without dew. Hence the necessity of a dif-
ferent course of proceeding.
Observation reveals to us the fact that on the same night,
and in the same spot, some surfaces are dewed, and others
not. ‘This holds out the prospect of an appeal to the Method
of Difference. On the surface of a plate of glass, there may be
dew, while on a polished metallic surface, there is none. Unfor- -
tunately, however, such a couple is not suited to the canon of
Difference. The points of diversity between glass and metal
are too numerous to comply with the stringent requisite of that
canon. We must, therefore, shift our ground once more.
It being apparent that the nature of the material enters
into the effect, let us expose a great variety of different
materials—metals, glass, stone, wood, cloth, &c. We now
find that there is a scale of degree ; between the extremes of
no dew and copious dew, there is a gradation of amount. The
enquiry then arises, is there any other property of these
different materials varying in concomitance with their being
dewed? Does their temperature (which is the clue that we
are going upon) change in exact accordance with the amount
of dew? There was here scope for a direct appeal to the
thermometer. We have not, however, to record the issue of
such an appeal; the history of the research pursues another
and more circuitous route for arriving at the conclusion. It
so happened, that the experiments, begun by Sir John Leslie,
upon the conduction and the radiation of heat, came in to the
aid of the present enquiry; and the use made of these is
sufficiently illustrative of the canons of Elimination. It
appeared, on the comparison of the various materials, that the
rate of becoming dewed varies inversely with the conducting
power of the substance; the good conductors—the metals—
are not dewed, the bad conductors are dewed according to
til
Re
RESEARCH ON DEW. 301
their badness as conductors. This is the method of Concomi-
tant Variations ; what it points to will be seeg presently.
It is next desired to ascertain how far difference of surface
operates, material being the same. The comparison shows
that rough surfaces are more dewed than smooth, and black
more than white. Instead of the direct test of the thermo-
meter, the appeal here also is to Leslie’s experiments on the
radiation of heat from surfaces; those surfaces that are most
dewed—rough and black—are the best radiators of heat. The
interpretation of this will be taken with the foregoing.
In the meantime, make another variation, namely, for tewture;
comparethe compact textures of metal, stone, wood, velvet, eider-
down, cotton, &c.; the compact bodies are little dewed, in the
comparison, the loose bodies, much. Now, as regards heat, the
loose bodies are very bad conductors ; they resist the passage
of heat through them, and are therefore chosen as clothing.
Let us now seek the interpretation of these three last re-
sults of Concomitant Variations. The first and third relate to
bad conduction of heat as a concomitant, the second to good
surface-radiation. Now, both circumstances point to one re-
sult, that is, swrface cooling, in a cold atmosphere. A surface
is cooled down by a cool contact, but if heat is rapidly sup-
plied from within (which is good conduction) the lost heat is
‘made good, and the fall of temperature is delayed, until the
interior has cooled also. In bad conductors, the loss is not
made good in the same way, and the surface temperature falls.
Thus, bad conductors sooner become superficially cold, in a
cold atmosphere. Next as to Radiation. The explanation
here is still more easy. Good radiation is, by implication, sur-
face cooling ; bad radiation, as from a polished metal surface,
is retention of surface heat. We thus come round to the con-
- clusion, which a series of trials by the thermometer would
have given at once, namely, that surfaces become dewed exactly
as they fall in temperature. To all appearance, therefore, we
have established a link of connexion between cooling and dew.
The appearance is not the reality. There is still outstand-
ing the fact that the same fall of surface temperature will not
always bring out dew. Neither the same absolute surface
temperature, nor the same difference between the surface
temperature and the air temperature, is constantly followed
by a deposit of moisture. We have here obviously a residual
circumstance, whose investigation should next follow. The
instances where the same thermometric difference is unattended
with dew need to be studied by exactly the same routine as
= ge ee Sass a a
Pen
.
302 EXAMPLES OF THE EXPERIMENTAL METHODS.
has now been followed. We must look out for the suggestion
of a possible agency ; and next subject that to experimental
trial, with a view to proof or disproof. This residuum would
have given rise to a very arduous research if it had been left to
experimental determination. The difficulty was conquered in
another way. Already (1799) had Dalton published his theory
of Aqueous Vapour, or the Atmosphere of Steam, which was the
missing link in the explanation of Dew. His positions were—
that the aqueous vapour contained in the atmosphere is vari-
able in amount, according to cireumstances, and that the
amount is limited by temperature. To each degree of temper-
ature corresponds a certain amount, which is the saturation of
the air at that temperature. An amount equal to one inch of
mercury is sustained at 80°, half an inch, at 59°. Supposing
the air saturated at any one moment, a fall of temperature
will lead to precipitation as visible moisture ; but as the air is
not always saturated, a fall of temperature will not bring
dew or mist, unless the fall extends below the degree corres-
ponding to saturation, called the temperature of the Dew-
point. This is the residual circumstance, the thing wanted to
complete the proof of the connexion of dew with surface cold-
ness.
The present instance is a case of Cause and Effect ; as may
be shown in various ways. In the way that the case has been
stated, there is not apparent any transfer of energy, which is
the best criterion of causation ; but underneath the appearance,
we find there is such a transfer. Heat is necessary to convert
water into steam, and this conversion is an instance of the
transmutation of power according to a definite rate of exchange.
The withdrawal of the heat is followed by the re-collapse of
the invisible vapour into water or visible moisture. So that
the production of dew is clearly a sequence under the great
law of transferred energy. Other proofs of causation are dis-
pensed with by this decisive consideration. Mr. Mill, however,
remarks, as a distinct criterion of cause and effect, as well as a
means of settling which is cause, and which is effect, that cool-
ing is a consequence of known and independent antecedents, —
and therefore cannot be set down as consequent on the occur-
rence of dew.
The next example is of value as showing the Experimental
Methods in their purity, or in the absence of all deductive
applications of laws, such as completed the enquiry into the
cause of Dew.
=
MUSCULAR IRRITABILITY AND PUTREFACTION, 303
On the 16th of May, 1861, Dr. Brown-Séquard delivered the
Croonian Lecture before the Royal Society, and took for his
subject the ‘ Relations between Muscular Irritability, Cada-
veric Rigidity, and Putrefaction.’ In this he adduced facts
to maintain the following position :—
‘The greater the degree of muscular irritability at the time of
death, the later the cadaveric rigidity sets in and the longer it
lasts, and the later also putrefuction appears and the slower tt
progresses.”
By muscular irritability is meant muscular power or apti-
tude for contracting. A man fresh in the morning for his
day’s work would be said to have a good store of muscular
irritability: at the end of the day’s work, the stock is com-
paratively exhausted. It would of course be still more ex-
hausted after protracted fatigues continued through many
days.
The cadaveric rigidity is a stiffening of the muscles that
occurs in all animals some time after death. The time when
the stiffening begins, and the duration of it, are variable, and
Dr. Brown Séquard tries to establish the law or cause or con-
dition of this variation. This he does by a series of observa-
tions, whose force will be appreciated by noting how far they
comply with the exigencies of the experimental methods.
First set of Experiments.—Paralyzed muscles. Here he has
two connexions to establish, in order to the end in view.
He first shows that the paralysis of a muscle leaves it for a
time with more irritability than the unparalyzed or exerted
muscles. He paralyzed the muscles of one leg in a dog, by
section of the nerve. Five hours afterwards the dog is
killed (by asphyxia). In the paralyzed muscles the irritability
lasted ten hours; that is, it was possible to induce contrac-
tions in them (by stimulants) up to that time. In the healthy
leg, the irritability lasted only four hours; in other words
was very much less. Now compare the results as regards
Rigidity and the delay of Putrefaction—
Duration of irrit. Duration of rigidity. a —
Paralyzed M. 10 hours 18 days 17th day.
Healthy ,, A Bren, 7th ,,
Here then is an experiment clearly of the nature of Differ-
ence; for two legs of the same animal were compared, and
the only difference was the paralysis of one of them. It is
true, as in all cases of vivisection, that an experiment of Dif-
ference must always be received with caution, seeing that
14
304 EXAMPLES OF THE EXPERIMENTAL METHODS.
other changes may be made by the means taken to produce
the difference. Yet, at all events, here is a strong presumption.
The doctrine is confirmed farther by another aspect of the
paralysis. If an animal is allowed to live a month after
paralysis of a member, the paralyzed muscles are then inferior
in irritability, and when compared under those circumstances,
they become rigid and putrefy sooner. |
Second set of Experiments.—LHffects of diminution of tem-
perature upon muscles.—Dr. Brown-Séquard had determined,
by previous experiments, that cold increases the vital proper-
ties of the nerves and muscles—a fact on which the stimulating
power of cold upon the animal system depends. He now
applies this fact to the enquiry in hand.
Two kittens of the same litter were placed in different tem-
peratures. After death, the following differences were discern-
ible. The one, kept at « temperature of 98°.6, assumed the
rigidity in 33 hours; this lasted three days, putrefaction
commencing in the fourth. In the other, which had been kept
so cool, that a thermometer inserted in the rectum stood at
77°, the rigidity was delayed till the 10th hour, and lasted
nine days, putrefaction commencing on the tenth. This experi-
ment was repeated with many animals, and is also an experi-
ment according to the Method of Difference. This is the
general principle of the fact known in hot climates, that the
dead putrefy almost immediately after death, and must be
interred without a moment’s delay. The relaxation of the
vital powers in hot climates is only a part of the same fact.
The full explanation of this point, or the resolution of the law
into still higher jaws is not yet fully made out.
Influence of death by lightning and galvanism.—It was —
thought by John Hunter that animals killed by lightning did
not stiffen. This has been found not the case. Still there are
instances where the rigidity has either not set in, or been of
so short duration, that its existence has not been traced.
Lightning may kill in various ways :—1st, By fright; 2nd, By
hemorrhage; 3rd, By concussion of the brain. In all these
three modes, ‘there ought to be a manifestation of the rigidity.
But there is a fourth mode, which is to convulse all the
muscles so violently as utterly to exhaust their irratibility ; in
which case the rigidity may fail to be noticed. This is the .
way that galvinism acts upon animals.
Experiments were accordingly tried by galvanizing the
limbs of Rabbits; comparing the galvanized with the un- —
galvanized limbs, with respect to the ‘time of rigidity.
[i
MUSCULAR IRRITABILITY AND PUTREFACTION. 305
Galvanized Limb. Not Galvanized,
Duration of Irritability, 7 to 20 minutes. 120 to 400 min.
a of Rigidity, 2 to 8 hours. 1 to 8 days.
Putrefaction advanced, within a day. After several days.
The experiments were repeated on dogs with the very same
results.
Also, guinea-pigs were subjected wholly to galvanism, but
in different degrees. In those powerfully galvanized, the
irritability lasted a short time, and the rigidity was correspond-
ing rapid and brief. With a less degree of galvanism, the time of
both phenomena was protracted. We have, therefore, an
additional corroboration of the law, still by the powerful
Method of Difference.
Influence of prolonged muscular exercise. — This, of course,
is a cause of diminished irritability. Now, there are well-
ascertained facts that connect prolonged exertion with rapid
putrefaction. Over-driven cattle and animals hunted to death
putrify speedily. So in cocks killed after a fight. Soldiers
killed in a very prolonged fight show the same phenomenon.
The rigidity is quickly over, and the putrefaction rapid.
These are instances of the Method of Agreement.
Influence of nutrition on muscles.—Dr. Brown-Séquard
here collects confirming instances, from the comparison of
cases where death happens in a well nourished condition of the
muscles, with cases where death had been preceded by inanition.
Thus, when men strong and fresh have been killed suddenly,
the rigidity and putrefaction have appeared very late. A case
is recorded of muscular irritability continuing twenty-six hours
in a decapitated man. Here is Agreement in presence.
Compare those instances with others of persons dying of slow
exhaustion, and the appearance is reversed. A man dying of
prolonged typhoid fever, for example, was found to show no
trace of rigidity, and putrefaction commenced in less than an
hour. This is Agreement in Absence.
Influence of Convulsions on rigidity and putrefaction.—It
appears that muscles much attacked with cramps before death
speedily give way to putrefaction.
Certain poisons (as strychnine) sometimes produce con-
vulsions before death, and in those cases the rigidity and
putrefaction progress rapidly.
Such is an ample body of evidence from observation and
experiment to establish the position laid down. The Methods
of Avreement, of Difference, the Joint Method, and the Method
of Variations, have been all brought into play. And if there
306 FRUSTRATION OF THE EXPRIMENTAL METHODS.
are any doubts about the decisiveness of the experiments on
the Method of Difference, from the possibility of making other
changes besides the one intended, these doubts are dispelled
by the coincidence of results from so many distinct experi-
ments. The research is purely Inductive. No consideration
of a Deductive kind has been introduced; although there
are general considerations that give great probability to the
conclusion. Muscular irritability is the living condition
of the muscle—its vitality—which may be greater or less;
and the greater it is, the longer the muscle will retain its
living characters, or the longer it will be in passing to the
characters of death, which are rigidity and putrefaction.
These, therefore, are delayed by fulness of vitality ; while loss
of vitality hands the system over all the sooner to the
destroyer.
When we form conclusions, on an insufficient employment
of the methods of elimination, we commit Fallacies of Induc-
tion. Of these, numerous examples might be given, and the ©
proper place for them is in the course of the exposition of the
Methods themselves. As it is still the custom, however, to
retain, in works of Logic, a separate chapter or book on
Fallacies, we shall reserve for that part of the subject, the
instances of Inductive fallacy.
CHAPTER VIII.
FRUSTRATION OF THE METHODS,
1. In the Inductive Methods as hitherto contemplated,
two conditions have been supposed; first, that an effect —
has only one cause, or set of antecedents; secondly, that
different effects are kept apart and distinguishable. Both
conditions may be wanting.
In the method of Agreement, for example, it is assumed, that
the effect a has only the cause A; should A and C both be
causes, the method would be defeated. The absence of A
would not prove that it is not a cause; for the effect might
still be due to C. The special difficulties attending this case
must now be considered. "
Aa Ue eet
re
PLURALITY OF CAUSES NOT FINAL. 307
Again, the effects a bc are supposed to stand out distin-
guishable. They may, however, be fused or united in one
simple effect 2ac, or 3a. This is the Intermixture of Effects ;
and is still more baffling to the inductive methods, as hitherto
given.
PLURALITY OF CAUSES.
2. In many instances, the same effect is produced by a
PLURALITY OF CAUSES : as Motion, Heat, Pleasure, Death.
Bodies are put in motion by all the different agencies termed
Prime Movers—animal strength, wind, water, steam, combus-
tion (asin gunpowder), &c. Finding a body in motion,
therefore, we cannot ascribe it to any special agent, merely
from the fact that it is in motion: we see a wheel turning and
doing work, but we may not be able to attribute its motion to
one agent rather than another. In like manner, there are
various sources of Heat; the solar ray and combustion are
the most familiar ; but friction and electricity are also-sources.
Hence the fact of the evolution of heat does not point out the
cause ; as an example, uncertainty still attaches to the immedi-
ate antecedent of animal heat.
There are numerous causes of pleasure and of pain: nume-
rous modes of stimulating the nervous system; numerous
agencies of good health and of bad health; numerous ways of
getting a livelihood ; numerous causes of death,
It is to be noted, however, that the plurality in some of
these instances is on the surface only. As regards Motion, the
law of the Persistence of Force assigns a common origin to all
the so-called prime movers; these, therefore, are prowimate, and
not the ultimate sources. The same law covers the produc-
tion of Heat, however various the apparent antecedents. The
causes of Pleasure can be generalized into a small number of
agencies, if not into one. Possibly all stimulants may, in the
last analysis, be found to have a common effect on the sub-
stance of the nerves. The ways to Wealth may be apparently
many, but we can cover them all by one general expression,—-
earning and saving. In Health and Sickness, there might
possibly be generalized expressions of the many proximate
causes. So with Death.
Nevertheless, for practical purposes, we have to ascertain
not simply the primal cause, but the special embodiment of
that cause, on a certain occasion. It is not enough, when a
man is found dead, to assign the. stoppage of the heart, or of
308 FRUSTRATION OF THE EXPERIMENTAL METHODS.
the lungs, or the extinction of the vital forces; we desire to
know in what form and circumstances these generalized causes
were specialized ; whether by cold, by inanition, by poison, by
mechanical violence, or otherwise.
3. The chief consequence of Plurality of Causes is to
frustrate the Method of Agreement.
The Method of Difference remains intact. Whatever be the
plurality of causes of motion, if we observe the imtroduction of
some one agent followed by the effect, we know the cause in
that instance. There may be many ways of keeping up the
animal heat, but the transition from the temperature of 60° to
30°, by causing an immediate sense of chilliness shows that the
external temperature is essential to comfortable warmth on
that particular occasion. |
The operation of Plurality is to give uncertainty to the
Method of Agreement. For example, we observe numerous
cases of unhealthy human beings whose parents were un-
healthy; this would be to a certain extent a proof from
Agreement. On the other hand, many unhealthy persons are
the children of perfectly healthy parents ; whence, concluding
by the strict rule of Agreement, we should affirm that
uuhealthiness in the parents is in no case a cause of unhealthi-
ness in the children; that the two facts are not in any way
connected as cause and effect. The conclusion is obviously
wrong; it would be correct were there only one cause of ill
health ; it is illegitimate if there be many causes.
Plurality is illustrated by our English spelling. The
method of Agreement is nullified in this instance. In certain
words, the letters ough agree with a peeuliar sound, as in
‘rough.’ The same word occurs with other letters, as in ‘ruff,’
and the same letters occur with a different sound, as in ‘hough.’
Whence, by the Method of Agreement, we should infer that
there was never any connexion between either sound and
‘ough.’ A similar illustration is afforded by ambiguous
words. The word ‘air’ is spoken in company with a musical
melody ; at other times it is spoken where there is no music;
any one unprepared for plurality, and following out Agreement,
would conclude that the connexion with music was purely
casual; that there was no fixed bond of union between the
two. We acquire the meanings of the vocables of our language
chiefly by the method of Agreement. We gradually eliminate
all accompaniments that may be absent consistently with the
employment of each word. We find, after a number of
FAILURE OF THE METHOD OF AGREEMENT 309
repetitions of the word ‘fire’ in various connexions, that the
one fact common to all is blazing combustion with heat. We
learn in course of time to extend the word to metaphorical
significations. These being conjunctions of pure co-existence,
without causation, they cannot be dealt with by any other
method, while the occurrence of plurality, even when under-
stood and allowed for, is a serious and painful distraction to
the inductive process.
Again, pressure on the brain is a cause of insensibility ;
yet, as we find insensibility where there has been no pressure,
we should say, according to Agreement, that pressure is not
a cause. In the same way, every one of the causes might be
_ proved not to be a cause—deficiency of blood, excess of dark
unhealthy blood, rupture of the nervous continuity, &.
Extraordinary facts have come to light showing the possi-
bility of exerting the mental powers, under disease of very
large portions of the brain. These facts would seem to
prove that such parts have no share in the mental functions.
The safer inference is that there is a plurality of nervous seats
or tracks for the same functions. It has long been supposed
that the two hemispheres have common functions.
The discussion of the problem of Beauty is often rendered
fruitless by the neglect of Plurality. The attempt is made to
assign some one circumstance present in all beautiful things—
as Colour, Harmony, Fitness, Unity, Suggestion of Mental
qualities. Now, by the unqualified method of Agreement,
every assignable circumstance could be disproved ; with refer-
ence to each one in turn, would it be possible to find objects
of unquestioned beauty where that one is not present. Jeffrey
_ thinks it a sufficient refutation of the theories he opposes,
to produce beautiful objects where the alleged source of beauty
is absent.
_ 4. The counteractives to the failure of Agreement, in
the case of Plurality, are (1) great multiplication of in-
stances, and (2) Agreement in absence, that is, the Joint
Method.
(1) One remedy for the failure of the Method of Agreement,
under Plurality, is multiplication of instances. This will
operate in various ways. It will tend to bring out all the
causes; which is one desirable issue of Plurality. An ex-
tended statistics of Crime or Pauperism will show us the pos-
sible agencies, by giving a wide scope for elimination. The
long experionce of medical practitioners has taught them
310 FRUSTRATION OF EXPERIMENTAL METHODS,
nearly all the possible causes of the greater number of
diseases. At this stage of exhausted plurality, the only point
for enquiry, in the special instance, is—Which of the causes
are present, and are these free to operate P Knowing, all the
contributing causes of Pauperism, we ask which of these occur
in England, in Ireland, or in Scotland, and are they free or
uncounteracted P Being aware of the various antecedents of
dyspepsia—bad food, too much food, too little food, hard labour,
waut of exercise, intemperance, mental wear and tear, bad air,
a hot climate, &c.—we can judge what brought on the disease
in a given instance.
If we do not know which causes are present on @ given
occasion, and whether those actually present are counteracted,
mere Agreement is wholly fallacious. The fallacy named post
hoc, ergo propter hoc, is an abuse of Agreement, where elimina-
tion is vitiated by Plurality, as in a great number of political
inferences. It is remarked that Protestantism is accompanied
with superior industry ; the instances attainable are insuffi-
cient in number to eliminate other causes.
(2) The other remedy is the Joint Method. We should seek
out cases of Agreement in absence, which are of a very decisive
nature. If in all cases where a particular effect fails, one par-
ticular cause is absent, there is, in spite of possible plurality,
a strong presumption that the two circumstances are cause
and effect in those instances. The reason grows out of that
close approach to the Method of Difference furnished by
Agreement in absence. Although there are various causes of
light, yet the union of agreement in presence with agreement
in absence is sufficiently decisive of the connexion of light
with a high temperature. The special connexions of light
with low temperature are not denied; they are admitted as
exceptions to agreement in absence, as a residwwm to be ac-
counted for. We know one cause thoroughly; we find there
are other causes, as yet imperfectly known, which have this
uncertainty, namely, that a body at the common temperature
of the air may possibly be luminous.
THE INTERMIXTURE OF EFFECTS.
5. The Methods of Elimination suppose different effects
to remain separate aud distinguishable ; whereas cases
arise where the effects of different causes unite in a homo-
geneous total.
When, in an aggregate phenomenon, distinguishable ante-
a ee
———
INTERMIXTURE OF EFFECTS. 311
cedents produce distinguishable consequents—A B C giving
abc, and A D E giving a d e, the experimental methods
operate to advantage. The combination of wind, rain, and
increased temperature, produces a combination of distinguish-
able effects—waves on the surface of water, flooding of streams,
the sensation of warmth.
In other cases, and these very numerous, the effect of the
several causes is homogeneous, and is merely increased in
amount by the concurrence. The sea is fed by innumerable
rivulets. The wind often concurs with tidal agency, so as
to produce a higher tide. A body propelled by several prime
movers, as when a train is urged by three locomotive engines,
shows only one effect, velocity of movement. The moon’s
path is a resultant of the attractive forces of the sun and
the earth combined with its projectile movement. The path
of a comet is the resultant of many influences; it does not
bear on the face of it the story of them all. An invalid repairs
to some salubrious spot, and plies all the means of restoration
to health; many influences combine to the result, but the
effect is one and indivisible.
A still more perplexing situation is the conflict of opposing
agencies. In an equal balance nothing is seen, and yet great
powers have been at work. In unequal contests there is an
effect ; but that effect does not suggest the fact of conflict. A
trader has a net profit at the end of the year; the statement
of that profit, however, gives no information of his expenditure
and receipts. The patient may be under various healthy
stimulants, each working its proper effect; but some one
noxious agency may counteract the whole.
Natural agencies can never be suspended; they may be
counteracted by opposite agents. The force of gravity is not
interfered with when a balloon rises, it is merely opposed by a
greater force ; it still operates butin a different form. Instead
of causing the usual appearance, namely, the descent of bodies
to the ground, it operates to diminish the effect of an upward
force, the buoyancy of the air (itself an indirect consequence
of gravity).
A counteracted force is technically said to exist in tendency.
There is a tendency in all bodies to descend to the ground; in
water to find its level ; in the moon to move towards the earth,
and towards the sun. Thereisatendency in human beings to
seek their own interest; in despotic sovereigns to abuse their
ower. The tendencies are not annihilated when they fail to be
realized ; they are only counteracted by some opposing tendencies,
7 S| = @r.s.* aso
cu6l ss
: “ eee
-
- —
812 FRUSTRATION OF THE EXPERIMENTAL METHODS,
A farther circumstance working to invalidate the operation
of the methods is the mutuality of cause and effect. In political
ciusation, this is illustrated by*Sir G. C. Lewis as follows :—
‘It happens sometimes that when a relation of causation is
established between two facts, it is hard to decide which, im
the given case, is the cause and which the effect, because they
act and re-act upon each other, each phenomenon being in
turn cause and effect. Thus, habits of industry may produce
wealth ; while the acquisition of wealch may promote industry: —
again, habits of study may sharpen the understanding, and
the increased acuteness of the understanding may afterwards
increase the appetite for study. So an excess of population
may, by impoverishing the labouring classes, be the cause of
their living in bad dwellings; and, again, bad dwellings, by
deteriorating the moral habits of the poor, may stimulate
population. The general intelligence and good sense of a
people may promote its good government, and the goodness of
the government may, in its turn, increase the intelligence of
the people, and contribute to the formation of sound opinions
among them. Drunkenness is in general the consequence of
a low degree of intelligence, as may be observed both among
savages and in civilized countries. But, in return, a habitof —
drunkenness prevents the cultivation of the intellect, and
strengthens the cause out of which it grows. As Plato
remarks, education improves nature, and nature facilitates
education. National character, again, is both effect and
cause; it re-acts on the circumstances from which it arises.
The national peculiarities of a people, its race, physical struec-
ture, climate, territory, &c., form originally a certain character,
which tends to create certain institutions, political and domes-
tic, in harmony with that character. These institutions
strengthen, perpetuate, and reproduce the character out of
which they grew, aud so on in succession, each new effect
becoming, in its turn, a new cause. Thus, a brave, energetic,
restless nation, exposed to attack from neighbours, organizes
military institutions ; these institutions promote and maintain
a warlike spirit; this warlike spirit, again, assists the develop-
ment of the military organization, and it is further promoted
_ by territorial conquests and success in war, which may be its
result—each successive effect thus adding to the cause out of
which it sprung.’ (Methods of Politics, I. p. 375).
|
6. The Intermixture of Effects is a bar to the Experi- —
mental Methods,
73 5
s
INTERMIXTURE OF EFFECTS. 313
If A B OC D conspire to yield, not abcd, but a; and if
ABC F yield still a, nothing is eliminated, there is no pro-
gress. If a were precisely measurable, and if its variations
corresponded definitely to the removal of particular agents,
the Method of Difference would cope with the case:. the
omission of A followed by the reduction of a to 2 a, would be
a proof that A produced ¢ a. But the Method of Agreement,
in its proper character of varying the circumstance by ex-
cluding some agents and including others, could not furnish
a decisive proof, so long as a represented the sum of several
effects.
Now, as in many departments, effects are thus inextricably
blended, we should be at a stand-still, were we not in posses-
sion of some method more searching than Agreement. Even
in the Inorganic Sciences, as Mechanics and Chemistry, we
have this complication; in Biology, Mind, and Society, we
have it still more.
—, © =
COMBINATION OF PROBABILITIES, 323
independent), the chance is # X 4 or $3; that is two for and
seven against. .
10. If. The probability ofthe occurrence of one or other
of two events that cannot concur is the sum of the separate
probabilities.
‘If one man in ten is over six feet, and one in twelve under
five; then in a large number, say 120,000, there will be about
12,000 over-six-feet men, and about 10,000 under-five-feet
men ; the sum of the two 22,000, will represent the number of
such as are one kind or the other.’
#
11. III. The rule for the cumulation of independent
Testimonies in favour of a fact, is to multiply the numbers
expressing the proportionate value of each Testimony.
If a witness is correct six times out of seven, or speaks six
truths for one error, his relative testimony is six for and one
against, or $. Two witnesses of this character concurring
would give a probability of 6 to 1 multiplied by 6 to 1, or
86 to 1, and so on.
12. IV. The rule for the deterioration of testimony in
_ passing from one person to another, that is, for the weaken-
ing of traditional evidence through lapse of time, is to
multiply the fractions expressing the separate probabilities.
If one witness speaks truth five times in six, the fraction is
£; if another witness speaks truth nine times in ten, the value
is 7%. Ifthe one repeats what he has heard from the other,
the testimony is weakened by the transmission to 2 x
fo = 63, or 3. Of facts attested by the second witness, de-
riving from the first, three will be true and one false. A few
such transitions bring the evidence below probability, and
render it worthless. Four successive witnesses each valued
#, would give 8, which would be a probability against their
testimony. Now, there are many cases where a testimony is not
put too low by the above fraction ; if a want of perfect veracity
is joined with inadequate comprehension of the statement,
weak memory, or other infirmity, a witness would not be correct
three times in four.
The application of the Theory of Probabilities to the induc-
tive determination of Causes is given in the following theorem
taken by Mill from Laplace.
B24 CHANCE, AND ITS ELIMINATION.
13. ‘Given an effect to be accounted for, and there being a
— several causes that might have produced it, but of whose
presence in the particular case nothing is known; the
probability that the effect was produced by any of these
causes is as the antecedent probability of the cause, multiplied
by the probability that the cause, if it existed, would have ri |
duced the given effect. ;
‘Let M be the effect, and A, B, two causes, by either of a
which the effect might have been produced. To find the pro-
bability that it was produced by the one and not by the other,
ascertain which of the two is most likely to have existed, and
which of them, if it did exist, was most likely to produce the
effect M; the probability sought is a compound of these two
probabilities.
‘Case I. Let the causes A and B be both alike in the second
respect : either A or B, when existing, being supposed equally _
likely (or equally certain) to produce M; but let A be itself
twice as likely as B to exist, that is twice as frequent a pheno-
menon. ‘Then it is twice as likely to have existed in thiscase,
and to have been the producing cause of M. 4
‘Case II, Reversing the last supposition, let us suppose that
the causes are equally frequent, equally likely to have existed, —
but not equally likely, if they did exist, to produce M; thatin —
three times that A occurs, it produces that effect twice, while |
B, in every three times produces it but once. Since the two ~
causes are equally frequent in their occurrence, in every six &
times that either exists, A is three times and B three times, —
But A in three occurrences produces M in two; while B in
three occurrences produces M in one. Thus, in the whole six
times, M is produced thrice, but twice by A and once by B. -
So that the probability is in favour of A in the proportion of —
two to one.
‘Case III. Let there be an inequality in both respects. Let
A be twice as frequent as B; and let A produce the effect
twice in four times; B thri ise in four times. Then the
antecedent probability of A to B is 2 to 1: the probability
of their producing M is as 2 to 3; the product is 4 to 3.
In other words the probabilities in favour of A being the
cause are as 4 to 8. And so on with any other combination.’ 4
The principle may be applied to distinguish casaal coin. a
cidences from those that result from law. ‘The given fact
may have originated either in a casual conjunction of ote .
or in a law of nature. The probabilities, therefore, that the
CHANCE APPLIED 10 CAUSATION. 325
fact originated in these two modes, are as their antecedent
probability, multiplied by the probabilities that if they existed
they would produce the effect. But the peculiar combination
of chances, if it occurred, or the law of nature if real, would
certainly produce the series of coincidences. The probabilities,
therefore, are as the antecedent probabilities of the causes.
One of these—the antecedent probability of the combination of
mere chances that would produce the given result—is an
appreciable quantity, on the principles already laid down.
The antecedent probability of the other may be estimated more
or less exactly, according to the nature of the case.
CHAPTER X.
INDUCTION AIDED BY DEDUCTION.
1, It is desirable at every stage to carry out Inductive
Jaws into their Deductive applications. Now, Deductions
cannot be made or verified without Observation of facts.
Deduction or Ratiocination, in its purely formal aspect, is
given in the Syllogism. In its material side, it involves the
comparison of facts, and is akin to Induction. We have yet
to view it as it plays a part in the Inductive Sciences.
2, The full scope of the Deductive Method comprises
three operations.
I, There must be certain pre-established INDUCTIONS.
We must somehow arrive at Inductive Generalizations, and
next prove them when arrived at. The Experimental Methods
have in view these two ends, and especially the last, namely,
Proof. Incidentally, the methods indicate the mode of Dis-
covery, but they have not been expressly aimed with that view.
It has been apparent, however, that the collection and study of
instances, under the Method of Agreement, must suggest the
points of Agreement, when we are ignorant of them, which is
to suggest a general law. Our examination of the problem of
Crystallization, and the enquiry into the cause of Dew, led
first to the discovery, and next to the proof, of generalized
coincidences. Still, it was not advisable to carry on a double
326 INDUCTION AIDED BY DEDUCTION.
illustration, by means of the Experimental Methods, to eluci-
date at once Discovery and Proof; of the two ends, the
logician has most to do with the second; Proof is his main
object, for which he can lay down definite laws; Discovery is
a valuable end, likewise, but it is not equally amenable to
prescribed rules.
In the management of particular instances, with a view to
the Discovery of generalities, assistance may be obtained in the
three following ways :— . .
(1) The number of instances should be as extensive as pos-
sible. In the comparison of a large number the mind. will be
struck with points of community, from the very fact of the
recurrence; aS in the examples collected in the research on
Dew. Moreover, there will start forth some one that contains
the circumstance sought, in startling prominence; these are
the glaring or suggestive instances. Such, in the case of
Dew, was the example of the warm breath upon a cold iron
surface, as a knife blade. ;
(2) When out of mere number and variety of instances, ihe
identity does not flash upon the mind, the next thing is to
select a few for careful scrutiny. Each instance should be
studied in isolation, should be gone over in every minute point,
and examined from every side; the features being exhaustively
set down in writing. After a few separate instances have been
considered in this thorough way, the resemblances (unless at
the time inscrutable for want of other lights) will become
apparent to the view. Newton’s study of the phenomenon of
the coloured rings of the soap-bubble, was an exercise of the
severe mental concentration now described. \'¢
(3) The general laws of phenomena must be sought in the
cases where they are least complicated or combined with other
laws. This is an obvious precaution conducing to Discovery.
The laws of motion are studied in simple cases, such as straight-
lined movemenis, or wheel-movements, under a single impulse.
Gravity is kest studied in bodies falling perpendicularly, where
there is no other force operating. Neither the first law of motion,
nor the law of gravity, could have been advantageously genera-
lized, in the flow of rivers, or in the motions of the planets.
These complications are not suited for inductive discovery, but
for deductive application, as at present contemplated. The
first principles of Optics are sought, not in the workings of the
eye, nor in complicated lenses, but in the simple mirror for
reflexion, and in the plane transparent surface for refraction.
So the more transceudental powers of light, in causing moles
eer et he
SIMPLE DEDUCTION. 327
cular change, are not studied on the retina of the eye, but in
the easier (although still obscure) cases—chemical action and
photography. The osmotic action of cells is illustrated by
Graham’s experiments on the passage of liquids through por-
celain partitions. The capillary circulation of the blood is
compared to the flow of liquids in capillary tubes. Salivation
and digestion are examined by withdrawing saliva and gas-
tric juice from the animal body, and subjecting different
materials to their action apart. The laws of Mind, which are
to be carried out deductively in resolving the complicated
situations of human beings, as in Society, are to be generalized
from observations of the individual man in favourable situa-
tions. For the laws of mental growth, we have to begin at
infancy ; for the germs of moral sentiment, we refer to the
uncivilized races.*
3. Il. DeEpucTIoN proper involves two stages of com-
plexity ; (1) The simple extension of an inductive law to
anew case, and (2) the combination of several laws in a
conjoint result, involving processes of Computation.
(1) Simple Deduction is the extending of an inductive
generalization to new cases. As in all enlargements of know-
ledge, so in this, there is both discovery and proof. The cases
have first to be suggested to the mind, and next to be rigor-
ously verified by the procedure suited to the case.
Without dwelling upon the means of suggesting new
applications of laws, let us consider the mode of proving such
applications. This resolves itself into a question of identity.
Supposing that the inductive preposition ‘all matter gravi-
tates’ has been formed upon solids and liquids, shall we apply
it to gases? This depends upon whether gases are matter—
whether any property of gases is identical with the defining
property of matter. Now, the defining property of matter is
inertia, and gases are proved to possess this property ; whence,
the proposition ‘matter gravitates’ is extended to them.
Again, Does Ether (the supposed medium of Light and Heat)
also gravitate? As before, we must test its identity with the
characteristic property of matter. Now, if, as seems to be
implied in the retardation of Encke’s comet, the ether is
a resisting substance, then it is matter, and accordingly
gravitates. |
* The Arts of Discovery, brought out by scattered allusions throughout
the work, will be systematic |!) given in AppEnpix H.
15
328 INDUCTION AIDED BY DEDUCTION. |
Questions of identity to establish a minor are necessarily
part and parcel of inductive research ; but they must not be
confounded, as they sometimes are, with the process of induc-
tive generalization to establish a major or a general law.
Thus, it is a moot point, whether any, and what alloys are
chemical compounds; which must be settled by examining
the characteristics of alloys, and comparing them with the
essentials or characteristics of chemical combination. Yi
We may instance important researches that have for their
end the proof of an identity. Thus, Dr. Andrews imsti-
tuted a series of experiments to identify Ozone (formed by |
Electricity) with the atmospheric constituent that decomposes
Iodide of Potassium. He selected three peculiarities of ‘i
ozone ;~—(1) the power of oxidizing mercury, (2) the destruc-
tion of ozone reactions by dry peroxide of manganese, (3) the:
destruction of its reactions at a high rate of temperature
(237° C}; and tried the element found in the atmosphere by
these tests. It answered to them all. The first, however,
(the oxidizing of mercury) is not conclusive, as other bodies,
besides ozone, tarnish mercury. The last of the three tests:
(high temperature), answers to no known substance, except
ozone. The three tests conjoined furnish superabundant
evidence of the identity of the so-called ozone of the air, with
ozone as obtained by electrolysis, and by the electrical machine.
Another remarkable discovery of Identity is seen in Graham’s
experiments on the relations of Hydrogen to Palladium.’
There have always been chemical reasons for believing that
hydrogen gas is the vapour of a highly volatile metal.
Graham has contributed new evidence in favour of the
identity. The metal palladium is capable of absorbing eight
or nine hundred times its volume of hydrogen gas; and,
when so charged, is found to undergo changes in Density,
Tenacity, Electrical Conductivity, Magnetism, relations to Heat,
and Chemical properties. On investigating these changes,
Graham shows that they correspond to the alterations made
on one metal when united in an alloy with another metal ; so
that, as far as metallic properties can be shown in such a union,
hydrogen is metallic. The metal ‘hydrogenium’ has a white
aspect, is of sp. gr. 2, has a certain amount of tenacity, and is
magnetic. The cumulation of proof is all but equivalent to
the separate production of the solid metal. 7
Sir G. C. Lewis confounds the establishment of a minor, as —
a part of Deduction, with the establishment of an Inductive
major by the method of Difference. He considers that the
COMBINATION. OF DEDUCTIONS. 329
Bost of a burglary in a Court of Law, or the proof that Sir
hilip Francis wrote Junius, is an employment of the Experi-
mental or Inductive method of Difference as one of the
Inductive methods. In reality, all such cases are the making
good of an identity to prove a minor. The kind of Difference
employed consists in bringing out successive details or cir-
cumstantials, to exclude by degrees every person but one;
and thereby to complete the identity of that one person with
the actor in the given case.
(2) The more difficult employment of Deduction is in the
concurrence of different agents to a combined result; as
when we deduce the path of a projectile from gravity, the
force of projection, and the resistance of the air; or the tides
from the united action of the sun and the moon. This is the
form of the Deductive Method, whereby we cope with the
otherwise intractable situation called Intermixture of Effects.
Physical Astronomy will ever remain the grand exemplar
of Deductive Investigation, as the computation of joint causes
producing an effect. The causes can be estimated with numeri-
eal precision, and their combined operation can be calculated
by the higher Mathematics. In other parts of Physics, there
are instances of the Deductive Method. The calculations
respecting Machinery, Fluid Pressures, Motions of Fluids,
Gaseous Pressure and Movements, Sound, Light, Heat, Hlec-
tricity,—proceed upon inductive laws, often united in their
operation, and requiring to be computed in their joint effect.
It has been seen, in the research on Dew, that Dalton’s
generalization of the laws and constitution of the atmosphere
of yapour, deductively applied, made up the wanting link in
the experimental investigation.
Equally telling examples of the Deductive Method may be
culled from the recent applications of Chemistry to Animal
Physiology. The laws of chemical combination enable us to
trace the metamorphosis of tissue, by means of the products
of waste. The single fact of oxidation is all-pervading in the
animal system, and the deductions from it clear up at once
many obscurities beyond the reach of experimental elimina-
tion. The difficult question of Animal Heat is to a great
extent solved already by this deductive application, and its
complete solution will probably depend on the same method.
We may quote farther the special applications of Chemistry,
under the great law of Persistence, to the phenomenon of
muscular power, of which no adequate account could be given
by mere observation or experiment. We now know that
330 INDUCTION AIDED BY DEDUCTION,
muscular expenditure represents a definite combustion of the
material of the food, although we do not know the precise
links of the transmutation. |
When purely Inductive or Experimental proofs are sup-
ported by reasons, or by a consideration of the nature of the
case, the meaning is that Deduction is brought to the aid of
Induction. The conclusion respecting the N. E. wind was
confirmed by the general operation of atmospheric impurities.
The result gained from the comparison of instances of Crystal-
lization, is in accordance with the theoretical views of the
two opposing molecular forces — attraction and repulsion.
The experimental facts as to the exhaustion of the mind along
with the body, are supported by what we know of the brain
as the organ of the mind. Our inductions respecting despotic
governments are aided by deductions from the laws of human
nature.
The applications to the Human Mind, to Character, and to
Society, will be more fully exemplified afterwards, in the
special chapters on the Methods of these Sciences.
4, III. The Deductive process is completed by VERIFI-
CATION.
This applies more particularly to the Computation of
combined causes.
The way to verify the deductive extension of a single law to
@ new case, is actual observation of that case. We appl
deductively the law of gravity to air, and verify the deduction
by observing whether the air has weight. As, however, we
may dispense with deduction when we have actual observation, —
such an instance does not show the power of the Deductive
Method. The thing meant is, that after verifying a deduction
by one or more instances, we shall be able to apply it to other
instances without farther verification; these last. instances
depending for their proof solely on the deductive process,
When an effect is the result of several conspiring causes, we
may deduce it from a computation of the causes; as, for
example, the lunar and planetary perturbations. To show —
that we have taken account of all the causes, that we have
obtained a proper estimate of each, and that we have correctly
computed their conjoined action, we must compare the deduced
effects with the observed effects in a variety of instances. If
the two precisely tally, the deductive machinery is verified; —
if not, not. A want of accordance points to a defect in one or —
other of the circumstances quoted :—the causes or agents ara
Bernd Kn — Vita oes
ey a
VERIFICATION OF DEDUCTIONS. 331
not fully taken account of; their exact amount is not precisely
obtained; or the calculation of their united action is not
perfect. Sometimes, the first point is defective, there being a
residual agent. In other cases, we know the cause but not its
exact numerical amount; thus, in Astronomy, we need to
know the relative masses of the sun, moon, and planets,
together with their mutual distances. Finally, it may happen
that the calculations are impracticable.
In Astronomy, where Deduction has gained its greatest
triumphs, verification has also been most thoroughly worked.
Upwards of fifty Observatories are incessantly engaged in
watching celestial phenomena; the observations have been -
the means of perfecting the deductive operation, and making
good all its shortcomings.
The deductive theory of projectiles combined gravity, pro-
jectile force, and the air’s resistance; the experiments on
gunnery are the verification.
The laws of the strength of materials are deduced trom
geometrical and mechanical laws, involving the size, shape,
and position of beams, &c. ; but however certain the principles
may appear, they cannot dispense with actual trials.
We have supposed the verifying tests to consist of detached
observations; they may be furnished by groups of observa-
tions, summed up into what are termed Empirical Laws.
Such was the verification of Newton’s planetary theory
(founded on gravity) by Kepler’s Laws. So, any theory or
generalization of the operation of refracting surfaces on light,
must be in consistency with Snell’s law of the proportion of
the sines of incidence and refraction.
The formule of fluid motions are of themselves insufficient
to predict the facts; experiments on the flow of rivers must
be conjoined in a matter of so great complicacy.
Newton calculated deductively the velocity of sound, and, on
- comparing it with the observed velocity, found a difference of
nearly twenty per cent. It is only of. late years, that the dis-
crepancy has been got over, by a more complete view of the
forces developed in the act of propagation. In sucha delicate
question, one verifying instance is too little. Newton himself
squared the results by arbitrary assumptions (as the thickness
of the air particles), which would have required for their con-
firmation an independent class of facts.
Very confident predictions have been made to the intent
that the Sun is cooling down in consequence of his enormous
radiation ; and that the earth’s rotation must ultimately decay,
3382 INDUCTION AIDED BY DEDUCTION.
through the friction of the Tides. The data and the calcula-
tions seem very secure in both instances ; yet, in order that
the deductions may be fully established, we need evidence of
an actual change, in past time, as regards both these moment-
ous facts. |
Combined Induction and Deduction expresses the full force
of scientific method for resolving the greatest complications.
Induction alone, and Deduction alone, are equally incompetent
to the great problems even of the Inorganic world; still more
so with Life, Mind, and Society. Induction, exclusively relied
on, is called ‘ empiricism;’ Deduction, without an adequate
basis and an adequate check in the Inductive Methods, ex-
presses the bad sense of ‘ theoretical,’
The two following chapters will continue the exemplification
of the Deductive Method, of which they merely vary th
aspect. |
CHAPTER XI.
SECONDARY LAWS—EMPIRICAL AND DERIVATIVE,
1. The importance of Secondary (as opposed to Ulti-
mate) Laws, grows out of their close adaptation to concrete
realities. ,
Speculation delights to attain ultimate generalities, which
give the key to a vast department of nature; as Gravity,
Conservation, and Relativity. These are highly satisfactory
to the mind in its craving after unity, simplicity, ‘ the one in
the many.’ A far more important use of these supreme
generalities is to perfect the statement of the Secondary Laws,
which are the more immediate guides of conduct, and the
expression of the phenomena in their actual or concreie
embodiment. The generalization of gravity did not supersede
Kepler’s Laws of the Planetary Motions. So long as the
concrete fact of planetary motion has an interest for us, so
long are we concerned with the. secondary laws representing
that fact. The use of the higher laws of Newton is to render
these indispensable secondary laws more precise.
The secondary laws are the ‘media axiomata’ of Bacon,
They were viewed by him (too exclusively) as the steps for
ascending to the supreme laws. Equally essential is the —
IMPORTANCE OF SECONDARY LAWS, 333
descending movement from the higher to the middle generali-
ties. No branch of knowledge is complete until it has
assembled all the secondary laws that express the more usual
configurations of actual phenomena, and until these secondary
laws have attained all the precision that induction and deduc-
tion can give them. :
We formerly had occasion to remark (p. 79), with reference
to Propositions, that, like the notion, they vary in regard to
the reciprocal properties— Hxtension and Comprehension. As
we increase the extension, we lose comprehension, and con-
versely. Now, of the two attributes, the one most important
for us practically is Comprehension. We have to deal with
small classes, and with individuals, and our interest lies in
knowing the whole of the specialities attaching to these. An
English statesman needs to know the peculiarities of English-
men. A physician has to deal with the diseases special to
humanity, and still more those special to his own sphere;
while even this degree of generality, is but to prepare him for
mastering individual cases.
Hence, the narrowing of a proposition, which may seem a
defect to the theorizing or speculative intellect, is the highest
merit in applications to practice: provided always that the
limitation of extent is accompanied with a corresponding in-
crease in amount of predication, that is, in meaning, connota-
tion, orintent. The full enumeration of the properties special
to iron, as it is found in a certain district, is essential to the
working of that particular ore; the account of the properties
common to all metals would be valuable merely as contributing
a quota to the highly specialized and exhaustive knowledge
telative to the particular substance.
It was a frequent remark of Aristotle that the finishing
stroke of knowledge is the tact that modifies all general pro-
positions according to the individual case. This of course is
in the more purely practical point of view.
The secondary laws are either Emprrican or Dertvative.
2. An EMpiricAu Law is a uniformity supposed to be
secondary, that is, resolvable into some more general uni-
formities, but not yet resolved.
That quinine cures a fit of ague is an Empirical Law. It
is a uniformity established by experience; it is, however, a
secondary uniformity; we have reason to believe that it is
334 SECONDARY LAWS.
capable of being resolved into higher uniformities, The pre-
sent inability to resolve it is a disadvantage, not merely in a
theoretical or speculative point of view, but as regards the
application of the law in practice.
3. When what was an Empirical Law has been resolved
into more general uniformities, or into highest laws, it 1s
termed a Derivative Law,
The occurrence of snow on high mountains was at one time
an empirical uniformity. It was established as an induction
from experience, but was not susceptible of being referred to
any higher generalizations, We can now resolve it into the
laws connected with radiant heat passing through the atmos-
phere. These may not themselves be the highest attainable
generalities ; still they are much more general than the induc-
tion connecting snow with height.
The converting of an Empirical Law into a Derivative
Law isa step gained both in scientific explanation, and in
practical facilities. The defects inherent in an Empirical Law
do not inhere to the same degree in a Derivative Law.
4, Empirical Laws are of various kinds. Their charac-
ters are judged from their appearance after being resolved,
that is, made derivative.
L. Many are obviously made up of the combination of
higher uniformities under definite arrangements or collo-
cations.
We see this class largely exemplified in the explained or
derived laws. The law of a projectile, Kepler’s laws, the tides,
the laws of wind and rain, the laws of geological action (igne-
ous and sedimentary), combustion, the nourishment of living
bodies—being formerly empirical laws, and now derived—we
can, from them, presume the character of those that are still
empirical.
These combinations have been already discussed under the
Deductive Method. They suppose certain ultimate laws, con-
curring in their operation, and also a certain definite arrange-
ment and amount of the concrete agencies or forces that the _
laws refer to,
5. II. Some secondary laws take the form of laws of
succession between effects and remote causes; they still,
however, possess the character last named.
ee
VARIOUS KINDS OF SECONDARY LAWS. 335
- When a sudden shower disperses a crowd, the shower is a
very remote cause of the effect; a number of. intermediate
links of causation are assignable. The taking of food is re-
moved by a good many stages from the renewal of the muscu-
lar strength. The sowing of a seed is followed at a long
interval with the maturing of an oak.
‘This is merely a superficial variety of the first case—com-
bination of agents, in definite collocation. Hach one of the
links is a distinct law of causation or coincidence, requiring to
be embodied in a definite collocation; and the combination of
the whole, in a suitable arrangement, is necessary to the
result.
6. ITI. Some are laws of Co-existence or of Succession
between effects of the same cause.
Such are the phases of the Tides, the flow of the Seasons,
Day and Night. Here also there is the same constant circum-
stance—a conjunction of agents and collocations. In every
case of a secondary law, there is, from the nature of the case,
more than one power at work. Only ultimate laws express
agents in isolation, purity, or abstractness.
In any complicated structure, a new agent produces a
variety of changes. The taking of food leads to concurring
alterations in almost every organ in the body. Every disease
has concurring symptoms. A country engaging in war has
its economy simultaneously disturbed in many different ways;
hence there are numerous empirical statements applicable to
the condition of war, which are co-effects of the one general
situation.
7. The aggregation of properties in a natural kind—a
mineral, plant, or animal—has something in common with
Empirical Laws.
As there may be uniformities of co-existence, not resolvable
into cause and effect, such uniformities stand solely on their
own inductive evidence, like empirical laws. They are proved
by the method of Agreement alone, and the proof extends no
farther than the cases observed.
8. The criteria of an Empirical Law are principally
these :—
If a uniformity is established only by Agreement, it is
not shewn to be a law of causation; and (if not an ulti-
mate law of co-existence) it is an empirical law.
336 SECONDARY LAWS.
Agreement does not single out a cause when there is plurality.
It is at fault, besides, in discriminating cause and effect from
effects of the same cause. Moreover, unless the variation of
the circumstances has been thorough and complete, there is
an uncertainty even in cases where there is but a single cause,
‘and where the antecedents contain that cause.
The Method of Difference does not at once lead to ultimate
laws. The swallowing of alcohol is followed by a certain
sensation; this is proved by the Method of Difference to be
cause and effect, yet it is not an ultimate sequence; it is an
empirical uniformity.
9. ‘The other criteria arise out of the characters already
mentioned.
Thus, when phenomena are obviously complicated, and
when there are intermediate links of operation, the laws of
such phenomena are not ultimate but secondary ; they are
empirical, or, if resolved, derivative,
The law that connects the fall of the barometer with wind
or rain is plainly empirical. We can see that many different
agencies enter into the sequence; and, also, that there are
many intermediate steps between the antecedent and the
consequent.
We presume the action of a drug to be an empirical law,
because we know, from the complication of the human body
and the plurality of attributes of natural kinds, that there
must be many concurring processes, each one governed by its
own law or laws of causation.
LIMITED APPLICATION OF DERIVATIVE AND EMPIRICAL LAWS.
10. A Derivative Law, and still more an Empirical Law
must not be extended beyond narrow limits of ‘Time, Place
‘and Circumstance. |
It being supposed that such laws are established by all th
evidence that the case admits of, still they are applicable only
a certain way beyond the narrow sphere where they have been
observed to operate.
The reasons are those already stated under the Deductive
Method. A uniformity depending on several higher uniformi-
ties, and on a definite collocation of agents, that is, on certain
special co-efficients, must fail, first, if any of the concurring
uniformities be counteracted, and secondly, if the proper ad- —
justment of the agencies is departed from. The elliptic
APPLICATION TO ADJACENT CASES. BOL
motion of the planets would be defeated, if some great dis-
turbing body were sufficiently near to counteract solar
attraction, or if the tangential force were made different from
what it is. Hence we cannot extend the law of the ellipse to
ae body that may now or at any future time revolve about
the sun.
This limit to the extension of secondary laws—whether
Empirical or Derivative—is the all-important fact respecting
them, in the logical point of view. A large number of pre-
- vailing errors might be described as the undue extension of
Empirical Laws. We shall presenta few examples of secondary
laws, calling attention to the difference of our position in
regard to them, according as they are Empirical or Derivative.
The rise of water in pumps was an empirical law, previous
to the discovery of the pressure of the atmosphere. The
application of the Method of Agreement in different countries,
and with pumps of different bore, proved that no pumps could
draw water beyond about 33 feet. The law could be relied on
within the wide limits of place and circumstance where it had
been tried. It could not have been extended to other planets ;
but it might be extended, with apparent safety to any part of
the earth.
Since the law became derivative, the limits of its operation
are precisely defined ; we can tell exactly where it would have
failed. We know that on the tops of high mountains the
maximum height would have been much below 33 feet; that
the exact height would not be the same at all times; that
other liquids, as alcohol, sulphuric acid, solutions of salts,
mercury, vary in the height attained. Now, probably none
of all these limitations had been actually discovered in the
empirical stage ; they might have been obtained by sufficiently
wide and careful experiments; the derivation superseded the
laborious task, which was probably beyond the competence of
an unscientific age.
It is an empirical law that the temperature of the earth
increases, as we descend, at a nearly uniform rate of 1° of
Fahrenheit to 50 feet of descent. This law has been verified
by observations down to almost amile. We might extend the
law inferentially to the adjacent depths, as far perhaps as
several miles; but we are not at liberty to extend it to the
centre of the globe. We do not know that the requisite col-
locations extend so far.
Yet this law is not wholly empirical. It is a derivative
uniformity. It is connected with the known facts—that the
838 SECONDARY LAWS,
earth has a high temperature in the interior, and 1 is cooled at
the surface by radiation in space. Knowing these, we are yet
unable to deduce the law of decrease from the higher laws
concerned, because we are ignorant of the degree of central
heat, and imperfectly acquainted with the laws of its conduc-
tion through the unknown materials of the globe. We under-
stand the general situation, but do not possess the numerical
and other data requisite for computing the effects.
That air-breathing animals are hot-blooded, is a law formerly
empirical, now derivative. It comes under the general law of
the dependence of temperature on the oxygenation of the blood,
and may be extended widely on the faith of that great
generality.
The Law of Continuity—‘ Natura non agit per saltum ’—is
an Empirical Law. In the continuity of Vegetable and Animal
Life, there would be, under the Doctrine of Development, a
reason for the fact, and it would be in that case Derivative.
Also, in the transition from one state of matter to another,—as
in melting, boiling, and their opposites—there must be a ~
certain amount of continuity owing to the greatness of the —
transition. But except where there is some presumption of
this nature, the extension of the law is wholly unsafe; we are
not to expect, for example, that the simple bodies of nature
should be arranged in series with continuous or shading pro-
perties. We find the greatest gaps in almost all the propertane
_ of the elementary bodies. :
In medical science, there is hardly such a thing as a single —
effect produced by a simple cause. What is worse, there are
scarcely any great inductive generalities relating to the cure of —
disease, except through hygienic or constitutional treatment.
Thus the use of drugs is almost exclusively empirical, —
The limitation in this case operates variously. It forbids 4
our inferring that two medicines of close kindred will have —
the same effect; thus bark and quinine are not interchange-
able, although the one is the crude form and the other the
essential extract. It also forbids our extending a mode of
treatment to a closely allied ailment, as in reasoning from
one species of fever to another. Lastly, it forbids the applica- —
tion of the same treatment to the same disease, in different
persons.
Hence, medicine is of all sciences the one most completely
tentative. Experience gives a probability to begin with; but
until the effect is tried in the new case, we CON Oly as @
general rule, rely on it. | ling
EMPIRICAL LAWS IN MEDICINE, 339
Until the day arrives when the operation of medicines is
made derivative, the only progress possible is to obtain through
multiplied experience, a more exact.statement of the conditions
attending on the successful application of certain modes of
treatment; as for example, the constitutional or other circum-
stances in the patient favourable or unfavourable to special
drugs.
The treatment of tape worm by male fern is of old date in
medicine. In the early period, the failures were frequent ;
at present, the oil of the fern is extracted and given instead of the
root, with an almost uniform success. This empirical unifor-
mity is to a certain extent derived or explained ; the substance
is a poison to the parasite. After such an explanation, there
is afforded a clue to other remedies for the disease; previous
to the explanation, the uniformity was confined to the one
remedy.
As an empirical law in Medicine, we may instance Bright’s
discovery of the connexion between albuminous urine, and
degeneration of the kidney. The law is as yet unresolved
into any higher law of structure and function; the kidney
degeneration is not associated with degeneration in any other
tissues of the body ; and no account is given of the temporary
production of albumen without the permanent disease.
It is an empirical law that about 250 persons in a year
commit suicide in London. This law may be extended a little
way into the future, but it may not be extended into a remote
time, when moral habits may be different, nor to other cities
and populations.
The Statistics of Mortality show a remarkable coincidence
between the rate of mortality and the density of the popula-
tion. A high degree of longevity is found in thinly peopled
districts, notwithstanding even the poverty that sometimes
occurs in sterile tracts; and mortality reaches its maximum
in the most crowded parts of cities. If we knew nothing of
the causes of this uniformity, if it were as empirical as the
medicinal action of mercury on the system, we could not
extend the law into other countries and other circumstances of
the population. But it is a derivative law, and knowing what
agents the effect depends on, and what circumstances would
defeat their operation, we apply it without scruple to every
portion of the human race. We should, however, refrain from
applying it to animals very differently constituted from man
as to the necessities of breathing pure air. All animals require
oxygen, but some need it in smaller quantity, and are indif-
340 SECONDARY LAWS.
for ‘ent to impure gases ; while warmth and the opportunities of
better food might more than compensate for the close atmos- —
phere of a confined habitation. et
In regard to the Human Mind and character, we have
uniformities that cannot be extended to the race generally.
Thus, the universality of sympathy or fellow-feeling is liable to
exceptions. Mr. Samuel Bailey, after quoting, from a travel-
ler in Burmah, the incident of a drowning man being beheld
by a crowd as an amusing spectacle, and being allowed to
sink without an attempt at succour, makes the following
remarks :—
‘Incidents of this kind (and the example might be easily ;
parallelled from other nations) serve to show that when we
ascribe certain sentiments to human nature or to men univers-
ally on given occasions, because they exist amongst ourselves
on those occasions, it is by no means a safe inference; we
cannot safely ascribe them except to men under analogous
circumstances of knowledge and civilization.
‘We may attribute with confidence to most men and to most
races of men, the rudimentary feelings which I have shown to
originate and to constitute moral sentiment; and some of them
with equal confidence to all men: namely, sensibility to cor-
poreal pleasure and pain; liking the causes of one and dis-
liking the causes of the other; the propensity to reciprocate
both good and evil; the expectation of the same reciprocation;
and more or less sympathy with other sensitive beings; but
the direction and intensity of these emotions respectively it is
often difficult and even impossible to assign: there are so
many causes at work to counteract, or modify, or cop y
such of these common susceptibilities as can be counteracted, —
or modified, or suppressed—to call them forth or to cea
them in, that, unfurnished with precise knowledge of national —
and social circumstances, we cannot predict with confidence —
how they will manifest themselves on particular occasions. —
Without specific information of this kind we cannot safely —
pronounce that the people of rude or distant and imperfectly _
explored countries would, under given circumstances, share in
those affections and moral sentiments which it seems contrary —
to our own very nature, under such circumstances, not to have.
That ‘ the mind of man is by nature conciliated and adapte¢
to his condition’ was formerly an empirical law. We may
now consider it as a deduction or derivation from the law of —
Universal Relativity. The principle has been greatly abused. —
It has been loosely extended far beyond the limits where it is
POLITICAL RULES, 341
observed to hold true ; indeed those limits were never correctly
marked in its empirical state. As a derivative uniformity, we
may assign its limits with tolerable precision.
The laws of Political Society are all secondary laws, either
empirical or derivative. Hence the necessity for limiting their
application. The politician is, like the ancient sailors, obliged
to sail close by the shore, rarely venturing out of sight of land.
We are not at liberty to transfer to our own time the maxims
suitable to the ancient world, supposing even that the ancients
really attained any political rules highly salutary in their own
case.
‘The distinction between ancient and modern history,’ says
Mommsen, ‘ is no mere chronological convenience. Modern
History is the entry on a new cycle of culture, connected
at several epochs of its development with the perishing or
perished civilization of the Mediterranean States, but destined
to traverse an orbit of its own.’ It would be a vicious extension
of secondary laws, to predict the extinction of modern nations,
because the great ancient empires are perished.
We cannot transfer at once the practice of one nation to
another nation. Hardly any political device has been so much
copied as the British constitution. Yet, its advantages being
not purely empirical, but toa certain extent derivative, it may
be extended to adjacent cases with some confidence.
_ It is suitable to the complicacy of the political structure to
make changes in the direction of existing institutions, and to
confide in them only when introducing a state of things nearly
adjacent to the present. After seeing the working of a ten-
pound franchise in this country, the inference was fair that
the lowering to eight, seven, or six pounds could not depart
very far from actual experience. |
The use of precedents in Law and in Politics exemplifies the
rule of limitation. Bacon, remarking on legal precedents, lays
it down that the more recent are the safer, although, on the
other hand, they have a less weight of authority. ‘A prece-
dent is at its maximum of proving force when it is sufficiently
near our own time to ensure similarity of circumstances, and
sufficiently distant to ensure the consolidation of practice, and
the experimental exhibition of the practical result.’ (G. C.
Lewis).
11. The rule may be farther illustrated under the second
form of the Secondary Laws— Uniformities of remote
connexion between cause and effect.
342 SECONDARY LAWS.
Of these, the most prominent examples are the results of
slow processes in the arts, protracted treatment in disease, the _
growth of plants, the development of animals, the formation of
the human character. That all empiricisms of this class must _
be precarious and liable to frequent defeat is apparent. Hven
when derivative to the full extent, they are rendered uncertain
by the number and complication of the agencies.
1
hn.
12. Lastly, with reference to Uniformities suspected or — i
known to be effects of a common cause.
The principle of limitation is still the same. a
As an example, the case is put—what reliance are we to —
place on the sun’s rising to-morrow ? s
Suppose, in the first place, that this were an empirical —
generality, we being ignorant of its derivation. Suppose, —
also, that we have authentic evidence that the sun has risen
daily for the last five thousand years. How far intothe future —
are we at liberty to extend the law; to what limits of time
should we confine it? The answer is, we may count the con- —
tinuance in the future, on the same scale as the continuance —
in the past; we may fairly assume a period counted by ©
thousands of years; we may be tolerably certain for one ~
thousand years, and have a considerable probability, for three,
four, or five thousand ; but we should not be safe in extending -
the scale to tens of thousands, still less to hundreds of —
thousands. For anything we should know, a catastrophe may -
be preparing that will speedily interfere with the regularity of
day and night; still, long continuance in the past reduces, —
without annihilating the chances. «cn
Let us next look at the case as a derivative uniformity. We
know that the phenomenon will continue so long as these
circumstances are conjoined, namely, (1) the luminosity of
the sun, (2) the earth’s being within a proper distance of the
sun, (3) the earth’s rotation, and (4) the negative condition of
the absence of any intervening opaque body to act as a screen.
Now, we know from past experience that all these conditions
are likely to be perpetuated for a period of time, to be estimated
by not less than hundreds of thousands of years. The sur
may be cooling, but the rate, judging from the past, is
extremely slow; the earth’s rotation is believed to be subject
to decay, but the rate of decay is infinitesmally little; the
removal of the earth out of the solar influence is in oppositio n
to our very best guarantees ; and the permanent intervention of
an eclipsing body is the most unlikely incident of all. Thus
any
eo at aa Fe
INDUCTION OF CAUSE 343
then, while, as an empirical law, we cannot well extend the
rising of the sun (or day and night as we now have it) beyond
thousands of years at most, we may extend it, as a derivative
law, to hundreds of thousands, if not to millions.
EVIDENCE OF THE LAW OF CAUSATION,
13. It may be shown that the Law of Causation, the indi-
spensable ground work of all Induction, itself reposes on
the highest evidence suitable to the case—uncontradicted
Agreement through all nature.
We have hitherto taken for granted that sufficient evidence,
of the only kind suited to the case, has been obtained in favour
of the law of Universal Causation, on which law have been
grounded all the processes of experimental elimination. A
summary of this evidence will farther illustrate the logical
processes detailed in the foregoing chapters.
The uniformity of successions was first observed in easy
instances, such as the more obvious mechanical effects. A
body at rest was observed never to move from its place without
the application of some force to move it; a body in motion
was observed not to stop abruptly without interference and
obstruction. The fact of the descent of unsupported bodies
is invariable. So light and heat display obvious regularities
that could be counted on. Even in the instability of the winds
there would be discovered circumstances of constancy. The
most complicated of all things, living bodies, were seen to
have numerous points of striking uniformity.
That change of every kind whatsoever follows on a definite
prior change, could not be affirmed in early times, except by
the mere instinct of generalization, which is no proof. Hence
in ancient philosophy, there were alternative suppositions.
Aristotle allowed an element of Chance, along with the reign
of Law.
Modern science has extended the search into natural se-
quences, collecting new examples of uniformity, and removing
exceptions and appareat contradictions. Investigations have
been pushed into every department of nature; and had there
been any decisive instances where change grew out of nothing,
or where the same agent, in the same circumstances, was not
followed by the same effect, such instances must have been —
brought to light.
14. Inthe form of Persistence of Energy, under definite
344 EVIDENCE OF THE LAW OF CAUSATION.
laws of Collocation, the Law of Cause and Effect has been
subjected to the most delicate experimental tests.
By irrefragable observations it was shown that Matter i is
indestructible, which is one element of nature’s constancy.
Farther observations have proved the numerical Persistence
of Force throughout all its transformations, and also the unifor-
mity of the collocations or arrangements for transferring it.
The first contribution to this result was the proof of the
Laws of Motion, as respects both the continuance of motion
once begun, and the conservation of the total moving force in
case of transfer by impact. These mechanical verities make
up one department of uniform cause and effect, Next came
the proof of the equivalence of mechanical force and heat—
the constancy of the amount of one produced from a definite
amount of the other. Joule’s mechanical equivalent of Heat
testifies to nature’s constancy in a very wide department.
Following on this is the mumerical estimate of the heat of
Chemical combinations, also admitting of numerical statement,
from which there is no deviation; a third great department
of constancy is thereby established,
If numerical equivalence has not been arrived at in Nerve
Force, and in Light, the subtleties of the phenomena are
sufficient to account for the deficiency. We have reasonable
ground to presume that, according as these phenomena are
fully understood, they will show the same constancy as all the
rest; the burden of proof lies upon any one maintaining the
contrary.
The only exception usually claimed to the Law of Causation
is the alleged Freedom of the Will. But whatever be the
mode of dealing with this long-standing enigma, there is a
statistical testimony in favour of the constancy of human
motives. The actions of men have a degree of regularity
compatible only with uniform causation.
Mr. Mansel has characterised as a ‘paralogism’ the doc-
trine that ‘the ground of all Induction is itself an Induction.’
He might have called it a paradow or an epigram, an apparent
contradiction needing to be resolved: it is not a paralogism
unless it can be made out a self-contradiction.
If the account given above of the methods of Proof and
Elimination is sufficiently intelligible and conclusive, nothing
farther is necessary to resolve the paradox. There is one fun-
damental mode of Proof—Agreement through all nature—by —
which all ultimate laws are established, including Causation, —
ee ee ee
d
-,
CAUSATION RESTS ON AGREEMENT ALONE, d45
There are several derivative, deductive, or dependent methods
of Proof, the special Methods of Elimination—Agreement
(according to Mill’s Canon), Difference, and Variations ; these
are called by courtesy Inductive Methods; they are more
properly Deductive Methods, available in Inductive investiga-
tions. The special form of Agreement described in the canon
is not quite the same as the fundamental method of Agree-
ment, on which alone repose all the ultimate generalizations.
That canon, as supposing Causation, would be inapplicable to
the proof of Causation. The method of Agreement that proves
Causation is not a method of elimination. It does not proceed
by varying the circumstances, and disproving successive
antecedents ; it can only find A followed by a, wherever the
two occur. Until the law is first proved, we cannot establish
A as the cause of a, by omitting successively B, C, D, and all
other accompanying circumstances, leaving nothing constantly
joined save A and a; even if this were done, there must still be
a search through all nature for A followed by a, when the ques-
tion of causation itselfis atissue. Hence Agreement for estab-
lishing an ultimate law is not the same as the Method of
Agreement, in Mill’s canon, for establishing cases of causation,
after the general law is sufficiently guaranteed.
There is a certain propriety in comparing the establishment
of the Law of Causation (or any other ultimate law), with the
proof of an Empirical Uniformity, which has nothing but de-
tailed Agreement to found upon. True, an Empirical Uni-
formity is to be applied only a little way beyond the limits of
time, place, and circumstances But, now, as Mr. Mill
remarks, ‘if we suppose the subject matter of any generaliza-
tion to be so widely diffused, that there is no time, no place,
and no combination of circumstances, but must afford an
example either of its truth or its falsity, and if it be never
found otherwise than true, its truth cannot depend on any
collocations unless such as exist at all times and places; nor
can it be frustrated by any counteracting ageucies, unless by
such as never actually occur. It is, therefore, an empirical
law, co-extensive with all human experience; at which point
the distinction between empirical laws and laws of nature
vanishes, and the proposition takes its place among the most
firmly established, as well as largest truths accessible to
science.’
CHAPTER XIL
EXPLANATION OF NATURE.
1. The laws arrived at by Induction and Deductiott are
the proper EXPLANATION of natural phenomena, =
Explanation has various meanings. ‘These all agree in
affording us a certain satisfaction or relief when oppressed —
with the difficulty, obscurity, perplexity, contradiction, mys-
tery, of natural facts. But the human mind has at different —
times been satisfied in different ways; and individuals still”
vary as to the kind of explanation that satisfies them. . a
When all Nature was peopled with deities, and the various
phenomena partitioned among them, a sufficient explanation —
of anything was that a certain god or goddess willed it. The —
intervention of Neptune was a satisfying account of why a
storm arose. The wrath of Apollo was the explanation of the —
plague that broke out among the Greeks at the siege of Troy.* — oi
There is a special and every-day form of explanation that —
consists in assigning the agency in a particular occurrence; _— a
as when we ask— what stops the way ? who wrote Junius ?
who discovered gunpowder? These questions belong to our
practical wants and urgencies, but the answer does not involve
the provess of scientific explanation. If, however, we pro l
from the ‘who’ or ‘what’ to the ‘ why: "why does A’s —
carriage stop the way? why did the author of Junius write
so bitterly ?—there is an opening for the higher scientific
process.
2. The basis of all scientific explanation consists” in
assimilating a fact to some other fact or facts, It
identical with the generalizing DIOe that is, with il
duction and Deduction. 185
Our only progress from the cinibitie to the plain, from the
mysterious to the intelligible, is to find out resemblances among
facts, to make different phenomena, as it were, fraterniz e.
We cannot pass out of the phenomena themselves. We can
explain a motion by comparing it with some other motion on
* Bee Grore’s Plato (Phedon) tor the views of the ancient philosoph hers
with ae to Explanation, or the Id.a of Cause. —
*
“«
e
ea
EXPLANATION IS GENERALIZATION, 347
pleasure by reference to some other pleasure. We do not
change the groundwork of our conception of things, we
merely assimilate, classify, generalize, concentrate, or reduce
to unity, a variety of seemingly different things.
The phenomenon of combustion was considered to have
been explained when Priestley showed it to be the combina-
tion of oxygen with carbon or other substance ; in short, he
assimilated the fact to cases of oxidation, as the formation of
the red precipitate of mercury, the rusting of iron, &c.
Lightning was explained by Franklin’s assimilating it with
electricity. The polarity of the needle was explained by
assimilating the entire globe to a magnet or loadstone.
Explanation thus steadily proceeds side by side with
assimilation, generalization. Combustion was explained by
oxidation ; oxidation is explained by the higher generality—
chemical combination ; chemical combination is swallowed up
in the Conservation of Energy.
3. Mr. Mill distinguishes three forms of the explanation
of facts and laws.
I. Explaining a joint effect, by assigning the laws of
the separate causes, as in the ordinary Deductive operation.
The Deduction of a complex effect, by computing the sum
of the separate elements, is also the explanation of that effect.
By combining gravity with projectile impulse, we explain
the motions of the planets. This deduction once verified, is
offered as the explanation of the planetary motions. In other
words, the showing that these motions are made up of the
two causes—gravity and tangential force—is the explaining
of their motions.
In such cases, the explanation points out the simple causes
concurring, in the shape of forces or agencies, and also indi-
cates their amount and their due -concurrence. Jupiter's
orbit depends on the mass of. the sun, on the tangential force
of the planet, and on its mean distance from the sun. These
are, in the Janguage of Astronomy, the coefficients, which must
be given in order to our assigning the result of the operation
of the laws. A mere law, such as the law of gravity, is not
an explanation until it is clothed in the concrete statement of
two or more gravitating masses, with a given amount anda
given distance from each other. These numerical statements,
the coefficients of Astronomy, are also said to determine the
collocations of the agents concerned.
348 EXPLANATION OF NATURE,
To explain the rise of a balloon, is to give the lawa: a
gravity, of buoyancy, and of gaseous elasticity, and to steht 7
the exact weight and elasticity of our atmosphere, and the
specific oravity of the mass of the balloon. ricer x '
To explain genius is to refer it to general laws of the mind, ©
or to certain elementary powers—intellectual and emotional— 5 ~
whose higher or lower degrees and modes of combination —
produce the kind of intellectual superiority so named. v2
To explain the rise of free governments is to state the a
general principles of human action, and the definite collocation
of circumstances calculated to produce the effect. sole 4
The separate laws are obviously more general than the laws —
of the conjoint effect. Gravity has a much wider sweep than
planetary motions; the law of the perseverance of moving —
bodies in a straight line-is far more comprehensive than
tangential impulse. |
4, II. Explanation may assume the form of discovering
an intermediate link, or links, between an antecedent and —
a consequent. at Yous ¥
What seems at first sight the direct or immediate cause of a
phenomenon may, by the progress of assimilation, turn out
the remote antecedent. The drawing the trigger of a musket —
is followed by the propulsion of a “ball. The why of that
phenomenon is given by disclosing a series of intermediate —
sequences, each of which is assimilated with some known —
sequence. The trigger by concussion evolves heat; the heat —
ignites the gunpowder; the gunpowder is a mass adapted for
very rapid combustion ; the combustion evolve gases which,
being confined in a small space, have a very high expanaiiay
force ; the expansive force propels the ball.
Again, the contact of sugar with the tongue is the precursor _
of a feeling of the mind, the sensation called sweetness. The
explanation, so far as hithante attained, supplies the followi
series of closer links. The sugar is absorbed by the mucus.
membrane of the tongue, and comes in contact with the file .
ments of the gustatory nerve; there ensues a chemical or
some other molecular action on the nerve. This action | is
of a kind that can be propagated along the course of the nervy:
to the nerve centres, or the brain ; shania are diffused a multi
tude of nervous currents er ding in muscular movements, y )
the cerebral agitation attaches the mental state called the § sel nsé —
tion of swectness. ys
INTERMEDIATE LINKS. 349
The unexplained phenomena connected with the Law of
Conservation refer to the intermediate links, or transitions, in
the interchange of the mechanical and the molecular forces,
and of one molecular force with another. The molecular pro-
cesses in the conversion of mechanical energy into heat, heat
into electricity, chemical force into muscular power and
nervous power,—are not accounted for: and we see only a
beginning and an end where we have reason to believe that
there must be various intermediate stages, each susceptible of
being assigned and brought under some general law of causa-
tion.
The intermediate links, or sequences, are each one more general
than the combined sequence. Take the case of a sweet taste.
The absorptive power of the animal membranes for various
substances (the crystalloids of Graham) is a general law, of
which the action in tasting is merely one example or applica-
tion. The molecular disturbance from the contact of nerve
and sugar is but a case of chemical or molecular affinity.
The current action of the nerve force is a limited instance of
current actions; the electrical forces exhibit other cases,
the whole being comprehensible under some higher law.
Finally, the link that relates the physical actions of the brain
with the mental effect belongs to some wider statement that
relates mental states generally to their physical concomitants.
As observed, in the previous chapter, it is incident to such
many-linked sequences, to be more frequently frustrated than
the simpler sequences that make them. A circumstance
counteracting any one of the closer links counteracts the
whole phenomenon. If the lock of the musket makes an in-
sufficient concussion of the explosive substance; if the gun-
powder is rendered incombustible by damp; if the expanding
gases burst the piece :—in any one of these contingencies, the
ball is not propelled.
_ 5, Ill. The third mode of Explanation is termed the
Subsumption of one law into another ; or the gathering up
of several laws in one more general and all-comprehending
law.
This represents the upward march of generalization, pure
and simple. We have attained a certain number of inferior
generalities, by assimilating individual cases in ordinary in-
duction. We have assimilated the kindling of fires for heat
and for light and for the disintegration of compounds, under
one head, called combustion ; we have assimilated the tarnish-
350. EXPLANATION OF NATURE.
ing and corrosion of metallic surfaces under another head ;
we subsume both under the higher law of oxidation, which
both exemplify. We have also assimilated the action of acids”
upon alkalies under a general head: we find that this case
can fraternize with the foregoing and with many other
phenomena, under a still higher, or more general aspect,
signified by chemical combination.
So, again, terrestrial gravity and celestial attraction, each
the result of separate assimilations, being found to agree, are
subsumed into the illustrious unity of Universal Gravitation.
Magnetism, Common Hlectricity, Voltaic lHlectricity,
Electro-Magnetism, &c., are all strung upon the common
thread of Electrical Polarity. 3
Capillary attraction, solution, alloys (not chemical), cements,
&c., are subsumed under the general law of molecular attrac-
tion (not chemical) between different substances, named
heterogeneous or alien attraction.
Numerous laws of smaller compass are subsumed ence
Relativity. The pleasures of variety and novelty, the neces-
sity of contrast in works of art, antithesis in rhetoric, the
statement of the obverse or counter proposition in science,—are
minor laws generalized, but not superseded, by the tee
law.
When minor laws are thus merged in a greater law, the
mind feels a peculiar and genuine satisfaction—the satisfaction
of having burst a boundary to expatiate over a wider field.
We rise from a statement bearing upon a-small group of facts”
to a statement comprehending a much larger group; from a
ten-fold condensation, we reach a thousand-fold condensation.
The intellect, oppressed with the variety and multiplicity of
facts, is joyfully relieved by the simplification and the unity of
a great principle.
The charm of resolving many facts into one fact was acutely
felt by the speculative minds of antiquity. It took a power-
ful hold of the earliest Greek philosophers; and made them
almost unanimous in imagining that all phenomena whatso-
ever are at bottom one, or are susceptible of being represented
in some single expression, being merely the many-sidedness of. 3
some single central power, substance, agent, or cause. Such
unity was, according to Thales, Water; according to Anaxi-
mander, an Indeterminate Babetaies’! according to Anaxi-
menes, Air; according to Pythagoras, Number, 1 1
3
4
ww Toe le
ULIMATE PHENOMENA. . at
LIMITS OF EXPLANATION.
6. Scientific explanation and inductive generalization
being the same thing, the limits of Explanation are the
limits of Induction.
Wherever Induction (extended by Deduction) can go, there
legitimate scientific Explanation can go, they being the same
process differently named.
7. The limits to inductive generalization are the limits
to the agreement or community of facts.
Induction supposes similarity among phenomena, and when
such similarity is discovered, it reduces the phenomena under
acommon statement. The similarity of terrestrial gravity
to celestial attraction enables the two to be expressed as one
phenomenon. The similarity between capillary attraction,
solution, the operation of cements, &c., leads to their being
regarded not as a plurality, but as a unity, a single causative
link, the operation of a single agency.
So remarkable have been the achievements of modern times,
in the direction of lofty generalities, that some countenance
seems to be lent to the ancient dream of attaining an ultimate
centralized unity in the midst of the seeming boundless
diversity of nature.
It depends purely on actual investigation, how far all
phenomena are resolvable into one or into several ultimate
laws ; whether inductive finality leaves us with one principle,
with two, or with twenty principles.
Thus, if it be asked whether we can merge gravity itself
in some still higher law, the answer must depend upon the facts,
Are there any other forces, at present held distinct from
gravity, that we may hope to make fraternize with it, so as to
join in constituting a higher unity? Gravity is an attractive
force ; and another great attractive force is cohesion, or the
force that binds together the atoms of solid matter. Might
we then join these two ina still higher unity, expressed under
a@ more comprehensive law? Certainly we might, but not
to any advantage. The two kinds of force agree in the one
point—attraction, but they agree in no other; indeed, in the
manner of the attraction they differ widely; so widely that
we should have to state totally distinct laws for each. Gravity
is common to all matter, and equal in amount in equal masses
of matter whatever be the kind; it follows the law of the
16
Ye ngs ay ea ae oe ae
352 EXPLANATION OF NATURE.
diffusion of space from a point (the inverse square of the
distance) ; it extends to distances unlimited ; it is indestruc-
tible and invariable. Cohesion is special for each separate
substance ; it decreases according to distance much more
rapidly than the inverse square, vanishing entirely at very
small distances. Two such forces have not sufficient kindred
to be generalized into one force; the generalization is only
illusory ; the statement of the difference would still make two
forces ; while the consideration of one would not in any way
simplify the phenomena of the other, as happened in the
generalization of gravity itself.
Again, gravity, considered as a power to put masses in
motion, to generate visible or moving force, may be
compared, by way of an attempt at assimilation, with the
equally familiar mode of begetting motion by tpact, or the
stroke of a mass already in motion ; as in propelling a ball by
a mallet. Here too, however, we have, with similarity of
result, a total contrast in the mode. Gravity draws bodies
together from a distance ; impact must be supposed to urge
them through their atomic repulsions. When the expanding
gases of kindled gunpowder blow a bullet through the air,
there is no actual contact of the parts; there is merely the
operation of powerful forces of mutual repulsion, acting;
however, at very short distances, like the cohesion of solidity.
Now, there appears to be nothing in common to gravity and’
these atomic repulsions, except the result. We have, there-
fore, no basis for assimilation or inductive generalization in
such a comparison. The two modes of action must be
allowed to lie apart in physical science; they must be em-
bodied in different statements or laws, with no hope of being
ever brought together. — rt
It is because gravity does not assimilate with the propulsion
of impact from a blow or a stroke that people have accounted
it mysterious. In point of fact, there is no more mystery in
the one than in the other. Attraction, from great distances,
is one form of the production of force; Repulsion, at near i
distances, is another form. The last of the two is, on the
whole, most familiar to us; it is the genus that our own
physical force belongs to; and we, by a mere whim, suppose’
it a simpler and more intelligible mode of exerting power;
the truth being that, in all that regards simplicity and intel-
legibility, gravity has the advantage. It is only by confining
ourselves to the superficial glance of bodies coming into close:
contact, thence giving and receiving momentum, that we
= ———"
—
ULTIMATE FEELINGS OF THE MIND. 300
suppose this mode of exerting force a simple one; the inter-
polated links of molecular repulsion are much more compli-
cated than gravity.
A similar line of remarks would apply to any endeavour to
assimilate gravity with the Correlated Forces generally. These
forces by their nature counteract gravity. The various move-
ments in nature are explicable by the conflict and mutual
action of two great Powers; Gravity, on the one hand,
and the sum total of the Correlated Forces, molar and mole-
cular on the other. The Correlated Forces mostly appear
under the guise of repulsions, as, for example, heat ; so much
so that this must be considered their typical manifestation ;
the electrical and magnetic attractions are exceptional, and
are probably mere superficial aspects of the deeper fact of
repulsive separation.
Three departments of Force thus stand out so distinct as to
be incapable of assimilation :—Gravity, the Correlated Forces,
and Molecular Adhesion. This last appears under two
forms ;—the attraction between particles of the same sub:
stance—iron for iron, water for water; and the attraction
between two substances—as iron for lead, water for alcohol or
for common salt. There may be a possibility of generalizing
these two, or stating them as acommon force. Some approach
has been made to this in the fact that the second kind of
attraction holds between bodies nearly allied—as metals with
metals, earths with earths.
8. The ultimate laws of Nature cannot be less numerous
than the ultimate feelings of the human mind.
This, as Mr. Mill pointed out, is the insurmountable barrier
to generalization, and consequently to explanation. Whatever
number of distinct states of consciousness, not mutually re-
solvable, can be traced in the mind, there must be that number
of ultimate fects or elements of knowledge, and of ultimate
laws connecting those states with their causes or concomitants.
If the sensation of colour be radically distinct from the feelings
of resistance, of movement, of form, there must be a separate
law with reference to colour. The phenomenon called white-
ness cannot be resolved into the phenomenon of form, or of
motion.
Even if we found that the fact of whiteness is conditioned
by a certain molecular structure, and certain molecular move-
ments, we should not thereby resolve whiteness into movement;
the facts would be distinct facts, although joined in nature.
B54 . EXPLANATION OF NATURE.
So, we are aware that the sensation of sound is conditioned by
a vibratory movement of the particles of a sounding body ;
but the vibration is not the sound; all we-can say is that a
law of causation relates the vibration to the sound. Now
there must always remain one law connecting the molecular
movements of bodies with the sensation of whiteness, and
another law connecting molecular movements with the sensa-
tion of sound.
In so far as all sensations are generalized into a common
fact of sensation, having similarity with diversity, so far may
we generalize the laws that connect sensation with corporeal
activities. This is a real and important step of generalization.
Yet it does not supersede the necessity of other laws for con-
necting special and irresolvable modes of sensation with their
special seats of corporeal activity. We may have a law of
pleasure and pain generally ; yet we need laws for the distinct
modes of pleasure and pain—the pleasures of light, of sound,
&c.—inasmuch as these cannot be resolved into each other.
The great generalities relating to Force all refer to one
sensibility of our nature—the muscular, or the active side ;
owing to which fact, they may admit of unity of law, or a
common statement. Likewise, there may be unity of law as”
regards Light and Colour, provided all the modes and varie-
ties are resolvable into the variation in degree of some funda-
mental mode of consciousness. If there be several fundamental
modes, there must be a law for each; thus there may be
wanted one law for white light, with its degrees, and one for
each of the primary colours—four laws for the sense of sight. _
We may be able to discover how Heat causes Light to the
extent of generalizing the molecular condition of luminosity,
and connecting this with the molecular condition of high
temperature ; but that such molecular condition and its ac-
companiments—radiation, refraction, &c. — should yield the
sensation of light, must always be expressed in a distinct law,
a law uniting an objective with a subjective experience. Such —
is the proper goal or end of our knowledge in regard to the
phenomenon, a
FALLACIOUS AND ILLUSORY EXPLANATIONS.
9. One form of illusory explanation is to repeat the fact —
in different language, assigning no other distinct yet" |
parallel fact.
This is ridiculed in Moliere’s physician, who gives as eh
reason why opium causes sleep, that it has a soporific virtue. —
i Re i ss ay
afd
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A
ILLUSION OF FAMILIARITY. 355
Not much is done to explain the greenness of the leaf of
lants by saying that it is due to a substance named ‘ chloro-
phyll.’ The only step gained is the fact (if it be a fact) that
greenness in all plants is due to the same substance.
A simile is sometimes offered for an explanation. Black’s
Latent Heat was merely a re-statement of the fact: he might
have gone on to call it secret, concealed, embodied, shut-up
Heat; all which expressions would merely iterate the circum-
stance that a certain amount of heat no longer appeared as
heat to the sense, or to the thermometer.
It is with the great ultimate generalizations, such as the
Uniformity of Nature, and the Axioms of Mathematics, that
we are most prone to give as a reason, or proof, a mere
various wording of the principle itself. ‘Why must the
future resemble the past?’ ‘Because Nature is Uniform.’
The phenomenon, sleep, was referred by Whewell to a
law of periodicity in the animal system. This, however, does
nothing but repeat the fact to be explained ; there is no
assimilation with another fact, so as to yield a higher gene-
rality, which would be inductive explanation, and no reference
to a higher generality already formed, which would be deduc-
tive explanation. A step towards real explanation is made by
comparing it with the repose or quiescence of the organs
after any activity whatsoever. This is to assimilate the
phenomenon with another distinct phenomenon ; the two taken
together form a higher generality, which, so far as it goes, is
an explanation.
10. Another illusion consists in regarding phenomena
as simple because they are familiar.
Very familiar facts seem to stand in no need of explanation
_ themselves, and to be the means of explaining whatever can
be assimilated to them.
Thus, the boiling and evaporation of a liquid is supposed to
be a very simple phenomenon requiring no explanation, and
a satisfactory medium of the explanation of rarer phenomena.
That water should dry up is, to the uninstructed mind, a thing
wholly intelligible; whereas, to the man acquainted with
Physical science, the liquid state is anomalous and inexplicable.
The lighting of a fire, by contact with a flame, is a great
scientific difficulty; yet few people think it so. A soap
bubble is a conflux of unexplained phenomena Voluntary
action, from familiarity, has long been reckoned so simple in
856 EXPLANATION OF NATURE.
itself as to have provided a satisfactory explanation of all
other modes of generating mechanical force.
11. The greatest fallacy of all is the supposition that
something is to be desired beyond the most generalized
conjunctions or sequences of phenomena.
It is supposed by many that the possession of a supreme
generality on any subject is insufficient; the mind, it is said,
craves for something deeper, and this "craving (which can
never be satisfied) is considered to be proper and legitimate.
The generalization of Gravity leaves behind it a sense of
mystery unsolved, as if there were something farther that we
might arrive at if obstacles did not intervene.
Newton seemed unable to acquiesce in gravity as an ulti-
mate fact. It was inconceivable to him that matter should §
act upon other matter at a distance, and he therefore desired
a medium of operation, whereby gravity might be assimilated _
to Impact. But this assimilation has hitherto been impracti-
cable ; if so, gravity is an ultimate fact, and its own sufficing
and final explanation.
The acceptance of the law of universal gravitation as a full
and final solution of the problem of falling bodies, without
hankering or reservation, is the proper scientific attitude of
mind, There seems ne hope at present of making it fraternize
with a second force, and there is no other legitimate outgoing
of enquiry with reference to it.
In the same way the niysteriousness often attributed to
Heat, is partly resolved by the Theory of Correlated Forces,
under which ‘heat is assimilated to movement. The subjec-
tive fact of heat—the sensation of the mind so described, is a
fact coming under the general relationship of body and mind.
Light is still a mystery in the legitimate sense; it has been
but imperfectly generalized as regards its physical workings.
Every isolated phenomenon ‘is, in the proper acceptation, a
mystery. 7
Apparent contradiction is something that demands to be
explained ; investigation should never stop short of the attain-
ment of consistency. Thus, the glacial period of the earth’s
history, is at variance with the only hypothesis yet framed as —
wy the solar agency—the slow but gradual cooling in the course
of ages,
The molecular aspect of the Correlated Forces is repulsion
(as in Heat), yet in Magnetism and in Friction Electricity, it
appears as attraction. —
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MYSTERY OF BODY AND MIND. 357
Free-will is often stated as a hopeless and insoluble contra-
diction. To leave any problem in such a condition is un-
scientific.
The union of Body and Mind has long been considered the
mystery by pre-eminence. The prevailing opinion has been
that this connexion would for ever resist and paralyze explana-
tion. Yet, the scientific mode of dealing with the case is
clear. The material properties and the mental properties are
each to be conceived according to their own nature—the one
by the senses, the other by self-consciousness. We then en-
deavour to assimilate and generalize to the utmost each class
of properties ; we generalize material properties into inertia,
gravity, molecular forces, &c.; we generalize mental proper-
ties into pleasures, pains, volitions, and modes of intelligence.
We next endeavour to rise to the most general laws of the
union of the two classes of properties in the human and animal
organization. When we succeed in carrying this generalizing
operation to the utmost length that the case appears to admit
of, we shall give a scientific explanation of the relationship of
body and mind. Any farther explanation is as incompetent,
as it is unnecessary and unmeaning.
Such language as the following is unscientific :—‘ Conscious
sensation is a fact, in the constitution of our corporeal and
and mental nature, which is absolutely incapable of explana-
tion.’ The only meaning attachable to this is, that bodily facts
and mental facts are fundamentally distinct, yet in close
alliance. So—‘To this day, we are utterly ignorant how
matter and mind operate upon each other.’ Properly speak-
ing there is nothing to be known but the fact, generalized to
the utmost.
‘Is there’ says Hume ‘any principle in all nature more
mysterious than the union of soul and body ; by which a
supposed spiritual substance acquires such influence over a
material one, that the most refined thought is able to actuate
the grossest matter P’ 3
Again, ‘we know nothing of the objects themselves which
compose the universe; our observation of external nature is
limited to the mutual action of material objects on one another.’
What is the good of talking of a supposable, and yet impos-
sible, knowledge ? *
* See Fznnizr’s Remains (vol. II. p. 436), for some pertinent remarks
on the nature of Explanation.
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CHAPTER XTIL
HYPOTHESES,
1. Various meanings belong to the word Hypothesis,
I. It means the suppositions, suggestions, or guesses, as
to any matter unknown, leading to ‘experimental or other
operations, for proof or disproof.
In the course of a research, many suppositions are made,
and rejected or admitted according to the evidence. Kepler
made an incredible number of guesses as to the planetary
relations before he discovered the actual laws. Davy sup-
posed the alkalies to be compounds before he established the
fact by decomposing them.
In the Inductive operation of arriving at general laws, the
supposition made is some law that appears likely to explain
the fact, as Kepler’s Third Law (of periodic times and mean dis-
tances). Such suggested laws have to be duly verified
according to the Experimental Methods.
In the properly Deductive operation of carrying out a law
by bringing cases under it, the supposition is an identity, as in
the examples already giver under the Deductive Method.
The hypothesis of a man’s being guilty of a certain crime is of
this nature; the proof consists in the tallying or fitting of the
circumstances of the accused with the circumstances of the
crime (commonly called ‘circumstantial evidence’). Of the
same nature is ‘the hypothesis of Wolfe with respect to the
origin of the Homeric poems; the hypothesis of Niebuhr,
with respect to the derivation of portions of the early Roman
history from ballads or epic poems ; the hypotheses of Hich-
horn, Marsh, and others, with respect to the origin of the text
of the four gospels; the hypothesis of Horace Walpole, with
respect to the character of Richard the Third, and various
hypotheses with respect to the Man in the Iron Mask. So
there are hypotheses, in literary history, as to the authorship
of certain works, as the Aristotelian Gconomics, the treatise
De Imitatione Christi, the Letters of Junius. In each of these -
cases a supposition is made, the truth of which is tried by
combining it with all the circumstances of the case.’ |
A HYPOTHESIS DEFINED. 309
These cases contain no matters for logical discussion. They
do not raise the questions that attach to the Undulatory Hypo-
thesis of Light, the Development Hypothesis, the Atomic
Theory, and other celebrated hypotheses.
2. The definition of a Hypothesis (according to Mill) is
@ supposition made (without evidence, or with insufficient
evidence of its own) in order to deduce conclusions in
agreement with real facts ; the agreement being the proof
of the hypothesis.
Hypothesis, in this sense, is a defective kind of proof; there
is some missing link; and the question is raised, how shall
this be made good in other ways.
For example, in the geological investigation concerning the
transport of erratic boulders, there are various possible suppo-
sitions—icebergs, glaciers, water currents. Now, we may be
unable to get what we should desire, in accordance with the
strict course of experimental elimination, namely, proof of the
actual presence and operation of one or other of these agents.
The only resource then, is to compare the appearances
with what would result from the several modes of action.
If these appearances are consistent with one mode only, there
is a certain strong presumption in favour of that one. The pre-
sumption would obviously amount to certainty, if we have
had before us (what we cannot always be sure of having) all
the possible or admissible agents.
In the absence of proof as to a man’s real motives, on a
given occasion, we often decide in favour of some one, because
the man’s conduct is exactly what that motive would dictate.
The soundness of the criterion depends upon there being no
other motive or combination of motives that would have the
same effects.
3. It is manifestly desirable, in assumptions relating to
natural agencies, that these should be known to exist. The
Hypothesis is then limited to such points as—their pre-
sence, their amount, and the law of their operation.
Such are the hypotheses as to the erratic boulders. So, we
may ascribe an epidemic to excessive heat, to moisture, to
electricity, to magnetism, to animalcules, to bad drainage, to
crowded dwellings, or to some combination of these. The
agencies ure real; every one of them is what Newton termed
a vera causa, What is hypothetical is the actual presence of
ie ;
“i= 5 71, te
360 HYPOTHESES.
one or other, the mode of operation, and the sufficiency to
produce the effect. If all these could be established in favour
of one, the point would be proved. If the presence cannot be
proved (the difficulty in past effects), there must be shown an
exclusive fitness in some one to account for the appearance. —
The illustrious example of Gravity may be quoted in its
bearing on Hypotheses. Newton’s suggestion was, that celes-
tial attraction is the same force as terrestrial gravity. He
thus proceeded upon a real or known cause ; the hypothetical
element was the extension of gravity to the sun and planets.
The preliminary difficulty to be got over was the rate of
decrease of the force according to distance. From Kepler’s
laws, it was proved that celestial attraction diminishes as the
square of the distance increases. Was this true of the earth’s
gravity ? The fall of the moon was the criterion, and exactl
coincided with that supposition, Thus, then, the law of the
sun’s attraction and the law of the earth’s attraction are the
same. The earth’s attraction extends to the moon; may it
not extend to the sun, and may not the sun reciprocate the
very same attraction P
The wonderful amount of tallying or coincidence in this
case was sufficient in the minds of all men to justify the
assumption that the two attractions are the same. The
hypothesis was proved by its consequences. And, as no rival
supposition has ever stood the same tests, the Newtonian
theory is considered as beyond the reach of challenge.
The rival hypothesis to gravity, in the explanation of the
celestial motions, was the Cartesian vortices, or whirlpools of
ether, which floated the planets round, as a chip revolves in
an eddy of a stream. |
The identity here assumed is between the circular motion
of the planets, in what is commonly supposed to be empty
space, and the circular motion of # whirlpool of water or of
air,
The first obvious disparity respects the fluid medium. In
the whirlpool of water we have a liquid mass with density
sufficient to buoy up wood, and mechanical momentum sufli-
cient to propel it in the direction of the stream. No such
fluid mass is known to be present in the celestial spaces; the
very supposition is hostile to all familiar appearances. A
fluid sufficient to move the planets at the rate they move in
would have numerons other consequences that could not
escape detection. It would mix with our atmosphere as an
active element and produce disturbances on the earth’s surface.
ee i el
et i
~
ASSUMPTION OF A NEW AGENT, 361
In this vital circumstance, therefore, the comparison fails ; the
assimilation is incompetent.
A second disparity was brought to light in Newton’s criti-
cism of the scheme. The laws of a whirlpool are not the laws
of the p!anetary orbits; a whirlpool is incompatible with the
laws of Kepler. Now, we cannot assimilate two mechanical
phenomena, two attractions, for example, unless they follow
‘the same law of force. This is a vital point in a mechanical
comparison. The following of the same dynamical law was
the crowning circumstance of the likeness between gravity and
solar force.
It would be said, therefore, that the Cartesian scheme did
not assign a vera causa. It assigned, no doubt, a mode of
action quite familiar to us; whirlpools are a real fact. But
it assumed a material substance unlike anything hitherto dis-
covered ; water we know, and air we know, but the entity
demanded for the vortices is eutirely foreign to all our experi-
ence of material things,
4. As it would seem irrational to affirm that we already
know all existing causes, permission must be given to
assume, if need be, an entirely new agent. ‘The conditions
of proof are, in this case, more stringent.
The chief example of this kind of Hypothesis is the
Undulatory Theory of Light.
The supposition of an etherial substance pervading all space,
and by its undulations propagating Light and Heat, as the air
propagates sound, is in accordance with many of the facts of
Light, more especially what is called the Interference of Light,
a generalization of many distinct appearances. The hypothesis
also served to discover new facts of luminous agency.
Assuming what is not strictly accurate as yet, that the
undulatory hypothesis accounts for all the facts, we are called
on to decide whether the existence of an undulating ether is
ehereby proved.
We cannot positively affirm that no other supposition will
explain the facts ; what we can say is, that of all the hypotheses
hitherto suggested, this approaches the nearest to an exact
explanation. Newton's corpuscular hypothesis is admitted to
have broken down on Interference ; and there is at the present
day, no rival.
Still, it is extremely desirable in all such hypotheses, to find
' some collateral confirmation, some evidence aliwnde, of the
supposed ether. This is supplied in part by the observations
362 HYPOTHESES.
on the comet of Encke. If the retardation of that comet, and
other observations of a like nature, establish the fact of a
resisting or inert medium, there will remain, as hypothetical,
the properties of that medium, namely, the peculiar mode of
elasticity fitted for transmitting luminous and other emana-
tions.
There is farther to be urged, in support of the hypothesis,
its constancy with the other hypothesis that regards Radiant
Heat and Light as the propagation of molecular movements
from hot and luminous bodies. The transmission of these
influences through space, by the communication of molecular
impulse, is in harmony with their character as motions in the
molecules of the masses of ordinary matter.
An additional confirmation is supplied in the remarkable
fact that bodies, when cold, absorb the same rays (of the solar
spectrum) that they give out when hot. This is precisely
analogous to the law of musical strings, namely, that, of the
notes sounded by another instrument in their neighbourhood,
they assume each its own note.
5. Some Hypotheses consist of assumptions as to the
minute structure and operations of bodies. From the
nature of the case, these assumptions can never be proved
by direct means. Their only merit is their suitability to
express the phenomena. They are Representative Fictions.
All assertions as to the ultimate structure of the particles of
matter are, and ever must be, hypothetical. Yet we must not
discard them because they cannot be proved; the proper cri-
terion for judging of their value is their aptness to represent
the phenomena. That Heat consists of motions of the atoms
can never be directly shown; but if the supposition is in con-
sistency with all the appearances, and if it helps us to connect
the appearances together in a general statement, it serves
an important intellectual function.
The phenomena of the solid, liquid, and gaseous state of
matter can be represented by the opposing play of two sets of
forces—the attraction of cohesion inherent in the atoms of
each substance, and the repulsive energy generated by the
heat motions. Incrystals, the heat motions are at a minimum, —
and in that case, the cohesion assumes a polar character, or 1s —
concentrated at particular points, whose difference of relative
situation makes difference of crystalline form. ;
The Undulatory hypothesis of Light, even although it may —
never be fully established as fact, will have a permanent yalue
[are er, ct
ae oy
REPRESENTATIVE FICTIONS. 363
as a Representative summary of the facts of Light; and may
be gradually carried to perfection in this character.
In a paper by Graham, on the ‘ Molecular Mobility of Gases,’
published in the Transactions of the Royal Society, 1863,
there is put forward a hypothesis of the Constitution of
Matter. The assumptions are these :—
(1) The various kinds of matter may consist of one species
of Atom or molecule, having a different kind of movement in
each substance. This is in harmony with the equal action of
gravity upon all bodies.
(2) The greater the energy or swing of the primordial and
inalienable movements of the ultimate atoms, the lighter the
mass. The leading fact named Density or specific gravity is
represented by this assumption.
(3) These ultimate molecules, whose primitive movement
gives specific gravity, are supposed to be made up in groups,
each group having a farther movement, vibratory or other;
which second superinduced movement represents the gaseous
molecule affected by Heat, and leading to gaseous expansion.
This Graham also calls the diffusive molecule.
(4) Equal volumes of two forms of gaseous matter, irre-
spective of weight, have a facility of combining ; this is
Chemical Combination. It is a hypothetical expression of the
law connecting Atomic Weight with Gaseous Volume. The
gaseous state is expressed by Graham as the typical state of
matter; ‘the gas exhibits only a few grand and simple fea-
tures.’
The special point of the hypothesis consists in assuming
motions within motions, like primary and secondary planets,
There is no limit to the successive groupings and their charac-
teristic movements. For still more complex properties, new
groupings may be assumed.
A somewhat different hypotkesis of Molecular Motions has
been given by Mr. Clark Maxwell (Phil. Trans. 1866). It
might be superadded to Graham’s.
_ Under the methods of Cnemisrry, we shall advert to the
hypothesis named The Atomic Theory ; and under the methods
of Bionoey, there will «ccur other examples of celebrated
hypotheses. Also, in the Logic of Mepicinz, the representa-
tive conceptions are brought under review.
The political ficiion as to a Social Contract, determining
the rights of sover:ignty, is not entitled to the dignity of a
Hypothesis. It isa pure fabrication to serve a political, or
364 HYPOTHESES.
even a party purpose; and ranks with the loge in the ee
ancient Grecian states, relied on as giving validity to the
title of a tribe to its territory, or of a family to the ens
power.
6. It has been said (by Dugald Stewart and otbarts
that the reasonings of Geometry are built upon hypotheses,
The meaning is, that the figures assumed are abstractions,
or ideals, and do not correspond to any real things.
The word ‘hypothesis,’ is here employed in a somewhat
peculiar sense. It is identical in meaning with ‘ Abstract,’ as
opposed to actual or. ‘Concrete’ objects. The important
truth intended to be conveyed would probably be given much
better by avoiding the use of ‘ hypothesis.’
In Geometry, as in all Abstract Reasoning, the essence of
the operation is to view the things in one exclusive aspect, or
with reference to one single property, although, in point of
fact, no object exists possessing that property in pure isola-
tion. The geometrical Point is a mark of position; we reason
upon it solely as marking position. Every real point, and
even the point that we conceive in the mind, possesses at the
same time a certain magnitude, a certain colour, and certain
material substance. We, however, make abstraction of all —
these features; we do not assume them in any degree ; we
drop them entirely out of view; we consider ‘position,’ m
so far as ‘ position,’ and make ‘affirmations on that” special
assumption. When we come to deal practically with an
actual point, we must re-admit all these properties belonging
to it in its concreteness; we must allow for the fact that no —
actual point can determine an abstract position ; it covers an i
area, and therefore does not fix position except by an approxi- -
mation. ‘2
In Mechanics, there are convenient fictions that subserve
the abstract reasonings of the sciences; as, for example, the
supposition that the whole mass of an irregular body is con-
densed into its Centre of Gravity—an operation impossible in
fact, but having a practical convenience in mechanical demon- —
strations. It is desirable, for certain purposes, that we should | a
make abstraction of the form and size of a mass, and view ;
only its weight and its relative position to some other mass ;
and one way of compassing the end is to imagine the form and fi
the size non-existent, or that the mass exists in a m
matical point. We say there is a certain definite position ix
the Pe OF of the earth, wherein, if the whole mass vee
are
EXPERIMENTUM CRUCIS. 365
concentrated, the earth’s attraction for the sun and the moon
would be the same as it actually is. This is merely a verbal
aid to the process of reasoning in the Abstract. The remark
is applicable to all the other abstract centres—oscillation,
Suspension, gyration, de.
7. A fact that decides between two opposing Hypotheses
was called by Bacon an experimentum crucis.
The ‘Instantia Crucis’ of Bacon does not properly belong
to the Experimental Methods of Induction. It is the decisive
instance between two contending hypotheses. Thus, when
the Copernican system was brought forward in opposition to
the Ptolemaic, not only was there a necessity for showing that
the new system corresponded with all the facts; there was
farther required the production of some facts that it alone
could conciliate. The first fact of this decisive character was
the Aberration of Light, a fact incompatible with the earth’s
being at rest. Another fact, equally decisive, is furnished by
the recent pendulum experiments of Foucault with regard to
the motion of the earth. Bacon himself, who never fully
accepted the Copernican system, desiderated an ‘ experimen-
tum crucis’ of this nature, namely, a fact to show that the
velocities of bodies appearing to move round the earth are
ir proportion to their distance; which, he says, would be a
proof that the earth stands still, and that the apparent daily
motion of the stars is real.
The entire absence of mechanical energy in the rays of
light is regarded as decisive against Newton’s Emission
Hypothesis. The most delicate experiments fail to show any
moving energy in the concentrated rays of the sun; which
failure is inconsistent with a stream of particles of inert matter.
CHAPTER XIV.
APPROXIMATE GENERALIZATIONS AND PROBABLE
EVIDENCE.
1. Probable Inference is inference from a proposition
only approximately true.
Every certain inference supposes that the major is a pro-
position universally true, as ‘all men are mortal,’ ‘all matter
366 APPROXIMATE GENERALIZATIONS.
gravitates.’ When a minor is supplied to such propositions, a Ss
the conclusion is certainly true. 3 he
From a proposition true only in the majority of instances, __
the inference drawn is not certain, but only probable. ‘Most
(not all) phenogamous plants have green leaves; hence itis _—
probable that any given class of these plants has green leaves.
The word for such generalities is ‘most;’ the synonyms are
‘many,’ ‘usually,’ ‘commonly,’ ‘ generally,’ ‘ for the most —
part,’ ‘in the majority of instances.’
2. If we know the exact proportion of cases in an ap-
proximate generalization, we can state numerically the
degree of probability of an inference drawn from it.
It being known that a certain thing happens in nine in-
stances out of ten, the probability, in a particular case, is nine
to one, or nine-tenths. All the metals, except copper and
gold, are devoid of colour, (being either white or some shade
of grey). The probability that a new metal is white or grey
is as fifty-two to two. |
On the supposition that the majority of drunkards are never ~
reformed, the probability is against the reform of any indivi-
dual drunkard. The strength of the probability depends upon
our estimate of the comparative numbers. If this estimate is
vague and uncertain,—if we cannot say whether the reformed
drunkards number one fiftieth, one twentieth, or one-fourth of
the whole,—our estimate of the probability in the given in-
stance is correspondingly vague. ohh
What Hobbes says of Charles 1I— 59
Nam tunc adolescens :
Credidit ille, quibus credidit ante Pater—
is true of the vast majority of men even in the most enlightened _
countries. Hence a strong probability that any given indi- —
vidual has never exercised any independent judgment in —
politics or in religion. A hundred to one is a safe estimate of
such a probability. ; -
It is an approximate generalization that both intelligence
and independent thought are most frequent in the middle —
ranks of society. The generalization has in its favour deduc-
tive as well as inductive evidence. We know the circum-—
stances adverse to those qualities in the highest, and also in
the lowest, ranks. Still, it is but approximate, and yields
only probability in every given application. Like all proba-
bilities, however, if applied to masses, it gives certainty, The
PROBABLE INFERENCES. 367
collective action of a middle class body would be more intelli-
gent and independent than the action of the other classes,
The proposition is approximately true that the wealthy are
more yirtuous than the indigent. There are numerous excep-
tions, but the evidence is sufficient to prove the rule as an
approximate generalization. The only dispute is as to the
extent of it. Direct statistics on the great scale are wanting;
and the deductive argument consists in comparing the tend-
encies for and against virtue in the wealthy, as compared
with the poorer class—a comparison where, from the vague
nature of all estimates of human conduct, a certain latitude of
expression must be allowed.
The characters of men are described by such general terms
as energetic, timid, tender-hearted, irascible, truthful, intel-
Jectual, and so on. Even when most carefully generalized,
these characters are only approximate; they represent prevail.
ing tendencies, liable to be defeated in the complicacy of
human motives, So with classes, professions, and nations.
All the current generalities respecting the characteristics of
sex and of age are mere approximations. Literary and Art
criticism, as expressing the style and manner of authors or
artists, is of a like nature.
The operation of laws and institutions is at best but
approximate. We cannot affirm that the general good con-
sequences follow in every instance. The tendency of severe
punishments is to deter from crime; they may do so in nine
cases out of ten, or ninety-nine out ofa hundred. It is the
duty of the state to seek out the mode that approximates
most to the desired end. In such a case, statistics give a kind
of numerical precision to the general tendency, and a corres-
ponding exactness to the inference of probability.
The very best institutions have to be defended on the
ground of superior good, not of absolute or unexceptional
good. This is all that can be said for liberty as against re-
straints, for responsible government as agaihst despotism.
Proverbial sayings are for the most part but rude approxi-
mations to truth. Many of them can hardly be said to have
a preponderance of cases on their side. ‘The more haste, the
less speed’ is not true in the majority of instances; its merit
is chiefly as an epigrammatic denial of the universality of the
rule that activity succeeds in its object. We often take delight
in parading the exceptions to approximate generalities ; and
not a few of our proverbs are occupied with the representation
of minorities. Tallyrand’s ‘No zeal’ is incorrect as a rule ;
368 APPROXIMATE GENERALIZATIONS.
the rule that it crosses, however, is but approximate, and has
exceptions ; the point of the saying lies in suggesting these.
3. It is a legitimate effort to endeavour to make the
approximation of a rule as close as possible, before apply-
ing it to cases. This can be done in various ways.
(1) An approximate generalization is rendered absolutely
certain in its scope, when all the exceptions can be enumer-
ated; as in grammar rules, and in Acts of Parliament contain-
ing schedules of exceptions.
(2) A very near approximation can be made if we know the
exact occasions and circumstances where the rule holds. Thus
that ‘Honesty is the best policy’ is in the abstract only a
rough generalization ; it is far from the exact truth. But we
are able to assign the specific circumstances where it holds
good more nearly. The ‘honesty’ should exactly correspond
to the standard of the time, not rising above, and not falling
below the established code. It should be apparent and not
concealed from view. It should contribute something to the
advantage of persons of weight and influence. Thus limited
and qualified, the approximation is very near the truth; yet
not altogether true. The dishonest successful men are still
sufficiently numerous to constitute a standing exception to the
maxim.
The Proposition ‘ Knowledge is virtue ’ was maintained in
the Socratic school. It is an appproximate generalization,
giving a certain small probability in its applications. That it
has the truth on its side is proved by the statistics of crime ;
the majority of criminals coming from the least instructed
part of the population. Still, the exceptions are numerous.
We know from deductive considerations that virtue does not
spring directly from the knowing faculties ; the filiation is in-
direct or circuitous. The best application of so slight a pro-
bability is to take it with concurring probabilities. The
conditions of a virtuous character can be stated with consider-
able precision, while intellectual culture also is an element
whose value can be assigned. Hence, in applying the rule to
a known case, we can infer with a far higher probability, than
could be given by any one approximate generality, as to the
virtuous tendencies of knowledge, of parentage, of occupation,
and other circumstances. We can unite all the presumptions
into one still stronger. 7
It is a usual defect of empirical generalities that the sub-
ject of them is badly defined, or that the circumstances where
mee
INCREASED APPROXIMATIONS. 369
the predicate holds cannot be exactly specified. This is a
common defect in the practice of medicine. A drug has a
certain efficacy in the majority of instances, and is therefore
only probable in its consequences. A higher knowledge
would give the exact conditions wherein it succeeds, which
would be to convert the approximation into certainty.
Soin Politics. Certain institutions, as for example Tree
Government, are good for nations generally. In some cases,
they fail. It is for political science to specify accurately the
circumstances where they are suitable, and those where they
are unsuitable ; by which means we may attain to rules of a
certain, or nearly certain character.
It is commonly said that being educated at a public school
developes particular manly virtues, as self-reliance, courage,
&c. This is but an approximate generalization. If we had
the comparative numbers of the successes and the failures, we
could assign the probability in a given instance, Still better,
however, would be the enquiry, what are the circumstances
wherein the effect would arise ; what kind of youths would be
operated on in the salutary way ?
It is an approximate generalization that absolute sovereigns
abuse their power ; it is true, in a large majority of instances,
but not in all instances. It can be converted into a still closer
approximation, if we can assign the particular situation of an
_ individual sovereign—the motives operating upon him person-
ally, either as encouraging or as checking the despotic vices.
Hence, by a series of provisos (as Mr. Mill remarks) we may
render an approximate rule, an almost certain rule :—An
absolute monarch will abuse his power, wnless his position
makes him dependent on the good opinion of his subjects, or
unless he is a person of unusual rectitude and resolution, or
unless he throws himself into the hands of a minister posses-
sing these qualities.’
4, Approximate generalizations give an opening to the
bias of the feelings, and to the arts of a sophistical reasoner.
It is impossible to deal fairly with an approximate genera-
lization, except by forming some estimate, the best that can
be had, of the instances on one side and on the other. This
is often difficult even to the most candid and painstaking
irnth-seeker. Nothing then is easier than to turn away the
mind from a part of the instances, and to decide upon the
remainder. Any strong feeling has this blinding efficacy.
For example, our Patent Law has raised a certain number of
370 ANALOGY.
persons to wealth; it has stimulated a certain number to.
inventions, whether profitable or not to the inventors; it has
induced a certain number to waste their lives in unproductive
and hopeless enterprises : it has obstructed, in certain instances,
the introduction of improvements. Whether the law has
been good or evil on the whole, depends upon the relative
number of these various instances. Now, it would be most ©
difficult to attain an exact comparative estimate in such a ques-
tion. How easy then for any one to incline to the instances
favouring a preconceived theory, and to pay no heed to the rest ?
The arts of the pleader suit themselves to this situation.
By dwelling upon and magnifying the instances in one side,
by ignoring and explaining away those in the other, a skilled
advocate reverses the state of the numbers in the approximate
generalization, making the minority seem the majority. The
reply needs to be conducted so as to redress the distorted
estimate. (For the practical applications of Probability to
Testimony and other Evidence, see Apprnpix I.). ?
CHAPTER XV.
ANALOGY.
1. The foundation and justification of all inference is
Similarity. The similarity may exist in various forms
and degrees, and the validity of, the inferences will be
modified accordingly.
When two situations are exactly the same, the uniformity
of nature leads to the same consequences. Place equal weights
in a balance so as to make an exact equipoise. Shift the —
centre of motion to one end, and that end will rise and the —
other fall, every time that the change is made. A great deal —
of variety may be introduced into the experiment, with the
same result. The rod may vary in length, and in material,
and the weights may be small or great: so that we may have —
sameness in the result without sameness of the antecedents, _
Again, having seen a great many animals die, we infer that —
other animals living and to be born will die: the resemblance, —
together with nature’s uniformity, being the justification,
But there are often wide disparities between the instances
observed and the instances inferred, Mads
i
INDUCTION IN DIFFERENCE OF SUBJECT, STi
It was, however, the object of the experimental methods to
eliminate the essential parts of a causal situation from the
non-essential parts. In the midst of all the various forms of
the experiment with the balance, we find, by the use of the
methods, that the one circumstance that disturbs the equipoise
is to remove the point of suspension from its central position
in the beam ; that the size and material of the beam, the size
and material of the weights, are unessential cireumstances. So
with animal life ; the fact called organized life is the fact ac-
companied with mortality; the forms and sizes of animals,
their being vertebrate or invertebrate, are inductively elimin-
ated as unessential.
An inductive inference is thus an inference from sameness in
certain particulars, shown by induction to be the particulars
always present when some consequence or collateral is pre-
sent. This is an inference by identity, a perfect induction.
2. ‘There may be a radical difference in the subjects of
two compared phenomena with ut preventing a strict In-
ductive inference. ‘The sole condition is that the same-
ness apply to the attribute found by induction to bear the
consequence assigned.
To say ‘there is a tide in the affairs of men’ is to use a
mere metaphor, the subjects compared being totally distinct.
Now, to reason from one subject to another of a different kind,
might be called reasoning by Analogy; yet, the inference
might be such as to deserve the name of induction. Great
as is the difference between the march of human history, and
the flow of the tides, still, if the two phenomena exactly re-
sembled in the single feature of ebbing and flowing, and if no
inference were drawn, except what this feature involved, the
_ argument would be a sound and strict induction. If human
affairs in any way are truly describable as ebbing and flowing,
we are entitled from one movement to predict the following.
If periods of great public excitement in special topics as
Liberty, Religion, aggressive War, are followed by periods of
apathy, there is a species of tidal movement, and the laws of
the tides may so far be applied to the case, by a legitimate
induction, or else by a deduction founded on an induction.
The Chinese profess to found their government on the
paternal principle, and to justify their peculiar form of despot-
ism on the similarity of the state to a family. The argument
is not inductive; there is a failure in essential points. It is @
crude metaphor. There is a certain important similarity,
372 ANALOGY.
namely, the fact of government, involving authority, superior-
ity, and punishment; and any inferences drawn upon this
single circumstance would be valid. Certain of the merits
and of the demerits of government are identical in both
instances; the graduation of punishment to offence, consist-
ency and fairness on the part of the ruler to the ruled, are
equally required in the family and in the state. But it is not
an inductive inference to say that because the parent is
despotical, so should the state. The two cases do not agree
in the point whence the despotical relation flows; in the
family, the subjects of government are children; in the state,
the subjects are grown men, on a level with the rulers. The
inference would require the case of a very ignorant and
degraded community ruled by a wise and high-minded caste.
To whatever degree a nation approximates to this state of
things, there is an identity between it and the family relation-
ship.
Plato’s comparison of the state to an individual man is not
an analogy in the proper sense of the term. It is one of those
figurative resemblances where the points of agreement and of
disagreement are perfectly ascertainable, and where there 1s
noelement unknown. Any one can tell whether the inferences
drawn from’ the comparison follow from the points of agree-
ment. That there should be a three-fold classification of
citizens in the state, cannot be inferred or confirmed by an
analysis of the mind into three leading functions. The con-
stitution of a state has nothing in common with the divisions
of the mental powers of an individual man. .
The same remark is applicable to another fayourite com-
parison of Plato’s—virtue to health. The resemblance is
exceedingly slight; yet, if nothing were inferred but what
grew out of that resemblance, we could not object to the use
of the comparison. But Plato’s theory of punishment derived.
from it supposes. a likeness that does not hold; and the heen
is refuted by exposing the dissimilarity.
- The Ancient Philosophy was full of these misapplied com-
parisons, improperly termed analogies.
Speaking with reference to the early growth of Law, Mr.
Mayne observes: — ‘ Analogy, the most valuable of instru-
ments in the maturity of jurisprudence, is the most dangerous:
of snares in its infancy. Prohibitions and ordinances, ori-
ginally confined, for good reasons, to a single description of
acts, are made to apply to all acts of the same class, because
a man menaced with the anger of the gods for doing one
~
*
J
3
77
PROPER MEANING OF ANALOGY. 373
thing, feels a natural terror in doing any other thing remotely
connected withit. After one kind of food has been interdicted
for sanitary reasons, the prohibition is extended to all food
resembling it, though the resemblance occasionally depends on
analogies the most fanciful. So, again, a wise provision for
insuring general cleanliness dictates in time long routines of
ceremonial ablution ; and that division into classes which ata
particular crisis of social history is necessary for the main-
tenance of national existence degenerates into tle most disas-
trous and blighting of all human institutions—Caste.’
Analogy has been often defined ‘resemblance in relations :’
as when a wave of water is said to be analogous to an undu-
lation of air, or of ether; or a magnet is compared to a
charged Leyden jar because of the common polar condition.
This definition is objectionable chiefly on the ground of
vagueness. The word ‘relation’ is too general for a precise’
statement of the case. What truth or fitness there is in the
expression can be given in other ways.
3 Analogy, as different from Induction, and as a dis-
tinct form of inference, supposes that two things from
resembling in a number of points, may resemble in some
other point, which other point is not known to be con-
nected with the agreeing points by a law of causation or
of co-existence.
If two substances agree in seven leading properties, and
differ in three, the probability of their agreeing in some
eleventh property (not known to be connected with any of the
ten) is, with reference to the known properties, seven to three.
But this rule would be modified by the consideration of the
number of properties still remaining to be discovered, a cir-
cumstance necessarily indefinite. If we had reason to suppose
that a large number of properties still remained undiscovered,
the probability could not be stated with the same fixity or
confidence.
4. An argument from Analogy is only Probable. The
probability is measured by comparing the number (and
importance) of the points of agreement with the number
and importance of the points of difference ; having respect
also to the extent of the unknown properties as compared
with the known.
No Analogy can amount to full proof; very few give even
a high probability. ‘It may afford,’ says Reid, ‘a greater or
374. ANALOGY.
less degree of probability according as the things compared
are more or less similar in their nature; but it can afford
only probable evidence at the best.’
The natural Kinds afford the best examples of the typical
case of Analogy. They have numerous properties, known
and unknown; extensive agreements prevail among groups
of them, together with differences’ more or less numerous.
Thus, sodium and potassium have numerous points of agree-
ment, and a few points of difference. There would, theretore,
be a certain amount of probability that any effect due to
sodium, or a given compound of sodium, might arise from
potassium, or the same compound of potassium. |
The celebrated guess of Newton, as to the Diamond, which
was afterwards verified by experiment, was not an analogical
inference in the strict sense. Had the inference been from, a
single body, as an oil, to the diamond (the point of agreement
between them being unusual refracting power), the resem-
blance would have been too limited even fora gaess. The
application to the Diamond was the carrying out of an
Empirical Law, partially, if not wholly proved. The circum-
stance that arrested Newton’s attention was that the refracting
power of bodies is very nearly as their densities excepting that
unctuous and sulphureous bodies refract more than others of the
same density. Having obtained measures of the refractive
powers of the densities of twenty-two substances, varying in
density between air and diamond, he found that they fell into
two classes. In one class, were topaz, selenite, rock-crystal,
Iceland-spar, conmon glass, glass of antimony, common air: in
all which, the refracting powers are almost exactly as the
densities, excepting that the refraction of Iceland-spar is a
little more than the proportion. In the second class were :
camphor, olive oil, linseed oil, spirit of turpentine, amber, which
are, ‘he said,’ ‘ fat, sulphureous, unctuous bodies,’ and diamond
which ‘ probably is an unctuous substance coagulated ;’ all
these, compared together, have their refractive powers almost
exactly proportioned to their densities. But now, when the
two classes are compared, the refractive powers of the second
class (the unctuous substances) are twice or thrice as great,
in proportion to their densities, as the refractive powers of the
first class. Water has a middle position between the two
classes ; salts of vitriol may stand between the earthy sub.
stances and water ; and spirit of wine between water and the
oils. The suggestion as to the diamond thus arose from its
position among a number of highly refracting bodies that
~~ = ia
EXAMPLES OF ANALOGY. 375
in being of an inflammable or combustible nature.
The concurrence of high refracting power with inflammability
was an empirical law ; and Newton perceiving the law,
extended it to the adjacent case of the diamond. ‘I'he remark
is made by Brewster that had Newton known the refractive
powers of the minerals greenockite and octohedrite, he would
have extended the inference to them, and would have been
mistaken.
As an example of Analogy proper let us suppose the Balsam
of Peru to possess certain properties, medicinal or other.
Suppose next, that the balsam of Tolu agrees in a great number
of these, but differs in one or two important or unimportant
properties. On this proposition, we should ground a very
considerable presumption, that the one might replace the other
in new and untried applications in Pharmacy.
The illustration might be extended to Vegetable and to
Animal species. A quadruped resembles a human being in.
very many points of structure and function, but also differs
in a considerable number; while there may be undiscovered
properties in both. This reduces to a weak probability
all inferences from one to the other as to the suitable kinds of
food, liability to disease, or medical treatment. Hxperiments
on animals may cast light on the human subject, provided we
know that the particular organs are constructed nearly alike
in both, as in the connexions of the nerves, the breathing, the
digestion, &c. The function of the saliva and of the gastric
juice has been studied by experiments on dogs and on horses.
In a recent set of experiments on the action of mercury, dogs
were operated on; care having been first taken to ascertain
that they agree with human beings in the mercurial symptom
of salivation.
It is interesting to determine whether our inference from
man to the lower animals as to the possession of conscious-
ness, is an induction or only an analogy. We believe that, in
human beings, consciousness is always associated with certain
external manifestations, called the signs of feeling, and with
an internal structure of brain, senses, and muscular organs.
This we hold to be an inductive uniformity completely estab-
lished as regards human beings. The induction extends to
differences of degree; with fewer and feebler manifestations,
and a smaller brain than usual, we couple a feebler degree of
the mental functions. Now, the physical part is found in the
brutes ; some approximating more, and some less, closely to
the human type. It would seem, therefore, that by induction,
17 ;
376 ANALOGY.
and not by analogy, we are to infer the existence of conscious
ness in the animals, with modifications of degree only.
Mind and Body are of opposite nature ; they are the greatest
of all contrasts. Yet there are points of analogy that have
been made use of to furnish language and illustration from
the one to the other. As in material phenomena, we may
have a plurality of forces conspiring or opposing each other,
the resultant being arithmetically computable, soin mind we
have motives uniting or opposing their strength, the effect
being computable (although not with numerical exactness) by
adding together those on each side, and noting which is the
larger amount. Reid has objected to this comparison, re-
marking that ‘the analogy between a balance and a man
deliberating, though one of the strongest that can be found
between matter and mind, is too weak to support any argu-
ment.’ Yet, if the analogy is trusted only to the extent of the
similarity, there is no good objection to making an inference
from it. Now, the similarity is complete as far as regards the
cumulative effect of concurring motives, and the neutralizing
or frustrating effect of opposing motives. Whatever power a
given motive adds to a man’s volition when it concurs, it
must subtract or withdraw when it opposes.
The intrusion, by Aristotle and by Kant, of phraseology
derived from the intellect, into the domain of the feelings and
the will, may be pronounced an improper identification, or an
abuse of analogy. Aristotle’s syllogism of the Will, and
Kant’s categorical Imperative, point to no real resemblance ;
a syllogism expresses an argument conducted by the reason-
ing faculty ;' it has no relevance or suitability to express the
decisions of the will.
Reflex Actions may be profitably compared with Voluntary
Actions, if we confine ourselves to the points of similarity.
The Reflex is the voluntary with consciousness suppressed or
made unessential ; on the corporeal side, there is a considgr-
able amount of resemblance, or still better, a gradation or —
continuity. 2.
Until recently, the sun was considered to be only analogi- 4
cally compared to terrestrial fires. The points of agreement,
in giving forth radiant heat with light, are of the most essential —
kind; but there was supposed to be a disparity also vital. It
was conceived that the sun gave forth its vast flood. of
radiance, with no diminution of intensity. Now, every hot
body on the earth cools by radiation. Until this serious dis-
parity was got over, scientific men felt that all inferences from
ANALOGICAL HYPOTHESES. OTe
terrestrial bodies to the composition of the sun were rash and
unauthorized.
Much speculation has been expended on the question—Are
the planets inhabited? The argumentis at best analogical ;
and there is not even the force of analogy except with refer-
ence to a small number. Bodies, like the moon, possessing no
water and no atmosphere, must be dismissed at once, The
planets generally appear to possess atmospheres.
We seem justified, however, in making a summary exclusion
of the near and the remote planets, on the ground of temperature.
All organized life known to us, is possible only within narrow
limits of temperature ; no animal or plant can exist either in
freezing water or in boiling water. Now, the temperature of
Mercury must in all likelihood be above the boiling point,
even at the poles, and the temperature of Uranus, and of
Saturn, below freezing at the equator. The constituent ele-
ments being now shown to be the same throughout the solar
system—Carbon, Oxygen, Hydrogen, &c., we are not to pre-
sume any such departure from our own type of organized life as
would be implied by animals and plants subsisting in these
extremes of temperature. On the supposition that the sun’s
temperature has steadily decreased, and is still decreasing, by
radiation, the day of living beings is past for Uranus and
Saturn, and perhaps for Jupiter; it is not begun for Mercury.
Confining ourselves, therefore, to the neighbouring planets,
and referring to the others only for the periods, past or future,
when the capital circumstance of temperature is suitable, we
have an analogical argument as follows. Venus and Mars are
gravitating masses like the earth, containing, we may now say
with certainty, the same materials as this globe—solid, liquid,
and gaseous. But we cannot tell the precise arrangement of
the constituent substances ; and, seeing that with ourselves so
much depends upon the mere collocation and amount of such
elements as oxygen and carbon, we may consider that the un-
known properties of the supposed planets are considerable in
number, and serious in character. The probability arising out
of the points of agreement, if not greatly affected by known dif-
ferences, is reduced by this large element of the unknown.
Many Hypotheses are of the nature of analogies or compari-
sons, the degree and value of the resemblance being more or
less uncertain, Thus, to refer to the undulatory hypothesis
of Light. When Newton explained the waves of water, and the
vibrations of the air in sound, by the:oscillations of a pendu-
lum, he was assimilating phenomena of the same mechanical
378 CREDIBILITY AND INCREDIBILITY.
character, and reasoning only from the points of similarity.
But when we reason from the sonorous vibrations of the air
to the vibrations of an ether assumed as occupying space, and
conveying light and heat, we work by analogy. It would,
therefore, not be irrelevant to apply the rule of analogy, and
estimate the points of agreement, as compared with the points
of disagreement, and conclude accordingly. On this view,
the hypothesis would have but a small intrinsic probability ;
it would be left in a great measure dependent on the kind of
evidence already quoted in its favour, the tallying with the
special facts of the operation of light.
The first attempt to penetrate the mystery of nervous action
was Hartley’s hypothesis of vibratory propagation, based on
the analogy of sound. The comparison was crude and un-
satisfactory ; but there was a certain amount of likeness, and
the inferences founded on that were admissible. It realized
the fact of influence conveyed inwards from the nerves to the
brain, and outwards from the brain to the muscles, thus
suggesting a circle of action, which circumstance alone is
pregnant with valuable conclusions, as appeared after the
discovery of Bell gave new vigour to the conception. The
vibratory mode of communication had no relevance, and any
conclusions drawn from it were unsound. Next came the
analogy to the electric current, which was much-closer to the
facts, more fertile in suggestions, and less charged with mis-
leading circumstances. By taking liberties with current
action, something like the liberties taken with the etber in
adapting it for light, we are able to shape a view of nerve
force that fits the actual phenomena with remarkable close-
ness. A third mode of representing the action has been
advanced by Mr. Herbert Spencer, which departs from electri-
cal and chemical action and reposes upon the physical property
called allotropisin.
CHAPTER XVL
CREDIBILITY AND INCREDIBILITY.
1. There are propositions supported by a certain amount
of evidence, that are nevertheless disbelieved. From some
en i 2s Pee
CONSISTENCY WITH ESTABLISHED INDUCTIONS. 379
circumstance connected with them, they are pronounced
INCREDIBLE.
Irrespective of the evidence specifically adduced in favour
of a certain fact, we often pronounce it credible or incredible ;
in the one case we believe, and in the other disbelieve, under
the same amount of positive testimony. We believe, ona
slight report, that a fishing boat foundered in a heavy gale ;
we do not believe, without much stronger testimony, that a
fully equipped man-of-war was wrecked. It was lately
rumoured that the Eddystone lighthouse was blown down;
every one felt that the rumour required confirmation.
2. The circumstance that renders a fact Credible or
Incredible is its being consistent or inconsistent with
well-established inductions.
In simple cases, this is apparent. That a child initiated in
crime by its parents should become a criminal, is credible, be-
cause it is highly probable, being the result of a well-grounded
induction of the human mind. That sucha child should turn
out a paragon of virtue, as is sometimes described in romance,
we pronounce improbable and therefore incredible. In the
one case we are satisfied with a small amount of testimony,
in the other case, we demand very strong evidence.
We are thus often led to reject evidence at once on the
score of antecedent improbability. We may be in the posi-
tion of refusing a large amount of positive evidence ; as when
a number of respectable witnesses testify that a man after
being immersed in the water for an hour has been resuscitated.
It is to be remarked, however, that in all such cases the evi-
dence tendered is only probable ; it may have a very high
degree of probability, it may be 500 to 1, yet it does not
amount to certainty. It fails once in five-hundred-and-one
times, and is therefore, in certain circumstances, not safe from
rejection.
3. Such well-established scientific inductions, as the
Law of Gravity and the Law of Causation, render wholly in-
credible any assertion that contradicts them.
That Mahomet’s coffin hung suspended in middle air, that
a table of its own accord mounted to the ceiling of a room,
are facts to be wholly disbelieved.
All the alleged discoveries of a perpetual motion, or the
rise of force out of nothing, are incredible; they are opposed
350 CREDIBILITY AND INCREDIBILITY,
to Causation as expressed under the Correlation or Persistence
of Energy. All supposed modes of deriving motive power,
otherwise than from solar heat past or present, are incredible.
That any medium of force more economical than the combus-
tion of coal remains to be discovered is all but incredible.
If any one affirms that some change has happened without
a cause, we refuse to listen to it. An exception to this rule is
sometimes claimed in the case of the human will; but that
exception has never yet been established upon evidence suffi-
cient to cope with the evidence in favour of the law of causa-
tion.
The principle laid down by Hume, that nothing is credible
that contradicts experience, or is at variance with the laws of
nature, is strictly applicable to these completely proved induc-
tions. We cannot receive any counter evidence in their case,
unless of a kind so strong as to reverse our former judgment
and make them out to be mistakes. No mere probability is
- equal to this task in regard to the axioms of mathematics, the
law of causation, the law of gravity, and many others.
That every living thing proceeds from a previous living
thing, or as expressed by Harvey—ommne vivum ew ovo, is an
induction verified by simple agreement, through a very wide
experience ; rendering spontaneous generation, for the present,
incredible. It is an empirical law, true within all the limits
of human observation hitherto, although we may not be able
to extend it over an indefinite period of time.
Among facts antecedently incredible, we must rank the
spontaneous combustion of a human being, which is totally
inconsistent with the constitution of the animal body.
It has been alleged by witnesses that the mummy corn of
the Egyptian pyramids has been sown and been productive.
To a botanist, the assertion is wholly incredible. Seeds two
centuries old are so completely changed as to lose their
fertility.
There appears to be unexceptionable testimony to the prac-
tice of the Indian Fakeers, in allowing themselves to be buried
for a number of days, after which they are dug out alive.
This would be wholly incredible, but for the knowledge that
we have of such states as trance, or lowered animation, which
dispense with food altogether for a time, and require only the
minimum of oxygen.
It is alleged by travellers that certain tribes subsist upon
earth as food. This is admissible, only on the supposition
that the earth contains a quantity of organic products, such
eats
a
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COMPARISON OF PROBABILITIES, 881
as starch, sugar, albumen, or their equivalents. That any
human being or animal could live upon the purely inorganic
matters of the soil is to be wholly disbelieved.
The phenomena of clairvoyance are all in the position of
antecedent incredibility. That any one should see with the
eyes bandaged is at variance with the conditions of vision as
established by all the authentic experience of the human race.
Yet this has been affirmed by multitudes of witnesses. The
testimony of witnesses, however, in such a matter cannot be
received. The sole condition of admitting such a fact would
be (what has never yet been attempted) a rigorous verifica-
tion according to the methods of experimental science. So
with the other facts of the same class—prophetic dreams,
visions or intimations of events at a distance. These are all
opposed to well-established inductions.
4, When a fact with a certain amount of evidence in
its favour, is opposed, not to an established induction, but
to an approximate generalization or probability, the case
is one of computation of probabilities.
What is only probable, or approximately true, has excep-
tions; an opposite assertion, therefore, may be credited, if
supported by a still higher probability, or by a generalization
approximating still more to certainty. A fact true ninety-
nine times in a hundred is not to be set aside by an opposing
testimony correct only nine times in ten.
In an age when physical laws were imperfectly understood,
when the law of causation itself was not fully verified, the
phenomenon of witchcraft stood between opposing probabili-
ties. ‘There was no inductive certainty on the one hand, to
controvert the mere probabilities of human testimony on the
other. ‘The physical knowledge even of Bacon was not
enough to render the testimonies in support of witchcraft
wholly incredible, although it might have stamped these with
inferior weight and cogency.
5. The allegations of travellers as to new species of
plants, or of animals, are credible or incredible accord-
ing as they affirm what contradicts, or what does not con-
tradict, laws of causation or of co-existence.
There are certain peculiarities of structure that are involved
as cause and effect in the animal system. An animal species
must have an organ for receiving aud digesting food, a respirae
882 CREDIBILITY AND INCREDIBILITY.
tory organ, a means of reproduction. Any contradiction to
these must be absolutely rejected.
Next in point of evidentiary force are the typical peculiarities
of the order, as the four limbs in the higher vertebrata. An
animal of the higher tribes, with both wings and arms, would
present an incredible combination ; there might not be absolute
incompatibility, but there would be such a departure from the
type as experienced, that it could not be received on less
authority than ocular inspection fortified against every possi-
bility of delusion.
New combinations of compatible organs are improbable
only in proportion as they have been hitherto undiscovered.
Flying fish were improbable, but not to the degree of incredi-
bility. The extension of our knowledge of kinds, by showing
new variations, reduces the improbability in favour of other
kinds, within the limits of compatibility. That a ruminant
animal may be found without cloven hoofs is incredible, if
these are cause and effect, or effects of a common cause, it is
only improbable if they are co-existences without causation.
Such a co-existence has been widely verified, but not as yet
exhaustively.
A late distinguished historian for a long time doubted the
fact of persons having lived more than a hundred years. He
did not regard the fact itself as absolutely incredible; but in
the absence of authentic registrations, and the uncertainty of
memory and tradition extending to events a century old, he
considered that the improbability of so great an age had not
been overcome by sufficient counter probabilities. At length
he obtained what he deemed adequate evidence in favour of
centenarians.
6. The assertion of a fact wholly beyond the reach of
evidence, for or against, is to be held as untrue.
We are not entitled to put the smallest stress upon a fact
without evidence in its favour, because, from its being inacces-
sible to observation, no evidence can be produced against it.
To affirm that the centre of the earth is occupied by gold, is
for all purposes, the same as a falsehood.
On the Great Postulate of Experience, we are to believe
that what has uniformly happened in the past will continue to
happen in the future; we accept uncontradicted experience as
true. But where there has been no experience, we can
believe nothing. We are not obliged to show that a thing is
not; the burden lies upon whoever maintains that the thing is,
BOOK IV.
DEFINITION.
The processes having reference to the class, notion, or
concept, have been already enumerated. The chief are,
Classification, Abstraction, Naming eat a view to gener-
ality), Definition.
The class, notion, or concept as already explained, is a
product of generalization. -.It-may be constituted by one
common property, as resisting, moving, white, bitter; or by
more than one, as house, mind, man.
CLASSIFICATION, in its simplest form, follows the identifica-
tion of like things; that is, a class is made up of things brought
together by likeness. When the mind attends more particu-
larly to the points of community, it is said to put forth the
power of Ansrraction. A name applied to the class in virtue
of the class likeness, is a GeneraL Name. ‘The precise delinea-
tion of the likeness by a verbal statement is DEFINITION.
The three processes—Classification, General Naming, and
Definition—are what we are now to consider. The first-
named process, Classification, has a larger meaning than the
mere assemblage of things upon one or more points of likeness ;
it includes the arts for systematically arranging vast multi-
tudes of related objects, under higher and lower genera, as in
what are called the three Kingdoms of Nature. With a view
to this greater complication, we shall view the whole subject
of Classification last of the three.
As regards the generalization of the Class, or Notion,
in all its aspects, the fundamental principle is stated as
follows :—
Of the various groupings of resembling things, prefer-
ence is given to such as have in common the most numer-
ous and the most important attributes.
This is the basis of natural or philosophical classifications,
384 CANONS OF DEFINITION,
in contrast to insignificant and unsuggestive classifications ;
as in the distinction between the Natural and the Linnean
systems of Botany. It may be termed the golden rule of
classifying.
We are often disposed to prefer classes on account of their
extent, although the common attributes—the comprehension
or connotation, may have dwindled down to a limited and
unimportant resemblance. Thus, the class ‘land animals’ is
very extensive, with little comprehension; and more insight
is imparted by breaking it up into groups, as mammalia and
birds, each having numerous and important points of com-
munity. The class ‘adherents to a religious creed’ is so
wide as to impart very little information respecting the indi-
viduals ; the sub-classes Buddhists, Mahometans, Jews, Roman
Catholics, Calvinists, each connote a large circle of peculiari-
ties.
“
CHAPTER L
CANONS OF DEFINITION.
_1. Definition consists in fixing by language the precise
signification—the Connotation—of General Names.
Defining does not apply to the unmeaning name. An arbi-
trary name used for a particular object as ‘ Sirius’ for a star,
‘Snowdon’ for a mountain, ‘Samson’ for a locomotive, is ex-
plained only by showing or indicating the thing.*
Nevertheless, from the important consideration already
stated (Introduction, p. 6), that even a singular is conceived
by the mind as a conflux of generals, Definition becomes
eventually applicable to individual things. A particular star,
a mountain, a locomotive engine, may be represented and
marked off from all other things by a «cries of descriptive
names of general signification. For such an operation, how-
ever, the name Description is more appropriate.
It has been already explained (Part I, p. 71) that a perfect
Definition is the whole connotation of the name. Somenotions
have one point of community ; some two, three, or four; some
@ great many, as the often-mentioned Kinds; the proper and
* Hence the maxim of the old logicians, ‘Omnis intuitiva notitia est
definitio’—‘ a view of the thing itself is its best definition,’
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FUNDAMENTALS OF DEFINITION, 385
complete Definition must give an account of them all. The
singling out of one or two properties, for the mere purpose of
discrimination, is not a proper or perfect definition.
2. From the very nature of human knowledge, Defini-
tion appeals to the two fundamental principles—Agreement
and Difference, or Generality and Contrast.
I, Every generality must relate to particulars.
II To every real notion, as well as to every particular
experience, there corresponds some opposite, also real.
This is simply the Law of Relativity or Contrast.
As the statement of what is common to a number of parti-
cular things, Definition is essentially a process of generaliza-
tion; while neither particular things, nor their agreements,
have any distinct meaning, unless there be assignable a dis-
tinct opposite. The act of Defining, therefore, consists of a
generalizing operation, rendered precise at every step by
explicit or implicit opposition, negation, or contrast. If,
throughout the process of generalization, we avail ourselves
of explicit contrast, to render precise both the particulars and
the generalities, that one operation would be enough ; defining
would be generalizing pure and simple, and nothing besides.
But there is often a great advantage gained by viewing, in a
separate and distinct operation, the opposite or contrast of the
thing defined; and hence we may lay down two canons, or
two stages of the process—the first the canon of Generalization,
the second, the canon of Contrast or Relativity; or, as Gene-
ralization must enter into both, we may call them the Positive
and Negative Methods. Taken together they show that
Defining is rendered thorough-going, first, by generalizing the
Particulars of the Notion propounded, and secondly, by
- generalizing the Particulars of its Negative.
The method of Defining given in the ordinary works on
Syllogistic Logic contains no reference to a generalizing opera-
tion. The scholastic definition directs us to assign (1) a
higher genus of the thing defined, and (2) the specific differ-
ence, or the distinction between the thing and the other
species of the same genus (per genus et differentiam). No
mention is made of the way of obtaining either the characters
of the genus, or the differential characters of the species,
Suppose we were to define Chemistry in this way ; (genus) a
Science, (differentia) having reference to a peculiar kind of
Combination of Bodies, called chemical ;—it is obvious that
386 CANONS OF DEFINITION.
to give such a definition we must scan the subjects ordinarily
included in Chemistry, and, by generalizing them, find an
expression suitable to them all, and to none besides. Hence,
the direction to assign the genus and the difference, merely
relates to the form of expressing the result of a generalizing
operation.
Allusion is made, by Mr. Mill, to a mode of defining by
* Analysis,’ or by resolving a complex notion into its con-
stituent elementary notions; as when we define Hloquence—
‘the power of influencing men’s conduct by means of speech.’
Here, Eloquence is a complex property, resolved into the two
simpler properties, ‘exerting influence over men’s conduct,’
and ‘speech.’ If, however, the enquiry was made, how do
we arrive at this definition, the only answer would be, by
generalizing from the particular examples of eloquent address ;
so that, in point of fact, this method, if it be a method, does
not supersede the processes of generalization.
The analytic statement could, if we please, be thrown into
the scholastic form; we have merely to adopt one of the com-
ponent notions as a ‘genus,’ and call the others ‘ differentia ;’
influencing of men’s conduct (genus), use of speech (differen- |
tia). We might even reverse the notions; ‘speech’ (genus),
‘for influencing human conduct’ (differentia).
Thus, neither of these two modes of defining can come into
competition with the main circumstance insisted on, namely,
that to define is to generalize. On what occasions, the
generalizing process may be dispensed with, will be a matter
of future consideration.
Positive Method.
3. Canon. Assemble for comparison the Particulars
coming under the Notion to be defined.
By the Particulars are meant, not every individual instance,
but representatwe instances sufficient to embrace the extreme
varieties.
To define a species of Plants, the botanist collects recognized
examples of the species, including the widest extremes admitted
into it. He compares the several specimens, noting their
agreements, until he finds what characters pervade the whole ;
these he expresses in suitable language, which language is
henceforth the definition of the species. So, in dealing with
the higher groupings —genera, orders, and classes—he follows
pio ee
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GENERALIZATION OF POSITIVE PARTICULARS. 387
_ the same obvious plan. Likewise, the zoologist and mineralo-
gist have, in the last resort, no other method.
Further to elucidate defining by the generalization of
the positive particulars, we will select examples such as to
bring out the difficult situations, and will indicate, in the form
of subordinate canons, the modes of overcoming the difficulties,
Suppose we have to define a Monarchy. We must begin
by assembling instances of every institution that has ever
been called by the name: the kings of the heroic age in
Greece ; the Spartan kings; the Roman kings; the Persian,
Macedonian, Syrian, and Ezyptian kings; the Teutonic
king; the kings of modern HKuropean nations; the kings of
the negro tribes; the emperors; the reigning dukes, mar-
graves, counts, bishops, &c. To these we should have to add
the king-archon at Athens, and the king of the sacrifices at
Rome—mere relics of the ancient kingly government (Sir
G. C. Lewis, Methods of Politics, I. 86). Now, if we confined
ourselves to a certain number of these, we should find the
common fact of absolute or despotic government; this, how-
ever, fails to apply to other instances, as our modern constitu-
tional monarchies; and, if these are to be included, the
common features are greatly reduced in significance, being, in
fact, little more than (1) the highest dignity in the state, and
(2) a participation, greater or less, in the sovereign authority.
But again, if we look to the two last instances—the king-
archon at Athens, and the king of the sacrifices at Rome—we
shall not be able to apply to them even the attenuated com-
munity just given; there would be required a still farther
attenuation, reducing the points of agreement to utter insigni-
cance.
Now this is one of the most usual situations arising in
the attempt to generalize a notion with a view to definition.
We must be led in the first instance, by the popular denota-
tion of the name; yet, if we abide by that, we fail to obtain
any important community of meaning. It is in such a per-
plexity, that the golden rule must be called to our aid; we
must take some means to form a class upon a deep and wide
agreement. If need be, we must depart from the received deno- -
tation; leaving out some instances, and taking in others, until
we form a class really possessing important class attributes,
Thus, in the case of the monarch, we should cut off at once
the mere relics of old kingly power. As regards the rest, we
should divide the instances between the absolute and the
limited monarchies ; there is a large and important community
-
a
388 CANONS OF DEFINITION.
of meaning in the class termed ‘absolute monarchies,’ and —
this class should be isolated, and should make a distinct notion
in political science. The remaining individuals should be dealt
with apart; they (as shown by Sir G. C. Lewis) are far
better excluded from Monarchies, and classed with Republics,
‘By including in monarchies, and excluding from republics,
every government of which a king is the head, we make every
true general proposition respecting monarchies and republics
wmpossible.’ In this state of things an operation of re-classing
is the indispensable scientific corrective of the popular and
received generalities. . .
The definition of a Colony would afford a case exactly
parallel. Taking together all the things that have ever borne
this name in ancient or in modern times —the colonies of the
Phenicians, Greeks, Romans, Italians, Spaniards, Portugese,
Dutch, French, English—we should find these facts in common,
namely, emigrating from the mother country, settling in some
new spot, and displacing the previous government, if not also
the population, of the place occupied. With this small amount
of agreement, there are very wide disparities, and until we
narrow the instances, we do not arrive at a large and im-
portant connotation or meaning. If, however, discarding the
ancient colonies, we make the comparison among the modern
instances, we find the important circumstance of a sustained
political relationship with the mother country ; which is
better expressed by the word dependency. And by sub-divid-
ing the class, we can obtain inferior classes, with still more
numerous important points of agreement; as, for example,
the Canadian and Australian colonies of this country, which
exercise the powers of independent legislation, under the
least possible control by the home government. |
Let us next endeavour to define Food. According to the
canon, we assemble representative examples of all the sub-
stances ever recognized under thisname. We have before us,
the flesh of animals, the esculent roots, fruits, leaves, &ec.
We have also a number of substances of purely mineral origin,
as water and common salt. Our work lies in generalizing
- these, in detecting community in the midst of much difference. _
Were man a purely carnivorous feeder, his food might be
generalized as the flesh of animals taken into the mouth, and
passed into the stomach, to be there digested and thence to
be applied to the nutrition and support of the system. But
when we include vegetable and mineral bodies, we must leave
out ‘flesh,’ and substitute ‘animal, vegetable, and mineral
%y
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RULE OF IMPORTANT COMMUNITY. 3889
substances ;’ the other part of the statement being applicable.
Even as amended, however, the definition is still tentative, and
needs to be verified by comparison in detail with everything
that has ever been put forward as food. We must challenge
all informed critics to say where the definition fails. Thus,
nourishment is afforded by substances absorbed through the
skin, which would exclude the medium of the mouth and
stomach, and narrow the definition to nourishing or supporting
the system. . Again, it is doubted, whether alcohol, tea,
tobacco (chewed) really nourish the system. This is a far
more serious objection; and the manner of dealing with it
will illustrate the principles of defining.
In the first place, there may be a contest as to the matter of
fact. Could it be shown that these substances do give nourish-
ment, support, or strength to the system, the difficulty is at
once overcome ; in that case, they fall under the definition.
On the contrary supposition—that they do not nourish the
the system,—two courses are open. First, we may exclude
them from the class ‘ Food,’ and retain the definition. Or
secondly, we may include them, and alter the definition. As
modified to suit the extension, the definition would be ‘ sub-
stances that either nourish or stimulate the system.’ To de-
cide between those two courses, we must, as before, refer
to the golden rule of classification, which recommends the
adherence to a smaller class founded on a great and important
community, rather than to a larger where the community of
meaning is attenuated to comparative insignificance. Better,
therefore, to retain two groups—Foods and Stimulants,—
each with its own definition. In that way, we should derive
much more information respecting any individual thing de-
_signated either ‘ Food’ or ‘Stimulant,’ than if the word ‘food’
covered both. It may be that some substances combine both
functions; which would entitle them to be named in both
classes.
We may notice the definition formerly given of ‘ Axiom’
by way of remarking that a definition is obviously spurious
that does not distinguish the given notion from notions
already settled. Thus, unless an Axiom bea real proposi-
tion, it is not divided from Definitions; and unless it is
fundamental within the science, it does not difter from the great
body of Propositions so far as employed to prove other pro-
positions. ‘The characters proposed are alone sufficient to
constitute a separate notion bearing the name.
These cases sufficiently exemplify the situation where a
390 CANONS OF DEFINITION.
word is extended to denote things that have few or no im-
portant points of community. The next example will bring to
view a perplexity of another kind.
Suppose we seek to define a Solid. Summoning to view, if
not all the solids in nature, sufficient representatives of all the
varieties compatible with the name—metals, rocks, woods,
bones, and all the products of vegetable and animal life
denominated solid—we set to work to compare them, and
note their agreement. There is little apparent difficulty in
this instance. We see that, however various these bodies
may be, they agree in resisting force applied to change their
form ; so readily does this strike us at first sight, that the case
seems scarcely worth producing to exemplify a logical formula,
Let us, however, apply the Socratic test—exposing the defini-
tion to the cavil of every objector,—and we shall probably
soon be told of a grave difficulty. The quality, so very
decided in the great mass of instances, is found to have
degrees, to shade insensibly into the state called ‘liquid,’
where solidity terminates. Now, at what point does solidity
end, and the opposite state begin? Is a paste, a glue, a jelly,
solid or not? Is Hamlet right in talking of ‘this too, too
solid flesh ?
We have here not a mere cavil, but a frequent and serious per-
plexity. Many couples of qualities, unmistakeably contrasted in
the greater number of instances of them, pass into one another
by insensible gradations, rendering impossible the drawing of
a hard and fast line. Whoshall say at what moment day ends
and night begins? So, there has always been a doubt as to
the exact individual that ends the animal series, and is neigh-
bour to the beginning of the plant series. Sleeping and
waking may have an intermediate state, with difficulty as-
signed to either, The great chemical sub-division into metals —
and non-metals has an ambiguous border in the substances
arsenic and tellurium. In the animal system, the voluntary
shades insensib!y into the involuntary.
The Greek philosophers displayed to the utmost the in-
genuity that lights upon difficulties; and this example did not
escape them. They grounded upon it a puzzle named the
Soriies, or heap. A certain heap was presented, which was
fairly designated small ; it was then increased by very gradual
additions; and the spectator was challenged to declare at
what point it ceased to be small, and deserved to be accounted
large.
There is but one solution of the riddle. A certain margin
MARGIN OF TRANSITION. 391
must be allowed as indeterinined, and as open to difference of
opinion ; and such a margin of ambiguity is not to be held as
invalidating the radical contrast of qualities on either side.
No one would enter into a dispute as to the moment when
day passed into night; nor would the uncertainty as to this
moment be admitted as a reason for confounding day and
night. We must agree to differ upon the instants of transi-
tion in allsuch cases. While the great body of the non-metals
can be distinctly marked off from the metals, we refrain from
positively maintaining arsenic and tellurium to be of either
class ; they are transition individuals, the ‘ frontier’ instances
of Bacon ; in that position we leave them.
There is a margin of transition in the ethical distinction of
Reward and Punishment. ° In the great part of their extent,
these two motives are amply contrasted; to bestow a reward
for performance, is a different thing from inflicting punish-
ment for non-performance ; and the withholding of a reward
is not confounded with punishment Yet circumstances arise
when the one merges into the other.
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whe.
452 LOGIC OF PHYSICS.
MOLAR PHYSICS.
Divisions of the Subject.
2. The Abstract Branches, comprising Motion and
Force in general, and susceptible of Deductive and Matha,
matical treatment are these :—
Mathematics of Motion —Kinematics.
Forces (1) in Equilibrio —WStaties.
Forces (2) causing Motion—Dynamies.
The Concrete Branches are—
Mechanic Powers and Solid Machinery.
Hydrostatics and Hydro-dynamices.
Aerostatics and Pneumatics.
Acoustics.
Astronomy.
Notions of Molar Physics,
3. In Physics, are pre-supposed the Notions (as well as
the Propositions) of Mathematics. Only those special to
the science are here reviewed.
Motion—fest.—This antithetic couple is the fundamental
conception of Physics, and is probably an ultimate experience of
the human mind. We obtain the idea of Movement by a
peculiar employment of our active energies, assisted by sen-
sation. We also obtain a knowledge of the varieties of move-
ment—quick, slow, uniform, varying, straight, curved, con-
tinuons, reciprocating, pendulous, wave-like, &e. The
modes that depend upon degree, or Velocity, are part of the
ultimate experience of motion as such ; those characterized by
shape or Form have a property common to mere extension.
Force.—-This is without doubt the most fundamental notion
of the human mind; in the order of evolution, it concurs with,
if it is not prior to, both motion and extension. It cannot be
defined except in the mode peculiar to ultimate notions. The
feeling that we have when we expend muscular energy, in
resisting or in causing movement, is unique and irresolvable.
Inertia, Resistance, Momentum.—These names designate our
experience of force from the objective side, or as embodied in
the things of the object world. The occasion of calling forth
our feeling of energy when referred to an external factis Re-
sistance, Inertness, Momentum, or External Force—all signi-
‘ oe Bt
NOTIONS OF MOLAR PHYSICS, 453
fying the same thing. This great fact must be learnt, in the
first instance, by each one’s separate experience ; the best mode
of scientifically expressing it is a matter for discussion.
Matter is Hxtension, coupled with Force or Inertia. Any-
thing extended and at the same time possessing force, either
to resist or to impart motion is Material.
Mass, Density, Solidity, are derived notions; they are ob-
tained by putting together Force and Extension or Volume.
The Mass is the collective Force of a body, shown by its degree
of Resistance, and also by the amount of Lesistance it can
overcome when moving at a given rate. The Density is the
degree of space concentration; a given power of resistance,
_with a smaller bulk or volume, is a greater Density. Solidity,
when not signifying the solid state of matter generally, as
opposed to liquid or gas, is another name for Density.
Impact is a phenomenon expressed by means of Space or
Extension, Motion, and Force. It is one mode of imparting
visible or kinetic energy, and is a test or measure of Force.
Attraction is definable by Extension, Motion, and Force.
It is a mode of communicating Force, distinct from Impact,
and in some respects simpler. Among its specific examples
are Gravity, Cohesion, Adhesion, Magnetism, Electrical Attrac-
tion, (Chemical Attraction).
ftepulsion is definable by reference to the same fundamental
notions. It also is a mode of imparting or redistributing
force, and differs from Attraction only in the way that it
changes the relative situation of the masses concerned. It is
exemplified in the Expansive energy of Gases in their ordinary
state, in the Expansion of Liquids and Solids from rise of
temperature and after compression (called Elasticity). The
Polar Forces—Magnetism, Hlectricity, &c., exercise, along with
Attraction, a counterpart Repulsion.
By still farther combining these primary notions, we obtain
—Hquilibrium, Composition and Resolution, Resultant, Virtual
Velocity, Centripetal, Centrifugal, Tangential force, Projectile.
To Mechanics belong Specitic Gravity, Centre of Gravity,
Stability, Oscillation, Rotation, Percussion, Friction, Mechanic
Power, Machine, Work.
In Hydrostatics, occur Liquid, Liquid Pressure, Liquid
Level, Displacement, Flotation, Column of liquid.
In Hydro-dynamics, Liquid Motions, Efflux, Discharge,
Liquid Waves.
In Aerostatics and Pneumatics, Air, Atmosphere, Expansion
of Gases, Flow of Gases, Undulations, Atmospheric pres-
sure.
454 LOGIC OF PHYSICS.
In Acoustics, Sound, Pitch, Timber, Vibrations, Noise;
Note, Echo, Harmony.
In Astronomy, Sun, Planet, Satellite, Comet, Aerolite,
Bolid, Star, Nebula, Orbit, Ecliptic, Year, Month, Day, Eclipse,
Pranait, Parallax, Aberration, Right Anpeniiolig Declination,
Eccentricity, Node, Apside, Per ihelion, Perturbation, Libration,
Precession, N atadioin Tides.
Propositions of Molar Phystes.
4. These are of the following classes :—(1) The Indue-
tions of Force and Motion; (2) ‘Vhe Deductive Propria
asserting the quantitative relationships of Motion and
Force; (3) Empirical laws of the concrete phenomena.
(1) The great Inductions, commonly called the Laws of
Motion, are the axioms of the science. These will be con-
sidered afterwards. They are all quantitative in their expres-
sion. Another fundamental Induction is the Law of Gravity.
(2) The science being pre-eminently Deductive, its proposi-
tions are for the most part deductions from the axioms. Such
are—the propositions of the Composition and Resolution of —
Motions and Forces; the proposition called the ‘law of Areas;’
the principle of the Mechanic Powers; the principles of the
pendulum ; the law of liquid pressure ; the principle that con-
nects fluid motion with fluid support; the laws of the propa-
gation and the reflection of sound.
All these matters are stated in the form of real propositions,
which, however, may be deduce from the axioms or induc-
tions of the science applied to the particular cases as scientifi-
cally defined. For example, the law of fluid pressure is a
proposition to this effect. ‘At any point in a fluid at rest, the
pressure is equal in all directions ;’ the subject of the proposi-
tion supposes a fluid at rest, a point taken in it, and considera-
tion given. to the pressure; the predicate is ‘ equality in all
directions.’ The proof is deductive, and ultimately rests on
the axioms of motion and force, together with the definition of
fluidity, although the proximate majors are the propositions of
the Composition of Forces.
Subsidiary to the working out of the science are the propo-
sitions «xpressing the quantities of motion, force, &ec., existing
in actual things. Thus, besides the Law of Gravity, we have
a statement of the numerical amount of gravity at the earth’s
surface ; also the relative gravities of different solids and
fluids. These numerical propositions are called the “aa
‘DEFINITION OF MOTION. A455
cons‘ants, or co-efficients of the science, and are ascertained by
observation and experiment.
(3) There are certain empirical laws obtained by observa-
tion or experiment. Such are the laws of the Strength of
Materials (to some extent Deductive), the laws of Friction,
the Motion of Projectiles (partly Deductive), the Flow of
Rivers, the Spouting of Liquids, the Compression of Liquids
and of Gases, the Diffusion of Sound, the action of Vibrating
Strings, &c. These are all real propositions ; they are in their
nature propria, or deducible from ultimate principles ; but, in
the present state of knowledge, they must be gained by direct
experiment.
Definitions of Molar Physics.
d. As in Mathematics, so in Physics, there are certain
properties that are ultimate, and incommunicable by lan-
guage ; being known by each one’s independent experi-
ence. Nevertheless, it is open to us to consider the best
mode of generalizing and stating this experience.
The facts named Motion, Force, Matter, are understood only
by our concrete experience of the things denoted by the names.
But our crude observations may be rectified by more careful
comparisons, and may be reduced under precise general state-
ments. Moreover, as in Mathematics, we may select the
aspect most suitable as a point of departure for our deductive
reasonings.
Definition of Motion.—Of the fact of motion no knowledge
can be imparted; there is nothing simpler to express it by:
‘change of place’ is not more intelligible than ‘ motion.’ We
must assume that each one understands motion both generically,
and in its degrees (capable of numerical statement); and also
in such simpler modes as straight or divergent. The more
complex movements are then definable. Velocity means degree
of motion. The only thing needing to be expressed formally
is the measure of Motion or Velocity with reference to Space
and to Time; these last-named elements being presupposed as
themselves intelligible.
Matter, Force, Inertia. These are three names for substan-
tially the same fact. At the bottom, there is but one experi-
ence, although varied in the circumstances, namely, the
experience of putting forth muscular energy in causing or in
resisting movement. To this experience we give the names
Force and Matter, which are not two things but one thing;
456 | LOGIC OF PHYSICS,
of which Inertia is merely another expression. It is pure
tautology to define one of these terms by the others ; matter is
nothing except as giving the experience called also force; force
is only revealed by matter moving, or obstructing movement.
Matter, however, affects us in other ways than by the mus-
cular feeling of resistance or of expended energy. It is always
extended, and in most cases visible, and also tangible. Are
we not, then, to include these facts in the definition? No,
and for these reasons:—(1) Extension is not confined to
matter; it belongs also to empty space; therefore, though a
predicate of all matter, extension is not the exclusive charac-
teristic of matter. (2) Visibility and Tangibility belong to
many kinds of matter, but not to all matter; hence, these
properties cannot be the defining characters of matter in
general, or of all matter; they are to be reserved as properties
of the kinds of matter wherein they occur; solids and liquids,
for example. Accordingly, the only fact occurring in all
matter is the fact expressed by resistance, force, or inertia ;
all which are names for a single phenomenon. This phenome-
non, when fully examined, and generalized to the utmost, has
two different aspects, which we may separate in expression, but
cannot separate in nature ; the one is the resistance to move-
ment by bodies, whether at rest or in motion, and the other,
the imparting of movement or momentum by being in motion,
The first aspect of resistance is the more popular meaning of
inertia ; the second aspect, the imparting of movement, is the
popular view of force; but in the scientific consideration of
the subject, these are but one property.
The definition of Matter and of Inertia, or Inert substance,
is, therefore, but one. It generalizes our familiar experiences
of resisting motion and of communicating motion, which
always concur in the same thing. Fully expressed, it amounts
to the statement given in the First Law of Motion. We are
entitled to lay down as the fundamental or defining attribute
of matter, in whose absence matter is not, that if once at rest
it remains at rest, and if once in motion, it continues moving
in a straight line. To put it from rest to motion, moving
power must be employed; to arrest its course, matter, either
in motion or at rest, must be opposed to it. All this is
involved in the very meaning of matter, We cannot divide
these expressions, and assign one as the defining mark of
matter, and the other as a predicate distinct from the defini-
tion. No one has ever succeeded in constituting a REAL
proposition out of these properties. The appearance of a real
a:
-
se
DEFINITION OF MATTER, 457
3 proposition could be given only by assuming as the meaning of
matter the imperfect view entertained by the unenlightened
mind (which, owing to adverse appearances and imperfect
knowledge, does not fully recognize the persistence of moving
matter), and giving as the predicate the scientifically recti-
fied generalization of matter; but when this generalization is
attained, it is wholly embodied in the definition of matter; it
cannot furnish one fact as a defining property and reserve
another as a predicate. There is a definition of Inertia; there
is no law.
Thus, then, the persistence in a state of rest or in a state of
uniform rectilineal motion, is the meaning of Inertia, and of
Matter in general; in which meaning there is an unavoidable
implication of active resistance, and active communication of
motion. The difficulty is to find an expression to comprehend
all these aspects of one indivisible property. Matter at rest
operates at one time in dead resistance, at another time in
using up force by itself passing into motion ; matter in motion
may resist movement, or it may generate movement; but,
these are not a plurality of properties ; we cannot suppose one
of them separated from the others. The definition employs -
plurality of phrases in order to encompass a unity.
Matter and Inertia being thus defined by one stroke, Force
is merely another reference to the same fact. Inert Matter in
motion is the most characteristic expression or aspect of Force,
and is adopted as its numerical measure; but we cannot ex-
clude from the idea the consideration of matter at rest. In
measuring force by moving matter, we mean matter transferred
from rest to motion, or from one rate of motion to a quicker ;
this is force as generated. Again, the force is manifested in
the abatement of the motion, in reducing bodies to the state
of rest; this is force as expended.
As there is but one fact underlying Matter, Inertia, Force,
so there is but one measure. A larger quantity of matter, or
inertia, is the same as a larger expenditure of force to change
the matter from rest to a given pace of motion. The ultimate
measure is the human consciousness of expended. energy.
There is a palpable impropriety in the expression, given as a
law,—‘ The amount of inertia increases with the quantity of
matter ;’ the two properties stated are but one fact.
To sum up. Hach person by their own experience must
become acquainted with the concrete examples of matter and
force. A comparison of all varieties of the phenomenon re-
veals the presence of a common feature, at bottom one and
458: LOGIC OF PHYSICS.
indivisible, but variously manifested as resistance, as a source
of movement—as persistence in rest or in uniform rectilineal
movement. To this many-sided unity, we give the names
Matter, Inertia, Force, which have a commen definition and a
common estimate: The word Matter is the concrete name,
while Inertia and Force are the asbtractions for what is com-
mon to all matter.
Mass, Density.—Mass is the quantity of matter, measured in
the mode already described, namely, by the expenditure re-
quisite to change the body’s state by a given amount. When
the Mass is given, and also the volume, or bulk, we obtain the
Density. Volume and Mass rightly precede Density, in order
of definition. Messrs Thomson and Tait make Density pre-
cede Mass.
Momentum means quantity of motion; its measure is the
mass multiplied by the velocity. The unit quantity of
motion is some unit of mass, multiplied by a unit of velo-
city. Mass is usually estimated by weight, but this is to
anticipate the consideration of gravity, which should be ex-
cluded from the elementary definitions of motion, matter, and
- force.
The defining of the notions following on these—Impact,
Attraction, Repulsion, Gravity, Cohesion, &c.—presents no
logical difficulties. They are all derivative notions, their
elements being the above named primary notions coupled with
those of mathematics ; and they are defined as such, although
concrete examples may be given to aid the understanding of
the more difficult abstractions.
Thus, Impact is the transfer of force from one body to
another by momentary concourse; the direction communicated
being the direction possessed. Attraction is the continued gene-
ration of moving force shown in the mutual appreach of two
bodies ; Repulsion is the generation of force leading to the
mutual recess of bodies. Gravity is the attraction inherent,
persistent, and unchangeable in all matter, being proportioned
to the mass, and extending to all distances, at a uniform rate of
decrease.
Axioms of Molar Physics. |
6. The chief axioms of the science are usually stated
under the titleh—Laws of Motion. }
In the statement of these laws verbal and real proposi-
tions are confounded. |
NEWTON'S LAWS. OF MOTION. 459
- Newton’s First Law—‘ Every body perseveres in its state
of rest or of uniform rectilineal motion, unless compelled to
change that state by impressed forces ’—is merely the full
expansion of the definition of matter, inertia, or body. It no
doubt expresses more than the vague unscientific notion of
matter, but no more than is absolutely inseparable from
matter. It isa verbal and not a real proposition—a definition
disguised as a proposition. ‘Body’ means what Newton pre- .
dicates of it; withdraw from ‘body’ all that the law affirms
and implies, and there would be nothing left. If a body did
not persevere in its state of rest or motion, until disturbed by
another force, it would not possess the most elementary con-
ception that we can form of body, the property of resistance,
Of the various modes of exhausting the aspects of body,
matter, inertia, force, it may be doubted whether Newton’s is
the most felicitous. At all events, the attempt would succeed
better, if the statement were in the only legitimate guise—a
Definition.
Newton’s Second Law is—‘ Change of Motion is proportional
to the impressed force, and takes place in the direction of that
force.’ This law assumes the fact of the communication or
transfer of motion, and affirms, although not in the best
manner, the quantitative equivalence of the motion given
with that received.
The Third Law is—‘To every action there is always an
equal and contrary re-action; or the mutaal actions of any
two bodies are always equal and oppositely directed.’ More
shortly expressed thus—‘ Action and Reaction are equal and
contrary.’ Objections have often been taken to the word
* Re-action’ in thislaw. The meaning put upon it by Newton
is gathered from his own illustrations. His examples are of
two classes. The first puts the case of impact, as in pressing
a body, or in drawing it by some solid medium as a cord or a
rod. There is, to say the least, great awkwardness in repre-
senting the communication of force by impact, in these terms :
—‘ when we push a stone with the hand, the hand is pushed
back by the same force as the stone is moved forward ;’ or
‘a horse towing a boat is dragged backwards by the same force
as the boat is dragged forwards.” The more natural expres-
sion is that when one moving body gives motion to another,
it loses exactly the energy that it communicates; or that on
the re-distribution of force or moving power nothing is lost.
Now, if there be any real affirmation in the Second Law, it is
this and nothing else.
460 LOGIC OF PHYSICS,
_ The other class of examples given by Newton comprises a
distinct case, and the only case that gives the appearance of
propriety to the word ‘ re-action.’ It is the communication of
movement by distinct attraction (or repulsion). When one
body attracts a second, the second equally attracts the first ;
the attractions are mutual and equal; the momenta produced
are exactly the same in each. This is a fact of great import-
ance in nature and deserves to be singled out; indeed, it is
the only case of communicated momentum where the result is
_ unaffected by disturbances that interfere with exact calcula-
tions.
Now this is to be regarded as a separate induction. It is
fully consistent with the principle of the conservation of
energy, under re-distribution, as represented by impact,
and has some inherent probability in its favour, but still
requires the confirmation of experience. Ingenious reasons
might be given, why no other result should arise, but there is
no infallible deductive cogency in applying the Law of Conser-
vation, founded on impact, to the equality of mutual attrac
tions.
Searching thus through the three Laws of Motion, we
encounter only one principle—the principle of Conservation
of Force under re-distribution. The second law has no mean-
ing but this. That ‘change of motion is proportional to the
impressed force’ with difficulty escapes from being a verbal
proposition, for there is no other measure of force but ‘ change
of motion,’ imparted, or impartible movement. The assertion
would have no reality but for the circumstance that a moving
body encounters another body and changes the state of that
other body—urging it to move or arresting its movement.
This is a supposition not made in the bare definition of force;
and, therefore, we do something more than repeat the defini-
tion, when we affirm that the force imparted to the second
body is lost to the first. Now, this is all thav the Third Law
contains; only that law brings into prominence the distinct
case of force arising by attraction or repulsion at a distance.
Discarding, therefore, the present First Law, as being but the
definition of Inertia, we may condense the second and third
into a single statement declaring the Conservation motive
Energy, under re-distribution, whether by impact, or by
attraction or repulsion. This is the one axiom of the Science;
its foundations are inductive. It is a partial statement,
applicable to molar forces, of the all-comprehending law of the
Conservation of Force. Indeed in the limitation to molar
ONLY ONE LAW OF MOTION. 461
force, the principle is not strictly true; it is true with regard
to attractions and repulsions, and hence in Astronomy no
error is committed in applying it; it is not true of impacts ;
there is always force lost in a mechanical collision, or in the
transfer by machinery ; the lost mechanical energy re-appear-
ing as molecular vibration or heat.
Newton’s second law has been considered as a way of pro-
viding for the case of the communication of movement to a
body already moving in some other direction. A force impel-
ling in any direction will accomplish its full effect in that
direction, even although the body should be already in motion
in some different direction ; as when a ship sailing in a
westerly current is propelled by a north wind. This is the
foundation of the law of composition of Motion and Force, but
it is still only an application of the principle of Conservation
of Energy under re-distribution. Direction as well as amount
_are included in the principle; a body moving in a certain
direction and imparting motion, imparts it in its own direc-
tion, and in no other. Before affirming the Law of Conser-
vation in its full generality, we are bound to verify it for this
case as well as for mutual attraction; it has been verified,
and is affirmed accordingly.
The so-called ‘Principle of Virtual Velocities’ is a hypo-
thetical expression of the Law of Conservation suited to various
mechanical applications, such as the demonstration of the
mechanic powers. We cannot prove the statical proposi-
tion of the lever, without supposing it to move. Dynamically
the law of the mechanical powers is the only one consistent
with the Conservation of Force; and the dynamical proof is
given as the statical by the supposition of a very small motion.
7. The second great Induction of Molar Physics is the
Law of Gravity.
The Law of Gravity associates the two distinct properties—
Inertia and Gravity, and declares the one to be proportioned
to the other, throughout all varieties of matter. The Law is
sufficiently expressed thus :—LEvery portion of matter attracts
every other portion, the attraction in each being in proportion
to the mass (or inertia), and inversely as the square of the
_ distance.
This Law has been frequently referred to, in previous parts
of this work, as the one unequivocal case of two co-extensive
properties, constitut'ng a proposition fully reciprocating, and
convertible by simple conversion.
ee wee ae
462 LOGIC OF PHYSICS.
Our unit of force (so much inerta acting through so much
space) is thus the unit of weight, say a pound, moved against
gravity through the unit of space, say a foot.
Concatenation and Method of Molar Physics.
8. The branches of Molar Physics follow a Deductive
arrangement. The Abstract departments are purely deduc-
tive ; the Concrete unite Deduction with Experimental
determinations. |
The great division into Statics and Dynamics—Kquilibrium
and Movement—exhausts the abstract portion of the subject.
These are thoroughly mathematical in their structure; the
propositions and demonstrations are worked out according to
Geometry, Algebra, or the higher Calculus, respectively. A
preliminary mathematical department is constituted, which
has been termed ‘ Kinematics,’ containing propositions that
assume only the fact of Motion, together with mathematical
elements. The Composition and Resolution of Motions, under
every possible variety of complication, are mathematically de-
veloped under this branch ; it being also applicable to Optics.
The theorems are then found to be transferable to Statical and
to Dynamical Problems, which regard Motion as the result
and the essential fact of Force, whose full expression includes
as factors the Velocity and Mass.
The Concrete Branches are :—I, The Mechanic Powers, and
Machinery generally (fluid action not included). Here there
is an application of the deductive laws, but these have to be
modified by the molecular structure of bodies; and the modifi-
cations are ascertained experimentally. The laws of friction,
of stress and strain, of molecular transfer in impacts, &e., are
the subject of experiment almost exclusively. Where deduc-
tion is applied, it must be submitted at every step to experi-
mental confirmation. .
IL. Aydrostatics and Hydro-Dynamics, or abstract Statics and
Dynamics applied to Liquids. There is here also the employ-
ment of experiment to find ont the modifications of dynamical _
laws due to the molecular structure of liquids. There is a
farther use of experiment, in aid of the deductive process
itself, which is apt to be foiled by the complications of fluid
mobility.
III. Aerostatics and Pneumatics comprise the treatment of
gaseous bodies, to which the foregoing remarks also apply,
IV. Acoustics treats of vibrations of the air and other bodies,
-
CONCRETE DEPARTMENTS OF MOLAR PHYSICS. 463
constituting the agency of Sound. Here we have the transition
from the molar to the molecular; but the mode of dealing
- with the phenomenon (through the similitude of pendulous
and wave motions) has close alliances with the preceding
molar branches. In this department, however, j OmPAEIOS
predominates over deduction.
VY. Astronomy might be taken either first or last among
the Concrete branches. It departs the least from abstract
Statics and Dynamics; which is owing to the purity of the
gravitating force ; there being no friction and, in the celestial
region, no resistance. It is deductive throughout; yet, owing
to the great mathematical difficulties, the deductions must be
checked by continual observation; while to observation alone
we owe the knowledge of the co-efficients or constants,
In Astronomy, there are various problems that draw upon
the other concrete branches of molar physics, and even upon
molecular physics ; so that the position of priority among the
concrete branches has to be qualified. The tides, the physical
constitution of the sun and the planets, the theory of solar and
planetary heat and light—are examples of these far-branching
portions of the subject.
MOLECULAR PHYSICS.
9. In Molecular Physics, the phenomena have reference
to the action of the component molecules of matter.
The chief subjects are—
Molecular Attractions—Cohesion, §e.,
Heat,
Tight,
Hlectricity.
The primary assumption, axiom, or induction of Molecular
Physics is to the effect that the masses of matter are composed
of small particles, atoms, or molecules, attracting or repelling
each other in various modes, and possessing intestine motions.
This is a real proposition respecting matter, and not a mere
repetition of its defining property—Inertia. It is pre-emi-
nently hypothetical in its character ; that is, the evidence for
it is only the suitability to express the phenomena open to the
senses ; as, for example, the solid, liquid, and gaseous forms
of bodies, the heat or temperature of bodies, luminous and
electrical effects.
tt
se
Aa
St ee
ae
464 LOGIC OF PHYSICS,
Notions of Molecular Physics,
Molecule, Atom.— It is known asa fact that every kind of |
matter is made up of very minute portions, called atoms or.
molecules; the limit of minuteness being hitherto unascer-
tained. By supposing attractions and repulsions between the
atoms, we can represent the varieties of solid, liquid, and gas,
as well as the imponderable forces—heat, &c. The phenomena,
however, require that there should be different orders of
atoms or molecules; the ultimate atoms being grouped into
complex atoms, and those again, perhaps, into still higher com-
pounds. Thus, the Cohesion atom, the Heat atom, the Chemical
atoms, the Solution or Diffusion atom, are all hypothetically
distinct, the assumptions being varied to suit the appearances,
The definition of the atom or molecule,* therefore, is hypo-
thetical and fluctuating ; the only constant assumption is a very
minute element gifted with attractions and repulsions, by which
is brought about the aggregation into masses.
Motecunar Arrractions—Propertizs OF Marrer. Nume-
rous important notions arise out of this department of Physics, —
which discusses the various modes of aggregation of material
masses, and their causes, real or hypothetical.
Solid, Liquid, Gas.—These names for the three states of
matter, have already occurred under Molar Physics, and must
there have been defined up to a certain point. The exhaustive
definition of the various forms of solidity falls under Molecular {
Physics. I shall indicate, for ulterior ends, what seems the
best arrangement or succession of the properties of Solids,
Crystal.—Antithesis of amorphous. The crystal is not difficult
to define. The common fact is a regular and constant geo-
metric form as determined by the angles of the faces or
boundary planes. A substance, for example, always found in
cubes, or with right-angled solid angles, is a crystal; a sub-
stance that has no regular or constant form is amorphous;
such isa cinder. Subsidiary to the main idea, are the notions
—face, axis, nucleus, cleavage, fracture—and the several systems
* Although the adjective ‘ molecular’ is usedin the broad contrast with
the molar, while the substantive ‘molecule’ also conforms to the usage, a
more specific meaning has lately been attached to the mole. ule, in con-
tradistinction to the ‘atom.’ An atom is supposed to be chemically indi-
visible ; a molecule is the smallest combination believed to exist separately.
There is a hydrogen atom represented by H; but the hydrogen molecule
is HH, or Hy. The molecule of Phosphorus and of Arsenic is each
composed of four atoms. All this belongs .v the hypothetical part of
Chemical Combination.
a
MOLECULAR ATTRACTIONS. 465
of crystals—Tesseral, Tetragonal, &c.; also Isomorphism,
Dimorphism, Allotropy.
Hard, Hlastic, Tenacious, Ductile, Malleable. These are
names for a series of important attributes of solid bodies, to
which there is a corresponding series of contrasting properties
—soft or flexible, inelastic, brittle, inflexible, inductile or wnmal-
leable. They are mostly distinct properties, althongh to some
extent related. They are all strictly definable, and measurable
in amount or degree by given tests. Hardness is the resistance
to change of form, as by scratching or dinting; Elasticity is
the rebound from compression. Tenacity is opposed to being
pulled asunder. JDnuctility is tenacity under the process of
being drawn out into wire; if the hammer is employed, the
substance is called Malleable.
Viscosity is a softness approaching to liquidity. ‘ All bodies
capable of having their form indefinitely altered, and resisting
the change with a force proportioned to the alteration, are
called Viscous Bodies.’ (J. Clerk Maxwell).
Cohesion (Homogeneous attraction). Definable as the mutual
attraction of particles of the same substauce, as iron, flint, or
ice. The crystalline structure, hardness, and other qualities in
the previous enumeration, may be expressed as different
degrees and modes of cohesive energy. Cohesion is therefore
the hypothetical summary of the properties just named; and
its modes are to be accommodated to represent these with
accuracy. A crystal must have one mode of cohesion, a
lump of clay, a different mode. The limits of cohesion are
small; two pieces of plate glass will adhere strongly if in
close contact, but will not attract one another through a
sensible distance.
Adhesion (Heterogeneous attraction). A wide-ranging phe-
nomenon. It is defined — the attraction of particles of one
substance for particles of a different substance, as when glue
sticks to wood, mortar to stone, water to wood, &c. Cements,
Capillary action, Solution, Absorption of Gases, Alloys—all
suppose this mode of action. To express the full details—
which substances attract which, and with what degrees of
foree—requires a great many propositional statements, mest
conveniently given in the mineral or the chemical description
of each substance. Under the present head, the general
results should be presented.
Diffusion, Osmose.—These are properties extending beyond
what is implied in solution, and even anticipating Chemical
processes. Still, they are the immediate sequel to the preced-
466 LOGIC OF PHYSICS,
ing group of phenomena. Their definition is a generaliza-
tion of the phenomena brought to light by the researches of
Graham.
Crystalloid, Colloid, Dialysis.—By extending the application
of Osmose, Graham arrived at a distinction among bodies,
expressed by the antithesis—Crystalloid and Colloid, whose
definition is in the highest degree pregnant with important
attributes. (1) The colloid state is a mode of the anti-crystal-
line or amorphous modification of matter. (2) The colloids are
inert chemically, they are not powerful as acids or bases. (3)
In their own form, they have peculiar powers; as soft and
semi-liquid they allow other substances to diffuse in them.
(4) Still more important is their instability, their readiness to
pass into change, and gradually to sink down towards the
deadness and fixity of the crystal ; during which process they
are sources of molecular power. These two last peculiarities
fit them to play a part in living structures, into which they
enter largely as constituents (albumen, fibrine, starch, &., are
colloids). (5) Colloids, while permeable by bodies of the
erystalloid class, as salt and sugar, are impermeable to each
other; a most important law, on which Graham has founded
his method of Dialysis, and which is the explanation of many
interesting phenomena.
LH ffusion, Diffusion, and Transpiration (of gases).—These are
the phenomena parallel to the foregoing as manifested in gases ;
they have a modified definition accordingly.
Such is an orderly statement of the great leading notions of
the initial branch of Molecular Physics. They all demand
strict definition, and a separation of defining properties from
predicated properties, according to the best logical method.
Descending into the very depths of molecular action, they un-
avoidably anticipate other parts of molecular physics, and even
of Chemistry ; but this is not avoidable by any arrangement.
The priority of position is justified by the circumstance that
Cohesive Force is the inalienable attribute of all kinds of
matter, and is the counter-force to the great total of Huergy
expressed by the Correlated Forces- Heat, &c. Matter is what
we find it, on the one hand, through the opposing play of
internal cohesions, and on the other hand through the repulsion
derived from the transferable energy of the universe. It is
as Heat, Electricity, and Chemical Force, that this energy
ab extra counter-works internal cohesion; just as, in the
capacity of mechanical energy, it counter-works Gravity on
the great scale of molar movements, .
DEFINITION AND PROPOSITIONS OF HEAT. 467
-Heat.—The next department in order is the primary and
the typical form of molecular energy, in the great circle of
Conserved or Persistent Forces. The leading notion—Heat
itself is the only one attended with logical difficulties of defi-
nition. Properly speaking it is an ultimate, indefinable, in-
communicable notion, and its essential character is subjective.
Hach of us must be referred to our own sensations of heat and
cold in their different degrees, which sensations are unique
and not to be confounded with any uvthers. Nor is there any
perplexity in generalizing the particulars, with a view to a
comprehensive definition, as there is with matter and inertia ;
he that has one or a few experiences of change of temperature
knows all.
The physical or objective counterparts of this unmistakeable
subjective experience are numerous and various, and Lelong to
strictly physical investigation. The most obvious are the
increase of bulk by warmth, and the so called destruction,
(more properly re-construction) of material masses. A great
and protracted effort of generalization has been requisite to
encompass all the manifestations of this physical correlate of
a familiar feeling, and to embrace the whole in a unity of
expression. Hven at the present moment, the generalized
unity rests upon a hypothetical assumption, true in the main
fact, but uncertain in the shaping, and as yet imperfectly adap-
ted to the multiplicity of the thermal phenomena. Heat,
physically, is a mode of molecular motion, exchanging at a
definite rate with mechanical movement, as well as with the
other molecular modes termed Electricity and Chemical force.
If we define Heat by its subjective phase, the great physical
generalization is a predicate of concomitance, constituting a
real proposition. If we use the subjective fact merely as a
clue to the objective, and insist on making the definition ob-
jective, this property is then the defining property, from which
would flow innumerable deductive attributes (propria); while
there would be propositions (either propria or concomitants)
affirming the relationships of heat to other forces, and also the
material collocations or arrangements connected with the
transmutation.
The notions involved in the various phenomena of Heat, give
the heads of the science ; they are all definable by generaliza-
tion, and their elucidation needs abundant reference to facts in
the concrete :—Conduction, Convection, Radiation, Reflexion,
Absorption, Diathermacy, Refraction, Specific Heat, Latent
- Heat, Melting, Freezing, Evaporation, Condensation, Kbull-
468. LOGIC OF PHYSICS.
tion, Boiling Point, Distillation, Tension of Vapour, Dew
Point, Heat of Combination, Calorific equivalents.
Licut.—The exact position of this subject in a athiot hy
studied arrangement of topics is somewhat dubious. In some
important points, it has a close alliance to Heat; its manifesta-
tion in a body is almost always dependent on a certain
temperature. Moreover, as an influence radiating through
space, it has not only great similarity to heat, but also is
singularly open to mathematical treatment. Still, being as —
yet imperfectly understood in its reciprocation with the cor-
related forces, it does not stand to heat on the same footing as
electrical and chemical force. But for the close and easy
transition from Electricity to Chemistry, we might put Light
at the end of Molecular Physics. Or, as haying abstruse
chemical relationships, it might succeed to Chemistry. Thus,
the position actually accorded is owing to a seeming prepon-
derance in favour of one out of several alternatives.
Light, lke heat, must have a subjective definition to start
with ; and, in this view, it has the same freedom from ambi-
guity. But as Sight isa highly objective sense, we can incor-
porate with the subjective property the objective particulars
—radiation and transmission in space—which are revealed at
once to the luminous sensibility.
We may give the definition thus :—Light expresses a dis-
tinct state of mind known only to individual self-consciousness,
to which state is added the ‘objective experience of an emana-
tion from a material body to the eye, whereby we become
cognizant of the characteristic properties of matter named
visible.
The subsidiary notions are the main topics of the science :—
Transparent, opaque, translucent, shadow ; Incidence, Refrac-
tion, Index of Refraction, Tisai) Image, Reflexion, Mirror,
Caustic, Focus, Colour, Spectrum, Complementary Colours,
Dispersion, Chromatic Aberration, Diffraction, Rainbow,
Double Refraction, Polarization, Interference, Undulatory
Theory.
So far as these topics are concerned, the science of optics
depends upon no extraneous source beyond Mathematics, and
might have precedence of all the other subjects of molecular
physics. The connexion of Light with Heat, with Electricity,
and with Chemistry, would then fall under these peneae
departments.
Brecrrictry.—As the denotation of Electricity takes in—
Magnetism Voltaic Electricity Magneto-Electricity
Friction Electricity Electro-Maenetism Thermo- Electricity—
aya eae
CHARACTERS OF ELECTRIC FORCE, 469
it is no easy matter to find an exact connotation for the
general name. Two properties may be put forward: (1)
Polarity, and (2) Current action. As regards the first,
Polarity, there is uniform agreement in all the modes; and,
moreover, the polar attribute is prominent and pervading, and
imparts a destinctive character to all the phenomena. Still,
in carrying out the idea, we are met by the ambiguous phe-
nomenon, named by Faraday, Diamagnetism, a force mani-
fested by the magnet upon heavy glass and certain. other
substances, but without polarity, being equal repulsion by both
poles. This phenomenon, however, must be held in suspense
in the meantime, and not allowed to interfere with the defini-
tion on so vital a point.
The second characteristic of the Electric Forces, is their
being carried to any distance, through solid conductors, so as
to discharge themselves at any point. In ordinary chemical
action, as in the double decomposition of two salts, the sub-
stances must be in contact ; but by an electrical arrangement,
the oxidation of zinc in one vessel, may lead to the decompo-
sition of water in another. This important point of commu-
nity makes a strong alliance, although with differences, between
the electric forces.
These two leading features, coupled with subjection to the
great Law of Conservation, are all that can be at present
brought under the connotation of Electricity asa whole. The
different branches have each their special definition, attainable
by the same generalizing process. Definitions are also to be
provided for the subsidiary notions—Magnetic Poles, Meri-
dian, Declination, Inclination ; Electrics, Non-Electrics, Con-
duction, Insulation, Circuit, Induction, Charge, Discharge,
Electrica] tension ; Electrolysis, Electrodes.
Propositions of Molecular Physics,
Axiom of Conservation of Force.—At the threshold of mole-
cular physics, there must be provided a staterhent of the Law
of Conservation, in all its compass, or as embracing alike the
molar and the molecular forces. Although the law cannot
be fully comprehended at this stage, yet some attempt should
be made to exemplify its workings as Heat, as Hlectricity, and
as Chemical force, and also to point out the mutual conversion
of all the modes—molecular and molar. The law is the pre-
siding axiom of molecular Physics, and of Chemistry, and
through them reaches the domain of Physiology. It is every-
where the sufficing explanation of the origin of Force ; leaving
470 LOGIC OF PHYSICS.
to be investigated, the arrangements, situations, or circum.
stances, attending on the manifestation of force in each par-
ticular case.
Other propositions of Molecular Physics.—The various notions
or defining properties being clearly characterized, we may
readily ascertain what class of predicates usually go with
them so as to constitute the real propositions of the science.
Thus, with reference to the first department—Molecular Attrac-
tions, or the Properties of Matter, from which are excluded
whatever comes under Heat, Electricity, and Chemistry—the
atom or molecule being defined, we have, as real propositions,
the following: ‘ Matter is composed of atoms,’ ‘ the atoms of
matter attract each other.’ This last proposition being one of
wide generality, there fall under it many special propositions,
or modes of attraction, for different kinds.of matter ; but, in
this department, we are perpetually disposed to palm off
verbal propositions for real—as in affirming that hard bodies
have a powerful atomic cohesion. Hxamples of strictly real
propositions are these :—crystals are hard bodies, that is, the
cohesion of crystallization is intense in degree; crystals
are usually brittle, or the cohesion of crystals is of a short
range. Again, with regard to Adhesion, there is an import-
ant inductive generalization, that bodies of a nearly sumilar
nature are those possessing mutual adhesion; thus metals
adhere in solders and in alloys, earthy bodies, in cements and
in cohesive mixtures, and so on. Farther, the Diffusive
volume of a gas is inversely as the square root of its density.
These are propositions of co-inhering attributes, verified
only by wide and exhaustive agreement through the whole
sphere of the things concerned. |
Another large class of propositions under the same depart-
ment includes the numerical expressions of the degrees of the |
different attributes. These are the constants of the department,
and need no farther remark.
The propositions of Heat have the reality -arising in the
concomitance of subject and object facts. Apart from this,
they may be classified under the following heads. The first
class takes in the deductions from the law of Conservation,
confirmed by observation and induction :—such are the facts
of the dilatation of bodies by heat, of which fusion and eva-
poration are special manifestations. There is herein comprised
a wide field of natural phenomena; and many specific state-
ments are needed to cover the variety of modes in different
substances. Another class of propositions affirm, in their
a ee
et
PROPOSITIONS OF HEAT. 471
several modes, the great molecular property named Conduction,
_@ property with numerical degrees ; while important laws of
dependence or concomitance connect this property with the
molecular properties of bodies. Radiation next demands to
be considered, a fact with geometrical aspects and correspond-
ing predicates ; this part of the subject haviug a considerable
parallelism to the leading facts of Optics. The specific rates
of radiation of different bodies may be numerically ascertained,
and laws enounced, whose character is jointly deductive and
inductive. Absorption is another predicate, and similar
remarks apply to it.
The exhaustion of the consequences of the Law of Conserva- °
tion, would require a statement of the mode of deriving heat
from Mechanical force (crushing, collision, or friction), and
from the other ‘molecular forces; and also the situations or
arrangements whereby it returns to these again; the case of
producing mechanical force having been given under the great
fact of Dilatation.
On the whole, propositions of heat are (1) Derivatives from
Conservation ; (2) Constants, or numerical measures of the
various phenomena for different bodies; (3) Laws connecting
manifestations of heat with molecular structure; (4) Laws of
situation, or conditions of the transmutation cf Heat, to and
from, the other energies, with the constants, expressing the
rates of equivalence.
The foregoing account may suffice to exemplify the propo-
sitions of molecular physics. Were we to proceed to Liaur,
we should find a statement of definite phenomena—called
radiation, refraction, reflexion, dispersion, colour—all expressed
under numerical and geometrical relations. We should also
find some cases of concomitance of attributes, as Double Re-
fraction and Polarization. The connections of Light with
Heat and with Chemical Force, being underivable i om the
great Law of Conservation, must be given as empiiical induce
tions of co-inhering attributes, some of them of considerable
generality, as the connexion of light with temperature; others
narrow and special, as in the chemical relations.
Execrricity has the advantage of being fully correlated with
the other forces. It involves, however, great complexity of
arrangements, as conditions of its manifestation in the various
species ; whence the propositions are greatly occupied in stating
these arrangements or collocations ; many of them being hidden
in the molecular depths of bodies, and rendered in hypothetical
language.
21 e
ees
472 LOGIC OF CHEMISTRY.
Predominant Methods of Physics. |
10. Physics has been seen to be partly Deductive, and
partly Inductive. The Inductions principally relate to
Cause and Effect ; while, in Molecular Physics, there are
inductions of Co-inhering Attributes. The principles of
Definition are appealed to, and more especially for the
primary notions ; but there is scarcely any opening for
Classification.
As a Deductive Science, Molar Physics is a branch of applied
Mathematics, checked and controlled by the perpetual reference
to facts.
As an Inductive Science, Physics makes an unsurpassed
display of the machinery and resources of Observation and
Experiment. It also shows to advantage all the Methods of
Experimental Elimination. The facts being subject to the
great law of Conservation, the deeper experimental problems
consist in ascertaining the collocations or arrangements for
transmuting or evolving the different modes of force. The
researches and discoveries relating to Heat, Electricity, and
Light have this character to a very large degree.
The Hypotheses of Physics exemplify all the forms of Hy it
thesis formerly laid down. The chief instances—the Dynamical
Theory of Heat, the Undulatory Theory of Light—have already
been adduced in expounding the general subject. Another
hypothesis of inferior weight and character is the two Hlec-
trical Fluids, for representing the polar phenomena of Eleo-
tricity.
\
CHAPTER IIL
LOGIC OF CHEMISTRY. —
1. The relationships of Chemistry to all the departments
of Molecular Physics are intimate and sustained. The
special fact of the science is given in the name Chemical
Attraction.
Chemistry deals with the union and the separation of ae
ments ; it regards all the substances of nature as either simples
REAL PREDICATIONS OF CHEMISTRY. 473
or compounds; the manner of union or composition being
special to the science. There are unions not chemical; as
when bodies are pulverized and mixed together without farther
intimacy. There is a still more intimate union in solution,
which, however, also comes short of chemical union.
2. Chemical Attraction, or Union, involves these facts :
(1) The Properties are definite. (2) In the act of union,
there is Heat evolved. (3) The chief properties of the
elements disappear.
A fourth mark, which may either enter into the definition,
or be reserved as a predicate, is that chemical union takes
place between dissimilar substances, while solution or adhesion
is between similars. If reserved as a predicate, this property
will be one of the properties forming real propositions, as ex-
emplified in next section.
It is not necessary here to exemplify these defining proper-
ties. Ina work on chemistry, it would be advisable to offer
in advance a few illustrative cases, as a preparation for enter-
ing on the systematic detail.
This disposes of the leading notion of Chemistry, being the
essence or connotation of the name, the Definition of the
Science. A mistake in Logic is made when these properties
are stated as real propositions; they are not predicated of a
subject called Chemical Attraction, they constitute or make up
that subject.
3. The Propositions, or real predications, of Chemistry
relate (1) to the circumstances, or conditions of Chemical
change, (2) to the substances that undergo the change.
(1) When we have defined the fact of Chemical union,
(with its correlative and implicated facts, Decomposition,
Simple Body, Compound Body), we have to state the various
circumstances, conditions, or modifying influences of Chemical
change. This constitutes numerous real predications, of great
theoretical and practical moment.
(2) The enumeration of substances that combine together
chemically, or that bring about chemical decompositions yields
_@ large mass of real propositions, under the general predicate
of Co-existence, or Co-inhering attributes. Oxygen com-
bines with hydrogen, and forms water; sulphuric acid decom-
poses chalk, common salt, &c.
The expressions for the definite combining numbers are real
propositions, corresponding to the ‘constants’ of Physics.
4°74. LOGIC OF CHEMISTRY.
The relation of Chemical Force to the other Correlated
Forces may be re-iterated at the commencement of the subject ;
although, as with the other preliminary statements, the under-
standing of it will grow with the unfolding of the future details.
Arrangement and Methods of Chemastry.
4. The division of Chemistry is into [NorRGANIC and
ORGANIC.
Inorganic Chemistry is laid out under the succession of
the Simple Bodies.
The distinction of Inorganic and Organic would exemplify
definition with a broad doubtful margin. The basis of the
distinction is the circumstance that a large class of highly
important substances can be obtained only from living bodies ;
such are starch, sugar, albumen. This peculiarity of origin is
associated with two other peculiarities, namely, the limited
number of elements in organic bodies, and the great complexity
of the chemical constitution. There would be a.convenience in
adopting all the three facts as a complex definition of Organic
bodies, from which, by antithesis or negation, we have the
definition of the Inorganic.
The Chemistry of the Inorganic or Mineral world comes
first ; and its method of arrangement is to adopt some succes-
sion of the Simple Bodies, and under them, to distribute the
various Compounds,
Classification of the Simple Bodies or Elements.
5. The Simple Bodies, or Elements, are divided, in the
first instance, into Metals and Non-Metals. Although
there are transition elements, as Tellurium and Arsenic,
the distinction is founded on important differences. ,
The Metals have certain prevailing characteristics, but yet
in a varying degree, and with occasional exceptions. (1) Most
striking are the visible properties— Opacity, Lustre, and Colour.
Metals are opaque; they have thepeculiar lustre termed metallic;
and their colour is white or grey, with the exceptions —Gold,
Copper, and Titanium P which are yellow. (2) They are solid,
Mercury and Hydrogeff being notable exceptions. The solidity
is usually joined with compactness of structure, as shown in
the properties—hardness and tenacity. (3) They are com-
paratively good conductors of Heat. (4) They are conductors — 4
of Hlectricity. (5) They are Ei ectro-positive. (6) They com-
wa
METALS AND NON-METALS CLASSIFIED. 475
bine chemically with the Non-Metals. (7) Their compounds
with Oxygen are for the most part Buses, and not Acids.
The question is not here raised how far some of these pro-
perties are implicated in others. Since the implication is not
obvious, the properties are provisionally given as distinct. A
more important remark, from the logical point of view, is the
occurrence of exceptions to almost all the properties. In the
complex defining of natural objects, we must be prepared for
this circumstance, which does not render the classification vain
or nugatory. Although mercury is a liquid we neither sur-
render the property of solidity, nor exclude it from the class.
Solidity is wanting only in two; and mercury has all the
other six properties. This is probably one of the cases where
Whewell would desiderate a type, or average representative
Specimen, some metal possessing in fair measure all the
prevailing characters.
The Non- Metals are defined by the antithesis of the above
group of properties. As regards Light they are not uniformly
opaque, and when opaque, they are, except selenium, wanting
in lustre. There is only one Gaseous metal, there are four
gaseous non-metals. They are non-conductors of Electricity,
and Hlectro-negative. Their compounds with oxygen (one of
their number) tend to Acids, and not to Bases.
_ Whenever aclassification is possible, there must be common
properties, and these are possible to be stated. Still, in the
usage of Chemical writers, the statement of the generic pro-
perties of the classes ‘metal’ and ‘ non-metal,’ does not dis-
pense with the repetition of these in the detail of the species.
The Natural History methods, not being susceptible of exten-
sive application in Chemistry, are hardly attended to, even
where admissible. Nevertheless, as the situations arising in
the classification of the Simple Bodies are highly illustrative
of situations in Botany and in Zoology, we may follow out
the present case a little farther.
6. Both Metals and Non-Metals are sub-divisible into
smaller classes or groups.
In the Metals, there are certain groups that have important
affinities—such are the Alkali-Metals (Sodium, é&c.), the
_Alkaline-Earth Metals (Barium, é&c.), the Earth-Metals
(Aluminium, &ec.), the Noble Metals (Mercury, Silver, Gold,
&c.)remarkable for refusing combination.
sy :
480 LOGIC OF CHEMISTRY.
about one twentieth to one thirtieth of its bulk (.04114 at
32° F.; .02989 at 59° F.),
(+) Relations to Heat.—Rate of Dilatation not stated. As
regards the temperatures of Liquefaction and Freezing, has
never been liquified, although condensed to z}q of its bulk.
Specific Heat, about one fourth of water (.24.05).
(5) Relations to Hlectricity.—Is a magnet at common tem-
peratures. In the Voltaic series, it is at the head of electro-
negative elements.
(6) Chemical relations.—Speaking generally, it is the most
widely-combining element in nature. With a doubtful excep-
tion (fluorine), it combines with every known element; not
merely its natural opposites, the metals, but non-metals like-
wise. Classes of leading importance in chemistry are com-
pounds of oxygen with the other elements ; the oxides of the
metals are what are termed bases; the oxides of the non-
metallic elements are generally acids. With Hydrogen, it
yields water. The act of combining with Carbon, either alone,
or along with hydrogen, is the most familiar example of
violent and rapid chemical union, with evolution of heat and
of light, and is termed ‘ combustion.’
The peculiar circumstances attending the combinations of
oxygen vary with the character of the second element. Thus,-
in the leading fact—Heat of combination—the maximum
evolved is with Hydrogen; Carbon yields one fourth of that
amount; Phosphorus, about a sixth; Sulphur, about a
fifteenth ; Zinc, Iron, Tin, about a twenty-sixta.
Atomic number, 16. .
As regards the conditions of entering into combination,
there is great variety, from the extreme of readiness at the
ordinary temperature of the atmosphere, to the extreme of
indifference, conquered only by the aids to combination,
namely, artificial condensation, heat, the electric spark, the
contiguity of chemical action already begun, &c. Part ofthe —
peculiarity is due to the state of oxygen itself:—which may
be either in the ordinary atmospheric dilution; or prepared
apart free from any other gas (whereby all combinations are
acclerated) ; or, lastly, in combination with other bodies as
in water (a powerful oxidizer); in the nitrates, in chlorate of
potash—which salts permit of the liberation of their contained
oxygen in a highly concentrated form.
Local spread of Oxygen.—Need not be here detailed.
Modes of obtaining Oxygen.
I doubt the propriety of including, under Oxygen, any more
OXYGEN DESCRIBED. 481
detailed account of the oxygen compounds. There are better
opportunities afterwards, under the several elements that form
the other members of the compounds,—carbon, hydrogen, the
metals, &c. Nor is it necessary to bring forward Combustion,
of which a sensational use is commonly made, in the descrip-
tion of oxygen. A disproportionate prominence is thereby
given to what is, strictly speaking, incidental only to some of
the modes of oxidation, and is found in other chemical com-
binations if they happen to be rapid and energetic. Combustion
is a special thesis under the general head— Chemical Union, its
conditions, and circumstances—and is of great importance
both theoretically and practically, but it need not be appended
to Oxygen. If involving too much anticipation of details to
be given in the preparatory view of Chemical Combination
(where, however, it might be briefly indicated), it might be
brought in at some convenient point, by way of digression,
as for example, at the end of Carbon, the chief element in
ordinary combustion.
Ozons.—A supposed allotropic form of Oxygen, under
which the oxygen is rendered more active in entering into its
various combinations.
The specific gravity of ozone is greater than of oxygen.
Adhesion.—It is not soluble in water, nor in acids or in
alkalies; but it is soluble in iodide of potassium.
- Relations to Heat.—Its active character is destroyed by a
temperature not much above boiling water.
Relations to Hlectricity.—The transmission of a series of
electric sparks through dry oxygen is one of the modes of
producing it.
Odour.—It has a characteristic odour, whence its name.*
Chemical properties —While it does not combine with any
substance but those that oxygen combines with, it combines
at temperatures, and under circumstances where oxygen does
not combine. Hence it is a powerful oxidizing agent—ain oxi-
dizing metals, in destroying vegetable and animal compounds,
in bleaching, in purifying the air from miasmata, in stimulating
the respiratory organs.
Modes of preparing Ozone.
Remarks on Ozone.t—lt is interesting to note the power of
electricity to give a new combining aptitude to oxygen.
* Taste and Odour may provisionally be given after Electricity, and
before Chemical properties. They are doubtless a consequence of Chemi-
cal re-actions.
4 The heading ‘ Remarks’ is intended, among other uses, to avoid the
A o eg egrey Se
482 LOGIC OF CHEMISTRY.
Nirrogey.—A gas. ,
As regards Light, transparent, colourless; Refracting In-
dex, 1.0093.
Specific gravity.—.9713. Atmosphere 1.
Adhesion.— Water dissolves about a thirtieth of its bulk at
ordinary temperatures.
Relations to Heat. —Dilatation not stated. Never been
liquefied. Specific Heat, slightly less than Oxygen, .2368.
Relations to Llectricity—Next to oxygen in the EHlectro-
negative series.
Chemical relations. —Nitrogen enters into a very limited
number of compounds. Where it does combine, it is sin-
gularly inert, or indisposed to enter into combination; de-
manding to be placed in the most stimulating conditions.
Many interesting consequences in vegetable and in animal life
are traceable to this peculiarity.
Compounds with Oxygen.—Recited in so far as illustrating
Nitrogen.
Compounds with Hydrogen.— Ammonia, &e.
Compounds with Carbon.—Cyanides. |
Spread of Nitrogen.—Modes of obtaining it. Remarks :—
bearings upon Chemical theory.
The next example is a solid element.
Carpon.—A solid, in two states—crystallized Diamond, and
amorphous Graphite. These occur in such a degree of purity
that they may be taken as typical of the element.
(Diamond).—The Crystallization, Optical Properties, Speci-
fic Gravity, need not be here recited.
Cohesion.—The hardest body known; hence at the top of
the scale of mineral hardness. .
Adhesion. —A very important circumstance as regards other .
forms of carbon, but not ascertainable in the diamond itself. j
Relations to Heat.—Is not fused or volatilized by the highest |
known heat; is not known to exist'either as liquid or as vapour.
An intense heat merely reduces it to a black opaque mass.
Relations to Hlectricity.—A non-conductor. Carbon has a
high relative place in the Electro-negative series (place given),
Before stating the chemical relations, a similar recital should
be given for the other form, Graphite.
Chemical relations. The range of elements combining with
carbon comprises—Oxygen, Nitrogen, Hydrogen, Phosphorus,
Sulphur, and many Metals, especially Iron. It does not enter
confusion and perplexity of introducing speculative considerations inte
the methodical description, .
ee
DESCRIPTIVE METHOD. 483,
into combination unless at high temperatures, and then com-
bines with rapidity and copious evolution of heat.
Compounds with Oxygen.—Carbonic Acid, Carbonic Oxide
(described at full length).
With Nitrogen.—Cyanogen ; alluded to.
The other compounds may be postponed.
Spread and Sources of Carbon.—Impure Forms.
Remarks on Carbon.—Combustion.
These examples are suflicient for the purpose of indicating
a systematic mode of describing the elementary bodies. They
would apply equally to compounds. In them, however, the
chemical relations involve another circumstance, namely, the
modes of decomposition.
In certain of the elements, the chief practical interest is
found in impure forms—alloys, or mixtures with other in-
gredients; for example, Iron. Still, itis desirable, for theo-
retical completeness and consistency, to advert, in the first
instance, to a pure or typical form, in order to know what the
substance is in itself, both physically and chemically. The
alloys or mixtures may then be given; but before their
practical bearings are touched upon, their properties are
to be recited as illustrating the changes brought about by
mixture, thereby contributing facts to the inductive laws
of Adhesion.
8. In Descriptive Method, it is of importance not to
mix explanations and theorizings with the description.
In deseribing a quality, the first thing is to state precisely
whatit consists in, or how it is discriminated. Moreover, the
whole series of qualities should be gone through, in the first
instance, and no attempt made to connect them with one
another, or with other properties, in general laws. This
last operation should always be kept distinct. The remark
applies to every science where description enters.
9. When bodies are closely allied in their nature, and
are in consequence grouped as genera, their differences
should be exhibited in marked contrast.
The Halogens among the non-metals, the Metals of the
Alkalies, &c., make groups or genera, with agreeing peculiari-
ties. These points of agreement are stated at the outset, so
as to abbreviate the details of the species. Attention should
next be given to contrasting pointedly the agreeing members
among themselves. Thus Sodium and Potassium agree to a
Veer
,
484 LOGIC OF CHEMISTRY.
very large extent; and after the agreements, the differences
should be given in a tabular antithesis. epttiel
10. The generalities of Chemistry are H’mpirical Laws.
The Atomic Theory is commonly said to be the highest
generalization of Chemistry. This, however, must) be
guardedly stated so as not to confound definition with pro-
positions. The nature of Chemical Attraction is expressed in
a complex definition (Definite numbers, Production of Heat,
Merging of elements). There may be real predication in
declaring these three facts to be conjoined; and their con-—
junction may be resolved into higher laws, or converted from
an empirical to a derivative conjunction.
The propositions, in connexion with Chemical action, that
have in the highest degree the character of real concomitance,
are those that affirm the conditions, arrangements, or situa-
tions attendant on combination and on decomposition.
For example, Combination requires proximity of the ele-
ments, and is favoured by all the circumstances that aid
proximity, as liquefaction ; it is resisted by strong cohesive or
adhesive forces, and proceeds as these are released. It is
brought on by elevation of temperature in numerous instances.
It is induced by the electric spark; which may operate by
mere rise of temperature, but more probably by polarizing the
atoms. Itis promoted by concurring combinations ; it accom-
panies decompositions. These are all empirical laws. They
are, moreover, statements as to general tendency, and need to
be accompanied, each with a schedule, stating the individual
substances and situations of their applicability.
Many other laws might be cited:—The celebrated law of
Berthollet, regarding the double decomposition of salts; the
laws that simple substances exhibit the strongest affinities,—
that compounds are more fusible than their elements,—that
combination tends to a lower state of matter—from gas down
to solid. |
As Empirical laws, these have no other verification but
Agreement ; they are only surmised to be laws of causation ;
they are limited to adjacent cases. |
11. The ultimate generalizations of Chemistry must fall
under the Law of Conservation of Force, and must express
the most generalized conditions of the re-distribution of
Chemical Force. |
The Law of Persistence over-rides every phenomenon of —
1
]
‘
‘
:
'
HYPOTHESES IN CHEMISTRY. 485
change, but it must be accompanied in each case with laws of
Collocation. In Chemistry, there must be indicated the pre-
cise conditions of chemical re-distribution, whether in com-
bination or in decomposition. It is necessary to find out, in
the most general form, the situation or situations that bring
about chemical change, in either direction. If this can be
comprehended in one law, that will be the highest, the ulti-
mate law of Chemistry, the Chemical appendage of the Law of
Conservation. The Empirical laws above quoted will then
have the improved character attaching to Derivative laws.
12. Chemistry contains, as a part of its nature, nume-
rous Hypotheses. These are mainly of the class named
Representative Fictions.
To express in the most general terms the numerous pheno-
mena of combination and decomposition, certain arrangements
of the component elements of the compounds are assumed
hypothetically. It is a fact that sulphate of potash contains
certain proportions, by weight, of sulphur, oxygen, and potas-
sium; it is a hypothesis that the salt is made up in the
particular way shown by the formula KO,SO;, being a binary
compound of two other compounds.
The Atomic Theory of Dalton contained a generalization of
facts embedded in Hypothesis. The facts were the fixed pro-
portions of bodies combining chemically; the hypothesis, that
each substance is composed of atoms, and that, in chemical
union, an atom of one substance joins with one, or with two,
or with more atoms of another; there being always a neat
numerical relation without remainder. No one now regards
this as more than a representative fiction, unsusceptible of
any other proof than its facility in expressing the facts.
The Constitution of Salts is the great battle ground of
chemical hypotheses, being the key to the entire structure of
chemical representation. There is, however, a perfect under-
standing as to the nature of the proof to be offered for the
rival hypotheses, namely, the suitability to comprehend the
greatest number of chemical re-actions, or combinations and
decompositions. It is a question purely chemical, and not in
anywise logical in the sense of demanding attention to be re-
elled to neglected logical principles.
As examples of the subordinate hypothetical points, we may
quote the singular idea of supposing an element to combine
with itself—hydrogen with hydrogen, chlorine with chlorine,
and so on; a very great stretch, seeing that opposition of ele-
‘ as a. : e
486 LOGIC OF CHEMISTRY.
ments is a predicate of chemical union. A better example of
a likely hypothesis is the proposal to assign to bodies of dif-
ferent properties, having the same ultimate constitution, a dif-
ferent proximate constitution; as formic ether and acetate of
methyl. The bold hypothesis of Gerhardt and Griffin—to re-
gard as two substances, iron when entering into proto salts,
and when entering into sesqui-salts, and the same with all other
elements producing sesquioxides—was considered as a relief
from otherwise inextricable difficulties.
The hypothesis of the Atom, or lowest chemical constituent
is now coupled with another hypothetical entity—the molecule
representing the smallest number of atoms of each substance
supposed to possess separate action. Thus the molecule
- of nitrogen is said to be made up of 2 atoms; the phosphorus
and arsenicum molecules, 4 atoms, and so on.
When a number of different salts are in the same solution,
as in a mineral water, it is a matter of hypothesis which acid
is attached to which base. (Miller’s Chemistry, II. 824.)
The class of Scientific Hypothesis consisting of unverified
theories, does not require special mention in Chemistry, Apart
from the representative fictions, essential and permanent in the
science, there are no hypothetic forces or agents. The great
prevailing agent or cause of chemical change is, and can only -
be, a molecular aspect of the great primeval force named under
the Law of Conservation. Until the supplement of this law,
as regards chemical transformation—the universal conditions
or collocations—be worked out, there will be many hypotheti-
cal collocations, which will be susceptible of final proof or
disproof.
Nomenclature and Classification of Chemistry.
13. The Nomenclature and the Classification of Chemi-
stry involve these points :—(1) The use of a symbol for
each elementary substance; (2) ‘lhe expression of the
ultimate constitution of compounds; (3) an expression of
the supposed proximate constitution of each compound in
a manner suited to its re-actions with other bodies.
(1) The symbolical notation has the advantage of affording
a brief and yet full expression to the most complicated com-
pounds, rivalling, in this respect, the notation of Mathematics.
It also enables bodies of like composition to be readily classed,
and their class indicated to the eye.
The nomenclature for expressing in terms the various bodies
a
CHEMICAL NOTATION, 487
is made up of the names of the elements—Oxygen, Carbon,
Tron, Silver—and of a systematic mode of uniting these in
compounds—carbonic acid, carburet of iron, &e. Only binary
compounds are stateable in this way ; a higher combination is
expressed in some supposed binary resolution—sulphuric acid,
acetate of potash, chloride of formyl. Substances like sugar,
starch, albumen, are given in their familiar names. Hence
double naming is, in Chemistry, a special and limited process ;
and has no analogy to the names of species in Botany and
Zoology.
(2) The notation exhibits the ultimate constitution of all
compound bodies, by stating their constituents and the pro-
portions of each ; H, O is the analysis of water; F O, protoxide
of iron; F, O;, peroxide or sesquioxide.
(3) The symbols are farther accommodated to give the
hypothetical upbuilding of the elements in complicated com-
pounds ; as in the theory of Salts. The ultimate analysis gives
the amount of oxygen in a compound, and the formula states
in what ways the oxygen is supposed to be distributed; an
oxygen salt, in the old theory was a binary compound of
two oxidized radicles, the oxide of a non-metal (as sulphur)
and ofa metal (as iron); sulphate of iron (proto=ide) S O; Fe O.
The analytical (or Empirical) formula of acetic acid is C, H, 0,4;
of the rational or hypothetical formula, there are no less than
seven renderings (Miller’s Chemistry, vol. TLL o. OL
14. A desideratum in Chemical Nomenclature is the
statement of the structural Heat of the bodies.
The formula H, O is given indifferently for steam, water,
and ice; although the exact difference of structural heat in
the three admits of numerical statement. Calling ice H, O; -
we may call water H,O + 180°; steam H, O + 1180", on
the usual reckoning of the heat of boiling and of evaporation.
Farther, when Hydrogen and Oxygen combine, there is
a great evolution of structural heat, which is lost to the com-
pound; a provision might be made for indicating the exact
figure, which has been found out by experiment; a certain
minute quantity would be attached to H, O, on this account,
_ and about one fourth of that quantity to © O;
LOGIC OF BIOLOGY.
1. Biology is the Science of Living Bodies—Plants and —
Animals ; its exact definition is the definition of Life. -
Definition of Life.
2, Life is to be defined by a generalization of what is
common to Living Bodies.
The Denotation of the term Living Body is well fixed ;
there is scarcely even a debateable margin between the
Organic and the Inorganic worlds.
Choosing Assimilation as a characteristic fact of bodily life,
and Reasoning, as an example of mental life, and contrasting
both with the characters of dead matter, Mr. Herbert Spencer
arrives at the following highly complex definition :—
1. Life contains a process or processes of change.
2. The change is not a simple or individual act, but a series
or succession of changes.
8. Life involves a plurality of simultaneous, as well as suc-
cessive changes.
4, The changes are heterogeneous, or various in character. —
5. The various changes all conbine to a definite result. .
6. Finally, the changes are in correspondence with earternal
_ co-existences and sequences.
In sum :—Life is a set of changes, simultaneous and succes-
sive, combined toa definite result, and in correspondence witb
external circumstances. Or, in a briefer form, Life is the
continuous adjustment of internal relations to external rela-
tions.
So carefully has the comparison been conducted, that no
exception could be taken to any part of this definition. Hvery
one of the particulars occurs in all living bodies, and in no
kind of dead matter. The apparent defect of the definition is
omission ; it does not express or seem to suggest points that
strike the ordinary observer. For example, there is no allusion ~
to the organized structure, at the foundation of which is the —
peculiar constituent known as the cell, or nucleated corpuscle.
Again, there is no mention of the individual and independent
SO ee Jere hen
ELEMENTS OF LIVING BODIES. _ 489
existence of living bodies; with which is also associated the
cycle of birth, growth, and death.
These omissions, real or apparent, might be defended or
explained on one of three different grounds.
First, it might be said, that the facts mentioned, although
present and conspicaous in many or in most living bodies, are
not found in all, and therefore cannot be adopted into the
general definition, They can be taken notice of only in
defining the classes or subdivisions of the whole kingdom of
animated nature. This remark would be a sufficient justifica-
tion, if it were true; but it is not true, at least to the extent
of excluding the mention of the circumstances from the
definition.
Secondly, it might be said, that the definition does not aim
at being e:haustive, but only at being discriminative ; while
it is based on essential characters, it does not profess to give
all the essential characters. Enough is given to prevent us
from ever confounding a plant or an animal with a stone;
but there is no intention of stating every feature that separates
living bodies from the inanimate world.
To this the obvious reply would be, why should all the
essential characters not be given? There is no apparent
reason for omitting in the statement whatever can be dis-
covered as common to the whole department of animated
nature.
Thirdly, it might be alleged, that the aspects in question
although not appearing on the surface of the definition, are
yet implicated on it, and are unfolded in the due course of the
exposition. The definition, it may be said, goes to the root of
the matter; while all else branches out from that, and is duly
unfolded in the subsequent exposition of the science.
Tn order, however, to bring forward at once whatever can be
assigned as general characters of living bodies, whether
primary or derived, we shall re-cast the definition, and dis-
tribute it under the heads—Constituent Elements, Structure,
and Functions.
3. I. Living bodies are constituted from elements com-
mon to them with the inorganic world.
The chief constituents of Living bodies are these four—
Carbon, Hydrogen, Oxygen, Nitrogen ; the last, Nitrogen,
being most abundant in animals. To these are added, in
smaller proportions, Phosphorous, Calcium, Sulphur, Chlorine,
Fluorine, Sodium, Potassium, Iron, Magnesium, Silicon.
490 LOGIC OF BIOLOGY,
The various properties, Physical and Chemical, belonging
to the several elements are found operative in their organized
form. All the mechanical and molecular laws are traceable
in living bodies.
Chemically considered, organic bodies, are exceedingly
complee compounds. The department of Organic Chemistry
is devoted expressly to these compounds. According to the
chemical reckoning, a single atom of an organic substance, as
sugar, starch, albumen, contains hundreds of simple chemical
atoms; the atom of albumen is said to be made up of 880
atoms of the four chief organic elements.
Il. With reference to STRUCTURE.
(1) Living bodies possess a peculiar structural complexity,
commonly called the Organized Structure. Associated with our
notions of life is a certain mechanism, or machinery, very
various in its extent and complication in individuals; attain-
ing in the higher animals a degree of complicated adjustment
unequalled in any other department of nature. Such strne-
tures as the eye, the ear, the brain, of human beings are, in
our conceptions, the very acme of structural mechanism.
It is now known that the ultimate constituent of all the
variety of structures is a microscope element called a cell, or
nucleated corpuscle ; by whose aggregations and transforma-
tions, tissues are formed, which tissues make up the organs.
It is true that in certain low forms, both plants and animals,
the cellular structure is not apparent, and therefore its visible
peculiarities — namely, the bounding pellicle and internal 3
nucleus—are not absolutely essential; still, we cannot omit q
from the definition an arrangement so completely bound up
with all living nature, the few apparent exceptions being
equivocal.
(2) Another prominent feature of the living structure is
Indwwiduality, or individuation. Living matter instead of exist-
ing in vast continuous masses, like rock, is separated into
distinct individuals. As with other peculiarities, however,
there is an ambiguous margin here also. In animal life gene-
rally, and in plant life generally, we have no misgiving as to
individual existence ; men, sheep, forest oaks, are all distinet
and separate. Still, a scientific definition must grapple with
the whole field of cases, having merely the requisite latitude
of a small doubtful margin. Mr. Spencer defines the indi-
vidual, with reference to his definition of Life, as any concrete
whole performing within itself, all the adjustments of internal
LIVING STRUCTURE AND FUNCTIONS. 491
to external relations, so as to maintain its own existence.
This definition, to a certain extent anticipates Function, but
so does :.ny adequate statement of Structure; the separation
of Structure and Function is one of great logical convenience,
but, in nature, the two things are inseparable.
With Individuality there is closely associated, in our con-
ceptions of living beings, the Cycle of existence, the derivation
of one living being from others, and the necessary termination
of each individual’s existence, after a definite career. Here,
too, we may seem to anticipate what belongs to Function.
(3) We may not improperly state in connexion with struc-
ture, and as following on Individuality, a circumstance so
notorious, that to omit it from the comprehensive statement of
hfe would appear inexplicable, namely, the vast Variety of
Forms and Structures. Uniformity, comparatively speaking,
pervades dead matter; variety is the characteristic of living
substances. The different forms of Plants and of Animals
count by thousands; there are upwards of one hundred
thousand species of Plants, and a still greater number of
Animal Species; while of every one of these distinct species,
there is an indefinite unceasing multiplication of individuals,
nearly, although not absolutely alike.
One of the chief demands of Biological science is to find an
orderly arrangement for such a host of various forms. This
makes Biology, inter alia, a science of Classification.
III. As to FUNCTIONS.
The living structure is naturally active, changing, produc-
tive, and its most characteristic points must have reference to
these activities. Here we may embrace the substance of Mr.
Speneer’s definition, in two principal heads—Change, and
Adjustment to external circumstances.
(1) A definite combination of changes, simultaneous and
successive.
(2) An adjustment to external circumstances.
(3) It must seem unpardonable, however, not to bring out
into prominent statement at the outset, that very remarkable
phenomenon of living bodies, to which there is no exception,
namely, Assimilation, or the, power of an existing organized
- particle, to impart its own organization to an adjoining particle
having the proper chemical constitution. This magic touch
of vitality, has only a faint parallel among inanimate bodies ;
combustion, and chemical combinations generally, make but a
small approach to it. Its lesser manifestations are in the
A9Q LOGIC OF BIOLOGY.
renewal, by nutrition, of the living tissues; its culmination
is in the throwing off of the germ, or seed, apparently homo-
geneous and structureless, but possessed of interior markings
that decide whether its future is to be a man or an oak; a
white man, or a negro; a flat nosed or an aqulline-nosed man
or woman. We may not be able to consider whether this
great property be essential and fundamental, or whether it
be derived from other properties, already given in the defini-
tion. ney te
We may repeat under this head, the peculiarity abov
adverted to, under individuality of structure—the Cycle of
existence, or birth, growth, and death. .
(4) It cannot be irrelevant to the comprehensive definition
to advert to the connexion of Mind with Living Bodies.
True, this is not a concomitant of all living bodies, yet it
appears only in connexion with the living form. When we
make the first great division of life, into Plants and Animals,
we obtain the more precise boundary of the mental manifesta-
tions. Still, at the very outset, we are interested to know
that this characteristic manifestation appears only in the
department of living structures. .
The foregoing definition professes to leave out no fact that
can be found inhering in all living bodies. The first requisite
in defining is to be exhaustive; it is an after operation, of
_ great scientific interest, to trace the dependence of one or
more properties upon the others, and to assign what appears
to be the ultimate and underivable properties. At present,
however, all such derivation is but tentative and hypothetical,
and therefore, is not suitable to be brought forward at the
commencement of the subject. Provisionally, these various
peculiarities are to be held as distinct; no one being assign-
able as a derivative of another. é
Divisions of Biology.
4. The Divisions of Biology are in conformity with the
Definition. |
The first part of the Definition refers to the Organic Chemi-
stry of Life. This subject is partly given under Chemistry,
and partly as the Introduction to Biology. |
The two other parts of the definition suppose a separate
consideration of Structure and of Function. We should fully —
understand the reasons and the limits of this separation.
STRUCTURE AND FUNCTION VIEWED SEPARATELY. 493
_ These two facts are inseparable in the reality. But as, in
less complicated subjects than Life, we have often to make
_ abstraction of some qualities to the exclusion of others where
there is no actual separation possible, so in the present case
we find it advisable to consider Structure by itself, before
* viewing it as connected with Function.
Yet this separation may be carried to an unjustifiable
extreme. As soon as the mind has perfectly comprehended a
structural arrangement, we are prepared to enter upon the uses
or functions of that arrangement. Indeed, while the know-
ledge of the structure is still fresh, the knowledge of function
should be imparted. Function completes and fixes the idea
of structure, in so far as the two are manifestly connected.
The only reason for not following up the account of structure,
_ with the account of function, for every distinct living organ,
would be the necessity of viewing Function as a connected
whole, and therefore not to be entered on unless it could be
given as a whole. For example, the Function of Digestion
could not be entered on till the entire group of alimentary
organs were structurally described.
The separation of the two subjects is carried to a question-
able extreme in the special Biology of man; Anatomy and
Physiology being, by present convention, treated in distinct
works, and taught by distinct teachers in the schools. The
just middle plan would be to include both in one work, and
to append to the Anatomy of each organ—Bones, Muscles,
Heart, &c.—the Physiology or function.
In the usual treatment of Plant Biology, Structural Botany
is given first, Physiological Botany next (in the same treat-
ise); the student being made to wait for the account of
Function in any organ until Structure has been gone through
in every organ. The justifying reasons are probably these :—
(1) It is possible to carry provisionally the whole structure
in the mind, without the assistance that function would give ;
and (2) there is a convenience in treating function as an un-
broken whole.
In Animal Biology, the branch called Comparative Anatomy
takes each organ apart, giving both structure and function,
and exhausting the varieties of each through the animal series.
Structure has to be viewed, in its successive moditications,
through the cycle of the individual life. This is called
Embryology. A still more extended view is the considera-
tion of successive structures in the hereditary line, where
there may occur changes requiring to be taken account of,
494. ; LOGIC OF BIOLOGY.
being the initial step of the new biological department called
Evolution.
It is proper to generalize to the utmost the wide variety of
structures, and to exhibit all the generalities apart as giving
a mental command of the entire field. Such generalities
would be cclled General Morphology, and General Embryology.
Function, or Physiology, is an account of all the living pro-
cesses, in the most convenient order; all those changes con-
stituting Life—changes simultaneous and successive, contri-
buting to a definite result, and adapting each organism to the
environment. Here there isan unlimited scope for inductions,
and for deductions, confronting and correcting one another.
The high generalities of Function comprehending all Life, if
such there be, would form a General Physiology.
The subject of Evolution involves the mutual actions and
modifications of Structure and Function. It deals with the
general truth that when external circumstances demand and
prompt an increase of function (as when an animal is called to
exert unusual muscular energy) the structure is liable to be
increased, and thus to increase the function apart from stimu- ’
lation. This is one way of the supposed re-action of Structure
and Function. Another way is by Mr. Darwin’s Natural
Selection, or Survival of the Fittest. The carrying out of these
principles is the substance of the great Biological Hypothesis
of Development or Evolution.
Biology can to a certain extent be treated as a whole, there
being certain things common to living beings—Conistituents,
Structure, Function and Evolution; it would then have to be
divided, as has always been usual, into Plant Life and Animal
Life ; each of these subjects being subdivided according to the
plan above laid down for the whole.
Remaining Notions of Biology.
The general definition of Life has been seen to carry with
it the definitions of Organization, Cell, Protoplasm, Assimi-
lation, Individual, Germ, Reproduction, Growth, Death.
The specializing of the structures and functions introduces
many other Notions.
Plant—Animal.—The greatest line of demarcation in living ;
bodies is between Plants and Animals; these are the two »
highest genera of living bodies, a perfect dichotomy of the __
whole. Allowing for a doubtful margin, the distinctive
characters are numerous and important. As in all dichoto-
mies, we have the advantages of a definition by Antithesis.
PARTS AND PROCESSES OF PLANTS, 495
The leading characters may be stated in contrast thus :—
PLANT. ANIMAL.
Number and complewity of Tissues, Organs, and Functions.
Small Great
. Local habitation.
Fixed Moveable (Locomotion)
Food matervals.
Inorganic Organic
Mode of reception of Food.
Absorption Reception into a mouth
and stomach
Process of nutrition.
| Deoxidation Oxidation,
Tissue. Organ. Vessel.—These are comprehensive parts or
constituents of the organized structure, as made up of cells;
they are common to all living bodies, and admit of exact
definition. There is a difference between the Tissue and the
Organ; one Organ, as the stomach, may contain several
tissues. Hach Tissue is analyzed into a distinct cell structure,
which is its defining peculiarity as regards structure, to which
there also corresponds a certain kind of activity or function.
Thus, the nervous tissue is made up of nerve fibres and nerve
cells, in a special aggregation; these are connected with the
peculiar activity or function called nerve function, or the
manifestation of nerve force.
The view of Plant Life contains the definitions of the
structural parts of the plant.
Cellular Tissue Integument (Stomata, Hairs, Glands)
Vessels Root
Vascular Tissue Stem
. Leaves
Inflorescence (Flower, Fruit, Germ).
From the enormous number and variety of plants, a great
effort is needed to present these parts in their widest gener-
ality; while the general idea must be accompanied with a
classified detail of modifications.
ann must also be given of the processes of Plant
e.
Osmose Flowering
Exhalation Vigils of Plants
Transpiration Sexual union
Secretion Impregnation
Irritability and Contractility Fecundation
Defoliation Germination
Circulation, sap, capillarity Propagation,
ane
yes et"
496 LOGIC OF BIOLOGY.
A set of notions, parallel but more numerous and compli-
cated, belong to the description of Animal Life as a whole.
The modifications of the ultimate materials are described as
blustema or matrix, crystals, protoplasm, granules, homogeneous
membrane, vesicles, nuclei, nucleated cells, simple fibres, nucleated
fibres, compound fibres, and tubes. These are compounded into
the characteristic Tissups—Cellular, Adipose, Vascular, Carti-
laginous, Osseous, Muscular, Hlastic, Epithelial, Nervous. The
OrcGans are Bones, Muscles, Alimentary Canal, Respiratory
Organs, Heart and Blood Vessels, Sympathetics, Skin, Brain,
Senses, Reproductive Organs. The Functions follow the
Organs; and in several instances, give these their distinctive
names.
The Classification of Plants and of Animals gives scope for
Definition as applied to the several grades.
5. In these detailed Notions, we have the analysis of the
Living Organism—Plant or Animal.
An organism is by its very nature a complexity. Ina
scientific consideration this complexity has to be resolved into
the related parts—organs, tissues, constituents: The laws of
structure are laws of relations of the parts to each other;
and if our analysis has hit the natural partition, it is the basis
of our subsequent statements, in propositions, of the natural
relations. If the analysis is inexact, no exacé propositions can
be grounded on it.
Propositions of Biology
6. The Laws and Propositions of Biology differ in their
logical character, according as they relate to Structure or
to Function.
First, as to STRUCTURE. ‘y
The propositions or laws of Structure, affirm co-existence,
as order in place, between the different parts of living bodies.
Human Anatomy is a vast congeries of such propositions.
How far the co-existences are ultimately dependent on Causa-
tion, rests with the theory of Evolution. In the meantime;
they are to be regarded mainly as Co-existence without Causa-
tion. .
These propositions may be special to individuals and limited
groups of individuals ; or they may be generalized over very
wide areas. The narrow class is exemplified in human Ana-
tomy, and in all specific descriptions whether of plants or of ©
a a a
4
cr
. a
: "
PROPOSITIONS OF ANIMAL STRUCTURE, 497
animals. High generalities, realizing the scientific ideal of
Biology, are not wanting. For example, in Plants—all the
parts are homogeneous in structure; or, as otherwise expressed,
the flowers are modified leaves; the monocotyledonous mode
of germination co-exists with the endogenous mode of growth ;
flowering plants are generally multiaxial ; complexity of struc-
ture is accompanied with permanence of form. In Animals,
we have the anciently observed coincidence of ruminant sto-
mach, cloven hoof, and horns; the grouping of mammalian
characteristics—mamme, non-nucleated red blood-corpuscles,
two occipital condyles, with a well-ossified basi-occipital, each
ramus of the mandible composed of a single piece of bone and
articulated with the squamosal element of the skull.
Viewed, in the first instance at least, as co-existences with-
out causal connexion, these propositions must be verified by
agreement through all nature, and held as true only to the
extent observed.
There are numerous and striking co-existences between
Structure and External circumstances, the so-called Adapta-
tions of one to the other; but in these there is a great pre-
sumption of cause and effect; they furnish the best support to
the doctrine of Evolution.
There are likewise laws of causation, more or less traceable,
in the operation of all the outward agents. Thus, Heat,
Light, Air, and Moisture, are essential or causal conditions of
the growth of plants. Light is necessary to the colour of the
leaves. The oxygen of the air is an indispensable condition
of all animal life. Many other laws of causation are occupied
in expressing the agency of different kinds of food, of medi-
cines, &c.
There are laws of cause and effect, in the mutual actions of
different organs, in each individual plant or animal. Thus,
in animals, the digestive organs affect, and are affected by
the circulation, the muscles, and the brain.
7. Next as to Function, or Physiology.
The propositions here affirm Cause and Effect. The process
of Digestion, for example, is an effect of the contact of food
material with the complicated alimentary organs. In like
manner, every organ of every living being has a function,
more or less assignable.
It is a deduction from the permanence of Matter, established
since the researches of Lavoisier as a law of nature, that what-
ever materials exist in plants and in animals, must be sup-
498 LOGIC OF BIOLOGY.
plied asa condition of their growth. Plants being constituted
from Carbon, Oxygen, Hydrogen, Nitrogen (in small portions),
and Saline bodies,—must find all these elements in the earth
or in the air. The animal tissues being highly nitrogenous,
animals must have nitrogenous food. The gastric juice con-
tains hydrochloric acid, whence the necessity of salt as an
article of food.
8. The law of the Conservation of Force, and all the
subordinate generalizations of Molecular Physics and
Chemistry, are carried up into Biology.
The law of Conservation holds true in organic changes, and
is a deductive key to the phenomena, Every manifestation
of force in a living body—mechanical energy, heat, decom-
position of compounds,—is derivable from some prior force of
exactly equivalent amount.
The laws of Cohesion, Adhesion (in all the forms—Solution,
Capillary Attraction, Diffusion, Osmose, Transpiration), Heat,
Light, Electricity, and the laws of Chemical combination and
decomposition, are carried up into organic bodies. In the
present advanced state of knowledge respecting these laws,
there are many deductive applications of them to the pheno-
mena of life. The complications of Biology are thus, in part,
susceptivle of being unravelled by pure deduction.
So far as concerns Force, or energy, in any shape, there is
nothing special to living bodies. As regards Collocation,
there is the peculiarity of the organized structure. It is not
correct to speak of Vital Force in any other sense than the
molecular and chemical forces, operating in a new situation.
It would be strictly proper to speak of a Vital Collocation of
elements, under which the molecular forces put on new
aspects, although never inconsistent with the primary law of
Conservation. Thus the nerve force is something new, not as
regards its derivation from an antecedent equivalent of force,
but as regards the singularity of the nerve structure, which
leads to a new mode in the manifestation of the force.
9. In the department of Function, there are necessarily
many Empirical Inductions.
Excepting the deductions from Physics and Chemistry,
every law of Biology must be considered as empirical. There
are, however, some empirical laws established by an agree-
ment so wide and sustained that they are considered, for the
present, as laws of nature. Still, no such laws can be held as
oe eee
peer
PROPOSITIONS OF FUNCTION. 499
absolutely certain. Notwithstanding the agreement in favour
of the derivation of living beings from germs or seed, there is
yet a possibility of spontaneous generation.
The following are examples in Plants. Vegetable cells
absorb fiuids, elaborate secretions, and form new cells; they
also unite to form vessels. Roots absorb material from the
soil, in part by osmotic action. The sap circulates under the
influences of heat and light, and the actions going on at the
surfaces of the leaves and of the roots. In flowering plants,
reproduction is performed by the access of the pollen to the
ovules. Fruit succeeds to fecundation. Seeds germinate in the
presence of heat, moisture, and air, with absence of light.
_ There is something very unsatisfactory in the inductions of
Vegetable Physiology. Some of them are now obvious results
of the law of Conservation; as for example, the influence of
Heat at all stages of vegetable growth. The great lack is in
the intermediate steps of the process ; what happens in the
interval between the incidence of heat and air in the leaves,
and the elaboration of the sap, the setting free of oxygen, &e.
But this is the defective part of our knowledge of all the
organic processes.
In the functions of Animals, there are numerous empirical
inductions. Thus the conditions of Muscular contractions are
well known by experimental research; they are the presence
of blood, and the stimulus of the nerves. That blood should be
necessary is a consequence of the law of conservation; muscular
force must be derived from some prior force. That non-azotized
materials are sufficient for causing muscular energy could be
known only by experiment. Again, the circumstances affecting
the heart’s action, are empirical inductions ; so is the fact
that the red corpuscles of the blood carry the oxygen for the
tissues. The processes of Digestion are stated in the form of
empirical inductions, The same holds of Urination and Re-
spiration. Farther, the multiplied actions concerned in
Impregnation, Germination, and Growth, are ascertainable
only as empirical laws. All the functions of the Brain and
the Senses are given in propositions of the same character.
That exercise (within limits) strengthens all the animal
organs has long been established as an Empirical Law. Mr.
Darwin is dissatisfied with the physiological reason or deriva-
tion of the law; to him, therefore, it remains empirical.
These empirical inductions are to a certain small extent
controlled by high generalities, and are in so far derivative.
The law of Conservation is a check upon many of them; and
500 LOGIC OF BIOLOGY.
the special laws of Molecular Physics and of Chemistry are
seen at work in some. But in such a process as Digestion, the
recognized physical and chemical actions are thwarted by
deeper forces, of which we have only an empirical statement.
The most potent instrumentality of deductive explanations at
present known is that furnished by the researches of Graham
on Transpiration, Diffusion, Osmose, and Capillarity.
Animal Mechanics, and the propulsion of the fluids by the
heart’s action, are susceptible of a complete deductive treat-
ment, through the applications of Mechanics and Hydrostatics.
This is well exemplified by Dr. Arnott, in his ‘ Elements of
Physics.’
Logical Methods of Biology.
10. In Biology, the facts are open to Observation and
to Experiment ; although with some limitation owing to
the peculiarities of the living structure.
The difficulties attending the observation of living beings
are greatly overcome by such instruments as the microscope,
stethoscope, laryngoscope, ophthalmoscope, &c., and by the
chemical examinations of the various products. Accident
sometimes lays open the interior, as in the case of Alexis St.
Martin, through whom was obtained invaluable results as to
digestion.
11. Through the variety of the cases presented by Biology,
there is great scope for elimination by the methods of
Agreement and Concomitant Variations.
The means of varying the circumstances by the comparison
of instances, agreeing and yet disagreeing, is very extensive.
From the number of different vegetable and animal species,
each structural peculiarity is presented under the greatest
possible variety of accompaniments. And this is only one part
of the case. In every individual there is scope for additional
comparisons in the different stages of its existence, the method
of Embryology. Lastly, the occurrence of monstrosities still
farther contributes to the desired variation of circumstances.
In these three ways, the opportunities of plying the Methods
of Agreement and Concomitant Variations are exceedingly
multiplied.
Thus, an examination of the structure of the eyes, in their
oa
ae
rudimentary types in the lowest animals, and in their succes-
sive phases of growth in the higher, has both suggested and
Re
CHANCE AND PROBABILITY. ; 501
proved (as some believe) that an eye is a modified portion of
the skin,
Mr. Owen enumerates seven different modes of carrying out
comparisons of the animal structures (Vertebrate Animals,
Vol. I. Preface).
The use and limits of the Deductive Method in Biology have
been sufficiently adverted to in previous remarks. Some
notice may be taken of the applications of Chance and Proba-
‘bility.
12. There are many biological conjunctions of wide,
but not of uniform concurrence. Such cases must be dealt
‘with according to the rules for the Elimination of Chance.
When a concurrence, although not universal, is, neverthe-
less, more frequent than chance would account for, we are
bound to recognize a natural tendency, or some law of nature
liable to be defeated by other laws. [or example, the con-
currence of superiority of mental power with superior size of
brain, although liable to exceptions, is yet very general, and
far more than chance can account for. Hence we must regard
this as an established law, with occasional liability to be
defeated. Weare not at liberty to predict it of every instance,
but only with a probability proportioned to the observed fre-
quency as compared with the failures.
13. It is a result of the great complicacy of vital pro-
cesses, that many inductions are but approximately true ;
and, therefore, are to be reasoned on according to the
principles of Probable Evidence.
The prevalence of approximate generalizations is a mark of
the increased complicacy of the Biological processes, as com-
pared with the processes in Physics and in Chemistry.
The best that can be done, in this state of things, is to ob-
tain statistics of the actual occurrence of certain conjunctions.
There is a large department, of modern creation, termed Vital
Statistics, which enables us to reason on vital phenomena with
the degree of probability belonging to each case. It is thus
that we can infer the proportions of mortality at different ages,
_ and the proportion of male to female births. When Agricul-
tural Statistics shall have been continued for a sufficient time,
the recurrence of good and bad harvests will be capable of
being stated with numerical probability.
14. Many of the propositions of Biology are defective in
numerical precision.
502 LOGIC OF BIOLOGY.
In Physical and Chemical facts, it is usually possible to
measure numerically the degree of the qualities. Thus most
of the properties of a mineral can be stated with numerical
precision ; others, as colour, and fracture, can be referred to
a known type. But when we say a certain amount of exercise
streagthens the organs, while a greater amount weakens them,
we leave the estimate very vague. Change of air is said to
invigorate the powers, but there are no precise reckonings,
either in the general or in particular cases, of how much invi-
goration may be expected from a definite change. So, the
influence of altered circumstances on breeds and on races is
given in vague indeterminate language, and must be taken
with great latitude. ,
Hypotheses of Biology.
15. The character of the science requires the utmost
aids that can be afforded by well-contrived Hypotheses.
Biology has all the difficulties of Molecular Physics and
Chemistry as regards the impalpable nature of the constituent
parts in living bodies, and its own additional complications
from the organized structure.
The hypotheses of Biology are of all the varieties enu-
merated in the general chapter on the subject (Inpuction,
chap. XIII.). Some assume a real cause, as the Development
Hypothesis ; others assume unreal or unknown agencies, as
the supposed adherence to ly pe or plan; a third class would
claim to be Representative assumptions.
Of the first class, we may cite, as instances involving the
smallest amount of peril in the assumption, the unverified
deductions from general laws of the inorganic world, such as
the molecular and chemical laws. These powers of cohesion,
adhesion, solution, osmose, &c., are assumed as operating in
the living body, but the deduction from them is not sufficiently
exact to be fully verified. Hence there is much that is hypo-
thetical in the theories of oxidation, of animal heat, of secre-
tion, &c. From the known chemical inertness of Nitrogen,
Mr. Herbert Spencer draws some remarkable inferences in
explanation of the vegetable and animal processes (Biology,
I. 8).
Development Hypothesis—This renowned speculation, with
all its boldness, has the characters of a legitimate hypothesis ;
it assumes a real agency, a vera causa; its difficulties lie in
showing that the supposed agent is equal to the vastness of
the results.
HYPOTHESES. 503
. _ Properly speaking there is no rival hypothesis. The Special-
Creation view is a phrase that merely expresses our ignorance.
Its power of explanation is confined to making a comparison ;
it assigns to the living species that have successively appeared -
in the course of ages the same mode of origin as the earliest
species of all, and asthe whole framework of the universe ; an
origin that must for ever be inconceivable to the human mind.
As the physical theorists who speculate upon cosmical develop-
ment—the formation of suns and planets—start with the
assumption of matter spread out over a great amplitude of
space, and coming together by gravity, so the biological theo-
rists assume a primeval start, either of living broods, or of
matter ready to become organized under particular circum-
stances. Now the value of any scientific explanation of life is
measured by its capability of tracing the whole of organized
nature to the fewest primitive assumptions.
The modification of plants and animals in the course of
generations is a fact. It happens even in the same external
circumstances ; while under alteration of circumstances, the
changes become vastly greater. Now, if any means can be
assigned whereby some of the modified forms are kept alive
while all the others perish, the deviations are rendered per-
manent. Mr. Darwin provides an instrumentality of this
nature in what he calls Natural Selection, or the preservation
of the fittest in the struggle of life. It has been his endeavour
to accumulate a vast multitude of facts showing the principle
in operation, many of them inexplicable on any other supposi-
tion. Herbert Spencer, Huxley, Hooker, Wallace, and others,
have contributed to the support and elucidation of the hypo-
thesis.
The occurrence of allied species in the same geographical
area, and the wide differences in character of the species in
localities widely apart, are adapted to the doctrine of deve-
lopment and not to any other view as yet provided. Again,
says Mr. Darwin—‘ How inexplicable is the similar pattern of
the hand of a man, the foot of a dog, the wing of a bat, the
flipper of a seal, in the doctrine of independent acts of
creation ! how simply explained on the principle of the natural
selection of successive slight variations in the diverging
descendants from a single progenitor!’ In the course of
time and change, certain parts originally useful have become
superfiuous ; and their retention in the useless condition is
intelligible only on « hypothesis of descent.
So long as the Development Hypothesis tallies with a very
504 LOGIC OF BIOLOGY.
large number of facts, and is not incompatible with any, itis -
a legitimate and tenable hypothesis; and its worth is propor-
tioned to the extent of the phenomena that it explains, com-
pared with those that it fails to explain.
Hypothesis of Iteproduction.—The reproduction of each living
being from one or from two others, through the medium of a
small globule which contains in itself the future of a definite
species, is the greatest marvel in the whole of the physical
world ; it is the acme of organic complication.
Mr. Herbert Spencer and Mr. Darwin have recently pro-
mulgated hypotheses to represent this process. (Spencer,
Biology, L, 253; Darwin, Domestication, II., 357). The two
views have a good deal in common, and might be taken
together. Mr. Darwin’s, however, ventures farthest, and
may be here quoted ag exemplifying a biological hypothesis.
He prepares the way by generalizing all the different modes
of reproduction—whether unsexual or sexual. The unsexual
modes, as buds and fissure, are to be held as identical with
the processes for maintaining each organ in its integrity, for
the growth or development of the structure, and for the
restoration of injured parts. And it seems to be a tenable
supposition that the sexual mode of reproduction is a mere
modification of the same general fact.
The hypothesis then is that each egg, or seed (of the female)
and each spermatozoon, or pollen grain (of the male) is already
a vast aggregation, a world in itself. It is made up of a host
of smaller bodies, which may be called gemmules, with all the
properties of growth or reproduction commonly attributed to
cells in general ; this host is different in each species. For
every separate part of the animal or plant to be formed; down
to a feather, there are distinct gemmules of the type of that
part, and unfolding to produce it by ordinary growth. Hvery
animal contains circulating through it the undeveloped gem- —
mules of all its organs, and parts of organs; a complete set is
bound up in the ovum of the animal (or plant), and by due
expansion reproduces the new individual complete at all points.
Something must be assumed as determining them to fall into
their places ; but that there is no absolute fixity in this respect,
Mr. Darwin shows by the frequent occurrence of misplaced
organs; this, he thinks, favours the view of the multitudinous
gemmules, and refutes any hypothesis of a formed microcosm —
existing in the seed, to which supposition there are many other
hostile facts.
To grasp, reconcile, and generalize the facts, is an ample
HYPOTHESES, 505
justification of this bold venture; by the nature of the case,
we can never hope to penetrate the precise operation, nor yet
to arrive at a supposition that shall exclude every other. It
is, however, an important appendage to whatever hypothesis
may be formed of the great vital fact named Assimilation.
CHAPTER V.
LOGIC OF PSYCHOLOGY.
1. Psychology, or the Science of Mind, comprises both
Mind proper, and its alliance with Matter, in the animal
y-
Definition of Mind.
2. The ultimate antithesis of all knowledge is called the
antithesis of Object and Subject.
The object world coincides with the property called Exten-
sion ; whence the Subject, or Mind, is definable by antithesis
asthe Unextended. A tree is extended ; a pleasure, a thought,
a desire, have nothing in common with extended things.
3. By the method of Particulars, Mind is definable as
possessing the three attributes named Feeling, Volition,
and Intellect.
_ Feeling is exemplified by pleasures and pains; Volition is
action prompted by Feelings ; Thought, or Intellect, contains
the processes known as Memory, Reason, Imagination, &c.
All our emotions are included under Feeling; our sensa-
tions are partly Feelings and partly Intellectual states.
The positive definition of the Mind is also a Division, and
must conform to the laws of Logical Division.
| Concomitance of Mind and Body.
4, To the Definition of Mind, we must add the Con-
comitance of the Body.
The concomitance of Mind and Body is a conjunction alto-
gether unique. The extreme facts of human experience—the
subject and the object, mind and extended matter—are found
in union. We cannot say with certainty whether the unionis
Yn ee
506 LOGIC OF PSYCHOLOGY.
@ case of causation, or a case of co-inhering attributes. It
stands apart.
5. The union of Mind and Body must hold throughout,
While many, from Aristotle downwards, have held that
portions of the mind are unconnected with bodily processes,
no one denies that mind is to some extent dependent on the
body. But all have failed in every attempt to draw a line
between the functions that are dependent, and those that are
supposed independent of bodily organs.
6. The concomitance of the two radically distinct
phenomena gives the peculiar characteristic of the science.
Every fact of mind has two sides.
Every feeling has its mental side known to each one’s own
consciousness, and its physical side, consisting of a series of
physical effects, some superficial and apparent, others deep
and intricate.
It depends upon circumstances whether, and how far, these
physical adjuncts should be brought forwaed in the scientific
exposition of the mind. On the one hand, if they are
unvarying in their concomitance, they can hardly be excluded
without impairing our knowledge of the mental part. On
the other hand, it is a bare possibility that the mental pheno-
mena, being radically distinct and unique, may be studied
better by making entire abstraction of the physical accompani-
ments. Moreover, much depends upon the degree of insight
actually possessed respecting the nervous system and the
various organs related to the mind. It might be expedient at
one stage of knowledge to drop these from the view, and at
another stage to take them up,
In point of fact, until the present century, only a very small
number of philosophers gave systematic attention to the
physical implications of mind ; the chief being Plato, Aristotle,
Hobbes, and Hartley. In spite of the crndity of their know-
ledge of physiology, they all (with perhaps the exception ot
Plato) gained most valuable psychological hints by means of
that knowledge. The physiology of the present century —
having placed the whole subject on a new vantage ground, -
the attention to the physical side may be expected to be much
more rewarding. '
Thus, on one side, Psychology is a department of Animal
Biology, and subject to biological laws. The all-pervading —
law of Persistence of Force extends to the physical concomi- ‘
Roe is. =
DEFINITION OF MENTAL PROPERTIES. 507
fents of mind, and is pregnant with consequences of the
utmost practical value.
On the other side, Psychology presents a unique phenome-
non—individual self-consciousness—to which there is no
forerunner in any of the previously enumerated sciences.
Still, the methods and spirit of scientific enquiry, as exhibited
in these other sciences, are of value in the study of mind in
its psychical side. States of consciousness have degrees of
intensity and duration; they are single or compound; they
aid or thwart one another ; they have their laws of emergence,
increase, decline; in all which particulars they observe
analogies to physical forces; so that the intellectual habits of
accurately estimating physical agencies may, with due allow-
ances, be of service in dealing with the complications of mind.
The two-sidedness of the phenomena appears in language.
The terms of mind had all an objective origin; and, while
some of them have now an almost exclusively subjective
meaning—as pleasure, pain, feeling, thought, sweetness, fear,
conscience, remorse,—others have also an objective reference,
as shock, emotion, excitement, avidity, irritation. Jn these
last, the language is ambiguous; we cannot always tell
whether the physical or the mental is aimed at. There is,
morover, a liability to represent the mental fact as a physical
fact.
Other Notions of Psychology.
Consciousness.—The most difficult word in the human voca-
bulary. It concentrates in itself all the puzzles of metaphysics.
If it were strictly synonymous with Mind, it would be defined
accordingly. But the object, or extended world, is inseparable
from our cognitive faculties; so that a word that expresses
every conscious state whatever is wider than mind, strictly so
called; it comprises both matter and mind. Hence, if ‘ con-
sciousness” be the name for all sentient states, it is the widest
word that we can employ, in fact, there is no meaning corre-
sponding to it; like Existence, it is a fictitious addition of the
two highest genera. To state these separately, we must have
the double epithets Subject-consciousness and Object-con-
‘sciousness; which, however, give only the meanings—Object
and Subject, ;
Sensation.—A word with several distinct meanings. In the
first place, it may either cover the physical operations con-
nected with the exercise of our senses, or it may be restricted
to the purely mental state arising therefrom. In the next
508 LOGIC OF PSYCHOLOGY.
place, inasmuch as the senses give us feelings in the purest
form (pleasures and pains) and also intellectual discrimina-
tions, the ground work of our ideas,—sensation may be used
for either class. In the third place, there is a contrast of
Sensation with Perception, or between the immediate effect
on the mind, and the associated effects; colour and visible
magnitude are sensations, distance and true magnitude are
perceptions.
The special modes of sensation, together with muscular
feeling, are ultimate states of the mind, to be defined solely
by individual reference. Resistance, Motion, Warmth, Diges-
tive Sensibility, Taste, Smell, Touch, Hearing, Sight,—as
states of feeling, must be known by independent experience.
Emotion.—The emotions are a department of the feelings,
formed by the intervention of intellectual processes. Several
of them are so characteristic that they can be known only by
individual experience ; as Wonder, Fear, Love, Anger. These
stand very near the ultimate elements of human feeling.
Many, however, are evidently derived; such are, in an emi-
nent degree, the Aisthetic and the Ethical emotions.
Phases of Volition.—The definition of the Will, or Volition,
is a part of the definition of mind as a whole. Will, as con-
trasted with Feeling, is a unity, indivisible. Yet, there are
various aspects or modifications of it, that receive names.
Motive is the feeling that prompts the will in any one case;
the motive to eat is the pain of hunger, or the pleasure of eat- __
ing, or the pain of defective nutrition. Deliberation supposes
conflicting motives. Resolution is a volition with the action
adjourned. Desire is ideal volition, either as preparatory to
the actual, or in lieu of it. Belief is preparedness to act,
for a given end, in a given way. |
Intellectual States.—In the Intellect, we have three fun-
damental processes—Discrimination, Similarity, Retentiveness
or Revivability ; all requiring actual experience in order to be
understood. Discriminationis another word for the fundamental
fact called Relativity and also Contrast. Similarity, or agree-
ment in difference, is a distinct fact of the mind; the sensi-
bility corresponding to it is unique; and it is one of the most
iterated of human experiences. Retentiveness and Revivability
describe a great characteristic of our mental nature, for which
we have other designations, as Idea, Memory, Recollection ; it
ean be defined only by reference to actual experience ; al-
though the figurative words—retention, revival, resuscitation, —
seem to be a definition by the medium of other notions.
- ———
ESSENTIAL AND REAL PREDICATION. 509
The complex intellectual faculties—Reason, Imagination,
&c., are defined each by its proper department of exercise ;
thus, Reason is the power of drawing conclusions from pre-
mises, or the scientific faculty. To this definition may be
appended, as a real predicate, the derivation from the ultimate
intellectual elements just named.
Psychology contains scope for Classification, both according
to Logical Division, and according to Ramification or Compo-
sition. The ultimate sensibilities—namely, the Senses, the
elements of Intellect, and the Simple Hmotions—are classiied
as genera and species, and according to Logical Division.
The compound faculties and sensibilities, as the popularly
named Intellectual Powers, and the Complex Emotions, are
classified solely by Ramification; their classes do not comply
with Logical Division.
Propositions of Mind.
7. The complexity of many of the Notions of Mind
gives rise to Essential Predications.
Mind itself being defined (positively) by the union of three
distinct and irresolvable characteristics, there may be proposi-
tions affirming the concomitance of these three facts; as
Feeling is accompanied with Volition and with Intelligence.
When we say that Mind (as a whole) feels, wills, remembers,
we give a verbal or essential predication.
So with many other notions. Such simple feelings as fear,
love, anger, if defined, would have a plurality of circumstances.
That such circumstances are united, may be a real predica-
tion ; but when any one of them is predicated of the name,
the proposition is essential. ‘Anger makes one delight in
retaliation ’ is a purely verbal predication.
Our common talk on mind is full of Essential propositions.
His vices were condemned, his virtues praised. Prudence
keeps a man out of difficulties. The strongest motive deter-
mines action.
8. The conjunction of Mind and Body is a real predi-
cation ; it being understood that the definition of Mind is
restricted to subjective facts.
This holds throughout the detail of feelings, volitions, and
thoughts. When the name for an emotion is the subject of a
proposition, and the physical accompaniments are affirmed,
the predication is real :—‘ Fear depresses the vital organs’ is
510 PSYCHOLOGY OF LOGIC,
an affirmation of concomitance. ‘The hope of the reward
quickened his speed.’ conjoins a motive to the will (a feeling)
with the bodily part of a voluntary act.
9. The three leading functions, given as the Definition
of Intellect (Discrimination, Agreement, Retentiveness),
are unfolded in predications.
That Mind discriminates is an Essential proposition ; yet the
full account of the fact of Discrimination, Relativity, or Con-
trast, demands numerous propositional statements, many of
them real. Not to re-iterate the double-sidedness of every
mental fact, the conditions, circumstances, and limitations of
each of these leading properties are enounced in propositions
that are in no sense verbal.
(1) Thus, we speak of the law of Ielativity, expressed as
the concomitance of consciousness with change of impression,
This is the general statement ; and constitutes a real predication
by virtue of the distinctness of the two facts—change of im-
pression (physical, in great part), and consciousness (strictly
mental).
(2) Retentiveness, Revivubility, Contiguous Association, are
names for a fundamental property of mind, which in its expo-
sition takes the form of a law. A certain condition or situa-
tion has to be assigned (the reception of present impressions),
and to this is attached as a real predicate, the property of
being retained, revived, remembered. The various modifying
circumstances (engagement of attention, physical vigour, &.)
are real propositions in subordination to the main principle:
It is a grand generalization, resuming, explaining, and ren-
dering precise the media axiomata of acquisition, as regards
intellectual growths, emotional growths, and volitional growths, —
Under it are given numerous affirmations as to the derivation
of complex phenomena from simpler, the unfolding of thoughts _
and emotions, and the evolution of the mature mind from its
primary elements. This is commonly called the Analysis of
the Mind. The proof of such assertions rests partly on the
consciousness of the hearer, and partly on indirect reasonings.
Thus, the proof that Beauty is a compound, and not a simple
Emotion, is that we can consciously identify its constituents.
The same with the Moral Sense. ‘The indirect prodfs are, the
absence of the Feeling prior to certain opportunities of mental
association. (See § 12.)
(3) The Law of Similarity, or Agreement in Difference, is, —
for the same reasons, an inductive generalization of real
LAWS OF MIND. SEE
concomitance. ‘ Present states of feeling, &c., tend to revive
their like among former states, notwithstanding a certain
amount of difference.’ As before, there are required many
subsidiary propositions to express all the qualifying circum-
stances of this wide generality.
Another important law of the mind is sometimes described
as the law of the Fixed Idea, namely, that ideas tend to act
themselves out ; as when the sight of yawning makes us yawn,
merely by giving us the idea of the act.
10. There may be laws of the rise, continuance, and
subsidence of Feelings.
The connotation of each distinct mode of feeling, whether
sensation or emotion, indicates both its character as feeling,
and its mental antecedent. The laws connecting mind and
body, predicate its physical side; the laws of Relativity and
of Retentiveness contain additional predicates. ‘To all these
may be added inductions as so the rise, continuance, and sub-
sidence of Feeling ; which laws, like every other, have a physical
side, and may possibly, on that side, be generalized into still
higher laws.
Like all sciences where simple elements contribute to form
compounds, Psychology contains affirmations respecting the
composition of feelings and other states. The assertion is
made, for example, that Beauty, Conscience, Imagination, are
not simple facts, but are compounded of certain assignable
elements.
Among the ordinary predications respecting living beings,
we may mention the passing of the various capabilities into
action. Thisextendstomind. I walk, speak, reason, wonder,
desire, &c., are examples; to all such belongs the reality of
predication.
Logical Methods of Psychology.
11. In Psychology, special importance attaches_to the
ultimate Analysis of the phenomena.
In all sciences, we desiderate an accurate and thorough-
going analysis of the phenomena. It is only an ultimato
analysis that can be the groundwork of the most general pre-
positions respecting them.
In proportion to the difficulty of ascertaining and proving
the facts in detail, is the valne of an ultimate analysis, whereby
we can reduce to a minimum the number of independent
512 LOGIC OF PSYCHOLOGY,
assertions. When we know the component parts of an Emo-
tion, for example, Beauty, the Moral Sentiment, or Veneration,
we can apply our experience of the parts to correct and con-
firm our experience of the totals.
12. The proof of a Psychological Analysis is (1) the
feeling of identity between the compound and the parts.
This must be a matter of individual self-consciousness. _
That the Moral Sentiment contains a feeling of obedience
to authority, under dread of punishment, is proved by each
one’s being conscious of the presence, in the compound, of
that special element.
13. An Analysis is proved (2) by the identity of the
consequences and collaterals of a feeling. ‘This will
afford an Objective proof.
That the Religious Sentiment contains an element of Fear, _
is proved by identity in the eRe and the Actions |
dictated by the state.
14, The greatest difficulty is felt in establishing the
sufficiency of an Analysis.
This is a difficulty in all cases where there is great com-
plexity in the phenomena. We may identify the presence of
certain elements, without being able to show that these are
the whole. Where the quantity of the elements can be
measured, as in Chemistry, we can prove the analysis by
casting up their sum. Where quantity is not exactly esti-
mable, as in many biological facts, and in nearly all psycho-
logical facts, this check is indecisive.
For example, some have maintained that Benevolence is
exclusively made up of self-regarding elements. Others,
while admitting the presence of these elements, deny that
they account for the whole. Owing to the vagueness of our
estimates of quantity in mind, the dispute cannot be decided ~
by a process of summation in ordinary cases. We must —
proceed by varying the circumstances, and by finding —
Instances where self-regarding elements are either wanting, or
so small in amount, as to be obviously unequal to the effect
produced. Such an instance is found in the pity called forth
by the punishment of great criminals.
15. The Inductions of Mind bring into play the Experts
mental Methods.
LOGICAL METHODS IN MIND, 513
The great Law of Concomitance of Mind and Body must be
proved by the Method of Agreement. We must show that
the whole of the facts of mind—Feelings, Volitions, Thoughts,
are at alletimes accompanied by bodily processes. The case
has something of the peculiarities of the Law of Causation.
We can prove the concomitance in a vast number of cases ;
while in many mental exercises, as in meditative reflection,
the physical processes almost escape detection from their
subtlety. These instances, however, although unable to
confirm the proposition, are not opposed to it; and they
do nothing to invalidate the force of the unequivocal in-
stances.
We can do more than establish a law of concomitance of
mind and body generally. We can, by the methods of Elimi-
nation, ascertain the exact bodily processes connected with
mental processes. On this determination, we can bring to
bear all the Hxperimental Methods.
The Law of Relativity is established by Agreement, and, in
a remarkable manner, by Concomitant Variations.
The Intellectual Laws, called Retentiveness and Similarity,
are established, both in general terms, and as respects their
peculiar conditions, by all the methods.
16. From the circumstance that, in Psychology, we have
attained to laws of high generality, there is great scope for
the Deductive Method.
While every one of the great laws above enumerated is
fruitful in deductive applications, the instance that perhaps
best exemplifies the Deductive Method of enquiry, considered
as a Supplement to Induction, is the Law of Conservation or
Correlation, applied to Mind, through the physical supports.
By this law, every mental act represents a definite, although
not numerically expressible, physical expenditure, which must
be borne by the physical resources of the system. The deduc-
tive consequences of this fact are innumerable.
13. From the circumstance of passing through the
Linnean classification, so well adapted to the ready deter-
mination of plants, Botany affords the best example of
an Index Classification. ie z
We may retain for se purpose the Linnean system in qo
literal form ; or we may have recourse to the modified schemes ~
of recent Botanical writers. The principle is the same. We -
commence with certain characters, having alternative modes ; 17
and the key or index informs us what classes each mode points 7
to. A second character is then examined, its alternatives —
found, and the corresponding classes discovered. (See tote
ley’s Vegetable Kingdom, Bentham’s British Flora, &c.) _
LOGIC OF ZOOLOGY. ' oe a
14. The difficulties of Zoological Classification rolatal
to the multitude and the complication of the Animal King
dom.
The multitude of the objects to be arranged, and the com-
plication of even the lowest forms, distinguish Zoology from
all other classificatory sciences. There are certain partial s
compensations. As compared with Minerals, the organs of
Animals present numerous relations of concomitance ; and as
compared with Plants, the Animal Kingdom falls ina ‘remark= ;
able degree, under a lineal series, or consecutive development.
I. Characters of Animals. he a ui
15. We must look for the characters of Animals in the
division of the animal system into constituent Organs. - -
The Animal, like the Plant, is made up of Tissues and ‘
Organs, which have a certain amount of sameness, with
variety, throughout the entire Animal Kingdom. The enu-
meration of these belongs to Biology ; Connective tissue,
Elastic tissue, Adipose tissue, Cartilage, Bone, Muscle, Nerve,
Vascular tissue, Blood corpuscles, &c. In Zoology, howe
the Tissues are viewed mainly in the Organs; and Zoolog
characters are characters of organs. There is not the san
use made of distinction of Tissue, as we have seen in B
The basis of Zoological Classification is the division 9
ie oe ae | A
Whites in: ; P
COMPARATIVE ANATOMY AND ZOOLOGY. 5389
Animal system into Organs. These, with their functions, may
be variously arranged, there being two natural groups; (1)
the Vegetative Organs and Functions (Nutritive and Repro-
ductive) — Digestion, Absorption, Circulation, Nutrition,
Secretion, Excretion, Respiration, Generation, Development ; i
(2) the higher Animal Organs — Locomotion, the Senses,
the Brain.
In all these various organs, characters may be sought;
there being none but what are subject to variation throughout
the Animal series. The Anatomy of Vertebrates comprises
the following parts:—Skeleton, Muscles, Brain and Senses,
Teeth, Alimentary Canal and Appendages, Absorbents, Circu-
lation, Respiration, Urinary organs, Skin, Generative Organs.
The Blood is also a source of distinction in the larger divisions—
as between Vertebrate and Invertebrate, Warm-blooded (Birds
and Mammals) and Cold-blooded (Fishes and Reptiles).
The grand separation, common to all classificatory sciences,
between the General and the Special Departments, in the
Animal Kingdom, gives birth to the two subjects,—Compara-
tive Anatomy and Zoology. As in Mineralogy, and in Botany,
these should repeat and support one another, giving the same
information in two different forms.
The Comparative Anatomy arrangement, besides settling
the selection and the order of Zoological characters, is a most
powerful instrument of generalization. The exhibition of each
successive organ in.all varieties and modifications, discloses
many aspects otherwise hidden; and places the more general
and fundamental peculiarities in a strong. light. Much of
the insight that we at present possess regarding the brain ‘is
due to Comparative Anatomy. Too great pains cannot be
* given to the perfecting of the Comparative Method; and the
grand secret is the lucid presentation of agreements and of dif-
ferences.
16. There being, in Animals, a number of distinct
_ organs, a search is made for Laws of Concomitance be-
tween them.
It is a part of Biology, and an indispensable aid to Zoology,
to find out the correspondences or laws of concomitance
between the different organs—Moving Organs, Nervous
System, Digestion, Reproduction, &e.
These laws occur under various aspects. Some are empiri-
cal generalizations, such as the coincidence of the ruminant
characteristic with the cloven foot and horns on the frontal
540 - LOGIC OF ZOOLOGY.
bone. Other coincidences are mutually related, and are
and parcel of the development of the species; as the adv:
of the brain with the muscular system, the reproductive
organs, and the organs generally. The fact of increase of — :
organization as a whole implies laws of concomitant ae
ment of all the leading organs. The connexion between an
animal’s organs and its circumstances or conditions of life is
not a law of co-existence, but of mutual implication; it does not — ¢
give us two independent facts, but the same fact on two sides, —
All references to the element of each species—water, air,
earth, the body of another animal—are to be held as not G
illustrating the nature of the organs. 63 >
The best established laws of concomitance in the asia s
organs, on which depends the existence of a science of Zoo- —
logy, as distinguished from a Comparative Anatomy of ani- —
mals, are liable to exceptions. Sometimes a single species —
will mar the unanimity of an entire Division, like Amphioxus | ‘
among fishes. It is clear, however, that such exceptions are —
to be mentioned, and then disregarded. They do not even —
prevent us from supposing that the characters whose con- a
junction they violate are united by cause and effect; for
although causation permits no exceptions, it may be ocasionally
counteracted.
The more we can exhaust the relations of conespoactil
or concomitance, and the more precisely we can express them,
the better are we prepared for the great classifying operation |
that makes up Zoology. The full import of the remark will
appear under the next head. (hae
It might seem superfluous to insist on preserving a regular
order in the statement of Characters throughout the whole
scheme—whether in the Comparative Anatomy or in the >
Zoology,—seeing no one ean follow out comparisons that ¢ are
not uniformly expressed. 4 im '
TI. The Maximum of Affinity as gwing the Classes. — ng
a
17. The choice of Classes follows the maximum of ag 2.
ments in the several organs.
The existence of Laws of Concomitance indicates “he “possi
more organs, or important modifications of organs.
zoologist grasps at this circumstance, in order 0 forn
leading classes.
In appearance, but only in appearance, there i is. ay
BASIS OF CLASSIFICATION. 541
principle of grouping. Some one organ is chosen as the basis
of classification ; for example, the Reproductive system, which
gives the name to Mammalia. In reality, however, such choice
is made not on account of the organ by itself, but on account
of the number of its alliances.
An extreme supposition will place this fact in a clearer |
light. Let us imagine that every one of the leading organs,
or systems,—Nervous, Reproductive, &c.—was wholly uncon-
nected in its modifications with every other organ; that the
nervous system might vary through all possible modes
without any corresponding variation in anything else. Under
such circumstances, we might have a comparative anatomy of
each organ, but no concurrence of organs. Zoology would
be incompetent and non-existent. The only possible classifi-
cation would be according to the Comparative Anatomy of the
several organs. We might assign a superior dignity to
same one organ, as the Brain, and give it a priority in arrange-
ment, and a preference in study; but after the entire animal
kingdom had been exhaustively arranged under thecomparative
anatomy of the Nervous System, the same operation would
have to be repeated under the other systems ; the work would
then be finished ; being substantially the present science of
Comparative Anatomy, without the relief that is at present
afforded, to the overwhelming mass of details, by laws of
Concomitance.
Accordingly, the justification of preferring one organ as the
classifying basis, is avowedly its alliances. The taxonomic
value of the ‘ placenta’ in Mammalia is the number of charac-
ters that it carries along with it. ‘Man, the Apes, the Insec-
tivora, the Cheiroptera, the Rodentia,—are all as closely con-
nected by their placental structure as they are by their general
afjinities’ (Huxley). The real motive to the grouping is not the
placental structure, but the general affinities.
We may make another illustrative supposition. If all the
organs were strictly co-equal in development and in modifica-
tions; if the Nervous System, the Muscular System, the
Reproductive System, &c., were all modified in strict concomi-
_ tance, there would be no such thing as a preference organ
whereupon to base classification; the Reproductive organs
could be no more a clue to the ‘ general affinities’ than the
digestion, or the respiration. There would be no mention of
a special basis ; general affinity would alone be prominent.
It would appear, however, that the constituent systems of
the animal organization are not co-equal and concomitant in
549 LOGIC OF ZOOLOGY.
their changes; some carry with them more, and some less, me 3
general affinity or concomitance. Taking the whole Animal —
Kingdom, we find that the Nervous System is by far the most _
important basis of classification; the reason being that the
organs generally cannot advance without a corresponding rise
‘in the regulating and co-ordinating organ. There cannot be
an extension of the muscular apparatus without an extension
of the brain; while the muscular apparatus itself implicates
many other parts of the system. ,
Next to the Nervous System is that part of Reproduction,
embracing the mode of Development of the animal from the
germ upwards. We have already seen how far this governs
the divisions and sub-divisions of the Mammalia; their very
name is founded on it. Y
If, for the sake of illustration, it were asked what would be
the worst organ for classifying upon—the one that undergoes
the greatest degree of unconnected or isolated variation,—the —
answer would probably be the Heart.
IIL. Classification by Grades.—Spectes.
18. It being assumed that each class is formed on the —
maximum of affinities, the number of grades is regulated —
by the occurrence of a succession of suitable groupings.
The grades, or halting-places, are a relief to the burden of
numerous common characters; but there is no need tocon-
stitute them where the amount of resemblance is inconsider- __
able. 5
In the higher Vertebrates, a succession of six, seven, ormore
grades is admissible and advisable; while the attempt to con-
stitute Natural Orders, Genera and Species, in the Protozoa, —
is misplaced and savours of pedantry. -
In Mammalia, the distinctions of Species may be numerous —
and important; profound differences separate the Lion and —
the Tiger, the Horse and the Ass. In Birds, on the other
hand, the species often turn upon small and nice peculiarities. -
Of the three hundred species of Parrots, it is impossible that —
there can be specific differences either numerous or important; _
the Psittacos erithacus, for example, is distinguished as grey, —
with tail red! The domesticated varieties of the horse, dog, —
and cat, have wider differences than many species, or even —
genera, of the lower animal tribes. The differences between
a Negro and a Caucasian (varieties of the Species—Man) pro
AGREEMENT AND DIFFERENCE, 543
bably surpass in number the distinctions between two Natural
Orders of Infusoria.
Iu some cases, there occurs a single character so bold and
remarkable as to satisfy our utmost demands for a specific
distinction. Such is the extraordinary electrical organ in cer-
tain fishes. The species of the Gymnotus named eleciricus, is
sufficingly marked by this single feature, in whose presence
the describer abstains from all further specification.
IV. Marking of Agreement and Difference.
19. Zoology depends greatly on the rule of parallel
array for Agreements, and of pointed contrast for Differ-
ences.
The characters of classes, high or low, should be thrown
into the form most advantageous to the reader, that is, the
tabular arrangement, with appended remarks and comment-
aries in ordinary typography.
For example, the characters of Aves (reckoned sufficient for
discrimination, although inadequate asinformation) are these:—
Reproduction :—oviparous
Respiration :— air-breathing
Heart :—four cavities, as in the Mammalia
Integument :—feathers
Teeth :—wanting ; substitute horny jaws
Locomotive Organs :—the anterior limbs are wings.
Besides these characters much is to be said as to the points
of community, in the Nervous System, the Digestive System,
and other parts.
For the statement of Difference we may select Mr. Huxley’s
primary division of Birds into three classes ; an instance where
the pointed contrast may be extended to three members :—-
SAURURE RATITA CARINATS
Metacarpal Bones
Not ankylosed §Ankylosed Ankylosed
Caudal Vertebree and Tail
Longer than body Shorter Shorter
Crest of Sternum
None Present
Barbs of the Feathers
Disconnected Connected.
There are several other characters of the second and third
classes, and no more of the first. Hence, we might have put
the first against the two others as a whole, and then worked
out the present contrast upon these two.
Ov ann
3} Lye , or
“Pn
te
A a
544 LOGIC OF ZOOLOGY. oa.
te
Not merely in the formal exhibition of generic and specific
characters, but in every incidental comparison of one class
with another, the statement of Agreements and of Differences
should always be clear, emphatic, and ostentatious.
V. Index Classification.
20. An Index Classification for Zoology might choose
between the two alternatives—-the tabular and the dichotom-
OUS
The Tabular method has already been suggested for Mine-
ralogy, and will again be brought up for Diseases, The
Dichotomous method is carried to perfection in Botany. a
A tabular plan could be based upon Comparative Anatomy ;
there being given, under every peculiar mode of each organ, a
complete list of all, animals possessing that mode. Thus,
there would be a table of the species conforming to each
grouping of the Teeth, so that the discovery of such grouping
in any given specimen would decide the animal as one of the —
list. A second character being noted as present in the speci- __
men would direct to a second list, where the animal must —
appear; the choice is now narrowed to such as are common
to both lists. A third, and a fourth character, being followed —
out in the same way, would reduce the choice to still smaller
limits ; and eventually the enquirer would be guided to the
proper Species. pong
The dichotomous method of Botany, if fully adapted to —
Zoology, as it might obviously be, would be still better, =
The want of an Index is less felt in Zoology because of the —
better marked specific distinctions, at least until we descend —
to the inferior tribes, where there are numerous species, —
slightly marked. It would be pre-eminently necessary for
Birds, among Vertebrate animals, and for the Invertebrate —
Orders generally. It is less necessary for Mammalia, except ,
in a collection of unusually vast extent, ei
CHAPTER VIL
LOGIC OF PRACTICE.
1. The Practical Sciences are defined by their several
ENDs.
Medicine is the practical science having for its end Health.
Grammar and Rhetoric have for ends the perfection of the
instrument of Language.
2. There is one crowning end, the sum of all other ends,
namely, Happiness or Well-being,
People desire Health in order to be happy. There can be
no end beyond human enjoyment—the gaining of pleasure
and the averting of pain.
3. ‘The final end of all pursuit must be assumed or
granted ; it cannot be proved.
No proof can be offered of the position that Happiness is
the supreme end of human conduct. We must be satisfied
with the fact that mankind make it the end. As all proof
consists in referring the point in question to something more
fundamental, there must be at last something taken for
* granted on its own account. Such is Happiness, the highest
crowning end. Men desire Happiness, either for themselves
or for others, as the goal of all endeavour.
4. There is, however, a want of perfect unanimity as to
the final end. Some even deny that Happiness is the end;
while there may be great difference of opinion as to the
nature of the happiness to be sought.
The end set up by some, as the final end of all, is Virtue.
To those that embrace this view consistently, there is no
reply; there is no possible appeal from a fundamental end.
We may, however, enquire whether any class of persons do
consistently and thoroughly maintain virtue, and not happi-
ness, to be the sole end of all endeavours. Wherever there is
inconsistency, an argument is possible.
Now, in reply to the setting up of Virtue, or mere self-
denial, as an end, we may urge, first, that the conduct of man-
kind shows that, in the great mass of cases, they regard virtue
546 LOGIC OF PRACTICE.
asa means to happiness. The virtue of Howard consisted not
in the fatigues and privations suffered from his journeys, and
from visiting squalid dungeons ; it was in the amount of human
misery that he relieved.
Secondly, the position that Virtue is an end is almost
uniformly coupled with the assertion that, in the long run,
Virtue is Happiness; which is merely another way of assign-
ing Happiness as the end.
Thirdly, the thorough carrying out of the position that
Virtue, in the form of ascetic self-denial, which is Virtue
dissociated from Happiness, is the ethical end, would be tanta-
mount to abolishing the difference between good and evil,
with which virtue itself is identified. Virtue, in the sense sup-
posed, flourishes in misery ; the more miserable we are, the
greater scope we have for virtue; the more miserable we
make other people, the more scope we give them for virtue.
Again, Happiness may be allowed as the end, and yet there
may be wide differences of view in the interpretation of the
end. The partizans of virtue may re-appear on this ground,
affirming that Happiness is only to be found in Virtue or
Duty, not in enjoyment and in the absence of pains. The
reply proceeds as before; are these reasoners thoroughly
consistent with themselves? If they are, they cannot be
refuted; if they are not, they may.
Great variety of opinion may be held as to the beings whose
happiness is to be sought. Are we to seek our own happiness
solely, or the happiness of others solely, or partly the one and
partly the other? How far are we to extend our regards—
to our own kinsmen, to our fellow citizens, to humanity in
general, to the lower animals? In none of these points is
argument possible, unless where people are inconsistent, which
they need not be. We cannot reason a person into the adop-
tion of other people’s happiness as an end, unless such person
has already of his own accord embraced some doctrine that
involves this, as for example, the profession of Christianity.
Neither can we offer any reason for extending sympathy to
the lower animals. An education of the feelings is the only —
mode of enlarging people’s sympathies. Noman can be argued —
out of a consistent selfishness.
CHAPTER VIII
LOGIC OF POLITICS.
1. Politics, in the largest sense, refers to the action of
human beings in Society.
The notion of Society can be gained only by each one’s
individual experience. The first example of it is the Family,
which contains a plurality of persons in mutual co-operation,
withcommand andobedience. The earliest notions of authority,
law, command, obedience, punishment, superior, inferior, ruler,
subject,—are gained from the various aspects of the small
domestic circle.
The larger aggregations of the school, village, parish, town-
ship, church, &., repeat all those aspects of the family, while
dropping the incidents special to the family.
2. Thescience of Politics, as a whole, is either Thanraan
cal or Practical.
Under the Theoretical Science of Politics must be described
the structure or organization of Political Society ; this being
equally essential as a preparation for the Practical Science.
All the leading terms of Politics must be defined ; all the parts
of the Political system explained. To this preliminary branch,
Sir G. C. Lewis applies the designation ‘ Positive Politics,’
In the second place, the Theoretical Science traces cause
and effect in political institutions, as facts of the order of
nature; in the same way as Physics and Chemistry describe
cause and effect in inorganic bodies, and Biology in living
bodies. The theoretical department of Society would state,
upon evidence of fact, conjoined with reasonings from human
nature, what are the consequences of given institutions. To
quote from Sir George Lewis :—
‘It assumes that we know what astate is ; what are its functions ;
what are the conditions necessary for its existence; by what in-
struments it acts; what are its possible relations with other states.
Starting from this point, it inquires how certain forms of govern-
ment, and certain laws and political institutions, operate; it seeks.
from observed facts and from known principles of human nature,
to determine their character and tendency; it attempts to frame
propositions respecting their probable consequences, either uni-
* 548 -- LOGIC OF POLITICS. | a
versally, or in some hyyothetical state of circumstances, Thus it
may undertake to determine the respective characters of monarchy,
aristocracy, and democracy ; it may show how each of these forms
of government promotes the happiness of the community, and
which of them is preferable to the other two, It may inquire into the
operation of certain modes of preventing crimes—as police,—of
criminal procedure, and of legal punishment, such as death, trans-
portation, imprisonment, pecuniary fines,—and it may seek to
determine the characteristic advantages and disadvantages of each,
in certain assumed conditions. It may inquire into the operation
of different systems of taxation—of laws respecting trade and-
industry—of modes of regulating the currency—of laws regulating
the distribution of property with or without will—and other
economical relations. It may lay down the conditions which
render it expedient to govern a territory as a dependency; or q
which tend to promote the prosperity of a new colony. It may
define the circumstances which ensure the permanence of national
confederacies, and it may inquire what are the rules of interna-
tional law which would tend to promote the uninterrupted main.
tenance of peace.
‘It seeks to lay down general theorems respecting the operation
and consequences of political institutions, and measures them b
their utility or their capacity for promoting the welfare of the
national community to which they are applicable. Propositions
of this sort may lead (though not by so direct a road as is often
supposed) to preceptive maxims ; but they are themselves merely
general expressions of fact, and they neither prescribe any course
of conduct, nor do they predict any specific occurrence; though,
from the generality of their form, they may relate as much to the
future as to the past.’
The Theoretical Science of Society is sometimes expressed
as the ‘ Philosophy of History,’ or the accounting upon general
principles of cause and effect for the actual course of political
events, the growth of institutions, the progress and decay of
nations. History, in the ordinary signification, recounts these
things in the detail; the Philosophy of History generalizes the
agencies at work, and endeavours to present the whole as fol-
lowing out certain great leading ideas. A few writers have
aimed at establishing such generalities—Vico, Montesquieu,
Millar, Condorcet, Auguste Comte, &c.
Practical Politics consists of maxims of political practice.
Here we have to suppose an end,—the welfare of the com-
munity, or any other mode of stating the political end.
This necessarily appears with more or less prominence in all
political treatises. Aristotle’s work is a search after the best —
government. Machiavel’s treatises are preceptive or practical. —
Locke does not formally enquire after the best constitution,
SCIENCES COMPRISED IN POLITICS, — 549
but under the guise of what is necessary to a state, he insinuates
certain political forms, and certain legislative principles.
Sound method requires that a writer should, in the first
instance, separate the Theoretical from the Practical.
3. The entire department of Political Science at the pre-
sent day comprises several sciences.
It has been found practicable and convenient to withdraw
from the wide region of human society, certain subjects that
can with advantage be cultivated apart, and thus to reduce the
complication of political enquiries.
(1) The first of these is Jurisprudence. This is a distinct
branch bearing on the form of Law, as apart from its substance.
It teaches how laws should be expressed, with a view to their
satisfactory interpretation by the Courts ; it embraces evidence,
* and the principles and procedure for the just administration
of the laws. It does not consider the choice and gradation of
punishments, but explains how they should be legally defined,
so as to be applied in the manner intended by the legislator.
(2) International law is the body of rules agreed upon by
independent nations for regulating their dealings with each
other, both in peace and in war. It includes, for example,
questions as to the Extradition of Criminals, and the right of
Blockade at Sea.
(3) Political Economy, or the science of the production and
distribution of Wealth, relieves the political philosopher of a_
considerable part of his load. The legislation regarding Pro-
perty in Land, Trade, Manufactures, Currency, Taxation, &c.,
is guided by the enquiries of Political Eeomony. Within its
own sphere, this science has the same logical character as the
mother science. It has its definitions, its principles or laws,
partly inductive and deductive, and its methods, which are
the ordinary logical methods.
(4) Statistics is a branch of the Science of Society, admit-
ting of being cultivated separately. It furnishes the facts and
data of political reasoning in the most complete and authentic
form.
4, The subjects remaining to Political Science, are (1)
the Form of Government, and (2) Legislation on all topics
not otherwise embraced.
The different Forms of Government, their precise defini-
tion, and their several tendencies, constitute the foremost
preblem of the political science. The discussion of Monarchy,
550 LOGIC OF POLITICS.
Aristocracy, Democracy, enters into every treatise called
political.
In immediate connexion with this subject, if not a part of
it, is the distribution of the functions of government, into
Legislative, Administrative and Judicial; the delegation of
the powers of government to subordinate authorities, as in
provincial, local, or municipal government.
These subjects are sometimes considered as exhausting the
sphere of Politics; but ina very narrow, although distinct
signification of that sphere. Thus, Mr Mill remarks,—‘ To
attempt to investigate what kind of government is suited to
every known state of society, would be to compose a treatise
on political science at large.’
It must, however, be matter of enquiry how a government,
when constituted, is to discharge its functions. This supposes
that the functions are classified and defined; an operation
involving one very important enquiry in Politics, namely, the
proper Province of Government.
There are certain things that Government must undertake,
in order to fulfil its primary ends; such are Defence, and
the Preservation of Life and Property.
There are other things that government may or may not
undertake—as the Support of Religion, Education, Postal com-—
munication, the maintenance of Roads, main Drainage, aiidi
other works of general utility.
5. The curtailment of Individual Liberty is a necessary
effect of government ; and the degree of this curtailment
is a vital consideration i in Political theory.
In order that men may act together in society, each must
in part subordinate their own actions and wishes to the
general scheme. Obviously, however, individual liberty,
which is in itself a chief element of well-being, should be
restricted in the least possible degree; and the burden ei
proof must always lie upon the proposer of restraint.
The Structure of Political Society.
6. The preliminary branch of the Social Science, con- 4
tains the Definition of Political Society, and of all the —
Relationships and Institutions implied therein. r
This is the part of the subject entitled by Sir G. C. Lane
Positive or Descriptive Politics. It teaches what is essentially '
involved in the idea of political government. It an the —
THE POLITICAL STRUCTURE, 551
necessary instruments of government; as a law, rights and
obligations, sanctions, executive commands, and the like. It
neitlier enquires into the operation and tendency of institutions
(which is Theoretical Politics), nor urges the preference of
one to others (Practical Politics). It explains the meaning of
monarchy, aristocracy, democracy, but does not teach which
is the best form. It shows what is the nature of punishment,
bust does not say which punishments are the most efficacious.
It expounds the relations of master and free servant, and of
master and slave, but does not trace their bearings on the
welfare of the parties concerned. It explains the nature of a
dependency, without arguing the question—Should colonies
have a separate government. It shows what are the acts
constituting an exchange, and the difference between barter
and a money equivalent, but does not dwell upon the advan-
tages of exchange in facilitating trade. (Methods of Reasoning
in Politics, vol. I., p. 54).
The fundamental notions of Political Society—Sovereignty,
Law, Command, Duty, Sanction, Obligation—are treated of
by John Austin as a part of the special science of Jurispru-
dence. That these notions are at the basis of Jurisprudence
is beyond doubt. Still, in a completely formed Political
Science, they would be given once for all at the outset, under
the head of the Structure of Political Society, and would need
only to be referred to by the Jurist.
7. The very fact of Political Society involves a series of
primary notions, forming a mutually implicated, or corre-
lative group.
Government.—This is the essential fact of political society ;
to define it, or any one of its numerous synonyms—NSovereignty,
Authority, Ruler, Political Superior—is to define political
society. The definition must be gathered from the Particulars
common to Political Societies. It is given by Sir G. C. Lewis,
as follows :—‘“ When a body of persons, yielding obedience to
no superior, issue their commands to certain other persons to
do or to forbear doing certain acts, and threaten to punish the
_ disobedience of their commands by the infliction of pain, they
are said to establish political or civil governinent.””
Closely examined, this definition contains the very terms to
be defined—for example, superior and command—so that it is
not a definition suited to inform the ignorant. It is rather of
the nature of the first definitions of geometry (Line, Angle,
&c.) which do not communicate notions, but employ terms to
552 LOGIC OF POLITICS,
fix with more precision the boundaries of notions already
gained from experience. We should require, in the first
place, to know political societies, in concrete instances; and
the definition would teach us the corresponding abstraction or
generality.
Austin (Province of Jurisprudence Examined) endeavours
to build up the definition from its simplest assignable elements.
Starting with Command, he defiues this as ‘ the expression or
intimation of a wish, to be followed with some evil, if not
complied with.’ This involves only such facts of human nature
as wish, expression, non-compliance, infliction of evil. In the
notion of Command, as thus defined we have nearly all that
is signified by Government, Sovereign, Superior, Authority.
We have only to specify the persons intimating the wish (to
some other persons) and following up the non-compliance with
the infliction of pain.
The supposed command is a Law. The evil to be inflicted
is a Sanction, Penalty, or Punishment. 'The persons addressed
are Subjecis, Inferiors ; they are placed under Obedience, Duty,
Obligation. The aggregate of persons comprised within the
scope of the same commands, is a Political Socvety, a Community,
a People. They are in the Social state, as opposed to the state
of nature.
Moral Right and Wrong must be referred to the same com-
plex fact.
8. Government is usually said to have three distinct
functions—Legislative, Executive, and Judicial ; each one
giving birth to a numerous class of notions.
iad od ie coe
Sa hea
Legislature-—The power of making general commands uni-
versally applicable, under given circumstances, is called
Legislation ; it is the most extensive and characteristic func- —
tion of government. The process is very different under —
different forms of government. In every shape, there are —
implied as subsidiary notions—statute, and its synonyms, pub-
lication or proclamation, enactment and repeal, &c. ~
Huxecutive, Adminisiration.—Implies performance of the speci- —
fic acts occurring from day to day, in the exigencies of society —
—organizing and directing the military force, negotiating with
foreign governments, appointing the officials of government,
erecting public works, &c. In this function, the government
is said to use ministers, to issue orders, to receive and i issu
despatches, reports, to suwpermtend all functionaries. i
Judicial,—A distinct function of government, delle en-
a as
-*
Rie
THE POLITICAL STRUCTURE 553
trusted to a separate class of persons. It supposes impedi-
ments to the commands and operations of government, either
in the way of misunderstanding, or of disobedience. These
are removed by Judicial Institutions, called Courts of Law,
presided over by Judges, said to administer Justice, according
to a definite Procedure, and rules of Hvidence. The ramified
arrangements belonging to these several heads are detailed and
defined by the special science of Jurisprudence.
With all varieties of government there must exist these
three functions ; in rude governments, they are exercised by
the same persons ; in civilized governments, they are more
or less divided between different persons.
9. Under ‘ Form of Government,’ there is a number of
structural modes, for which there are specific designations.
The Form of Government brings out the designations
Monarchy, Aristocracy, Democracy, Republic, Mixed Govern-
ment, Balance of Power, Constitution.
The logical division of Forms of Government is into the
government of one person (Absolute Monarchy) and the govern-
ment of more than one (Republic or Commonwealth). If, in
the second alternative, the governing body is small, the
government is an Aristocracy ; if the power is lodged in the
majority of adult citizens, the gorenment is a Democracy.
Such names as Limited Monarchy, Constitutional Monarchy,
mean either Aristocracy or Democracy; they indicate the
form of monarchy, but the reality of another power. A
Mixed Government is a mere semblance; some one of the con-
stituents is in point of fact the sovereign.
Aristocracy, where it prevails, makes a division of the
people into Nobility and Commonality. Often the governing
body is a hereditary nobility.
Representative Government, the growth of modern Democracy,
is a leading notion of Political Science. The meaning is that
the whole people, or a large portion, exercise the ultimate
controlling power, through the deputies periodically elected by
themselves. In the ancient republics, the corporate or col-
legiate action lay with an assembly of all the citizens, or of as
many as could be got together.
The operations of corporate government give birth to the
political elements expressed by assembly, deliberation and
debate, decision by a majority, chairman, election, suffrage.
10. The Functions or Business of government introduce
many structural elements.
554 LOGIC OF POLITICS. ou aN
The first function of a political society being defence, there
is a large institution corresponding, called the War eget
tion—Army and Navy. “
The protection of the members of the society from one
another is either by an application of the War force, that
is the soldiery, or by a separate force called Police. =
These two leading institutions involve many others. An
official machinery, or bureaucracy, is interposed between the
sovereign power and the actual instruments. For paying the
cost, there must be a levy of Taxes, with a bureaucracy
corresponding.
If the government undertakes public works—roads, bridges,
public buildings, means of communication—it becomes a sort of
industrial management on the large scale.
The coining of money is a proper function of government.
The regulation of bargains and contracts of every description,
as well as the enforcing of them, is a matter for the state. The
marriage contract, in particular, the relations and rights of the
different members of the family, are under state control.
A Church Establishment, whether incorporated with the
civil government, as is most usual, or existing apart, is a vast
social machinery with elements and terms corresponding, all
admitting of definition. -
11. In a society spread over a wide territory, there must
be a division into local governments, duly subordinated
to the chief or Central Authority.
This originates the terms Central, Centralization, and Local, _
Provincial, or Municipal government and institutions. Asmall
locality may represent in miniature nearly all the features of —
the entire society. The delegation of power to the loc .
may be small or may be great. Moreover, the Form of
- Government of the entire society repeats itself in the localities. —
If the sovereign is an absolute monarch, the local authority is.
absolute in the local sphere; such is the oriental satrap, an
the viceroy of the absolute European monarch.
12. The Province of Government marks the line between
Public and Private management. | eke
The habitual industry or every day avocations of the mass
of the people must be left to themselves. Their manner bo
subsistence, their recreations and amusements, are also their —
own choice ; although governments have often anne es to
regulate all such matters.
ORDER AND PROGRESS. 55D
13. The mutual bearings of Public and Private Institu-
tions are so numerous, that a statement of the Political
structure is incomplete without the Private Institutions.
The Industry of the People is an important element of the
state politically. So are their Recreations, Tastes, Opinions,
Literature, and Science. However much the government ab-
stains from control in these matters, its operations in its proper
sphere are influenced by every one of them. An agricultural
community gives a peculiar character to the entire action of
its government. A community largely occupied in foreign
trade involyes the government in relations with foreign coun-
tries.
14. The good or ill working of the Political system
leads to a variety of situations, requiring the consideration
of the political reasoner.
When the government fails to accomplish its main functions
—defence, protection, justice, &c.- -it receives the designations,
‘bad government,’ ‘mis-government.’ Its badness may con-
sist in partiality to individuals, which is injustice; in not
adhering to its own published regulations; in the capricious.
introduction of changes ; in preying upon the community by
exactions, or by affronts, .
When the government is excessive in its restraints on indi-
vidual movements, it is called despotical, tyrannical, oppressive ;
and the re-action or. revolt is Political Liberty. When it
meddles with what might be left to private management, it is
said to over-govern ; the euphuistic phrase is a paternal govern-
ment.
The emphatic expression Social Order means, in the first
place, that the government, whether good or bad, is obeyed ;
the opposite state is Anarchy, Revolt.
Order is also contrasted with Progress, Improvement, or
Owwilization. .Those things that maintain the existing structure
in its integrity are said to minister to Order; while the agen-
cies that raise the society to a higher pitch of improvement,
are said to minister to Progress. In point of fact, the opposi-
tion between the two is very slight; what is good for one is,
with very trifliug allowances, good for the other (Mill’s Re-
presentative Government, chap. II).
+556 LOGIC OF POLITICS,
| he
THEORETICAL POLITICS. er “a
15. The Laws, Principles, or Propositions, of political 4
society, together with the Methods of invesiaaae consti- | a
tute Theoretical Politics. ‘ite i
The foregoing head, including the Analysis of the Social ;
Structure, the meaning of State of Society, the Notions of —
Politics—is preparatory to the enunciation of the Laws of —
Society, so far as known. These Laws are best discussed in |
the theoretical form; they may afterwards be changed into
the practical or preceptive form, that is, nto maxims of the a
Political Art. 7 4
16. The Laws of Society may be either Laws of Co- |
existence, or Laws of Succession, of the different parts of a
the Social Structure. In both cases, they are laws of
Cause and Effect. a
The complex structure of Political Society involyes many
relationships of Co-existence and of non-coexistence. Soned
arrangements always carry with them some other ane a
ments ; some things are repugnant to other things. Ther
mark was made by Volney that the ‘plains are the seat c
indolence and slavery, the mountains of energy and ooo
But whatever co-existences and repugnances can be predicna
generally are dependent on causation. 4
Again, we may take any one part of the social structure a8
a cause, and lay down the laws of its effects; as when w
describe the consequences arising in a given state of =
from an absolute monarchy or from a state church.
We may even take up an entire state of society, with all's it os
mutual actions, and endeavour to trace its future destiny. .
This is the large problem of the Philosophy of History.
But for devices of simplification, such problems would be
wholly unworkable ; the complication of elements could
be embraced by the human mind. We should need to fas
upon some single agency, either comprehending, or outwei
ing the others, whose solitary operation will give the ke.
the entire problem. The state of opinion and enlightenm
of a community is an example of those over-masterin
cumstances. fi re
‘ie
Human Character as a Political Element.
17. As the subject-matter of Political Science is humar
a
es *
"vid oye An
aaa
ae a
¥, i
oils
POLITICAL ETHOLOGY. ‘ 557
beings, the characteristics of humanity must enter as a
primary element.
If all human beings were alike, either wholly or in those
points concerned in political action, the construction of a
political society, whether easy or not, would be but one pro-
blem. But there are wide differences as regards peculiarities
of character essential to the working of the political scheme.
The differences between an American Indian, a Hindoo, a
Chinaman, a Russian, an Englishman, an Irishman, an Italian,
taken on the average, are such as to affect seriously the struc-
ture and the workings of political institutions. Given a certain
Form of Government, or a certain constitution of Landed
Property, the tendencies would alter greatly under these
various types of character.
The theory of Society consists in stating how human beings
will act under a given social arrangement; it is, therefore,
essentially a special application of the laws of mind and char-
acter. Hence a thorough knowledge of whatever Psychology
can teach would be a preparation for this study.
Yet, all parts of human nature are not equally concerned in
political action; the ethical qualities of Honesty, Industry,
Steadiness of Purpose, are more vital than the Artistic sensi-
bilities.
Moreover, Politics is concerned only with the characteristics
that appear in collective bodies. The politician leaves out of
account all those individualities that are merged when men act
together in a body; that is, the qualities occuring merely
in scattered individuals and in minorities. Whence, national
character is a much simpler phenomenon than individual
character ; as the flow of a river in mass is a simpler physical
problem than the molecular adjustments of the liquid state.
18. A Political Ethology would be a modified science of
character, consisting (1) of a selection of the qualities that
appear in national character, and (2) of the laws of their
operation,
(1) Following the divisions and subdivisions of character,
as formerly sketched (p. 518), we should have to bring out into
prominence all that arise in human beings when working
collectively.
Thus, to commence with Action, in the form of Spontaneous
Energy. Prior to an account of the various motives that
induce men to activity, there is a notable peculiarity of cha-
558 ' LOGIC OF POLITICS.
racter in the degree of the energetic disposition itself.
this shows itself, as high or as low, in whole nations, na s
importance as respects both the Form of Government
many other political arrangements. The inhabitants of tempe
rate climates are superior in natural energy, irrespective of al all
modes of stimulation. to the dwellers either in the roma r
in the arctic circles. The English and Anglo- -Americ
peoples are probably at the top of ‘the scale.
Now this attribute has numerous social bearings. It iansieeh
private industry and the accumulation of wealth, an effect
leading to many other effects. It is both directly and indirectly ee
hostile to monarchical or despotical rule, and is, therefore, the ‘
parent and the guardian of liberty. 3
In like manner, we might survey in detail the FEELING <
Sensibilities, or Emotions of the mind, and mark those that
have social significance, and those that appear in men eae =
lectively. Thus, the Tender Sentiments, or the Sociability of re
the Mind, when strong, draw human beings together in society, —
and favour the cohesion of states as well as of families. Again, a
the strength and the mode of the Sentiment of Power may be —
a collective peculiarity, with national consequences. The fig
conjunction of tender feeling, as patriotism within our own
nation, with the love of domination beyond, is a pecntay by
often repeated. aa
The InrELLEcTUAL qualities that stand out in national pr O-
minence are too numerous to be touched upon. It was an
intellectually minded people, the Greeks, that began all the
civilization flowing from science or philosophy, “There is a
certain depth of ignorance and incapacity that renders th
higher modes of Political society impossible. A signal fail e
in either of the intellectual virtues—prudence and sympath >
is incompatible with political union. "i
(2) The next part of Political Ethology is an account of
tendencies of these various characteristics, and of the me
whereby they themselves are modified. The general scie
of character embraces this investigation on the wide scale, :
the present department is a special application of the panei Ss.
Propositions of Theoretical Politics.
19. The Political Structure, or Organism, being defi net
the Laws of Theoretical Politics are the laws of Causi
Effect, traceable in the working of the several Instit
What are the consequences of Absolute Monarchy
~~
iyo.
:
CAUSE AND EFFECT. 559
Democracy ; of Castes; of Hntails; of Free Trade; of Poor
Laws; of Indissoluble Marriage ; of State Churches? These
are a few of the enquiries of Political Science ; they are strictly
enquiries of Cause and Effect. Given any of these institutions
as causes, the effects may be sought. Again, given certain effects,
as the repression of agrarian crimes, the impartial administra-
tion of justice, the encouragement of trade,—we may seek for
causes. This is really the same problem in a. different form.
To all intents and purposes, the one enquiry is—Given a cause,
required the effect ?
t is not uncommon for political philosophers to entertain
such problems, as What are the effects of Monarchy, Aristoc-
racy, Democracy, in general; what are the effects of Slavery
in general, that is, under all circumstances, under every possible
variety of human character. Now, with such strongly-acting
causes as Absolute Monarchy, there may be assigned certain
universal tendencies so decided as to be seldom wholly defeated.
There are points in common to the despotism of a single person
in all countries and times. The possession of power, whether
_ on the great scale or on the small, operates with remarkable
uniformity. This is a psychological tendency whose free
course is best seen in politics; where, by the necessities of
the case, individuals have to be entrusted with power in a
large amount. The same consideration renders the workings
of slavery uniform to a high degree.
20. The Propositions of Political Science range between
two extremes; on the one extreme are propositions affir-
ming vniversal tendency, and, on the other, propositions
affirming specific effects in limited cases.
(1) The propositions affirming a universal tendency are
exemplified above. Similar propositions may be found respect-
ing every institution of human society. In many institutions,
however, the tendencies are difficult to find out, and are so
liable to be defeated by other causes, that their enunciation
has scarcely any value. For example, the operation of guilds,
or privileged corporations, admits of no definite statement
with reference to all possible circumstances. The division of
land into large or small properties may have opposite effects
in different social states.
Nevertheless, the attempt should be made to generalize the
tendencies both of the Forms of Government, in their detailed
varieties, and of all the leading Institutions growing out of
legislative action. It is equally indispensable to estimate the
560 LOGIC OF POLITICS.
precise worth of this class of propositions, to be aware of the
infirmities, and of the cautions needed in applying them. ~
There are prevailing tendencies of every important Institution
—of the Succession of Land, of Direct or Indirect Taxation, —
of Religious Endowments, and the rest. The affirmations re-—
specting these are only probable; they afford a certain Pe
sumption of what will actually happen in individual cases.
The special departments—Political Economy and Jurisprae
dence—share the burden of these difficult problems. == a
(2) Propositions confined in their range to limited cireum- _
stances, to a narrow field of observation, may be so qualified —
as to state the causation with almost perfect exactness. Thus
if we confine our views to communities in similar climates, of
the same race, of nearly the same advancement in general —
intelligence, we can formulate with comparative precision the
tendencies of a given institution, whether the Form of Govern- —
ment, or any of the other leading social elements. These —
Limited or Partial Theories are the really valuable parts '€:
Political Science ; they afford the guidance in the art or pre
tice of Politics.
With a view to these propositions, there must be a aiviieal
and subdivisions of communities into classes. An example of —
such a classification is given by Sir G. C. Lewis, as follows:— _
‘One large classification of communities for the purpose of
a common predication is—1, those communities which are in
a wild and unsettled state, ‘such as the African and Indian
savages, the Bedouin Arabs, the Nomad Tartars; 2, those
Oriental communities white live under a regular polit al
government, but whose social state is nevertheless fixed and
unprogressive, such as the Turks, the Persians, the Hindt /
the Chinese, the Japanese; 3, Christian communities partaki
of the modern European civilization.’ i
Setting aside the first class, as affording too een a fi
for political data, Sir G. C. Lewis institutes a comparison ¢
contrast between Oriental and European communities, show
each of the two classes as a whole. The following are sc
leading points of the contrast. |
ORIENTAL. EUROPEAN.
Government.
Despotical Free oe
By Delegation _ Direct from the centr re
International Law. ?
Rude Intricate, forming : i
LIMITED OR PARTIAL THEORIES, 561
Laws—Civil and Religious codes,
Interwoven Distinct
Marriage.
Polygamy Monogamy
Women.
Secluded At large
Status of the Labourer.
Slavery Civil Freedom
Punishments.
Cruel Mild
Dress.
Loose Closely fitting
Alphabet.
_ Intricate Simple
Form of Interature.
Poetry and mystical prose Argumentative prose.
Numerous propositions of Cause and Hffect could be laid
down respecting these peculiarities, connecting them with
one another, and with the Climate and Physical Situation, the
Physical and Mental Constitution, and the Historical Ante-
cedents of the oriental races.
Methods of Theoretical Politics.
21. As in all other sciences, there must be Observation
of Facts.
In Political Observation, there are special peculiarities
amenable to logical canons. The education of a political
observer is scarcely in any degree, as in the physical sciences,
an education of the senses; it consists mainly of intellectual
habits.
22. The Facts of Politics coincide with authentic His-
tory or Narrative.
The individual occurrences that, when generalized, make
up political principles, have to be correctly recorded, with all
the circumstances essential to the link of causation. The
sequence of events in a revolution must be stated exactly as
they occurred, and in sufficient fulness to give the conditions
of canse and effect.
The rules of historical evidence are a branch of Inductive
Logic, and as such they are given elsewhere (Appendix, I).
They have in view principally the number and the nature of
the testimonies needed to establish the truth of a past event.
562 LOGIC OF POLITICS.
A farther exercise of discrimination is requisite in the polit ti
historian, namely, to include all the circumstances enter
into the chain of causes, and to separate accompaniments —
that have only a poetic interest. To do this, the his-—
torian must be himself a_ political philosopher ; he must
know that the dazzling glitter of spears in the sun has nothing |
to do with the fighting strength of an army, that the stature, —
complexion, voice, or dress of Charles I. had no bearing upon —
his quarrel with his parliament. In short, as regards the —
relevance of facts and circumstances, the narrater must under- —
stand what it is to trace cause and effect in history. Tn ;
order to frame a coherent narrative, some theory of causation >
is necessary ’ (Lewis).
23. In Politics was first developed the reducing es
observations to the form called Statistics ; definable as the
observation, registration, and arrangement of such facts as |
can be given in numbers. i
The cultivation of statistics was first owing to the impeltatl
given to political economy by the French economists ; it being |
possible to state in numbers the most material facts regarding —
trade, currency, taxation, production, population, &c. The —
subject now comprises matters relating to all branches o} f
political observation ; Population, Births, Marriages, Deaths
~ Occupations, Diseases, Crimes, Pauperism, Education. :
Statistics gives an entirely new precision both to Theoretical AG
or Speculative Politics, and to the operations of government.
The increase or diminution of pauperism or of crime, in a la
country, could be judged only in the vaguest manner with
statistical returns from the officials concerned. The govert
ment would be at the mercy of accidental displays, and of
circumstances where the impressions are exaggerated. —
bread riot in a particular locality, an outrage of appal
accompaniments, would distort the judgment of the nation, as
to the general state of destitution or of crime.
24. The causes of erroneous observation in Politics,
partly common to the sciences generally, and para arg
to the political science. 7
Indolence and inattention, the love of the marvello
esthetic likings and dislikings, the support of a fay
theory, are operative in politics as elsewhere. The
special sources of bias in the political department are admira
tion of individual actors, party feeling, and, where practice i
r feos
POLITICAL EXPERIMENTS. . 563
concerned, direct personal interest. As a matter of course,
these corrupting motives extend their influence to the general-
izing no less than to the observing of facts.
Politics deals with human beings, whose springs of action
are in the mind; while observation relates only to outward
appearances, from which the mental states are obtained by
inference. The right performance of this process of inference
is an operation based on Psychology, and guided by the rules
of Inductive Logic. That Charles I. was executed is a fact ;
the motives of Cromwell and the Puritans in executing him
are a matter of difficult inference ; requiring us to apply laws
of human nature (veracity, bias, &c.), to what the actors said
and did in connexion with the fact. The secrecy of motives
is the characteristic of many ethical maxims.
Eaperiment in Politics,
25. Experiment, in the strict scientific meaning, is usu-
ally regarded‘as inadmissible in Politics. The substitutes
are (1) the sudden introduction of extraordinary influences,
and (2) the practical operations of government.
It is not possible to submit a society to the process em-
ployed in studying a metal, or in detecting the laws of Heat
or Magnetism. A political community cannot be manipulated
with a view to excluding artificially this or that agency, iso-
lating it from all but known circumstances.
(1) Some of the advantages of experiment are derivable
through the introduction of a new and extraordinary influence
into the society—such as a famine, a commercial crisis, an
insurrection, an epidemic, an invasion, a new invention, as the
steam engine, a religiousrevolution. The Irish potato famine
of 1845, is adduced by Lewis as a casein point. The influence
of this terrible calamity laid bare the evils in the state of the
Irish poor, and disclosed the secret springs in the social
economy of the people, as effectually as could have been done
by an artificial experiment contrived for that purpose.
(2) It is the very nature of government, especially an im-
proving government, to be trying experiments. Every new
law is an experiment.. There being an object to be achieved
by the law, the public is supposed to be interested in watching
the effects of the measure. A Police is organized, and the
effects upon crime observed. A Poor Law is introduced, and
the consequences traced. So every great innovation is a new
agent in society, which is followed by definite effects. The
564. LOGIC OF POLITICS. Bae
experiments are not always free from ambient thesed
be concurring agencies either defeating or exaggerating the
results; hence a demand for the precautions of the various —
Inductive Methods, Sau a
Causation in Politics, Wee
26. In Political Causation, the predominating fact is”
Collocation ; there is seldom, yet occasionally, an eee
to Conservation, 7S aa
tee
A political sequence is always immersed in a host of arranger
ments, positive or negative; and although impelling forces |
must always be present, the result is dependent in a pre-emi-
nent degree upon the direction given to these forces. Thus,
a political rising depends less upon the greatness of an impel-_
ling force, than upon the direction given to forces always
present. The demand for thirty shillings of ship money from —
John Hampden was the turning point of the English Revell 4
tion.
. Yet in dealing with human nature, whether as individuals
or political masses, any omission to allow for the principle of
Conservation, in the form of Limitation of Human Energy,
will lead to mistakes. Thus, a politician that would expe ct
an Art-loving people like the Italians, Germans, or French, to’
take on the energy of the English in business and in politics,
without becoming less artistic, would be guilty of overlooki ng
the law of Limitation. x :
a
(Oo
27. In Political Causation, it is especially necessary
keep in view the entire aggregate of conditions, positiv re
and negative, entering into the cause. ;
ff
When Luther preached against Indulgences, and when
Hampden refused to pay ship money, these were merely a sin
condition out of a large assemblage concerned in bring
about the great events that ensued. Hence, the histo
considers it requisite to describe the whole of the surroundi
in the state of society at the time, but for which the conse
quences would not have arisen. ae
To seek the cause of a political event in a single cir
cumstance is a perversion of the political problem. The
most enlightened reasoners and historians are accustomed t
state the case as an enquiry into the causes of a phenom
The phrase is not strictly correct; the entire aggre
antecedents is properly the cause; but as bringing forw
o
ae =| CF
wae
i
DEFECTS OF THE METHOD OF AGREEMENT. 565
idea of plurality of circumstances, conditions, or collocations,
the mistake is on the right side. The causation of the French
Revolntion was a vast aggregate of prior arrangements in the
state of the French nation, together with numerous circum-
stances in the world at large.
The Method of Agreement in Politics,
28. The Method of Agreement enters into political
investigation, but not without shortcomings.
Like every other inductive enquirer, the political reasoner
first collects his facts; then compares them with a view to
attaining laws of concomitance, which he farther verifies by
_Agreement, as a method of Elimination.
This has always seemed the obvious course. When Aris-
totle enquires into the effects of Despotical or of Democratical
_ government, he collects examples of each, and looks out for
the attendent peculiarities. By an inductive determination,
founded on Agreement, we are accustomed to connect differ-
ent forms of government with lower or with higher stages of
civilization.
The first peculiarity of the inductive problem of society, as
affecting the sufficiency of the Method of Agreement, is the
mere number of concomitant circumstances in a state of
society. The cause A, say Despotism, works in conjunction
with such a large variety of other circumstances,—climate,
race, history, institutions in detaili—B C DE F, &c.,—that
we can hardly find in the whole area of our experience a
sufficiently diversified series of instances to eliminate them all,
and find A followed in every instance by a.
Worse than the mere number of accompaniments is plurality
of causes with intermixture of effects. _ Whatever results might
really flow from Despotism—whether discontent and insurree-
tions, or the repression of men’s energies and the arrest of
prosperity and progress—could flow from other social agencies; .
the effect a, an actual effect of A, might also be an effect of
C, F, H. This would not prevent a Honk being always present
with A; it would rather in some instances make it supera-
bundantly present ; yet, as proving too much, it would be fatal
to the evidence. An apparently more paralyzing instance would
be, when the effect a, properly belonging to A, is neutralised
by some accompanying agent D; one of the commonest of all
occurrences in politics. Hardly any effect of absolute monarchy
is better substantiated than the discouragement of intellectaal
566 LOGIC OF POLITICS.
activity generally; yet this did not follow at once on the —
imperial despotism of the Roman Empire; the prior impeti
acquired under free institutions was for a long time unspent.
So, a law designed to produce a certain effect, may really be
acting as intended; but the effect may be frustrated by
evasions, or by passive resistance to its enactments. Restric-
tions on trade are adverse to commercial prosperity ; yet the
effect may happen to be counteracted by other circumstances.
The United States of America, in the abundance of land to be
occupied, can prosper under many arrangements that would be
ruinous to Great Britain.
The other Experimental Methods,
29. The Method of Difference may be exemplified in
Political Cause and Effect. j
The introduction or withdrawal of a single agent, followed at —
once by a definite change in other respects, is our most cogent, —
as wellas our shortest proof of causation. In the complications —
of Political Society, we cannot always be sure that only the
one innovating circumstance is present; so many unseen —
operations being always at work. ‘This source of ambiguity is
practically overcome when an agent suddenly introduced, is _
almost instantaneously followed by some other change; as when
the announcement of a diplomatic rupture between twonations —
is followed the same day with a derangement of the money 4
market.
According as the supposed change is more gradual in i
introduction, and the consequences slower in their deen
ment, the instance is less and less a decisive example of differ ‘4
ence. The deterioration of value is saved only when we are a
sure that every other thing has remained the same. A new
religion introduced into a nation, remarkably stationary in its”
other institutions, would be held as the cause of all the oe a
quent changes. ;
30. Agreement in Absence may be advantageously re ;
sorted to in Politics,
tions ; and if any circumstances uniformly present in the
are uniformly absent in the other, the force of proof is” gre atl
augmented.
DEDUCTION IN POLITICS, 567
30. Concomitant Variations is employed in tracing
political causation.
There is a marked concomitance, in the History of England,
between the growth of Free Institutions, and the progress of
the nation, both materially and intellectually. This may be
compared with the inverse instances of Greece and Rome,
where, by a gradual process, the extinction of liberty was
ultimately followed by intellectual and social decay. Even
all these instances, in the complications of Politics, may not
be final ; yet they afford a very high presumption of cause and
effect
The Deductive Method.
31. The Deductive Method, in conjunction with the
Inductive or Experimental Methods, must be regarded as
the mainstay of political investigation.
Neither the Deductive Method alone, nor the Inductive
Methods alone, can be trusted in the complications of the
social science. Their mutual consilience or confirmation, is
requisite in order yield trustworthy conclusions.
Pure Deduction appears to most advantage in following out
the tendencies of separate agents. This is the motive for
subdividing the Social Science into branches, as Political
Economy, &c. The tendency of the single motive of the
desire of wealth can be studied apart from other tendencies.
An essential part of political deduction consists in tracing
the wide operation of the Sentiment of Power, in the various
degrees of its development among human beings, and under
all circumstances. The deduction should comprise a wider
area than mere political situations.
The Sociability of mankind, their Sympathies, the grades of
Intelligence, have consequences traceable by a purely deduc-
tive operation.
We might even venture a certain way in the second deduc-
tive process—Calculation or computation of concurring agen-
cies; as Wealth, Power, Sociability, Sympathy, with Habits,
Customs, &c. Here, however, we become aware of the help-
lessness of the deductive method by itself. Having no correct
quantitative estimate of the separate agents, onr attempt to
combine them in a quantitative sum, isentirely hopeless. The
errors of calculation may be so wide as radically to vitiate the
conclusions.
It is the third step of Deduction—Verification—that gives
25
568 LOGIC OF POLITICS.
the method all its weight, by joining it with Inductions, In
point of fact, politicians in applying the conjoint methods
usually have an inductive or empirical generality presented in
the first instance ; which induction they compare with the
deduced tendencies of the agents concerned. ‘Thus the work-
ing of despotism is first given as an empirical generalization
from history ; we then compare these alleged results with the
deductive consequences of the love of power, and all other
human motives, both of the ruler and the ruled, entering into
the situation. Such maxims as the following require, for —
their verification, the consilience of induction and deduction.— __
‘The possessors of supreme power, whether One, Few, or
Many, have no need of the arms of reason; they can make ~
will prevail.’ ‘The governments most distinguished for
sustained vigour and ability have generally been aristocracies.’
The deductive reasons in favour of this last position are
founded on the consequences of devoting a small number of
men exclusively to public business.
Thus, the usual course of the Deductive Method is to lay
hold of a number of empiricisms, derived from history and
political experience, and to subject them to the test of deduction,
thereby converting them into derivative laws. Considered as
inductive generalities, everything should be done for them
that can be done by strict compliance with the Inductive
Methods; after which they are to come into comparison with
the deductive results of the tendencies concerned.
Among Empiricisms demanding to be confronted ith
deductive conclusions, we may instance thefollowing—‘*modern
civilization tends to collective mediocrity,’ (J. S. Mill); ‘unity —
in religion is unfavourable to civil interests’ (G. C. Lewis); —
‘there is no necessary connexion between hereditary royalty —
and hereditary nobility > (ib); ‘the human race is on the >
whole progressive’; ‘ there is a constant relation between the —
state of society and the state of intellectual per i —_
(Comte).
Deductive confirmation is especially needed in oscenieainallll
causes of some one historical event. Unless there happen to —
be other events closely analogous, our inductive basis is of the -
slenderest kind ; succession may be taken for causation with-—
out any check. Thus, the account of the rise of free institu: |
tions, in modern Hurope, must be far more deductive than
inductive. Si:
The introduction of Christianity into Europe co-existed ie
so many other changes, that its consequences cannot easily be
EMPIRICAL AND DERIVATIVE LAWS, 569
eliminated. Our only means of varying the instances is to
take the separate nations apart; but in none of them was this
one cause introduced singly. Hence any inference as to the
political and other results of Christianity would want much
deductive confirmation; and we find that this method is
largely appealed to. The tendencies of the Christian religion
__ are laid out deductively, and the attempt is made to show their
_ coincidence with the facts. To be properly checked, a similar
deduction should be made of all other tendencies—as Greek and
Roman influences, and the mental endowments of the European
races ; which subtracted from the total would give a case of
the Method of Residues.
In the foregoing brief allusion to the Deductive Method is
included a reference both to Empirical and to Derivative Laws.
The subject of Politics furnishes pertinent examples of the
limitation of Empirical Laws, and ina less degree of Derivative
Laws, to adjacent cases. There is safety in extending an em-
pirical law only to the same territory, the same time, and
similar circumstances. Whena ten pound suffrage had sub-
sisted in Britain for thirty years, with good effects, it was a
small matter to risk the extension to a seven pound or a six
pound franchise, on the mere faith of the empirical coincidence ;
whereas, the sudden transition to universal suffrage, could not
be relied on from the same empiricism. The consequences of
such a step, if computable at all, could be computed only by
the aid of deductive reasoning—by the establishment of a deri-
vative law. A well-informed, sagacious, and unbiassed reasoner,
might be trusted to predict, within certain limits of error, the
probable issue of such an extension of the franchise; but only
by a superior handling of the deductive method.
The Method of Residues being properly a Deductive Method,
is occasionally valuable. It takes the problem ona varied
aspect; as in the case of Christianity already referred to.
In applying the methods of Agreement and of Difference, to
single out a cause, our prior knowledge of the general adequacy
of the cause, prepares us to receive the inductive evidence,
without the misgivings that we must feel when we know
nothing on this head.
Hypotheses tn Politics,
32. In Politics, we are seldom under the necessity of
assuming an unknown agency ; the known forces of human
nature are the sufficing causes. Our assumptions refer to
570 | LOGIC OF POLITICS.
the presence, and the amount, of the supposed agent ; and
these may be proved by their exactly tallying with the
facts, pe
Assumptions are perpetually made regarding the conduct
of human beings under all circumstances, The passions of
Power, Pride, Fear, the Self-interest of men, their Sympathies,
- are all real or genuine causes, ‘There may be doubts which of
them produced a certain line of conduct ; and we may apply the
logical conditions of hypotheses to solve the doubt. If any one’s
actions tally precisely with the consequences of Love of Power,
we receive this coincidence as so far a proof of the hypothesis.
But the proof is completed only by showing that the action
does not tally with any other motive ; a thing that we cannot
always be certain of. The execution of Charles I. might have -
resulted from the fears of the Puritans, from their revenge,
from their ideas of justice, from their interpretation of the
designs of providence.
Definition of specific Diseases—The very general states
above quoted exemplify definition under the greatest simplicity,
as respects the number of characters, although not as respects
the generalizing and seizing of the true characters. When
we proceed to the more concrete forms of disease, Typhus,
Gout, Pleurisy, Neuralgia, Jaundice, &c., we have the general
processes, Fever and the rest, with many various accessories,
constituting the specific characters of the individual affections,
Consequently, the definitions are apt to be voluminous in their
statement; and there is still more need of method.
Examples have now been given of the two different modes of
medical definition; the one corresponding to Diagnosis, and
framed with a view to identify a disease by such signs as are
best accessible ; the other, the most complete generalization of
the essential fact or facts of the disease, which facts may or
may not lie upon the surface. The first is requisite for
distinguishing diseases ; the second, for understanding them.
Let us take an example. Gout is defined by Dr. Garrod— ~
‘A specific form of articular inflammation, invariably accom- —
panied with uric acid in the blood, and the deposition of
urate of soda in the affected tissues.’ The positions given to —
the words ‘specific’ and ‘accompanied’ suggest what was
probably not in the author’s mind, Strictly interpreted, the
er
DEFINITION OF SPECIFIC DISEASES. 587
language means—Gout is articular inflammation of a specifie
character (not described); it has, for concomitants, uric acid
in the blood, and deposits of urate of soda. The real mean-
ing must be presumed to be—Gout is articular inflammation,
specifically marked by uric acid, &c.
This definition is one of those advanced generalizations,
attained in some diseases, which penetrate to the essential
features of the disease, without fully expressing the symptoms.
A detailed account of the symptoms is therefore added, first
under the title ‘ Description of an attack of Gout, and of the
progress of the disease’ (a sort of popular history of a case),
and secondly, under ‘ Phenomena occurring during an acute
Gouty Attack,’ where there is a more rigid and systematic
analysis into (1) Febrile Disturbance, and (2) Local Appear-
ances.
Again, Small-Pox is thus defined (Dr. Aitken). ‘The pro-
duct of a specific and palpable morbid poison, which is
reproduced and multiplied during the course of the malady.
(1). After a definite period of incubation a remittent fever is
established and followed by an eruption on the skin, and
sometimes on the mucous surfaces, with other concomitant
and occasionally succeeding affections (2). The eruption on the
skin passes through the stages of pimple, vesicle, pustule, scab ;
and leaves marks or cicatrices on its site (3). The disease
runs a definite course, and, as a rule, exhausts the suscepti-
bility of the constitution to another attack (4).’
Here we have, in sentences (2) and (3), the leading symp-
toms of the disease, which, when elucidated at full, make up,
as far as book description can go, the characters whereby the
disease is known and discriminated. Sentence (1) does not
properly belong to the definition, but to the predication ; the
cause of a disease must always be accounted a predicate.
Sentence (4) contains two statements, first, ‘the disease runs
a definite course,’ which surely is true of many other diseases,
if not of nearly all; second, ‘it exhausts the susceptibility of
the constitution to another attack,’ a most pertinent circum-
stance, but still better reserved for a predicate or concomitant,
than mixed up with the defining marks.
Influenza is thus defined by Dr. Parkes :—‘ An epidemic
specific fever, with special and early implication of the naso-
laryngo-bronchial mucous membrane ; duration definite of
from four to eight days; one attack not preservative in future
epidemics.’ The transposition of the epithet ‘ specific’ is
desirable :—* An epidemic fever, specially characterized by
588 LOGIC OF MEDICINE.
early implication, &c.’ This definition also isa summary of
symptoms, and nothing more. The author proceeds, under
the head ‘Symptoms’ to describe the general course’of the — 2 :
disease, and under ‘ Consideration of the Special Symptoms’
‘to analyze them in the detail; Temperature, Condition of the _
Skin, Nervous and Muscular ‘Symptoms, ee System, a
Circulation, Digestion, &c. aa
All the facts stated in the Definition may be fairly allowed
as defining circumstances, with the exception perhaps of the
last ‘ one attack not preservative in future epidemics,’ which
might be reserved for predication. Doubtless, if we hada —
generalization of the central or fundamental fact of the
disease, this would take place among deductive consequences,
or propria. But we do not need it in a definition consisting
of a summary of the symptoms.
The following sentence commences Dr. Buzzard’s definition
of Scurvy : tt A peculiar state of mal-nutrition, supervening
gradually upon the continued use of a dietary deficient in
fresh vegetable material, and tending to death, after a longer
or shorter interval, if the circumstances under which it arose
remain unaltered.’ Here we have first a theory or hypothesis _
of the essence of the disease (a state of mal-nutrition), secondly, _
its cause, and thirdly, an announcement of its dangerous
character. All this is extraneous to the definition, whichis
given unexceptionably (as a summary of symptoms) in what
succeeds to the above quotation.
Propositions of Medicine.
10. The Real Predications of Medicine, as ‘sonhanteeet 2
guished from the Essential or Defining Propositions, fall |
under distinct heads. ;
The coupling of the Essential characters, even atchodge a
numerous, is Definition, and not Real Predication. Nay
farther ; the modified characters shown in different constitu- —
tions dnd different circumstances, should be held as a part, or.
as an appendage, of the Definition. Real propositions may —
arise in connexion with these modifications when certain cir- ¥
cumstances are alleged to intensify or to resist the diseased 4
action. Ls.
ease. ‘m+ BCC
PROPOSITIONS IN MEDICINE. 589
Having given the defining marks, in their ultimate state-
ment, together with the important moditications and varieties,
we can by the help of general principles—Physical, Chemical,
Biological, or Pathological—draw many conclusions bearing
on the treatment of the disease. It would be easy, for ex-
ample, to unfold a great many facts respecting Fever, from
the Law of Conservation, the laws and facts of Organic Che-
mistry, &c. The maintenance of an excessive temperature,
with less than the ordinary nourishment, involves waste or
inanition of the organs, and the formation of special products
of wasted tissue; with many other consequences under given
situations. This deductive process, when based on well
ascertained generalities, affords propositions capable of great
precision and certainty.
12. The second class of Real Predications consists of
the Causes of Disease.
A Disease is one thing, its cause is another thing; proposi-
tions of Causation, are, therefore, in their nature, strictly real.
Their importance demands a distinct and separate enunciation.
Implicated with the great subject of Hygiéne, or Health
preservation, there is a body of information respecting the
General Causes of Disease. It is all one thing to know what
are the means to keep the body in health, and what will cause
loss of health.
Many forms of disease are due at once to the disproportion
between the expenditure and the nutrition of the system.
The diseases of exhausted organs—functional weakness and
degeneration of the muscles, the brain, the stomach, the lungs,
the heart, the kidney—are of this class.
To the same general head should be referred nearly every-
thing meant by Predisposing Causes of Disease. There are
many diseases that do not spring up unless by poison or infec-
tion from without; called Zymotic Diseases. As the poison
of many (but not of all) such diseases may be resisted by a
healthy system, any circumstances that destroy general
vigour, or weaken particular organs, are called predisposing
causes; as when cholera attacks constitutions exhausted by
_ intemperance, or by insufficient food, or by ill-ventilated
dwellings.
Tt is less easy to generalize the various influences expressed
as Infection, Epidemic poison, Miasmata, &c. This is one
great field for Representative Hypotheses in Medicine.
Under each separate Disease, an account is given of the
590 LOGIC OF MEDICINE.
Cause, as far as known, whether general or special. Where-
ever there is a loss of power from the predominance of waste
over supply, Causation in Disease appears as ‘ Conservation ; ”
it, however, still more largely implicates Collocations.
13. There may be a distinct class of Real Propositions,
expressing the effects of Disease.
The full definition of each disease comprises its whole
history to the termination; the temporary prostration of
Typhus is not an effect of the disease, it is the disease itself.
When, however, a disease, besides accomplishing its course,
makes permanent changes in the organs or constitution of the
patient, this is a distinct fact, and may be enrolled under the
head of Causation. Such are the after effects of Small Pox,
Measles, Scarlet Fever, and Syphilis. While a few diseases
have a wholesome efficacy, the greater number weaken the
system at some point, and are therefore predisposing causes of
future disease.
14, The Remedies of Disease constitute Real Propositions.
All the previous classes of assertions prepare the way for the
present. ‘The remedy of a disease may be suggested by its
Characters, whether primary (Definition), or inferred from the
primary (Propria) ; ; or by its Causation, on the principle of
‘remove the cause.’ Diseases of functional degeneration, or
premature decay of organs, involve in their cure ‘repaying
the debt to nature’—the restoration of the balance of nourish-
ment and waste.
In many instances, the remedy consists in something differ-
ent from either treating the symptoms, or removing the cause.
The Specifics that have been discovered for particular diseases,
as quinine, colchicum, lime juice, cod liver oil, are affirmed as
independent facts, resting on no deductive inferences from
Cause and Effect in Disease, but on the experience of their
efficacy. | |
The Experimental Methods in Medicine,
15. All the Experimental Methods are applicable to
Medicine, with certain cautions and qualifications.
The ultimate problem of Medicine is to find a remedy for
every remediable disease ; and the apparently direct solution
is to try various remedies upon actual cases. If by Agreement,
under a wide variation of circumstances, a certain remota ik
THE EXPERIMENTAL METHODS. 591
found to succeed uniformly, or in a great proportion of
instances, there is proof that it is the remedy.
Still, we cannot but remark the very serious difficulties that
weset all the Experimental Methods in thisattempt. Plurality
of Causes and Intermixture of Effects occur in the most aggra-
vated shape. Moreover, drugs, being natural Kinds, have so
many possible ways of acting, that the elimination of the
precise property that affects the system is all but hopeless.
Without, therefore, abandoning the tentative process, as
applied to actual disease, modern medicine has advanta-
geously approached the problem in circuitous ways; and has
instituted researches where the experimental methods are less
likely to be defeated. Thus—to take the example that departs
least from the empirical method—the mode of action of
medicines and of remedies is studied by experiments, not re-
stricted to special diseases, but applied to the system in health
and in disease alike, under every variety of conditions. This
is a far more thorough and searching procedure; and the
Method of Agreement will, of itself, give trustworthy results
under so great an extension of instances; while by superad-
ding Difference, Inverse Agreement, and Variations, there
may accrue results of the highest certainty. I may cite, among
this class of Researches, the Report of Dr. Bennet on the
Action of Mercury on the Biliary Secretion, and Dr. Harley’s
work on the Old Neurotics. By such researches is built up
that part of Materia Medica relating to the Therapeutic action
of medicines.
Again, the Pathology of Disease, the concurrence and se-
quence of symptoms, studied, in the first instance, apart from
modes of treatment, is open to experimental enquiry, and may
lead to results having ali the precision attainable in the
science of Medicine. For such enquiries, the Kxperimental
Methods are suitable; the endeavour being made to bring
each one of them into play, by searching for the approp-
riate class of instances. Mere Agreement is usually what
suggests itself to the untutored mind; the force of Agreement
in Absence and of Variations is apparent only to such minds as
have reflected largely on the conduct of scientific researches.
The influences commonly called Hygienic, and the simpler
Therapeutic agencies, as cold and heat, change, exercise and
rest, stimulants, &c., not only present fewer difficulties to ex-
periment, but are also within the scope of the Deductive
method. In like manner, the proof of noxious agencies—as
impure water, and the efiluvia of decay —is easy and complete.
> 26
592 LOGIC OF MEDECINE.
16. The Elimination of Chance is of great value in -
Medicine. Its groundwork is Medical Statistics. th
Nowhere more than in Medicine may laws of Causation be
defeated ; there is rarely such a thing as a simple cause yield-
ing a simple effect. Hence, the necessity of ascertaining =
whether a coincidence is more frequent than would be ac- ;
counted for by chance. Thecinchona bark sometimes fails to
cure ague, yet its general efficacy is satisfactorily established.
To prove the efficacy of medicines as a whole, in opposition :
to some speculators that ascribe all cures to nature (aided by
repose and regimen) the physicians of a French hospital
made the experiment of withholding drugs from all the patients
for a certain time. ‘The conclusion seemed to be that the
mortality was not increased, but the recoveries were more
protracted. This was a competent inference from statistics.
The difficulties in obtaining a statistical proof of the action
of a remedy in a given disease are exactly those already
mentioned respecting the use of Agreement in the same
determination.* A large hospital statistics is better than the
inferences of a single physician in private practice, and yet
may come short of the proof. There should always be obtained,
if possible, a parallel statistics—cases with, and cases without,
the treatment in question. The statistics of cholera treatment
may be alleged in favour of many modes; but none appear 19
be decisively established.
Statistics, as applied to Scarlet Fever, has shown that a
second attack is extremely rare; that the ages of two and
three are most susceptible to the disease; and that the maxi-
mum of prevalence is in October, November, and December,
and the minimum in April, May, and June. I
The Deductive Method.
17. The scope of the Deductive Method in Medicine is
co-extensive with the number of well-established generali-
ties than can be appealed to.
The sciences applicable to Medicine—Physics, Chemistry,
and Biology—yield a considerable number of these fertile
generalities. The science itself contains few of a very com--
manding character, but a considerable number that have a
sufficient range for deductive operation, and for converting.
empirical into derivative laws. All the propositions of general
* See an estimate of these difficulties in Dr. Barclay’s work on Medidél! ,
Erro1s, p. 35. y ough /
OO ee SS ee ee eee ee ee
HYPOTHESES. 5938
cansation in medicine, the laws of general Therapeutics, the
laws of the action of drugs on the system generally, have
sufficient breadth to control and correct empirical practice ;
and the mastery of these, as well as of the more commanding
principles of the preparatory sciences, increases the power of
the physician. The physiology of Food as regards the various
forces of the system, muscular, heat-giving, nervous, &c.,
and the products of elimination,—is pregnant with deductive
consequences, both in warding off and in curing disease.
The experimental methods are greatly at fault with slow-
acting causes; and hence deduction is pre-eminently desirable
in such points as the influence of alterative medicines, stimu-
lants, climatic influences, and modes of life. Only a thorough-
going statistics, or a deduction from general principles, can
dispose of the doubts that arise on such points.
Hypotheses in Medicine.
18. Medical Science is largely dependent on Hypotheses.
As a department of applied Biology, Medicine needs all the
aids rendered by hypotheses in the mother science, and some
special to itself. The great biological fact—Assimilation—
takes on a new aspect in the production and spread of Disease.
The first and simplest case of Hypothesis, the assuming of
an agent known to exist, but not known as present in ade-
quate amount in the given case, is abundantly exemplified.
Thus, the origin of contagious disease is ascribed hypotheti-
cally to various real agents, and among others, to actual
living organisms. The effects tally in a general way with
such an agency. What remains is to find whether they tally
closely at all points. The hypothesis, however, receives a
powerful support from individual cases where the presence of ~
an animalcule, or living germ, appears to be actually estab-
lished. The alternative, and older, hypothesis is that organic
particles, in a state of change or activity, are thrown off from
one living body and infect another, such particles not being
complete organisms or the germs of organisms. This bhypo-
thesis may seem to assume less than the other, but in reality
it assumes a class of particles not distinctly proved to exist.
A strong analogy may be pleaded for them, in the supposed
communication of morbid action within the system; the action
of the poison of small pox must be the same on the blood
of the innoculated patient as on the original patient. Yet the
aerial effluvia of typhus may consist of something more
594 ; LOGIC OF MEDICINE,
definitely organized than the supposed active particles. Fer-
mentation by yeast is found to be due to an animalcule.
The Representative Fiction is indispensable in Medicine,
and its rules and properties need to be well understood.
Diseased appearances, like all manifestations of living bodies,
are the superficial outcome of a vast concatenation of hidden
changes. These intermediate links are in great part unknow-
able; yet, by following the clue of what we know, we may so
conceive or imagine them, as thereby to unite the appearances
in a consistent whole. When an organ is liable to derange-
ment from slight causes, we prononnce it weak, which is merely
to express the fact in another word; when, however, we assign
such circumstances as that its tissue has degenerated or
changed, that it has very little tendency to assimilate nutri.
ment from the blood, or that the superior exercise of all the
other organs of the body withholds from it the fair amount of
blood and nerve force,—we employ convenient hypotheses,
which are more or less in keeping with the facts,
As regards the two leading diseased processes—F'ever, and
Inflammation—probably no hypothesis yet framed adds any-
thing to the facility of conceiving or of generalizing the facts.
Supposing the different fevers generated each by a specific
virus, or animated body, we cannot even in imagination sup-
pose a connexion between the structure of the infecting
element, and the specific characteristics of the fever; as in the
difference between typhus, scarlet fever, or intermittent fever.
Indeed, we cannot form a plausible supposition as to the
intermediate link that connects a certain infecting substance
with the febrile state generally. The difficulty here is exactly
the difficulty in representing the facts of living action,
Hypothesis appears to more advantage in connexion with
what is termed Functional Degeneration, Functional weakness, —
strength and weakness of parts. Great convenience attaches
to the use of such phrases as healthiness, robustness, vigour,
constitutional foree—which are modes of stating the absence
of disease under circumstances that usually provoke it. We
may increase the value of this class of terms, by pak Seigers +r
interpolations, to the following effect :—
Assuming an average healthy system to begin with, we
know by reasonable inferences, (1) that every one of the organs
needs an equable supply of blood, with more or less aid from.
the nervous centres, and (2) that each organ is capable of a cer-
tain amount of exertion. Suppose now, that by any cause,
either the nutrition is below the mark, or the exertion above
i el
HYPOTHESIS OF DEGENERATION, 595
it, or both. It is the nature of the system not to show im-
mediately the effects of such a mal-proportion, yet there must
be an immediate effect ; the overwork, or the defective nutri-
tion, of asingle day does not leave the organ exactly asit was;
we are entitled to assume that there is superinduced a minute
structural change, or degeneration, perceptible only after many
repetitions, but actually realized. Suppose the disproportion
of expenditure and supply to continue for a length of time;
the first outward symptoms will probably be, that the organ is
enfeebled in some duty that is required of it, and becomes
positively disordered under influences that, in its regular con-
dition, it would have successfully resisted. At this point,
degeneration or structural change has made a decided ad-
vance ; another equal advance would bring down the organ to
the bare performance of its functions; a third would be utter
suspension and death. Now, we have here scope for a
great variety of suppositions, as to the relative condition
of all the organs in the body. We can represent the constitu-
tioual peculiarities at birth, by the proportionate dispositions
of the several organs—nerves, muscles, lungs, digestion—to
appropriate nutriment, and to become vigorous or the oppo-
site ; we can state to ourselves the practical mode of redressing
the inequality, namely, by restraining the vigorous organs from
their tendency to impoverish the rest, and by giving greater
opportunity to the nourishment of the weak. We can also state
the rationale of the constitutional treatment of diseases, viz.,
the placing of the weakened organs in such a position as to
increase their nutriment and abate their over-exertion. We
can give a hypothetical account of the degeneration of or-
gans such as the heart and kidney, which often show no
signs until the structure has reached a mortal disease. We
should, moreover, feel no surprise at the sudden breaking down
of constitutions reputed strong ; the popular eye sees only the
prosperity of those organs that cast a dash and a glare—the
muscles, the stomach, and the brain. The deeper glance dis-
closes the degeneracy of the heart, the lungs, the kidney,
following on the very strength of these ostentatious members
of the system.
Classification of Diseases.
_19. There being upwards of one thousand recognized
Diseases, they may, like other great aggregates, come
under a regular Classification.
596 LOGIC OF MEDICINE.
Diseases may fall under a classified arrangement, like
Minerals, Plants, or Animals, attention being given to the
peculiarities of the department. ,
I. Order of Characters.—In Mineralogy, and in Botany, a
strict order of characters is observed. This is disregarded in
Zoology, and also in Medicine, from difficulties that can be
readily assigned. There is every likelihood, however, that
both sciences would gain by a systematic arrangement of char-
acters, avoiding the sacrifice of the spirit to the letter.
In a work to be afterwards referred to (p. 597), the remark
is made ‘ that the labour of analyzing and comparing clinical
observations would be greatly lightened, and the precision of
the observations themselves increased, if the records of these
were in every instance arranged on an uniforny plan.’
One obvious precaution is to make the outward symptoms
precede the subjective. Thus, of the usual marks of inflam-
mation, the pain should come last. In nervous diseases, the
physical symptoms should be fully enumerated before entering
upon the mental symptoms ; the two classes are then viewed in
such a way as to check and confirm each other.
Il. Maximum of Affinities. — The propriety of classing
Diseases by their closest resemblances is sufficiently allowed
in the abstract ; the difficulties in execution are not logical,
but pathological. icity
III. Arrangement by Grades.—The formality of Grades is
observed in the classification of Diseases, but without the full
carrying out of what it involves. There is something of lax-
ness attending the use of the method even in Chemistry, the
statement of the points of community of the higher grades —
being sometimes given, and sometimes not, without any
apparent reason. .
Occasionally there is vacillation as to whether diseases ar
different in species, or mere varieties. Little importance
attaches to the question; and the workable criterion is the
comparative number and persistence of the distinctive marks.
IV. Statement by Agreement and Difference.—Hverything
already said on this head applies to the exposition of Diseases.
The systematic and orderly stating of Agreements, and the
pointed contrast in Difference, have the same efficacy here as
elsewhere. Under the heading ‘ Diagnosis,’ it is usual to
mention the closely resembling diseases, and to indicate the
diagnostic marks. For example, Roseola is distinguished
from Scarlet Fever, thus :—the eruption in Roseola is gene-
rally confined to the chest. When the diagnostic points are
Pi a i nel a | aS il)
INDEX CLASSIFICATION, bOY
two or more, they might be set forth in the formal manner
already exemplified.
20. V. Index Classification.—For Medicine, an Index
Classification might be provided on the tabular plan.
This aid to the discrimination of Disease is still wanting.
Probably, it would be best attempted, in the first instance, on
the tabular plan. A basis is afforded in a small work, pub-
‘lished by the Medical Society of Observation, with the title
‘* What to Observe in Medical Cases.’
- The work professes to lay out in order an exhaustive state-
ment of all the appearances connected with each bodily organ,
besides adverting to the external circumstances of the patient.
The enumeration commences with the Skin, which is followed
by the organs of Locomotion, Digestion, Respiration, Circula-
tion, Lymphatics, Urinary Organs, Organs of Generation, Brain
and Nerves, Vascular Glands.
As an example, I quote the varieties of the Pulse :—‘ Radial
Pulse :—number ;—size and force; large, small, thready, equal,
‘unequal, strong, feeble ;—resistance; soft, compressible, hard,
-incompressible ;—rhythm; regular, irregular, intermittent ;—
time as compared with that of heart’s impulse ;—artery tortuous,
rigid.—Special characters of pulse; jerking, bounding, undula-
tory, continuous (one pulse appearing to run into the following),
‘vibrating, quick, tardy, vermicular, tremulous, reduplicate.—
Effects of posture on pulse (its number and other characters).—
Phenomena of pulse in one arm as compared with the other.’
The authors have evidently studied exhaustiveness to,
begin with. It is possible, however, to be too minute;
distinctions that are not marks of anything else are worthless
and may be an encumbranee. ‘The next step, therefore,
should be to abridge and group the symptoms with a view to
the maximum of significance.
There being obtained a methodical array of symptoms
under each organ, the mode of proceeding with a view to an
Index is to append to each symptom a list of the diseases
where it occurs. Should a symptom appear in only one
disease (as urate of soda in gout) the occurrence of the symp-
tom would decide the disease at once. Should a symptom
appear in three diseases, its occurrence points to one of those
three diseases.
By appending, to every symptom of value in diagnosis, a
complete list of diseases, there is provided a means of deter-
mining every disease according to the knowledge of the time.
One symptom refers us to one list, containing two, three, or
598 LOGIC OF MEDICINE,
four diseases ; a second symptom leads to another list. [fon
comparison, there is found only one disease common to the
two lists, the diagnosis is complete. Ifthere are two or three ©
common to both lists, a third symptom must be sought out
with its corresponding entries, by which the alternations are
again reduced ; and so on, till the concurrence of symptoms
points toa single disease.
Suppose, for illustr ation, that ‘Irrecularity of the Pulse’
appears as symptom. According to Dr. Watson, this may
attend (1) disease within the head ; (2) organic disease of the
heart ; (3) simple disorder of the stomach ; (4) debility, and
a pr elude to stoppage of the heart’s action from asthenia,
Now supposing the tabulation of symptoms and of diseases
complete upon this plan, and supposing a second symptom in
the case under enquiry had opposite to it a list, agreeing with
the first only in the entry ‘simple disorder of the stomach,’
the diagnosis is made out by two easy references.
Owing to obvious causes—the great number of diseases
accompanying particular symptoms, the occasional ambiguity
of actual diseases by the failure of some of their usual symp-
toms, and the imperfection of the terminology of symptoms,—
the best scheme that could be given would be imperfect.
This would not, however, prevent it from being a boon to the
student, and an occasional aid to the experienced practitioner.
It does not supersede, but indicates, the reference to the
systematic works on Medicine and Pathology, which arethe
authorities in the last resort
ciate eae
BOOK VI.
FALLACIES.
CHAPTER I.
MILU’S CLASSIFICATION OF FALLACIES,
Mr. Mill regards all fallacies as divisible into two great
heads—Fallacies of Stmpie INspEcTION, and Fallacies of INrER-
ENce. By the first class he understands those cases where a
presumption is created in favour of a fact or doctrine, on the
mere inspection of it, and without any search for evidence ;
natural prejudices are comprised under that head. By the
second class he understands erroneous conclusivns from sup-
posed evidence. This class is subdivided accurding to the
nature of the evidence simulated ; which may be deductive,
inductive, &c. A special division is indicated under the title
‘Fallacies of Confusion,’ where the error arises, not in the
link between premises and conclusion, but in the incorrect
handling of the premises themselves.
There are thus five distinguishable classes of Fallacy, as set
forth in the table :—
of Simple Inspection - e« e« 1,Fallacies a priori.
F Inductive | 2. Fallacies of Observation
ee °°) Fallacies F Fallacies of Generalization
conceived Deductive 4. Fallacies of Ratiocination
Fallacies
Fallacies
from evidence :
indistinctly 7 « - 5. Fallacies of Confusion
of Inference conceived
I. Fallacies of Simple Inspection, or a priori Fallacies.—Re-
fraining from the discussion of the question, which this desig-
nation might raise, what are the ultimate facts or premises at
600 MILL'S CLASSIFICATION OF FALLACIKS.
the foundation of all reasonings, Mr. Mill adduces first the
tacit assumption that the same order obtains among the objects
of nature as among our ideas of them—that if we always think
of two things together, the two things must exist together.
He illustrates this tendency by numerous popular superstitions,
as ‘talk of the devil and he will appear,’ &c. He also cites—
the philosophy of Descartes, which, from the mere conceptions
of the mind, inferred the existence of corresponding realities ;
the doctrines that ‘ whatever is inconceivable is false,’ ‘ that
a thing cannot act where it is not’ (applied by Newton to
show the necessity of a gravitating medium), that ‘ matter
cannot think,’ that ‘space is infinite,’ that ‘nothing can be
made out of nothing,’ that ‘nature always acts by the simplest
means.’ An allied Fallacy, or prejudice, is the tendency to
presume a correspondence between the laws of the mind and
the laws of external things, of which one form is expressed
thus :—‘ whatever can be thought of apart exists apart.’
From this springs the personifying or re-ifying of Abstractions,
as in the doctrine of Realism, and in mystical theories gene-
rally, whether it be the mysticism of the Vedas, or the mysti-
cism of Hegel; all which proceeds on ascribing objective
existence to subjective creations— feelings, or ideas.
Another kindred fallacy consists in representing nature as
under the same incapacity with our powers of thought ; the
great example being the celebrated Principle of Sufficient
Reason, adduced in explanation of many first truths, such as
the laws of motion. i
‘That the differences in nature correspond to the received
distinctions of language,’ is another wide spread and baneful
prejudice, which particularly weighed upon Greek philosophy,
being prominent in the reasoning’s of Aristotle, and from which
Bacon was unable to set himself free, as is shown by his futile —
attempts to find a common cause for everything that goes
under a common name, as heat, cold, &e.
Lastly, there has existed the prejudice that ‘ the conditions
of a phenomenon will resemble the phenomenon ’—like pro-
ducing like: as that motion must necessarily arise from the
impact of a moving body; that a sharp taste must be brought
about by sharp particles; that our sensations must be copies
of external things; that the law of causality can hold only
between what is homogeneous, whence there can be no causa=
tion between mind and matter; that the Deity must have the
exact perfections discoverable in nature, __
II. Fallacies of Observation.—These do not apply to the
. GENERALIZATION.—RATIOCINATION. 601
operation of observing, for which there is no logic strictly so
called, but to the omissions and partialities in collecting facts
with a view to the generalizing process. There may be Non-
observation, or Mal-observation ; the one leaves out pertinent
instances, the other distorts or misrepresents what is observed.
Non-observation explains the credit given to fortune-tellers,
to quacks, and to false maxims; the cases favourable being
noted, and the other forgotten. The motive in this class of
fallacies is a strong pre-conceived opinion or wish to find the
dictum true. Farther, the Non-observation may be, not of
instances, but of material circumstances, as when it is stated
that lavish expenditure alone encourages industry, the circum-
stances being overlooked that savings are capital for the
employment of labour.
Under Mal-observation may be placed the chief mistake
connected with the proper act of observing, namely, the con-
founding of a perception with a rapid inference, or the mingling
up of inferences with facts. This is the common infirmity of
uneducated witnesses and narrators of events.
Iil. Fallacies of Generalization.—These are errors in the
employment of the Inductive process. The chief instances
adduced are these:—All inferences extended to remote parts
of the universe, where no observation or verification can be
carried ; all universal negatives and propositions asserting
impossibility (not being contradictionsin terms) ; the theories
professing to resolve all things into some one element, of which
the most notable instance is the attempt to resolve states of
consciousness into states of the nervous system; the placing
of empirical laws, arrived at per enumerationem simplicem, upon
the footing of laws of causation, largely exemplified in reason-
ings upon society; the vulgar form of the same fallacy, desig-
nated post hoc, ergo propter hoc ; and the fertile class of False
Analogies. Under the same head are specified Bad Classifica-
tions, or the asserting under one term, things that have little
or no community ; of which the Greeks gave examples in such
terms a8 Motion, Generation and Corruption.
IV. Fallacies of Ratiocination. These comprise the errors
_ against the laws of the Syllogism. Mr. Mill, however, properly
includes under them the fallacies connected with the Conver-
sion and Kquipollency of Propositions; remarking that the
simple conversion of the universal affirmative, and the errone-
ous conversion of Hypotheticals are among the most frequent
sources of error. Of this last class, is the maintenance of some
favourite doctrine, on the ground that the inferences from it
602 MILL’S CLASSIFICATION OF FALLACIES.
are true. Connected with the Opposition of Propositions is
the confounding of the contrary with the contradictory of a
statement. Vicious syllogisms, whether from undistributed
middle, or from illicit process, are tke more noted instances of
this class of fallacies. There may be also included the fallacy
of changing the premises, occurring frequently in the argument-
ative discourses of unprecise thinkers (the schoolmen’s a dicto
secundum quid ad dictum simpliciter) ; exemplified in the once
favourite theory that ‘whatever brings in money enriches,’
Under the same head might be placed the misapplication of
general truths, or the supposition that a principle true in the
abstract must hold under all sets of circumstances. |
V. Fallacies of Confusion. The first class under this desig-
nation is Ambiguity of Terms, As there is no limit to that
form of confusion, a logician can only select a few random
instances ; those chosen by Mr. Mill are ‘scarcity of money,’
‘influence of property,’ ‘tieory,’ ‘the church,’ the ‘laudable’
ina Stoical argument in Cicero’s De Finibus, ‘1’ in Descartes’
argument for the being of God, ‘necessity,’ ‘same,’ ‘ force,”
‘infinite,’ ‘right ;? to which he adds examples of the fallacy
of Composition and Division, as strictly belonging to the same
class. foe
The second division is Petitio Principit, otherwise called
‘arguing in a circle,’ of which there are abundant examples.
A certain species of terms received from Bentham the desig-
nation ‘ question-begging appellatives,’ because they begged a |
question under the guise of stating it; such is the word * Inno-
vation.’ Plato, in the Sophistes, has an argument to prove
that things may exist that are incorporeal, because justice
-and wisdom are incorporeal, and they must be something:
thereby begging the question that justice and wisdom are
things existing apart or in themselves. One of the most re«
markable examples of fallacy is furnished by the political
theory of Hobbes and Rousseau, known as the theory of the —
‘social compact.’ We are supposed bound by the promise —
entered into by our ancestors before society was called into
existence ; but there is no such thing asan obligatory promise
until society has first been formed. he
The third class of Fallacies of Confusion is the Ignoratio
Hilenchi. It is exemplified in most of the replies to the popu-
lation doctrines of Malthus. A still more signal instance is —
the stock argument against Berkeley’s doctrine of the nom
existence of matter; Johnson’s kicking the stone was not the —
point denied in the ideal theory. 5 ae
a
CHAPTER IL
THE POSITION OF FALLACIES.
The setting apart of a distinct chapter to the consideration
of the errors against the laws of reasoning and evidence seems
at first sight an incongruous proceeding. We cannot separate
a law from its violations ; the one implicates the other. When
good reasoning is exhibited, there must be exhibited at the
same time the coresponding bad reasoning. If the rule be
given that the middle term of a syllogism must be distributed
once, whoever understands the rule must conceive, at the
same time, cases of its fulfilment and cases of its non-fulfil-
ment. If the method of Difference requires that the instances
compared shall coincide in every particular save one, we are
instructed by it that the method fails if any two instances do
not coincide to this extent. If a good classification involves
identity on one or more points of importance, there is implied
in the same statement that a grouping under one name, with-
out any important community, is a bad classification, a
‘fallacy ’ of classification.
_ Any one would recognize the absurdity of a grammar that
would reserve for a chapter at the end all the examples of
grammatical errors. Yet such is apparently the plan pursued
in Logic. The grammarian, indeed, frequently provides a
separate collection of errors by way of practice to the pupil,
but these are additional to what necessarily and properly
occur under the rules that they severally violate; this, how-
ever, is not avowed by the logician as the nature of his
chapter on Fallacies.
Without entirely exonerating works on Logic from the
- inconsistency of distributing between two departments of the
subject the fulfilment and the violation of the same rules, we
can assign certain circumstances that account for the prevail-
ing usage. The main circumstance is the narrowness of the
field of logical precepts, from Aristotle down to the present
generation. The part of reasoning reduced to rules was
almost exclusively restricted to the syllogistic or deductive
departments ; hence, in the exemplification of those rules, no
errors could come to light except such as violated the forms
604 THE POSITION OF FALLACIES.
of syllogism. But the Greeks had surveyed human knowleds
wide enough to be aware that many errors passed current —
that could not be reduced to errors of syllogism. The logician, a
therefore, was driven to one of two alternatives—to make no
allusion to some of the most notorious failings and mistakes of
the human understanding, or to provide a chapter for enumer- __
ating such mistakes entirely apart from the body of logical
theory. It was characteristic of Aristotle to choose the second —
alternative—to be inconsistent rather than to be incomplete.
His treatise on Fallacies comprises errors against the Syllo.
gism, which he could not omit noticing under the Syllogism 7
(Undistributed Middle, Illicit Process); but these are a small —
part of the mass of Fallacies; and the rest he had not
any theory for. He had no Inductive Logic (or only mere ~
traces which his followers wiped away), and therefore he had
no place for the exhibition of the rules siuned against by post —
hoc, ergo propter hoc. For want of a thorough-going discussion —
of the department of Classification and Definition, he could —
not exhibit the errors connected with general language under
precepts for the clheatyine of things and the defining of
terms. ‘
It has been ee however, that even the thorough-going
Logic of Mr. Mill does not dispense with a ‘ Book’ on Fallacies.
This is explained in part, but only in part, by the autho Hol
adhering to the usage of all former logicians, while using bis
own extended system to re-arrange the recognized examples, |
and to introduce new ones. Yet all the fallacies in the
second, third, and fourth classes (Observation, Genetalautione
Ratiocination) might with the utmost propriety be abeotbaail
into the body of the work. The account of the inductive and —
deductive processes unavoidably quotes derelictions from the
sound performance of these processes, which derelictions are
identical with the fallacies treated of under the heads just”
named.
The case is different with Mr. Mill’s first and last classes
(Simple Inspection and Confusion), The chapters on these
heads contain matter that would not readily find a place ey
the systematic exposition of the logical methods. To take the
first class, Fallacies of Simple Inspection, or a priori. Cnet
these, the author dilates on certain fallacious tendencies ¢
the mind, the generating causes of errors. Now, the logic ti n
might say that his business is to show how errors are to
checked and corrected, not how they arise in the imperfect
of the human constitution, If he is to handle this a, i, he
NATURAL CORRUPTION OF THE INTELLECT, 605
vould not with propriety take it up in the detail of the
Deductive and Inductive Methods; he would need to be
allowed a corner apart. The demand is irresistible. -It would
be most inexpedient to agitate, under the Syllogism, or under
the Experimental Methods, enquiries as to the fallacious ten-
dencies of the natural mind. Granting that all the deductive
and inductive fallacies, and the mistakes of classification and
definition, were taken up into the main body of the work, the
fallacies @ priori, if included at all, must receive a separate
handling. Some doubts might be raised as to the logician’s
title or obligation to enter upon the subject, but there could
be none as to his allocating a distinct chapter to the considera-
tion of it.
Socrates was the first person to urge strongly the natural
corruption of the human intellect, and the need of a very
severe remedial discipline, which, in the shape of personal
_ eross-examination, he was wont to apply to his fellow Athen-
ians. The theme was not again taken up in a vigorous
manner, until Bacon composed the first book of the Novum
Organum. The elucidation of the inevitable miscarriages of
the untutored understanding, itellectus sibi permissus, and the
classification of idola—false lures, in that renowned work,
instead of being laid to heart and followed up by fresh ex-
amples, became a matter of mere parrot repetition. The next |
person to treat the subject independently, and to go systemati-
cally over the ground, was Mr. Mill, in his chapter entitled
‘Fallacies a priort.. So important is the subject, and yet so
far is it distinct from the proper field of Logic, that it might
be embodied in separate treatises. It is a kind of homily or
preaching, a rousing address on human frailty ; and although
the logician is the person most likely to be impressed with the
evil consequences, he is not the only person qualified to illus-
trate them ; while the points to be adduced in the exposition
are not precisely such as fall under either the deductive or the
inductive logic.
Mill’s concluding head ‘ Fallacies of Confusion,’ still remains
extra-logical. The extension of the field of logic does not enable
this class to be absorbed. They caunot be adduced as violating
inductive, any more than deductive precepts. In reality, they
are owing to the defective acquaintance with the subject matter
of the reasonings, and toa low order of intellectual cultivation
generally, rather than to misapprehending logical method. A
considerable stretch of the logician’s province is implied in
the taking up of this class ef errors. The ground that they
the intricacies, the incoherences, the "sei platitian the per
ments, possible to the human understanding. The only
circumstance that justifies the attempt to handle them fie
matically is the great frequency of a few leading forms; in ~
consequence of which they can be, to some extent, treated —
comprehensively. Mr. Mill’s three classes of examples— ‘
Ambiguous Terms, Petitio Principii, Igroratio Elenchi—have —
this character of extensive recurrence. Moreover, in ‘the
elucidation of such classes, there come to view many prominent
and practical errors, thus opportunely laid bare. am
From these considerations, it follows that the most defensible
course to be pursued in regard to Fallacies is to absorb into
the main work all those that are the direct violation of logical | is
precepts ; and to handle, in the chapters apart, the Fallacious
tendencies of the human mind, and the Fallacies of Confusion. —
This is not to debar the assembling of additional examples in
a supplement or appendix ; it being understood that these’ are
merely in continuation of the examples already furnished in
the regular course, |
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CHAPTER IIL fie
FALLACIOUS TENDENCIES OF THE MIND.
a
The Fallacious tendencies of the mind may be traced throu gh
an enumeration of the sources of Belief. wP
The state of Belief is a form or manifestation of our nae vity.
The import and measure of Belief is the readiness to act in the
direction indicated by the thing believed. A man’s belief in
the wholesomeness of a regimen is shown by his energy f 1d
persistence in adhering to it. '
There are three distinct sources of belief. I. The inher
Activity of the System—the disposition to act through m
spontaneous vigour. II. The influence of the Fee
Emotions, or Passions. III. The Intellectual Associatio
acquired trains of thought. Excepting under the a
there is nothing to guarantee soundness of belief, or the a
ance of the thing believed with the reality.
OUR EARLY BELIEFS OVER-VAULTING. 607
I. Inherent Activity of the System.
From the spontaneous and inherent vigour of the system, we
are induced to act somehow, to change out of the passive into
the active condition, and to continue that activity while the
energies are unexhausted, and while there is freedom from obe
struction. There is no enquiry beforehand as to the proper
course or direction to act in; opposition is not presumed until
actually eneountered. A way now open is supposed to be al-
ways open; the mind does not anticipate any future termination
or obstacle. Blind confidence is the primitive attitude of our
mind. It is only through the teaching of experience that we
suppose any limit to our career of action.
This state of mind shows itself in our early beliefs, which
may be described generally as over-vaulting; as presuming
that what holds now and here, will hold then and there and
everywhere, The following are instances :—
We are disposed to assume that, as we feel at the present
moment, we shall feel always. After a certain number of
checks, the tendency is somewhat restrained, but it continues
very strong all through early life, and is seldom entirely
conquered at any age.
We begin life by reckoning with the utmost confidence that
other persons feel exactly as we do. After lengthened experi-
ence, this primitive tendency is greatly subdued, although
perhaps in few minds is it fully sobered down to the measure
of the actual facts, The consequences are shown in our not
allowing for differences of character, in our inability even to
conceive of types departing widely from ourselves. Without
being the sole origin.of intolerance, this tendency greatly
ministers to that prevailing vice of mankind. We can with
difficulty avoid judging all men, in all circumstances, by the
standard suited to ourselves and our own circumstances.
From one or a few instances we are ready to infer a law
applicable without limit. The mere infant parodies the induc-
tive process; the most ignorant of human beings are the
most unrestrained generalizers. From an acquaintance with
one or two Frenchmen, Italians, or Russians, we conclude the
characters of the entire nation. We feel assured that a
remedy found to answer in a particular case will answer uni-
versally. Happening to visit a place during fine weather, we
are led to suppose that the weather there is always fine. The
word ‘always’ isa familiar expletive to vent our generalizing
temper.
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and harmony. Pythagoras was entranced by the mystery of
number; Plato followed him; and Aristotle: was not exempt.
from the spell. But the predominant source of fallacy quotable
under the present head was the supposed Perfection, Dignity, —
and Becomingness of certain arrangements in nature, which
included numerical considerations among others. The superior
worthiness of fire was declared in the Pythagorean philosophy ;,
and even in the later Copernican controversy an argument was
founded on the circumstance that the new system placed fire,
the noblest element, in the centre of the universe. So only
Mind, according to Plato, in Philebus, is sufficiently dignified
to create the world. In the recital by Socrates, in Pheedon,
of the phases of his intellectual history, on the subject of Cause,
the doctrines of Thales and Anaxagoras are set aside because —
they do not recognise the becoming as a power in the world.
The adherence to the circular form of the planetary orbits,
because of its perfection, was inveterate in the cool mind of
Aristotle. The planets could be only six, because that was a
perfect number.
The dictation of a plan to Nature on a supposed orbshate
has run through all times. Even in hard business affairs of.
trade, Aristotle held it was against nature that money should
breed money, that is, pay interest on loans. Lamarck argues
that a Polype cannot have Sensibility, because it would be
contrary to the plan that Nature is obliged to follow in all her
works (Lewes’s Aristotle, p. 97).
The fiction of Unity, which carried away the early Greek
philosophers, partly proceeds from over-assimilation, and partly
ministers to artistic emotion. The absolute unity of mind
is still worshipped by German: philosophers. Herbart and
others, rather than admit the radically distinct nature of Feel-
ing, Will, and Intellect, insist upon regarding Intellect or
Cognition as the basis of the two others.
The artistic sublime dictates such exaggerations as ‘ Let
justice be done, though the world collapse;’ ‘ Truth is great
and all-prevailing.’ Only a mind driven off its calm centre —
by the sublime of Force can exclaim ‘ Might is Right.” The —
fallacy that makes Artistic Harmony the test of truth, almost —
inevitable in poetry, is deliberately maintained in Wordsworth’s,
Essay on Kpitaphs, and in his prose criticisms. ! gt
The allegation is often made, on instances garbled to chime 4
in with an amiable sentiment, that great men derive thei J
mental power chiefly from their. mothers, ae
The influence of «esthetic qualities—beanty, hi: har-
INTELLECTUAL ASSOCIATIONS. 615
mony, propriety—is constantly operating to twist the under-
standing. The architecture, music, and colouring employed
in religion, indispose the worshipper to canvass the validity of
the doctrines. The art of the orator involves the tickling of
the sense, and the charms of style. Such subjects as History,
Criticism, Morality, the Human Mind, where literary polish is
more or less attended to, are liable to distortion through that
circumstance. Of Rhetorical devices, only a few are subser-
vient to truth; while a great many are hostile,
The interests of Morality and Religion, have, in almost
every age and country, been thought to require a habitual
exaggeration of the pleasures of virtue and the miseries of vice.
Plato was the first openly to recommend the pious fraud of
‘preaching doctrines, in themselves false, as being favourable
to morals and social order. And although only one society in
modern times—the Jesuits—has formally avowed the same
principle, there has been a wide-spread disposition to put it in : i
practice. Various apologists for Christianity have contended —
that, even supposing it untrue, it ought to be propagated on —
account of its beneficial consequences.
III. Influence of Associations.
Belief is not founded in the intellect; yet the intellectual
associations confirm tendencies pre-existing, and contribute to
belief both in the true and in the false. When two things have
been often associated together in the mind, the impetus thus
acquired, in passing from the one to the other, counts as a
force of belief. We are disposed, by our inborn activity, to
proceed upon whatever we are told, there being no counter-
acting tendency present ; the frequent repetition of the same
declaration enhances our disposition to believe it. The force
of iteration is one of the leading causes of men’s beliefs. What
has often been said, and seldom or never contradicted, is all-
powerful with the mass of mankind.
Thus, one part of the iutluence of education, and of prevail-
ing opinions, is due to an intellectual link, whose growth could
be arrested by mere counter iteration. The same influence is
at work confirming our modes of looking at things. There
may be no reason, beyond the adhesion generated by length
of time, why a man is reluctant to entertain a new opinion,
and yet this may be enough to render his conversion impracti-
cable. It was remarked that Harvey’s doctrine of the circu-
lation was admitted by no physician past forty. Among our
habits, we are to reckon beliets. ‘lhe inveteracy of preconceived
Opinious is in great part due to their being long cherished.
27
CHAPTER IV.
FALLACIES OF CONFUSION.
These fallacies cannot usually be produced as direct contra-
ventions of logical method. Many of them depend on imper-
fect acquaintance with the subjects under discussion. A
certain number may be regarded as snares of language
(Bacon’s idola for). A logical discipline is good as against
many; and their detailed exposure may have a slightly forti-
fying influence. As already remarked, an exhaustive treat-
ment is not possible; but certain genera may be selactethes as
being both prevalent and deleterious.
Fallacies of Language.
Am Sitios and ill-defined terms.—The Fallacies of Equivoca-
tion of the scholastic logic are fallacies of ambiguous langu-
age; for which the remedy is an exact definition of all
leading terms, and an adherence to the meaning so settled.
It is one criterion of an advanced science to have its terms
defined. In subjects not raised to scientific precision, we may
expect vagueness in the use of language. The Mathematical
and the Physical Sciences were the first to make progress in
this direction; only in recent times has the progress been
extended to thd Moral Sciences—Psychology, Hthics, Polities,
Law, Political Economy.
The exemplification of ambiguous words has no limit, unless
we adopt some principle of selection. For a work on Logic,
the most appropriate examples are terms of leading importance
whose ambiguity is still a cause of error and perversion. ©
The word ‘ Nature’ is full of ambiguity. Butler pointed
out three meanings. Sir G. C. Lewis, after a lengthened
examination of particular uses of the word, found that they
fall under two classes:—(1) A positive idea, as expressing
essence, quality, or disposition ; (2) A negative idea as excluding
art, or human regulation and contrivance. This last meaning
occurs in the phrase state of nature, used to designate man’s
existence before the introduction of law, government, and the
arts of civilization. As human interference may sometimes be ~
AMBIGUITY OF TERMS. 617
good and sometimes bad, the meaning of nature varies accord-
ingly. When men’s ‘natural rights’ are spoken of, there is
great doubt as to whatis intended. ‘ Hvery man has a natural
right to his liberty ’—is a jumble of uncertain sounds ; ‘ natural’
being probably used in Lewis’s second acceptation, as the
antithesis of art, regulation, and interference.
‘Liberty ’ has various meanings. It isnot merely the absence
of coercion or restraint, as being at large instead of being impri-
soned ; it extends also to the possession of powers, rights, and
status; thus in a community where there are slaves, being impri-
soned ; it extends also to the possession of powers, liberty is a
distinction, and freemen compose a privileged order of the state.
The ambiguities of ‘Moral’ have been previously adverted
to, Even in the one specific meaning of ‘right and wrong,’
it has a fluctuating signification, and has given occasion to
erroneous views. The criterion of ‘moral’ and ‘immoral,’
in the accurate meaning, is Law; a moral act is imposed by a
superior; hence a supreme power cannot do an immoral, any
more than an illegal act. When the Deity is said to have a
‘moral’ nature, the word must be supposed to mean simply
* goodness,’ or else ‘equity,’ both which qualities may attach
to a supreme legislator; the sovereign power may do a mis-
chievous act, and may be guilty of partiality or unfairness as
between one man and another; which, however, is not the
connotation of immoral or illegal, according to the proper
definition of the terms. The sovereign has no moral duties ;
his acts create these for his inferiors.
_ The confusion of Law in the juridical sense, with Law as the
uniformity of nature, is exemplified in Butler’s chapter on the
Moral Government of God. Butler calls the ‘course of Na-
ture’ a government, merely on the ground that it induces
precautions to avoid pain. But these precautions have nothing
moral in them; they may be used for criminal ends. Guy
Fawkes most faithfully obeyed the laws of nature, when he
placed his barrels of gunpowder so as to ensure the blowing
up of Parliament, while he arranged for firing them in safety
to himself. It is the object of a Law proper to prevent men
from injuring one another; the uniformity of nature lends
itself equally to good and to evil conduct.
The word ‘ Utility’ has a narrow sense opposed to Art,
elegance, and refinement; and a wider sense (as in the Utility
theory of Morals), comprehending the whole circle of human
gratifications and well-being.
‘Self’ has several meanings, which have to be disentangled
in ethical reasonings.
618 FALLACIES OF CONFUSION.
The words ‘same,’ ‘identity,’ have often been commented
on. Similarity or sameness is a matter of degree, and in this
consideration alone lies the ambiguity. A human being is
called the same person all through life, although in many
respects changed.
‘Probability’ is not always used in its proper meaning,
namely, the expression of what is true, not in every case, but in
most. Not unfrequently, the two sets of cases, pro and con,
are called the probabilities for and against a thing. The
wind blows from the east, say three days in seven, and from
the west four days in seven; the proper expression then is,
there is a probability of four to three in favour of west wind
on a given day. To say that the probabilities are four in
favour of, and three against, a west wind leads to a confounding
of the probable with the improbable. A vacillation between the
meanings is observable in Butler’s Introduction to his Ana-
logy. He correctly expresses the nature of probability when
he speaks of there being a greater presumption upon one side
of a question than upon another, and remarks that if there be
the slightest preponderance, prudence requires us to act
accordingly. He goes on, however, to say that, in questions
of great consequence, we have to be content with probabilities
even lower; that is, where there is an equal balance on both
sides; nay, even to less than this; in other words, we are to
act with the majority of cases against us, which is to believe
in the improbable. .
The play of ambiguity is seen in the remark of Aristotle—
‘That which is naturally good is good and pleasant to the good
man ;’ an equivocation too closely resembling what occurs in
Plato’s argument to show that the wrong-doer, if unpunished,
is more miserable, than if he were punished. ‘The wrong-doer’
says Plato, ‘when punished suffers what is just ; but all just
things are honourable; therefore he suffers what is honourable.
Now all honourable things are so called because they are either
agreeable, or profitable, or both together. Punishment is not
agreeable; it must therefore be profitable or good. Whence the
wrong-doer when punished suffers whatis profitable or good, &e.’
Separate meanings ascribed to separate words.—This is one of
the greatest snares of language. There is a strong tendency
in the mind to suppose that each word has a separate meaning,
and to be misled by tautologies and alterations of phraseology.
The ramifications of this tendency are numerous and subtle;
they include the master fallacy of Realism, or the conversion
of Abstractions into Realities.
DREAD OF CHANGES IN LANGUAGE. 619
The strong verbal associations formed with all our opinions
and views make us alarmed when it is proposed to withdraw
the customary phrases in favour even of such as are more
suitable. Siillingfleet complained that Locke’s doctrine con-
cerning Ideas ‘had almost discarded Substance out of the
world.’ This feeling has been manifested against all the great
innovations of philosophy. Because the Cartesian doctrine of
Mind and Matter, as two distinct things, is declared to be.
gratuitous and destitute of proof, people are shocked as if
Mind were done away with. The same revulsion is experi-
enced towards Berkeley’s attempt to reconcile the contradic-
tion of the prevailing mode of regarding Perception. Whately
disposes of Hume’s objection to miracles ‘as contrary to the
Course of Nature,’ by the retort that, according to him, there
is no such thing as a Course of Nature, there being nothing
but ideas or impressions on the mind of the individual. The
unproducible entity ‘Substance’ is upheld in man’s minds by
the force of the word.
The fallacy of the Identical Proposition is due to there being
two different names for the same thing :—
There’s ne’er a villain dwelling in all Denmark,
. But he’s an.arrant knave.
Ferrier complains of the phrase ‘ Perception of Matter,’ as a
a duplication of words for one fact, leading people to suppose
that there are two facts. So, between antecedent and conse-
quent, in Causation, there is interposed the name ‘ power,’
to which there is nothing corresponding ; the fact being
sufficiently stated by the uniform sequence of the antecedent
and its consequences.
There is a difficulty in satisfying men’s minds that Resist-
ance, Force, Inertia, Momentum, Matter, are all one fact. So
with the terms Motion, Succession, Direction, Distance, Situa-
tion, Extension—which are modifications of one fundamental
faet— Movement and the possibility of movement,
The giving reality to Abstractions is the error of Realism
and is not as yet fully conquered. Space and Time are
frequently viewed as separated from all the concrete experi-
ences of the mind instead of being generalizations of these in
certain aspects. Certain things are said to be ‘ out of all relation
to Time,’ which should mean that such things have no suc-
cession and no endurance. ‘Time as the innovator,’ is either
an unapt metaphor, or nonsense. So, ‘Truth’ in the abstract
is a fiction; the reality is a number of true propositions.
‘ Chance’ lingers in men’s minds as an independent existence,
620 FALLACIES OF CONFUSION,
instead of an assertion of identity between certain concrete
situations.
The word ‘Existence’ in its most abstract form refers to a
supposed something attaching alike to the Object and to the
Subject, over and above Quantity, Succession, and Co-existence,
which are attributes common to both. The only meaning of
the word is the Object together with the Subject; for which
addition we also employ the synonymous names, Universe,
Being, Absolute, Totality of Things. To predicate existence
of matter or mind is pure tautology. ‘ Hxistence” means
matter or mind, or both, as the case may be. The only use of
the word is to express Object or Subject indiscriminately,
there being occasions when we do not need to specify either.
The valuable distinction, struck out by Aristotle, of Poten-
tial and Actual, is made the occasion of giving reality to
fictions. The potentiality has no meaning but by a reference
to actuality; the power of moving means motion in given
circumstances. ‘ Educability’ means education under certain
conditions. Hamilton has created a fictitious intellectual
faculty under the name ‘ Conservative Faculty ; @ pure re-
duplication of his ‘Reproductive Faculty.’ We know nothing
of the conservation of thoughts, except that under certain
circumstances they are recalled or reproduced.
Unsuitable phraseology and unreal questions.—Many purely
artificial perplexities have arisen from applying to a subject
terms incongruous to its nature. The words ‘true’ and ‘ false’
are properly applicable to knowledge or affirmations respect-
ing the order of the world; they cannot be applied to pleasures
and pains except by mere metaphor. A ‘false pleasure ’ is an
incongruous jumble, like a ‘loud circle’ or a ‘ bright toothache.’
Aristotle puts the question—‘ Is happiness praiseworthy P’—
to which there is no proper answer, because there is no apd
meaning,
The old puzzle respecting Motion is due to the improper use
of language. Motion means ‘change of place.’ The puzzle is
brought about by insisting that the phenomenon shall be
expressed as im a place, that it shall be either in one place or
in another. If we give way to this arbitrary restriction of
language, we must allow, with Hamilton and many others,
that Motion can be shown to be impossible.
Allusion has already been made (p. 364) to the unsuitability
of the word ‘hypothesis’ to express abstract notions, as the
definitions of Geometry. :
The application of terms of Extension and Local Position
FALLACIES OF SUPPRESSED RELATIVE. 621
to the mind has been the source of factitious puzzles and arti-
ficial mysteries. ‘How the immaterial can be united with
matter, how the unextended can apprehend extension, how
the indivisible can measure the divided,—this is the mystery
of mysteries to man’ (Hamilton’s Reid, p. 886). The answer
‘is, no attempt should be made to express the union of mind
and matter in the language that would be suitable to the
union of one extended thing with another.
The most conspicuous example of an artificial difficulty
created by incongruous language is the celebrated Free-will
theory. The sequences of the Will consist of feelings followed
by actions; they exemplify mental causes giving birth to
activity, and are broadly contrasted with the physical prime
movers—as water and steam —which are devoid of any mental
element. There is no mystery in these peculiar sequences
except the mystery of the union of mind and body, formerly
remarked on (p. 357). The introduction of the idea of Free-
dom or Liberty into the voluntary operation is totally without
relevance; and the consequence has been a seemingly insoluble
problem, a mesh of inextricable contradictions,
Fallacies of Relativity.—A large class of Fallacies consist in
denying or suppressing the correlatives of an admitted fact.
According to Relativity, the simplest affirmation has two
sides; while complicated operations may involve unobvious
correlates. ‘Thus the daily rotation of the starry sphere is
either a real motion of the stars, the earth being at rest, or an
apparent motion caused by the earth’s rotation. Plato seems
to have fallen into the confusion of supposing that both stars
and earth moved concurrently, which would have the effect
of making the stars to appearance stationary.
Every mode of stating the doctrine of innate ideas commits,
or borders upon, a Fallacy of Relativity, provided we accept
the theory of Nominalism. A general notion is the affirma-
tion of likeness among particular notions; it, therefore, subsists
only in the particulars. It cannot precede them in the evolu-
tion of the mind; it cannot arise from a source apart, and
then come into their embrace. A generality not embodied
in particulars is a self-contradiction unless on some form of
Realism.
Kant’s autonomy, or self-government of the will, is a fallacy
of suppressed relative. No man is a law to himself; a law
co-implicates a superior who gives the law, and an inferior
who obeys it; but the same person cannot be both ruler and
subject in the same department.
622 FALLACIES OF CONFUSION.
In Ethical questions there are examples of suppressed rela-
tives. Thus, it is often set down as essential to the highest
moral virtue, that law and obligation should embrace every
act of human life, that the hand ‘of authority should never,
unfelt. Now, authority means operating by penalties, an
appeals exclusively to the selfishness of men’s nature, _Uni-
versal obligation is universal selfishness, which is not what is
intended by the supporters of the doctrine.
The view is sometimes expressed that the civil magistrate is
bound to support (by public establishment) the true religion ;
which, however, can mean only what he thinks the true reli-
gion; and the correlative or consequence is that he is bound
to establish a false religion, provided he believes it to be the
truth. This is an offshoot of the fallacy arising from the
suppression of the subject mind in affirmations. An affirma-
tion correlates with an affirmer; a truth supposes a betianar.
(See Part First, p. 80).
A Fallacy of Relativity i is pointed out, by Mr. Voswes in the .
doctrine of Fatalism; a doctrine implying that events, depend-
ing upon human agency, will yet be equally brought to pass
whether men try to oppose, or try to forward them. (Logic
of Chance, p. 366).
The doctrine of Relativity is carried to a fallacious pitch,
when applied to prove that there must be something absolute,
because the Relative must suppose the non-Relative. If there
be Relation, it is said, there must be something Un-related,
or above all relation. But Relation cannot, in this sma be :
brought round on itself, ees by a verbal juggle... which
thy
or extended world). This is the final at of all ene oni
tion. We may view the two facts separately or pe
and we may call the conjunct view an Absolute (as Ferrier
does), but this adds nothing to our knowledge. A self-con-
tradiction is committed by inferring from ‘ encry idling is
relative,’ that ‘something is non-relative.’
Fallacies of Relativity often arise in the hyperboles_ of
Rhetoric. In order to reconcile to their lot the more humble
class of manual labourers, the rhetorician proclaims the dignity —_
of all labour, without being conscious that if all labour is ‘
dignified, none is; dignity supposes inferior grades; a moun- ‘
tain height is abolished if all the surrounding plains are raised
to the level of its highest peak. So, in spurring men to
industry and perseverance, examples of distinguished success
7h et”
‘i...
BEGGING THE QUESTION.—SHIFTING THE GROUND. 623
are held up for universal imitation ; while, in fact, these cases
_owe their distinction to the general backwardness.
Petitio Principii.
- Petitio Principii, Petitio Quesiti, arguing in a circle, begging
the question—are names for a fallacy always included by
logicians in the List of Fallacies. ‘To assume somewhere in
the premises the very point to be proved is frequent in dealing
with ultimate truths. The attempts to prove causation or the
uniformity of nature usually take it for granted in some form
or other. The inductive syllogism is a petitio principu. As
another instance, suppose, on the one hand, the continuity of
motion were given as the proof of Persistence of Force, and
on the other hand, the Persistence of Force given as the proof
of the continuity of motion, the argument would revolve in a
circle. |
A chemical writer (Gmelin) assigns as the cause of chemical
decomposition by superadded bodies leading to new com-
pounds, that the forces tending towards the new compounds
are stronger than those maintaining the old.
Hamilton remarks that Plato, in Phezdon, demonstrates the
immortality of the soul, from its simplicity, and in the Re-
public, demonstrates the simplicity from the immortality.
Ignoratio Elenchi.
_ Ignoratio Hlencht, shifting the ground, or answering to the
wrong point, is committed in many controversies. An example
is furnished in the controversy relating to a Moral Sense.
The opponents of the doctrine urge as an argument against
, primitive or intuitive moral standard, that different nations
differ widely in their notions of what is right and wrong.
The reply is, that although they differ in the substance of the
moral code, they agree in holding some things to be right and
morally obligatory. This, however, is shifting the ground.
The reason for appealing to an implanted sense of Right was
to obtain for certain moral precepts a higher authority than
human convention could give. It was not to prove us endowed
with a sense that something or other is a moral obligation, but
to establish the obligation of certain assigued rules (the
morality of our own time).
In books on Practical Ethics, there is usually a chapter on
‘Our duties to ourselves,’ Like the autonomy of the Will, this
is a Fallacy of Relativity, being a contradiction of the very
idea of duty, which implies a superior authority. The difii-
624 LOGICAL FALLACIES,
culty is met by shifting the ground; the allegation being
that the care of our person and our interests is a duty to
society and to God.
The ‘ Fallacia accidentis’ and the ‘a dicto secundum quid
ad dictum simpliciter’ might be brought under “shifting the
ground.’ The meanin g of a term is changed in its application ; ;
‘water quenches thirst,’ does not mean ‘ boiling water.’ So, the
pleasures of duty are not pleasures attaching to it as duty, or
as self-sacrifice, they are incidental consequences of the situa-
tion, through the reciprocal conduct of the other party.
False Analogies.
The irrelevant comparison, or unsuitable analogy, is a usual
form of confused and erroneous thinking, especially in the
older philosophy. It abounds in Plato (see especially Timeeus)
and is not unfrequent in Aristotle; it is also prevalent in
Bacon’s attempts at scientific investigation.
A familiar but highly illustrative example is the comparison
of the history of a nation to the life of man, in respect of birth,
growth, maturity, and inevitable decay. The comparison is
irrelevant; the likeness palpably fails in the most important
points. A nation’s losses are repaired ; the physical failure
of a human being is irreparable.
The reply to all such comparisons is to indicate the failure
of identity. They are false minor propositions ; and the fale-
hood is exposed by pointing out the dissimilarity of the subject
with the subject of the major. a are of the same nature
as a pleading in law where the relevance is unsound. The
remedy is found in hostile criticism.
CHAPTER V.
LOGICAL FALLACIES.
There may be advantage in providing a supplemental collec 4
tion of examples of Logical Fallacies properly so called, that is, —
violations of the prescribed Logical rules and methods; it being ‘a
fully understood that the exemplification of the roles thein- 4
selves, in the regular exposition, unavoidably affords instan-
ces of their neglect or failure. io
EQUIVALENCE, DEDUCTION, AND INDUCTION. 625
The proper arrangement of such an additional collection
(unless made promiscuous to test the ingenuity of the student)
is the arrangement of the general subject. Following the
order—Deduction, Induction, Definition—we should commence
with Deductive or Syllogistic Fallacies.
Since, however, a separate department, inaueahiahs to the
Piyibogiacn; is made up of Equivalent For ‘ms, called also Im-
mediate Inference, and since mistakes may be committed in
this department (some of them the proper sources of syllogistic
fallacies), the first clsss of Fallacies should be Fallacies of
EQUIVALENCE, or of IMmepIATE INFERENCE. ‘The chief heads where
fallacies occur are the Opposition of Propositions, and Conversion.
_ The acutest minds have been snared by confounding the
Contrary with the Contradictory, of Propositions. ‘The
reverse of wrong is right’ should be ‘The reverse of wrong
contains something that is either right or indifferent.’ ‘There
are objections against a vacuwm; but one of them must be
true:’ the guarded statement is, ‘if there be not a universal
plenum, there must be some unoccupied space, or vacuum.’
The chief fallacy of Conversion is Simple Conversion of A ;
‘all the geometrical axioms are self-evident; all self-evident
truths are axioms.’ The connection of this mistake with the
usual fallacies of syllogism, was sufficiently pointed out,
The proper Depuctive Faubacies are errors against the
syllogistic forms and canons. They are mainly resumed in
Undistributed Middle and Illicit Process, which again usually
involve the simple conversion of A. But for the snare of
language that leads to this inadvertence, a fallacy of syllogism
would be comparatively rare.
The Inpuctive Fauuactes include the most frequent and the
gravest of logical mistakes. Their exemplification would
naturally follow the expository order of the subject of Induc-
tion. We might commence with erroneous views of the nature
of Cause, such as the suppression of important conditions and
collocations. We might also connect with this part of the
subject the error of assigning more causes than a pbeno-
menon needs. It is involved in the very idea of cause, that
the effect is in exact accordance with the cause; hence,
_the proof that more causes were operative than the effect
needed, defeats itself. If we have an adequate cause for
slavery, or for the subjection of castes, or classes, in the mere
love of domination on the part of the stronger, the explanation
that the state of society demands such an arrangement is of
no value, This is the error called ‘ proving too much,’
626 LOGICAL FALLACIES. -
Next are the Fallacies from insufficient employment or
neglect of the Methods of Elimination. Under Agreement
falls the mistake (exemplified in Medicine) of confounding
induction with multiplication of instances, without variation
of circumstances. Mr. Mill’s Fallacies of non-observation
likewise sin against the methods. An induction is not com-
plete till all the instances, or representatives of them all, have
been examined. Paley, in affirming ‘ that happiness 1 is equally
distributed through all classes of the community,’ must have
left out of account the larger part of the facts.
The assertion that ‘Species are never transmuted,’ even
although not disproved by positive instances to the contrary,
would require an examination of facts far beyond what has
ever been made. Leibnitz generalize: his ‘ Law of Continnity ’
from a few unquestionable instances, without verifying it
through all nature.
The fallacious inferences named ‘ Non causa pro causa,’
‘Post hoc ergo propter hoe,’ are fallacies of the inductive
methods. Some circumstance coupled with an effect is held
to be its cause, without due elimination. Thus, the luxury in
the Roman empire is said to have been the cause of its down-
fall; commercial restrictions, in spite of which trade has
prospered, are made the cause of prosperity.
The fallacy of not recognizing Plurality of Causes will be
apparent from what was advanced on that subject. So, the
fallacy of trusting to the Inductive Methods in Intermixture
of Kffects was necessarily involved in the reasons given for
coupling Deduction with Induction.
Under Secondary Laws, there is obviously ‘ata the
fallacy of applying a general law to a concrete instance, or to
an intermediate law, without the due modifications; as if we
were to infer from the Law of Gravity that all the planets are
falling direct to the sun.
Fallacies of Explanation. were expressly exemplified. A |
non-compliance with the logical conditions of Hypotheses
would yield fallacies on that subject, wm a
Factactes or Derinirion would, in the first place, express —
the use of ill-defined terms. Again, the failure to satisfy the —
methods and rules of Classification is a sin against Logic.
We need but instance the wide prevalence of the error of
Cross-divisions. Bacon is prolific of divisions and sub-divisions, —
which are never logical. His four classes of Idola are not —
mutually exclusive; his Prerogative Instances will hee after-
wards remarked on, eloeote a
berg ©
APPENDIX.
A.—CLASSIFICATION OF THE SCIENCES.
It is here proposed to subjoin a short account of the different
modes of classifying Science or Knowledge. The subject has
various logical bearings. The concatenation of Knowledge is
in itself a Logic.
The mode of partitioning Knowledge that first gained atten-
tion was Bacon’s threefold division into History, Puitosopny,
and PoETRY; in correspondence with the three great modes
of intellectual production, or faculties—Memory, Reason, and
Imagination. History, the product of Memory, deals with in-
dividual things ; PaiLosopuy, the product of Reason, compares,
classifies, and works up these materials; Portry, the product of
Imagination, is the department of fiction, fable, or creation, as
opposed to the literal rendering of things in History and
in Philosophy.
In dividing and sub-dividing these leading departments,
Bacon displays his usual copiousness. History is divided into
Natural History and Civil History. Natural History is the col-
lective matters of fact of the world, laid out under Celestial
Bodies, Meteors, the Earth, &c. Civil History is Ecclesiastical,
Literary, Political, with minor sub-divisions.
Painosopny refers to God, to Nature, and to Man. The first
head gives Theology. The second is a somewhat crude sylla-
bus of Mathematics, Natural Philosophy, and Metaphysics.
The Philosophy of Man is divided and sub-divided in much
curious detail, but with no logical precision. He speaks of
man in a three-fold aspect—(1) Man in general, (2) the human
_ body, and (8) the human mind. The theoretical and the prac-
tical aspects of our knowledge respecting humanity are indis-
criminately mixed.
As a first attempt at partitioning the totality of Literature,
the scheme of Bacon deserves to be commended. But the
lines of demarcation are for the most part vague and unsatis-
factory. The distinction of Individual (as History) and Gene-
ral (as Philosophy) is wholly unsuited to a primary division
628 CLASSIFICATION OF THE SCIENCES,
of knowledge; we cannot divorce the particulars from the
generalities in the same subject matter.
The main outline, as regards the three-fold Division, was
maintained in the classification of D’ Alembert, intended for the ©
plan of the French ‘Encylopédie’; but with great improvements
in the sub-divisions. The sub- division of Philosophy, relating
to Nature, is a methodical arrangement of the Mathematical,
the Physical, and the Biological Sciences, together with the
more Scientific Arts, as Medicine, Agriculture, and Metallurgy.
The Natural History department of History includes Meteors,
Geography, Minerals, Plants, and Animals, very much on the
scheme of Bacon, with the curious detached addition (also
after Bacon) of a division for Prodigies, or deviations from the
usual course of Nature.
The Science of Man is distributed under the two heads
Logic and Morals. Logic comprises the arts of Thinking,
Retention, or Memory, and Communication. Morals is General,
that is, revards Virtue at large (Ethics); or Particular,—
including Law or J urisprudence. This is the mode of ap-
proaching the science of mind that has been embodied in our
Universities. Excepting in recently founded schools, there is
no chair for Psychology or the Theoretical Science of Mind ;
the subject is left to come under Logic and Moral Philosophy ;
the Intellectual Powers being described in the Logic miterne
the Active Powers in Moral Philosophy.
Thus, in D’Alembert, as well as in Bacon, there is total
confusion of the Theoretical and the Practical.
The plan of subjects in the ‘ Encyclopedia Motespaliiheed
(begun to be published in 1815), is worthy of being eo
There are four Divisions in the work.
The First Division includes PURE SCIENCES, divided
into Format—Grammar, Logic, Rhetoric, Mathematics, Meta-
physics; and Reat, Law, Morals, and Theology. ,
The Second Division is the MIXED SCIENCES ‘ch Mealiaiia
ics, Hydrostatics, Pneumatics, Optics, Astronomy [constituting
the larger part of our usual course of Natural Philosophy]. —
The Third Division is the APPLIED SCIENCKHS, sub-
divided into Experimental ParLosopay— Magnetism, Electricity,
Heat, Light, Chemistry, Acoustics, Meteorology, Geodesy ;—
Fine Arts; Userun Arts; Natura History (with applications - a
to Mchintnal \ ounedee
These are the properly scientific divisions; the other sub- ’
NEIL ARNOTT.—AUGUSTE COMTE 629
jects are History, Biography, Geography, Lexicography, and
Miscellaneous information.
The designations ‘ Pure,’ ‘ Mixed,’ and ‘ Applied’ Sciences
have characteristic meanings, although not precisely carried
out inthe above scheme. The Pure Sciences are the more
Abstract and Formal Sciences, not involving the consideration
of objects in the concrete; the two leading examples are
Mathematics and Formal Logic. The Mixed Sciences consider
the applications of the laws of the Formal Sciences to actual
things. The Applied Sciences, in so far as distinct from the
Mixed Sciences, should be equivalent to the Practical Sciences.
Dr. Neil Arnott, in his work on ‘ Physics,’ published in
1828, gave wide publicity to a division more in harmony with
our present views. He distributed the leading sciences under
four heads, representing the four classes of general Laws of
Nature—namely, Physics, Chemistry, Life, and Mind. He
viewed Mathematics as preliminary and indispensable to these,
being the Science of Quantity, or Measure, but not a depart-
mént of natural operations, in the same acceptation as Physics
or Chemistry. All the sciences give foundation to Arts.
_In his subsequent treatise, entitled ‘Survey of Human
Progress,’ Dr. Arnott brought out more decisively the distinc.
tion between Sciences and Arts, and between the Concrete and
the Abstract Departments of Science. Concrete Science he
calls the knowledge of TH1nas ; and he enumerates, under this
head, Astronomy, Geography, Mineralogy, Geology, Botany,
Zoology, the History of Man. Science, or Philosophy (Ab-
stract), is the knowledge of PHrnomena, and comprises the four
fundamental departments—Physics, Chemistry, Biology, Mental
Science. The Arts are classified as Mechanical, Chemical,
Physiological, and Mental.
The work of Auguste Comte, entitled ‘ Cours de Philosophie
Positive’ (1830-42), is both a classification of the sciences as a
whole, and a minute sub-division of each, according to certain
fundamental principles.
He first draws the primary distinction between the Abstract
and the Concrete Sciences, which he fully illustrates. The
Abstract Sciences, being the fundamental or departmental
branches of Knowledge, are susceptible of an orderly classifica-
tion on the principles of Generality, Simplicity, and Independ-
ence.
Accordingly, he commences with Maraemartos, whose truths
630 CLASSIFICATION OF THE SCIENCES.
are the most general of all, and wholly independent of the
truths of any other science, while all other sciences depend
upon it. Its sub-divisions are, the more abstract portion called
Number, including Arithmetic and Algebra, and the applica -
tions of these to Space (Geometry), and to Motion (Rational
Mechanics).
His second science is Astronomy, which is the ensbouimideik
of the Law of Gravitation. It receives this position because
the carrying out of gravity requires Mathematics alone, while
the phenomenon of gravity is a prelude to Physics.
Then come, in order, Puysics, CuEmistry, BioLoey, and
SocioLoGy, whose mutual position and interior arrangements
are governed by the same ideas of growing dependence and
complexity, and decreasing generality.
In addition to the singling out of Astronomy as a leading
science, Comte’s arrangement has these two farther peculiari-
ties, namely, the omission of Psychology, as a separate depart-
mental science, (it being appended to Biology, under ‘ Cerebral
Functions,’) and the inclusion of Sociology, or the Science of
Society, as a fundamental department.
Mr. Herbert Spencer, in his recent work entitled * The
Classification of the Sciences,’ has criticised the scheme of
Comte, and propounded one of his own, which he has devel-
oped with circumstantial minuteness. He deals exclusively
with the Theoretical sciences.
Mr. Spencer’s fundamental idea is the important distinction
of Abstract and Concrete, which he expresses in a@ variety of
forms ; it is the distinction between the Relations of pkeno-
mena and the Phenomena themselves, between the Analytical
and Synthetical ; it is the separation of one or a few sequences
from the total plexus of sequences; the wholly or partially
ideal as contrasted with the real.
Not content, however, with a simple binary division accord-
ing to this leading contrast, Mr. Spencer proposes a three-fold
division, by interpolating between the extremes a middle class
partly Abstract and partly Concrete, to be termed Abstract-
Concrete. The three classes are Absrract, ABsTRACT-CONCRETE,
and ConcreTs. The only way that this is competent is to sub-
divide the Abstract, according to degrees of Abstractness.
‘Concrete’ has no degrees ; ; it means the phenomena taken in
their full totality, or individuality,—Stars, Mountains, Mine-
rals, Plants, Animals; and there can be but one way of giving
these totals, one mode of concreteness. There may, however,
HERBERT SPENCER'S CLASSIFICATION. 631
be various degrees of the analytic separation—more or less
abstract relations indicated ; quantity and form are more ab-
stvact than weight, hardness, colour, life.
The Apsrract Sciences by pre-eminence, are those that deal
with the most abstract of all relations—Space and Time.
Wichout affirming that Space and Time are intrinsically mere
forms, conceived by us without any particular things extended
and enduring, Mr. Spencer holds that they have acquired this
character by hereditary transmission, and that we do actually
possess them in their empty condition, or apart from any con-
crete embodiments. Hence, whatever relations subsist with
reference to these great conceptions, are the most abstract that
the mind can possibly entertain; they are pure and proper ab-
stractions; their hold of the concrete world has been almost,
if not altogether, severed. Space is the abstract of all rela-
tions of co-existence. Time is the abstract of all relations of
sequence. Now there are two sciences that are occupied with
these abstract relations of co-existence and of sequence—Logic
and Mathematics ; which accordingly form a class by them-
selves, being removed from the next class by a wider interval
than separates the members of that class from one another.
Proceeding from the blank Forms of existence, to Existences
themselves, from the relations of phenomena, to the phenomena,
we find two divisions, having different aspects, aims, and
methods. In fact, we have the distinction of Abstract and
Concrete carried out, without the same absolute divorce as in
the previous class. Mr. Spencer illustrates the distinction
thus :—LHvery phenomenon is a manifestation of force, usually
a combination or complication of forces (the course of a pro-
jectile depends upon at least three forces). We may study the
forces either in separation, or in combination—the factors or
the product. On the one hand, neglecting all the incidents of
special cases (say of falling bodies), we may aim at educing
the laws of the common force (gravity) when it is uninter-
fered with. On the other hand, given all the incidents of a
phenomenon (as a river), we may seek to interpret the entire
phenomenon, as a product of the several forces simultaneously
in action. The truths reached through the first kind of en-
quiry, though concrete inasmuch as they have actual exist-
ences for their subject-matter, are abstract as referring to the
modes of existence apart from one another.
Mr. Spencer thinks it proper to point out farther that the
abstract must not be confounded with the general. Hach has
its peculiar signification ; ‘abstract’ means detachment from
632 CLASSIFICATION OF THE SCIENCES.
particulars ; ‘ general’ means manifestation in numerous cases. —
The law of uniform rectilineal motion is abstract; butitis —
never realized in any particulars, consequently it is ‘not gene-
ral; while rotation on an axis is very general, Accordingly,
he disapproves of Comte’s expression ‘ decreasing generality,”
as belonging to the phenomena of the successive sciences
—Mathematics, Physics, &c. This criticism indicates a pot —
worth noting, but as regards Comte’s remark it might easily
be evaded. There can be no abstraction without a prior
generalization; the abstract law of rectilinear motion, is a
generalization of the very highest order stating what would |
happen in every case when a body is projected into space and
left to itself. The other kind of generality is something more
special and concrete, in fact, much less of a generality _
this great primary law.
The Sciences, then, that treat of the forces of vhievsoasedill as
analyzed and handled in separation, are the ABsTRACT-CONCRETE
Sciences; as Mechanics, Physics, Chemistry. ‘The sciences
that view phenomena in their aggregate, or their full actuality,
are Concrete Sciences ; such are Astronomy, Geology, weap. j
Psychology, Sociology, &c.
A few words now as to the more precise definitions and
divisions of the leading departments, on which hang various
points of logical interest, 1 ah
ABSTRACT SCIENCE considers, first, what is common to all —
Relations, and next, what is common to each order of Relations. —
Between each kind of phenomenon and certain other kinds of —
phenomena, there exist uniform relations. It is a universal —
abstract truth—-that there is an unchanging order among —
things in Space and in Time. This is the most abstract truth —
ofall, the subject-matter of the highest division of Abstract
Sotonesi It has sub-divisions. First, and next in abstractness, ©
are the connexions of things in Space and Time, irrespective —
of the things connected. This is the subject-matter of Logie, —
where the nature and amounts of terms related are not
considered, but only the relations themselves. The other sub-
division takes in Quantity or amount, without any farther
qualities. This is Mathematics, which is a statement of laws of
quantity apart from any real things, that is, as occupying
Space and Time. This statement is made upon certain ultimate —
units occupying definite positions in Space and in Time. The-
divisions of Mathematics follow according as the units
simply separate, or according as they are both separate and
equal; the one gives birth to an indefinite Calculus (applied
wy
ABSTRACT AND CONCRETE SCIENCES. 633
in Statistics), the other to the Definite Calculus, whose sub-
divisions are Arithmetic, Algebra, and the Calculus of Opera-
tions. When the computation of units refers to occupation of
Space, the subject is Geometry. When Time is introduced, we
have Kinematics and the Geometry of Motion. .
_ So much for the sciences of pure Abstraction. The second
class, the Apstract-ConorETE, are occupied with the general
laws of Motion, Matter, and Force, in their disentanglement
from the concrete phenomena, where they re-act upon, and
modify one another. In Mechanics, for example, which is one
of the sub-divisions, the laws of motion are expressed without
reference to friction and resistance of the medium (?). So in
Chemistry, another sub-division, the laws are viewed upon
substances absolutely pure, such as Nature rarely supplies.
The partition of this group is conducted on the same prin-
ciple as in the former group. A distinction is drawn between
Force considered apart from its modes, and Force considered
under each of its modes,—a more abstract, and a less abstract
department. The first part contains a statement of the Laws
of Force, as deducible from the fundamental principle of the
Persistence of Force, together with the theorems of the Com-
position and Resolution of Forces. The second part comprises
Molar Mechanics or Molar Forces (Statics, Hydrostatics,
Dynamics, Hydrodynamics), and Molecular Mechanics—includ-
ing the properties and states of matter (Physical), and Chemis-
try ; together with Heat, Light, Electricity, and Magnetism.
[The arrangement is a questionable one, in so far as Chemistry
is interposed between the Physical properties and states of
bodies, and the agencies—named Heat, Light, &c].
The division of Abstract-Concrete Science is thus co-exten-
sive with what we have formerly termed Inorganic Physics.
The third great group, the Concruts Scienczs, as repeatedly
stated, embrace the totalities of phenomena. Astronomy is
placed in this group. The meaning is, that the astronomer
does not stop short after generalizing the laws of planetary
movement, such as they would be if there existed only one
planet; he solves this abstract concrete problem, as a step to-
wards solving the concrete problem of the planetary movements
as affecting one another. The ‘theory of the Moon’ means
an interpretation of the Moon’s motions, not as determined
simply by centripetal and centrifugal forces, but as perpetually
modified by gravitation towards the Harth’s equatorial protu-
berance, towards the Sun, and even towards Venus—forces
daily varying in their amounts and combinations. So the
634 CLASSIFICATION OF THE SCIENCES.
2 wy
geologist does not confine himself to the separate elements—
water-action, fire-action, he aims to interpret the entire structure ;
of the Earth's crust, And, in Biology, if different aspects of —
the phenomena of Life are investigated apart, they are all
helping to work out a solution of vital phenomena in their
entirety, both as displayed by individual organisms and by
organisms at large. The interpretation is no longer Syne z
cal but analytical.
These explanations premised, the enumeration of subjects in
the Concrete division is as follows :—First, and most general —
of all, are the Universal Laws of the continuous Re-distribution —
of Matter and Motion. Next follows the application of these —
toactual Matter. Asapplied to the Celestial Bodies (1) treated —
as masses, it is Astronomy ; (2) as made up of molecules—
Astrogeny (Solar Mineralogy and Solar Meteorology). On the
earth, the same actions result in Mineralogy, Metcortiae 3
Geology ; ; when causing organic phenomena, they make up —
Biology, which has various sub-divisions, Leruiareae im. 3
Psychology and Sociology. Dy
Such is the outline of Mr. Spencer’s scheme. By way of
criticism, the following remarks may be offered.
In the first place, objection may be taken to his longue
in discussing the extreme Abstract Sciences, when he speaks
of the empty forms therein considered. To call Space and —
Time empty forms, must mean that they can be thought of ~
without any concrete embodiment whatsoever; that one can
think of Time, as a pure abstraction, without having in one’s ©
mind any concrete succession. Now, this doctrine is in the
last degree questionable. For although we might concede the :
hereditary predisposition to fall into these conceptions, we do —
not thereby affirm that they can be bodied forth without any
concrete examples whatever. We might rather say with
Kant, and the later a priort schools, that when particulars are
given they start forth into full view, This much is certain, —
however, that without a very wide and familiar converse with —
particulars, the exceedingly abstract relations of these Abstract —
Sciences, are wholly incomprehensible to any human being.
The extreme generalities of Logic, in order to be intelligible,
need perpetual reference to particulars. The same is true wit
the first elements of Mathematics, which are the foundations
of all the rest. .
Mr. Spencer’s account of the subject-matter of Logic, the
first of all the sciences, is so extremely general that we can
hardly discover what is the precise scope he assigns to it.
LINES OF DEMARCATION. 635
From its position, however, it must be viewed as Theoretical
Logic purely ; under which there would be included the funda-
mental aspects of all knowledge—Difference (Relativity) and
Agreement (Generality), the Laws of Consistency, Mediate
Inference, the Uniformity of nature; and the various deduc-
tions or consequences of those primary facts. These are points
common to all sciences, and may therefore precede them all.
At the same time, it should be remarked that the ascertaining
of these very high generalities has been a great inductive
effort, considerably aided by the special study of the human
mind, or the science of Psychology. This observation slightly
qualifies Mr. Spencer’s statement that none of the truths of
the third group are of any use to the problems of the second,
while the second group are of no use to the first.
It may be farther noticed that, notwithstanding the strong
terms employed to contrast the Abstract with the Abstract-
Concrete Sciences, the contiguous subjects of each show but a
narrow boundary line. The geometry of Motion, the last of
the Abstract Sciences, comes very close upon the Universal
Laws of Force, the first subject of the Abstract-Concrete vroup.
These considerations, if they have any weight, tend to in-
validate the alleged distinction between Abstract and Abstract-
Concrete Sciences, a distinction without an adequate difference.
_ Practically, however, the matter isof no moment. The succes-
sion of subjects would probably be regarded as the same, and
the manner of sub-dividing and treating them would be very
much the same with or witbout this particular boundary.
Mathematics must precede Mechanics; and Logic, conceived in
its high theoretic aspects, may claim to precede Mathematics.
A much more serious dispute arises out of Mr. Spencer’s
proposed boundary line between the Abstract-Concrete and
the Conerete Sciences. No one ever drew the line as he has
done it. The Concrete Sciences have always been typified by
the so-called Natural History Sciences— Mineralogy, Botany,
Zoology, Geology—and by Geography. These are Sciences
whose marked teatures are Classification and Description.
They deal with large collections of objects, which they arrange
and describe by means of careful generalization.
It is, therefore, with a little surprise that we find inserted
among Concrete Sciences, not merely Astronomy, but the
whole of Biology, in which is included Psychology. Certain
parts of these subjects would be properly concrete ; as Celestial
Geography (under Astronomy); and the Races and Charac-
ters of men (under Psychology.)
636 CLASSIFICATION OF THE SCIENCES.
Let us consider how the case stands with Astronomy. This —
science, since Newton’s time, is avowedly based on Theoretical —
Mechanics. Newton, in the First Book of the Principia, which |
may be pronounced Abstract Mechanics of the purest type,
went far beyond Mr. Spencer’s limits to an Abstract-Conerete _
Science. These limits, indeed, are not a little arbitrary. We
can suppose a science to confine itself solely to the ‘factors,’ or —
the separated elements, and never, on any occasion, to combine —
two into a composite third. This position is intelligible, and
possibly defensible. For example, in Astronomy, the Law of —
Persistence of Motion in a straight line might be discussed in
pure ideal separation; and so, the Law of Gravity might be
discussed in equally pure separation—both under the Abstract- —
Concrete department of Mechanics. 1t might then be reserved —
to a concrete department to unite these in the explanation of a
projectile or of a planet. Such, however, is not Mr. Speucer’s —
boundary line. He allows Theoretical Mechanics to make this
particular combination, and to arrive at the laws of planetary
movement, in the case of a single planet. What he does not
allow is, to proceed to the case of two planets, mutually dis-
turbing one another, or a planet and a satellite, commonly —
called the ‘problem of the Three Bodies.’ This problem is |
not to be touched in Theoretical Mechanics, but to be remanded ;
to the Concrete Science of Astronomy. Yet, if we are allowed — ;
to combine the two factors—projectile motion and gravity to
one centre—why may we not take in an additional Saatod a
second gravitating body? The difference is not between
single factors and their combination, but between two grades of
combination.
In point of fact, such a line is never drawn. N ewton, i in the
First Book of the Principia, took up the problem of |
Three Bodies, as applied to the Moon, and worked it to ole
haustion. So writers on Theoretical M echanics continue to
include the Three Bodies, Precession, and the Tides. Nor is
any reason apparent for making the break that Mr. Spencer
suggests. Increasing complicacy of deduction and caleulation
attends the inclusion of new factors, but this special difficu
is not supposed to take the subject out of an abstract ten
ment and to insert it in some concrete department. <1
Again, Mr. Spencer remarks that in works on Mechanies,
the laws of motion are expressed without reference to fri¢
and resistance of the medium. Turning to ‘ Thomson
Tait’s Mechanics,’ we find the Laws of Friction intro .
with a reservation of the purely Experimental results to the
=
CHEMISTRY AND BIOLOGY. 637
department called Properties of Matter. In Newton’s Second
Book, and in all works of similar compass, the operation of a
Resisting Medium is handled.
The law of the radiation of light (the inverse square of the
distance) is said by Mr. Spencer to be Abstract-Concrete,
while the disturbing changes in the medium are not to
be mentioned except in a Concrete Science of Optics. We
need not remark that such a separate handling is unknown to
science.
Mr. Spencer’s illustrations from Chemistry are especially at
variance with usage, while it is difficult to reconcile them
with reason. Chemistry is an Abstract-Concrete Science.
What does this mean? The reply is, the chemist is never
satisfied with the crude substances of nature, but first purifies
them, and ascertains the properties in the pure state. This, of
course, is a necessary precaution. But if the insinuation be,
that Chemistry does not give, or ought not to give, the pro-
perties of any impure substance, or any alloy or mixture,
the fact is quite different.. Every chemical writer describes all
the prevailing species of carbon, including pure and impure
kinds; the same with iron, and with every substance found in
important varieties. Why should it be otherwise ? There is no
dereliction of logical principles in stating the properties. of
the iron ores, in connexion withiron. Thesame thing may be
repeated in Mineralogy, but is not out of place in Chemistry.
Again, no writer on Chemistry ever omits to describe the
Atmosphere, which is the actual or concrete combination of
Oxygen, Nitrogen, &c.
lt may be noticed in addition that a substance purified is
obviously not a substance in the abstract. Virgin gold, and
the purest diamond are still objects in the concrete.
These remarks on Chemistry pave the way for the conside-
ration of the place assigned to Biology among the Concrete
Sciences. Now, Biology is a science of increasing complica-
tion; living bodies are subjected to all the Physical and
Chemical Laws, and to Biological Laws in addition: so that a
rose is a more complicated object than a diamond. But the
objects of Chemistry and the objects of Biology are equally
concrete, so far as they go; the simple bodies of chemistry,
and their several compounds, are viewed by the Chemist as
concrete wholes, and are described by him, not with reference
to one factor, but to all their factors. The isolation of the one
_ property, named Chemical combination, which would be an
abstract handling of bodies in the chemical point of view,
638 CLASSIFICATION OF THE SCIENCES.
must be considered to be impracticable; at all events it is
never done. We may doubt whether anything would be gained
by attempting it. But, whatever abstractive operation of this
kind is possible in Chemistry, might be repeated in Biology ;
there might be general laws— isolated factors—of life, as well
as of inorganic matter. If so, to place one of these two leading
departments among Abstract Concrete Sciences, and the other
among the proper Concrete departments is to make a dis-
tinction without a sufficient difference. 1,
Nor is it possible to justify the placing of Psychology wholly ©
among Concrete Sciences. It is a highly analytic science, as
Mr. Spencer thoroughly knows. The totality of mind is sepa-
rated into factors, each discussed in isolation, before they are —
brought together. There are many strictly abstract discussions
to show the difference between the effect of a motive (as selfish-
ness) acting in ideal purity or separation, and the same motive,
combined with many others, in the concrete human being.
But the force of the remark would appear to be dissipated if
all the laws of Psychology are to be considered as expressions
of the concrete facts of mind.
A separation may be temporarily made between the purely
theoretical and deductive treatment of a science, and the ex-
perimental treatment. In Theoretical Mechanics, (as Hydro-
Dynamics), the laws of a resisting medium may be inferred
and computed from primary assumptions as to the nature of
fluid particles; while, on the other hand, the subject may be
investigated by experiments, as in gunnery. But the science
is not completely presented unless both are taken account of
together: the theoretical deductions have to be confronted,
checked and verified, by the experimental results, in order to
have any standing as laws of the department.
Yet another method is possible. A subject, as, for example,
Astronomy, may be exhaustively handled in a separate treatise ;
wherein there shall be brought together from every department
whatever bears upon the celestial bodies. This would be a
ughly mixed department, yet not, on that account, a strictly
concrete science. It would be full of the most abstract diseus-
sions ; witness the ‘Mechanique Celeste’ of Laplace. It would
draw contributions from various sciences, besides its parent
science, Mechanics ; it would introduce Optics, Heat, Magnet-
ism, and Chemistry; yet it would not treat the heavenly
bodies as Minerals are treated in Mineralogy, or Plants in —
Botany. It would have many practical bearings; in fact, it
would have considerable claims to bea Practical Science. Any —
‘
4
ee er ee ee ee Pes
Sabor
PRETENSIONS OF FORMAL LOGIC. 639
scientific department exhaustively treated would eschew purity,
and draw contributions from many sources.
Thus, it appears that Mr. Spencer, in abandoning the usual
partition of the sciences, into the departmental or fundamental
sciences, on the one hand, and the concrete or derived on the
other, has abandoned the more real distinction in search of a
fanciful and untenable boundary line of the Abstract and the
Concrete. We see reason still to abide by the old specification
of the Concrete Sciences, typified by Mineralogy, Botany,
Zoology, Geology, &c. These sciences have marks peculiar to
themselves; they are the classificatory and the descriptive
sciences. They embrace large collections of individual things,
which have to be classified, and to be described as concrete
wholes. Moreover, they contain no new fundamental operation
of nature; every variety of natural agent has been previously
exhausted in the departmental sciences—Mathematics, Physics,
Chemistry, Biology, Psychology.
B.—THE PROVINCE OF LOGIC,
It is contended by some logicians that the Province of Logic
is Formal Reasoning and Thinking; by which they mean
mainly the Syllogism, and what is subsidiary thereto. They
would exclude everything that refers to the Matter, that is to
say—Induction, and the greater part of Definition and Classifi-
cation.
We have, however, just grounds to complain that the dis-
_ tinction of Form and Marter is too vague and unsteady to con-
stitute a clear line of demarcation between the two departments
of Hvidence—Deductive and Inductive. It will be expedient
for us, therefore, to ascertain what precise meanings, if any,
can be assigned to these phrases.
Perhaps the most thorough and consecutive account of the
severance of Formal Logic from Material Logic is that con-
tained in the Introduction to Mansel’s edition of Aldrich. In
that work, the author adduces every consideration that is of
any avail in widening the distinction in question.
Adverting to the first question raised in the definition of
Logic, namely, whether it be a Science or an Art—whether it
is principally theoretical or principally practical—Mr. Mansel
holds that, in its essence, it is speculative or theoretical, and,
in its accidents, practical. ‘There would be a body of prin-
ciples or laws, although no one cared to apply them to the
discipline of the mind, or to the improvement of the thinking
faculties.
28
640 . . HE PROVINCE OF LOGIC.
_ Nevertheless, the science is susceptible of application to
practice; it may be brought to bear on our intellectual pro-
cesses. Such is its scope as expressed in the second part of
Whately’s definition— the Art of Reasoning ; which definition,
however, as regards the word ‘ Reasoning,’ Mr. Mansel, in
common with Hamilton and Mill, objects to as narrowing the
province too much. Even as a Formal Science, Logic in- —
cludes the processes named Apprehension and J udgment, and
these not as mere aids to Reasoning, but as independent acts
of thought. Accordingly, Mansel agrees with Hamilton in
substituting for ‘ Reasoning,’ with suitable eee the
larger term ‘Thought.’
He then proceeds to lay oat the distinction between the a
Form and the Matter of the thought. His first indication of
the difference is to this effect: Thought may violate its own laws,
and so destroy itself; something may be set up that turns out
wholly unthinkable. On the other hand, a Thought may be per-
fectly consistent with itself, but at variance with facts of
eeperience ; which, although quite thinkable, would be empiri- —
cally illegitimate, or wnreal. [This is the distinction between —
Self-Consistency—Immediate or Equivalent statements, and
Inductive or matter-of-fact certainty |. 4
The next remark is that there must be material data in Saat :
to thought of any kind, even formal thought; there must be
concrete experience of things external and things internal, in
order to understand even a syllogism. But the materials being q
given, there is a vital difference between two modes of using ~
them. The distinction of Presentative and Representative thought —
is an aid here; the distinction between the individual concrete —
things—a building, a man, a star, and the generalities or con- —
cepts—height, figure, brightness, which we may form by the —
comparison of the concrete objects. The consideration of the
Matter is the reference to the individual things; the considera- —
tion of the Form is the general concept, or representative —
thought. [So far we have the ordinary distinction between —
Concrete and Abstract, only it is apparently pushed to a kind
of Conceptualisn ; there being implied that the concept, or —
notion, is Something more than an agreement among individuals.
If it be true that a notion is unthinkable, except as one or
more individuals, the ‘Form’ is still ‘ Matter,’ only in a Somer
what different arrangement]. it es
But farther, the thinking process may be distinguished | as
material or formal. It is formal when the matter given is
sufficient for the product derived, with no other addition but
FORMAL THINKING EXPLAINED, 641
the act of thinking. It is material when the data are insufli-
cient, and the mind has to take in more matter, in the act of
thinking. Given the attributes, A, B, C, we can think them
as co-existing in an object, without any fresh appeal to facts ;
which is formal conceiving. [This is quite intelligible too; all
the operations of Arithmetic are formal in this sense ; we pro-
nounce six times four to be twenty four, without an appeal to
pebbles or coins, or any real objects. We have put together
from primary realities a machinery that can operate independ-
ently of the realities].
As conditions of formal conceiving, are laid down the laws
of Contradiction and Identity. We must not introduce Con-
tradictory attributes—A and not-A. The author is a little
more obscure as regards the condition of Identity. Thought,
he says, is representative of all possible objects ; but Intuition
(cognition of the individual, as opposed to Thought, or the
general) must be conscious of differences; every object of
intuition is marked off, limited, and individualized ; it is atsedf
and no other, To this circumstance corresponds the Law of
Identity, ‘Ais A’; ‘every object of thought is conceived as
itself.’ A somewhat novel rendering of that well-known Law
of Thought.
These laws are the key to logical conceiving (Conception is
the first logical product). Next, as to formal judging, or the
forming of Judgments. Affirmation takes place when one
concept is contained in another; Negation, when one contra-
dicts another. Here, too, are involved the laws of Identity
~ and Contradiction.
Finally, as to reasoning. This is formal when the given
judgments are connected by a middle term, under such condi-
tions of quantity and quality that the mere act of thought
necessarily elicits the conclusion. If there be required any
addition to the data, the consequence is material. Formal
Mediate reasoning, no less than Immediate inference, is achieved
through the laws of Identity (for affirmative syllogisms), and
of Contradiction (for negative syllogisms). In the immediate
inferences of Opposition [Obversion] and Conversion, there is
a further demand for the subordinate law of Excluded Middle.
Thus, then, if a thought professes to be based on formal
grounds, to be guaranteed by the laws of thought alone, its
pretensions can be adjudicated on by Logic; if it professes to
rest on sensible experience, or on suppressed premises, it must
come before another tribunal.
_ It is, of course, open, the author remarks, for any innovator
642 THE PROVINCE OF LOGIO,
to propose an extension of boundaries, by the inclusion of the
Matter of propositions; but he does so in the teeth of Kant’s
demonstration, that a criterion of material truth is not only ~
impossible, but self-contradictory. Moreover, the attempt to
enlarge the field renders impossible the assigning of any definite
field whatever. v7i5 eer
We are interested to know in what way Mr, Mansel makes
ood these very strong allegations. The steps are these. —
(1) The Aristotelian or Formal Logic seeks the laws whereby a
the mind thinks; the Baconian seeks the laws whereby the
phenomena of outward things take place; that is to say the one _
refers to mind, the ego, the other to matter, the object, or non-
ego. Consequently, the one enquiry is the interrogation of
self-consciousness, the other is an examination of external
nature. ‘3
Such is Mr. Mansel’s first position. Tt seems to involye some
confusion of ideas. We strongly doubt whether the contrast ae
Formal Logic and Inductive Logic can be reduced under the —
contrast of Subject and Object, or Mind and Matter. a
For one thing, the study of Mind, or Psychology, is, nm —
modern times, universally considered to be properly Inductive. _
How can we reach the important laws of Mind—such as Rela- _
tivity, Association of Ideas, the operation of the Feelings, and
the Will—except by observation and induction of the facts of —
- self-consciousness, occasionally aided by external indications. —
Again, the laws of Thought, called Identity, Contradiction,
and Excluded Middle, apply alike to the outer world and to —
the mind. If so, they may be gathered from either source. —
Probably, however, the supposition is that these laws are got
at without investigation ; that they work themselves out with- —
out being expressly studied. We unconsciously and irresistibly —
declare that the same thing is not at the same instant white
and black ; just as we walk without thinking how we walk.
These invincible tendencies of the mind, if such there be, are —
no doubt facts of our mental nature: but so is our belief that —
Nature is uniform, or that every effect must have a cause; on —
which reposes all Inductive investigation. In both cases, the
mind is the instrument, although the material may be some- _
times mental phenomena and sometimes phenomena of the —
outer world. Deduction and Induction have equally their seat
in laws of the thinking mind; and have equally, for their
field of operation, both mind and matter. ‘ae
(2) The next position is this—The Aristotelian laws are laws —
of thought as it ought to be; the Baconian laws are Jaws of
MANSEL’S ARGUMENTS. 643
nature as itis. The author adds, as explanatory and synonym-
ous statements, what seems to involve a new and distinct idea,
namely, that the one rest on their own evidence, the other on
the evidence of the facts concerned.
To this we may reply that ‘thought as it ought to be’ is
certainly not confined to Formal Reasoning. Wherever we
think wrong, and have to be put right, we are in the domain
of ‘thought as it ought to be.’ Lord Bacon’s inductive logic
professed to substitute right thinking for wrong. We commit
fallacies of Deduction and of Induction equally ; and if Logie
does not put us right upon both, it must be for some other rea-
son than the one now assigned.
The addendum given, professedly to explain the above posi-
tion, namely—that the Aristotelian laws are self-evident, and
irreversible in thought, while the Baconian laws are inductions
from facts and contingent or reversible—is merely a re-state-
ment of the general thesis as between self-evident or necessary
truth, and inductive or contingent truth.
(3) The third position is that the Aristotelian Logic pro-
ceeds from the law to the facts, constructing types or genera-
lities, and rejecting what does not conform thereto; while in
the Baconian Logic, the procedure is from the facis to the law,
rejecting every law that does not account for the facts. This |
is a direct opposition of Method.
Now, we may readily grant this position. But what is its
bearing on the question in dispute? The methodsare different,
but both are methods of arriving at truth; both may be alike
in want of precautions, and if so, both may, so far as appears,
equally receive attention from the logician.
(4) The fourth position is perhaps the most remarkable.
It is this: Law, in the Aristotelian system, implies a conscious-
ness of obligation; whereas, in the Baconian system, Law
means only uniform sequence.
Here is that confusion of thought, so well pointed out by
John Austin, in connexion with the term ‘ Law,’ whereby
there is introduced into the order of natural phenomena the
notion of authority and obedience. Law, as regards the order
of nature, whether in mind or matter, is purely figurative ; it
is applicable merely as expressing wniformity of sequence; the
Hthical and Political definition—a rule set by intelligent
superiors to intelligent inferiors, accompanied by the infliction
of pain on neglect—cannot be transferred to the sequences of
nature, whether mental or material; the application to these
contains only the single incident of law—uniformity. There
644 THE PROVINCE OF LOGIC.
can be no moral right or wrong in Logic, except only in so far
as we are all morally bound to seek the truth, an obligation
extending equally to truth Deductive and to truth Inductive. |
(5) A fifth position maintained by the author is, that, in the
field of Thought, the cause is the conscious self; the effects, the
thoughts produced by that self, through its own power, and
under its own laws. To which we may reply, that both causes
and effects are equally self, equally mental, but not thereby | ;
radically contrasted, in manner of investigation, with external
nature. Cause and effect in mind must be discovered induct-
ively, if at all. Should the sequences be very prominent, little
attention may suffice for their discovery; but that does not
alter the method of proceeding.
So much is Mr. Mansel carried away by the application of —
the term Law, in its Ethical sense, to the process of thinking,
that he censures Mr. Mill for applying ‘ physical causation ’
(meaning uniformity of sequence, ascertained by induction) to
the moral and intellectual world; as if there ever was any
other mode of discovering the facts and laws of mind than the
same processes, observation, and generalization, that apply to
the material world. In short, he brings us round by a series
of verbal ambiguities to the question of Free-Will and Neces-
sity, which becomes thus a principal turning-point of the
controversy as to whether Logic should, or should not, be
confined to Deduction.
The combined force of these five positions does not appear
to establish either of the two allegations, namely (1) that a
criterion of material truth is not only impossible, but self-
contradictory, or (2) that to enlarge the field of Logic, is to
assign it no definite field. We shall not here attempt a direct
reply to the first, inasmuch as the exact basis of inductive
truth will be fully considered in another place. (Appenpix D.)
The second allegation is a challenge to assign a definite boun-
dary to Logic, while over-stepping the limits of the Formal
Logic. ; Bhi
Mr. Mansel puts so much more stress on the Theoretical
than on the Practical side of Logic, that he would not be satis-
fied with a reply based on the practical side. Let us enquire, —
then, whether a Theoretical Logic, embracing Induction, could
be laid out and so circumscribed as not to be confused with
any other scientific department, such, for example, as Mathe- —
matics, Physics, or Psychology. Pa
In the InrropuctTioNn, we have indicated a field of Theoretical —
Logic, according to the larger meaning of the Province; and
SCOPE OF THEORETICAL LOGIC. 645
in Apppnpix A; we have given Mr, Spencer's survey of the
field in the same larger meaning. In summary, we may repeat
9 topics.
he Laws of ConsistEncy, or Equivalence of Propositions,
—€ understood as the Laws of Thought. These give
necessary (in the sense of analytic) inferences. They also
give, in the view of Hamilton and Mansel, the basis of the
Syllogism.
_ IL The Laws of Depucrivz or Mediate Inference, as repre-
sented by the Dictum de omni et nullo. This we hold to be
more than mere Self-consistency, or Equivalence. It might be
called Mediate Consistency, the consistency of a conclusion with
two conjoint premises, as contrasted with the consistency of
an equivalent transmutation of a single proposition. Mr.
Mansel would hold that this consistency is necessitated and
self-evident; and such an impression is not uncommon with
thinkers generally. In opposition to that view, we have con-
tended that nothing less than the induction of material in-
stances would justify the conclusion.
Ill. The Law of the Uniroxmity of Nature, which is the
basis of all material truth, and of all induction; consequently
the basis of the syllogistic axiom of mediate consistency. The
consideration of this law may well precede the ordinary sciences,
for itis an assumption running through themall. It may, there-
fore, receive its first announcement in the science that deals
with the criteria of all truth, namely, the separate science of
Logic. It is followed out into a series of formule, known as
the Inductive Canons, which, in their own sphere, may be com-
pared with the syllogistic forms, in the Deductive sphere.
Now, it seems to us, that a science may be constructed so as
to include the Laws and Formule of Immediate Consistency,
Mediate Consistency, and General Uniformity, without trans-
gressing the sphere of any other science. It need not run into
Mathematics, the kindred Formal Science; it need not trespass
on the Physical Sciences, merely because it considers the pos-
tulate necessary to them all, that is, Uniformity; it need not
run into’ Psychology, although it derives from that science the
_explanation of the ultimate nature of Knowledge, as Difference
and Agreement. And there does notappear to be any other
conterminous region.
But we cannot concede to Mr. Mansel that Logic is essen-
tially, or in the main, a theoretical science, and only incident-
ally practical. We contend that the science would never have
heen called into existence, but for its supposed practical utility.
646 THE PROVINCE OF LOGIC,
Indeed, the same might be said of its splendid giant brother, —
Mathematics. However agreeable and recreative to some ~—
minds may be the contemplation of this great creation of ages,
yet, but for the necessities and difficulties of measurement, it
would never have been heard of. Mr. Mansel supposes a race
of intelligent beings, subject to the same laws of thought as
we are now, but incapable of transgressing these laws; and
declares that in the presence of such a race, the Logie of the
Formal Concept, Judgment, and Syllogism, would remain the
same. Unfortunately even for the illustration, there is a
fallacy of Relativity in the very statement of the case. Toa
being that never committed an error, truth and error would
be alike unmeaning; to appreciate the valid moods of the
syllogism, as contrasted with the invalid, such a being would
have first to be told of an erring race, capable of confounding
the two. Only after Adam fell did he know good and evil;
only by committing fallacies is any one competent to under-
stand Logie.
Postponing for a little the enquiry into the prictioal oi
of the Inductive extensions of Logic, we shall advert more
particularly to the distinction of Form and Matter, on which
so much stress is laid in the present dispute. To some Formal
Logicians the distinction does not appear in all respects satis-
factory. Thus, Dr. Thomson (Outline of the Laws of Thought,
§ 15) remarks :—‘ The philosophic value of the terms matter
and form is greatly reduced by the confusion which seems in- __
variably to follow their extensive use. Whilst one writer ex-
plains form as ‘the mode of knowing’ an object, another puts _
it for ‘distinctive part,’ which has to do with the being or
nature of the thing rather than with our knowledge of it 5 8
where it means ‘shape’ in one place, which is often a mere
accident, in another it means ‘essence;’ so that it may be
brought to stand for nearly opposite things. I will add, that —
probably there is no idea which these terms represent that
ue be conveniently expressed by others, less open to con-
usion a
Mr, De Morgan says :—‘ When it shall be clearly vedical ae
out, by definite precept and sufficiently copious example, what
the logicians really mean by the distinction of form and matter, _
I may be able to deal with the question more definitely than —
I can do at this time.’ (Cambridge Transactions, vol. X. Part
II. p. 8.) Again, ‘ The truth is, the mathematician as yeh is
' the only consistent handler +f the distinction, about © es
'FORM AND MATTER. 647
nevertheless, he thinks very little. The distinction of form
and matter is more in the theory of the logician than in his
practice; more in the practice of the mathematician than in
his theory.’ (Syllabus, p. 48).
Hamilton illustrates Formal Truth in Mathematics thus :—
‘To the notions of Space and Time, the existence or non-
existence of matter is indifferent. If matter had no existence,
nay, if space and time existed only in our minds, mathematics
would be still true; but their truth would be of a purely
formal or ideal character,—would furnish us with no know-
ledge of objective realities.’ (Logic II, p. 66). But, in another
place, he quotes, with approbation, from Esser, a passage to
the effect that truth consists not in any absolute harmony of
thought, but in the correspondence of our thoughts with their
objects. ‘'Ihe distinction of formal and material truth is thus
not only unsound in itself, but opposed to the notion of truth
universally held, and embodied in all languages.’ (Logic L
106). And again (Reid’s works, p. 687), he remarks of
Reid’s eriticism on the Predicables, that Reid, like our British
philosophers in general, was unaware of the diiference between
the Logical or Formal, and the Metaphysical or Real. The
Predicables are forms or modes of predication, and not things
predicated: in the language of the schools, second notions, not
first.’
Let us adopt Mr. de Morgan’s suggestion, and refer to
Mathematics for examples of Form, in the opposition to Matter.
In so doing, however, we are merely taking up an old subject
under anew name. In Mathematics, we have the most com-
plete development of reasoning by Symbols, called also Abstract
reasoning. ‘There will be other opportunities for examining
the special processes of Mathematics (Loaic or tHe Sciences,
Mathematics). For the present, let us note what bears upon
the question before us. The abstractions of Mathematics, like
all other abstractions, are embodied in concrete instances; the
Form is always given in some kind of Matter. But the
matter needed is so very spare and attenuated, that, by a
stretch of language, we may say it is no matter at all. Yet,
the circles of Enclid are circles of printer’s ink; they have
colour and a definite size. If we compare them with the
round shield of Achilles, or a gorgeous centre ornament in the
roof of a palace, we may describe them as void of matter and
substance ; but they have their own substance, nevertheless.
The symbols of Arithmetic (still more, of Algebra) are
material, although their peculiar shape has nothing representa-
648 THE PROVINCE OF LOGIC,
tive in it. They are the signs of concrete facts—one, two,
three—which are inconceivable by us, except in concrete
instances. The simplest material will answer the purpose— _
bread crumbs, pebbles, mud specks; but we must have, in the
mind, a series of discrete impressions, derived somehow or
other ; even thoughts would do; but we find it easier to work
upon things of sense. Without some concrete basis, we cannot
possess in thought any number whatever. This is merely to
repeat the received nominalistic view of Abstract Ideas.
There is, however, an important step that can be made in
Mathematical Reasonings, whereby we can altogether leave out —
of sight the concrete things (which is to refrain from realizing
the very meanings of the numbers that we are handling). We —
can devise rules of operating upon the symbols, which, when ~
duly constructed and checked by the proper precautions, will —
give us the same results as actual experiments upon the con-
crete numbers. Having constructed our decimal notation,
we can base upon it a multiplication table, containing equiva-
lent formations of numbers; and by mere force of memory,
recalling these symbolical equivalents, we can perform opera-
tions of multiplying, without thinking of the concrete numbers
at all. In getting out the product of 94 by 116, we can leave
the world of numbered realities out of view for the time: com-
ing back to it only when the product has to be practically
turned to use. .
Now, by this dwelling among symbols, and rules and signs
of operation, we are as far away from Matter, or things in the ©
concrete, as we can possibly be. If anything represents pure —
Form, the multiplication table does. The higher operations of _
Algebra keep us for longer periods withdrawn from concrete
reality ; but the principleis the same. Thesymbolical creations
are more numerous, the rules of operation more complicated,
the operations themselves more protracted; yet there is no-
thing new in the principle of working. . hpet
The question then arises, Do these rules of operation upon —
symbols bear out the pretensions of Formal Logic, as to the —
self-evident, necessary, and non-material character of Formal
Thinking? Are all such rules, in their origin, completely
withdrawn from the tests of concrete experience, as they are in
the working? The full answer to this question is the theory |
of Deductive Reasoning in general, and of Mathematical Rea-
soning in particular. It is enough here to make two observa-
tions. First. If it be true, as the a posteriori thinkers maintain,
that the final axioms of all Mathematics,—on which repose th
FORMAL RULES OF OPERATION. 649
rules for Arithmetical sums, for Algebraic equations, and for
Geometrical demonstrations,—are inductions from experience,
then these various rules of operation have, after all, a purely
material source, and are not evolved by the mind in abstract
or formal thinking. .
But secondly. It is notorious and undeniable, that the rules
of operation, before they are trusted to, are tried and checked
by the results. A great many of them are so paradoxical, so
unpromising, and even repugnant, to the ordinary mind, that
they are admitted only because of their being instrumental in
bringing out true results (as proved by reference to the
matter). Who would put faith in such a rule as ‘ minus mul-
tiplied by minus gives plus,’ unless fully assured by concrete
trials that it leads to correct conclusions? The impossible
quantities of common Algebra, the infinitesimals of the higher
Calculus, have been a perpetual stumbling-block, as regards
their Form ; their sole justification is the test of actual facts.
Seeing how many ingenious tricks can be played upon us
_by formulas and formalities, the most unexceptionable in their
appearance, there probably is not a single rule in the whole
compass of Mathematics that any reflecting person would trust
to merely as a ‘ Law of Thought,’ without an appeal to the
matter by actual trials. The reason why we are so confident
in these rules, is that their verification is so easy, and has been
so complete. But in the absence of verification, we should be
very chary indeed in admitting such rules as the multiplica-
tion and division of fractions, vulgar and decimal, the extrac-
tion of the cube root, and the like. We have often been
deceived by more plausible formalities than these ; dolus latet
im generalibus, is true of all alleged ‘ Laws of Thought.’
The same remark as to the necessity of inductive verifica-
tion applies to Logical Forms. Not one of the valid moods
would be received by mankind upon formal evidence alone.
The dictum seems very evident, the nota note even more evi-
dent; but the nota note conducts us most plausibly to false
conclusions, until by examination of the actual cases we have
laboriously fenced it with circumlocutions and qualifications.
_ When we examine carefully the various processes in Logic,
we find them to be material to the very core. Take Conversion.
How do we know that, if No Xis Y, No Yis X? By exam-
ining cases in detail, and finding the equivalence to be true.
Obvious as the inference seems on the mere formal ground, we
do not content ourselves with the formal aspect. If we did,
we should be as likely to say, All X is Y gives All Y is X; we
650 THE PROVINCE OF LOGIC.
are prevented from this leap merely by the examination of
cases. itm N07
Again, the laws of Hypothetical Equivalence are dependent
on our knowledge of the material circumstance called Plurality
of Causes, but for which the formal directions as to Hypor
thetical Inference would be quite different. oa
Mr. Mansel complains that the rules of Definition commonly.
given in logical treatises are extra-logical; that is, they step __
out of Form into Matter. The charge is well founded; the _
writers obviously felt that Definition, confined within the —
narrow limits of the Formal, would be a very meagre affair.
What would be logical defining in strict form? Why,
this. A Formal Definition consists in giving, as the marks of —
the thing defined, the marks of some higher Genus, together
with the Diffinendei We have, then, these forms:—The
Genus together with the Difference (in Connotation) is the
Species; the Species minus the Difference is the Genus; the
Species minus the Genus is the Difference. Thisis the whole |
theory of Defining, according to Formal Logic; and it is worth |
nothing. me
Still more would a logic of Classification, to be of any value, a
trench upon material considerations. Logical Division is
another name for classification. The rules of Logical Division —
are Formal, but they have to be held in check by the —
otherwise they may lead us astray. >
It may be maintained that Deduction and Tndtiebteh are —
properly continuous operations; they are the parts of one ~
whole. Within certain small limits, Deductive processes are
possible, upon rules of symbolical operation solely, these having —
been well fenced by a study of the matter ; but real deduction, %
the extension of a principle to new cases, supposes an exami-
nation of the cases in their concreteness or actuality, exactly —
as in the inductive generalization of the rule. The judge who —
applies the law must look to the matter; he must not commit —
paralogisms of form; but he cannot stop short at mere formal A
correctness. sdf
Within the Inductive sphere, we might construct rales of
Formal operation, such as ought to commend themselves to ¢
rigid formalist. Thus, A, B, and C, being joint causes of an-
effect X; if A be foducadl: in sittin ts B or C must be corre
pondingly raised to keep up the effect; if A be increased; 4
others are so far dispensed with, and so on. These are e:
mathematical considerations, which: wa':kniows to. be corr
=
10 |
4
VALUE OF A LOGIC OF INDUCTION. 651
generally, and can therefore use formally without regard to
the matter.
But the question at issue cannot be adequately stated, unless
we view Logic as a Practical Science. If its practical character
is conceded, the propriety of extending the Province rests
upon the utility of rules for Induction. The presumptions in
favour of such rules are these :—
First. It is admitted that Aristotle included in his scheme
both Deduction aud Induction, however imperfect may have
been his view of their respective spheres, and however inade-
quate may have been his handling of Induction. Thus, the
testimony of the Founder of Deductive Logic is opposed to its
exclusive pretensions. |
Secondly. In the table of Fallacies, sketched by Aristotle,
and retained by the scholastic logicians, with slight modifica-
tions, there are comprised Fallacies of the Matter, and of
these some are fallacies of Induction (non causa pro causa, S§c.).
From this we may infer, that, in the opinion of logicians
generally, people are liable to commit mistakes in regard to
matter, no less than in regard to fourm. We may infer farther,
that it is not useless to give a reminder of these material and
inductive mistakes, which is, in fact, a Logic of Induction.
Thirdly. The scholastic period was marked by an almost
exclusive attention to the formal or Syllogistic part of Logic.
At the revival of letters and philosophy in the 15th and 16th
centuries, public opinion revolted against the narrowness of
the conception, and found a spokesman in Bacon, who inaugu-
rated, amid very general applause, a Logic of Induction. For
the last two centuries and a half it has been the pride of
both physical and metaphysical philosophers to call themselves
his disciples as regards the methods of pursuing science and
philosophy.
Fourthly. The renovated Physics, or Natural Philosophy, of
Galileo and Newton was accompanied with a professed Logic
of Induction—the famous Regule Philosophandi prefixed to
the Third Book of the Principia. These rules, meagre as they
are, were a guiding star in physical research to the enquiries
of the 18th century.
Fifthly. In the present day, when physical science has been
s0 far advanced as to exemplify sound methods of procedure,
the most distinguished physical philosophers still feel and ac-
knowledge the need of a systematic guide to research, for the
more abstruse and subtle departments. The Introduction to
652 THE PROVINCE OF LOGIC .
Natural Philosophy, by, Sir John Herschel, and the ssdoagil «
and Logic of the Inductive Sciences, by the late Dr, Whew ell
are testimonies to this want.
Sixthly. Since the publication of the work of Mr. Jahn. 4
Stuart Mill, in which the Inductive Logic is methodized with —
a completeness previously unknown, applications have been —
extensively made of the Inductive canons to the Experimental —
Sciences. The investigations of Medical science have especi- —
ally profited by Mr. Mill’s teaching; a higher and surer stan-
dard of evidence has taken the place of the loose eeaitiads 08
reasoning formerly prevalent. ui
Seventhly. The Science of Politics is an equally atribiniist >
ample. The valuable work of Sir George Cornwall Lewis on —
the ‘ Methods of Observation and Reasoning in Politics,’ makes _
perpetual reference to the Inductive Logic of Bacon, Her-
schel, Whewell, and Mill, and only once or twice alludes to ©
Formal Logic, although the author’s education was such as to
incline him to view that department with the utmost possible —
favour. He complains strongly of the wide-spread abuse. of
the Method of Agreement (the enwmeratio simplew of Bacon)
in Politics, as mm other subjects; and endeavours by Per
and by example, to counterwork the vicious tendency. ;
Kighthly. Sir William Hamilton occupies a considetablal j
portion of his Course on Logic (nine Lectures out of Thirty-
six), with Modified Logic, in which he considers Truth and —
Error, on the material side; Observation; Induction; the —
Credibility of Testimony ; and various other points related to,
the acquisition and communication of knowledge. The plan —
of his course would have allowed him, without contradicting
his views of the Province of Logic, to have gone as minutely —
as Mr. Mill does, into Induction, and the operations a
to Induction, such as Classification and Naming. ify heh
Dr. Thomson, in his Laws of Thought, follows the example
of Hamilton, in ‘the enlargement of the Province. In Part IV.,
entitled ‘ Applied Logic,’ he considers (shortly) the Search for —
Causes, the Inductive Methods, Definition, Analogy, Chance, —
Classification, Fallacies generally, and the Division ofr the
Sciences. | Alt
C.—ENUMERATION OF THINGS. ¢ S As
The Classification of Names (p. 61) leads.by a ‘paiell al
transition to the Classification of Things. Moreover, in order i
to establish the most generalized propositions, we must nee 288
correspondingly generalized Notions, tae
_ BASIS OF RELATIVITY. 653
_ The totality of Existing Things may be divided in various
ways, under different principles of classification and division.
We may partition the whole universe into Celestial Bodies
and Terrestrial Bodies; into Minerals, Plants, Animals ; into
Solid, Liquid, Gas; into Ponderable and Imponderable ; into
the Four Hlements of the ancients, which division crudely
gives the three states of matter, and the imponderables—Heat,
Light, &c. Lastly, we may make a division into Matter and
Mind. These various modes of sub-dividing the totality of
things are useful for their special purposes. The purpose of
the Logician is to arrive at a division that will correspond to
the distinct methods of enquiry, so as to partition the field of
knowledge according to the best division of intellectual labour.
We begin by re-stating, as an essential preliminary, the
principle of Universal Relativity, by which all objects of know-
ledge are two-sided, or go in couples. This statement is
necessary to obviate the error, committed by Aristotle and
others, of placing ‘ Relation’ in an inferior or subordinate
place in the classification. If Relation is recognized at all, it
is fundamental and independent; everything comes under it,
it comes under nothing. The supreme position given by
Logicians to the ‘ Law of Contradiction’ is a mode of admit-
ting this primary fact.
I. The deepest of all Relations is Opsecr and Sussect, com-
monly called Mind and Matter, the External World and the
Internal World.
When we pass from being engrossed itl pleasure or pain
to the consciousness of some extended thing, as a tree, we are
affected with a marked shock of difference; we have made a
transition the broadest and deepest that the mind can ever
pass through. These typify the two ultimate or final modes of
the human consciousness ; they mutually constitute each other,
on the principle of Difference or Relativity; they cannot,
therefore, be resolved one into the other, or into any more
fundamental experience. The contrast must be accepted as
the chief division of all things, on the principle of dividing
upon the maximum of difference. One portion of knowledge
we term the Object world, the Extended World, and, less
correctly, Matter, and the External World. The other portion
we call the Subject world, the Unextended Mind, and, less
properly, the Internal World. Indeed, when we talk of these
two departments as dividing between them the universe of
existence, we are using fictitious and unmeaning language;
the ultimate universe, according to the law of Relativity, is a
654 ENUMERATION OF THINGS.
couple; the highest real grouping of things is this ‘lag:
grouping, called Object and Subject, &e. These are “the
proper swmma genera. Hxistence is a mere name. .
If. Ossucr has been variously represented and aisle
Some have contended that it is an ultimate fact, given in our
earliest consciousness. Others have resolved it into simpler —
states of the mind. ‘The different views on this subject be- 3
long to the Metaphysical and Psychological question called |
the ‘Theory of External Perception.’ We here assume that the 4 =
notions expressed by ‘ Object’ and ‘ Subject,’ can be analyzed, a
and we give one mode of the analysis. Object means (ia
what calls our muscular and bodily energies into play, as Stipe | i
to passive feclings; (2) the uniform connexion of definite feel- 7
ings with defimte enerytes, as opposed to feelings unconnected
with energies; and (3) what affects all minds alike, as opposed
to what varies in different minds. wae
(1) The greatest antithesis existing among the phenomen a
of our mental constitution is the antithesis between the Active —
and the Passive ; the muscles (with the out-carrying nerves) —
being the bodily instrument for the one, the senses (with the —
in-bringing nerves) being the bodily instrument for the other.
To this fundamental antithesis we are able to link the opposi-—
tion of Object and Subject. Although developed by other
circumstances, the contrast appears to be rooted in our Grotaat t
Psychological contrast. ns
(2) The circumstance of our feelings being definitely cherie
with definite active exertions on our part is a most notable ac-
companiment of our objectivity. When we move across @
room, and feel our optical prospect definitely ante
passions and emotions.
(3) It is a characteristic of the Object world, that differ
persons are affected in the same way. Those definite ae
sense, accompanying definite movements, as in walking
a street, or in entering a room, arise in each person alike
other class of feelings—hunger, fatigue, fear—run a ditt
course in different persons. rs
These are probably the main features of the fandaindhel
trast of Subject and Object; other subsidary cinched
been pointed out, but their discussion is not suitable to this 5
ATTRIBUTES OF BOTH OBJECT AND SUBJECT. 655
_ IIL. The Supsecr is explained by what has been said of the
Object ; it concerns our passive states; our feelings not de-
finitely changed with definite energies ; and the states wherein
different persons vary in the same circumstances.
IV. There are attributes common to Object and to Subject,
and attributes special to each.
Notwithstanding the fundamental contrast of these two ex-
periences, we can affirm some attributes of both. Thus, within
the sphere of each, we are variously affected; we recognize
object distinctions and subject distinctions. So we identify
and compare object facts with one another, and subject facts
with one another. From the very nature of human know-
ledge, these possibilities of discerning agreement and difference
must hold in both departments. Hence :—
First. The contrasting attributes of Lixennss and UNLIkz-
ness belong equally to Object states and to Subject states. We
identify and discriminate magnitudes, forms, colours, &.,
which are object facts; we identify and discriminate pleasures,
pains, volitions, ideas, which are subject facts. Hence, affir-
mations of likeness or of unlikeness may apply to every kind
of knowledge whatsoever. Being in fact the fundamental cir-
eumstances that define and constitute knowledge, such aflfirma-
tions are analytical propositions.
Secondly. Quantity or Degree belongs to both states. This
is Agreement and Difference in one important fact or feature,
called more and less; the states of the subject mind are all
of varying amount or intensity, as well as the states of the
object consciousness, which we call object properties—size,
weight, hardness, &c. We may and do predicate quantity,
therefore, of everything knowable. The laws of Quantity, of
which Mathematics is the complete developement, pervade all
modes of existence. It is true that numerical calculations are
mostly confined to object properties—as space, dimensions,
weight, and so on; we have no numerical ratios in pleasures
and pains. This circumstance, however, which is a great
drawback to the science of mind, is not due to the absence of —
degree from mental phenomena, but springs from our inability
to set up an exact common standard of degree in the states of
the mind, and to take precise measures according to that stan-
dard. We are conscious of inequalities in our pleasures,
emotions, and desires, but we have a difficulty in fixing the
degrees in an understood expression, such as may be communi-
cated to others, and permanently recorded.
It is usual to specify the leading modes of Quantity under
656 ENUMERATION OF THINGS.
Intensity, Duration, and Extension: the last being a uaa
special to the object. Intensity and Duration apply in’ both |
regions of phenomena. Intensity is usually marked with Te-
gard to each special property—intensity in colour, heat, pres
sure, &c. Duration, which is a degree of continuance, is more
commonly abstracted from things, and enters into that great —
and all-comprehending generality, called Time, to be noticed z
more fully under next head. ninety
Thirdly. The great and important contrast named Co-existe
ENCE and Succession is found in both departments of pheno- — :
mena. Oy PRs
Co-existence is not an ultimate experience of the mind. |
We begin with modes of Succession, which are developed into |
Co-existences. vi
To the mind, which, with very slight qualification, can —
attend to but one thing at a time, all distinctive states of con-
sciousness are successive. Succession is the law of our mental
being. The succession may be rapid or slow, which accep gi
the estimate of duration above noticed. In succession —
grounded the important fact called Number or Discrete aca
tity, as opposed to the measure of continuance, or Continuous”
Quantity. We identify groups of successions as twos, 0
threes, fours, and so on. Thus the forms and modes of Quan- —
tity are involved in the modes of succession of our sensations,
feelings, and thoughts. to TS ae 7
Duration and Succession (with Number) thus belong alike
to states of the Object and states of the Subject. The eleme nb
of Time, which is duration and succession generalized to the
utmost, ‘and reduced to a common measure, 1s @ propel if
both worlds ; ; a circumstance that has been noticed Pon the
very beginning of philosophy. “aE
The predicate of Succession also involves order of ped rity,
which can apply to object and to subject states equally,
Co-existence is an artificial product, a peculiar mode of suc es
cession, which in its highest form is Simultaneity in Speen r
Extension, a property of the Object sphere exclusively. There
attaches to Mind an inferior mode of Co-existence, the 20+
existence of two or more awakened sensibilities at one momen
of time. bsanids : oe
Of Attributes common to both spheres, we naval thus - uike
Unlike, Quantity, Succession, Co-existence ; but as the predi
cation of Like-Unlike in the widest sense is, from the nature
of knowledge, a purely identical proposition, we need stat
only Quantity, Succession, and Co-existence. These ar
ATTRIBUTES SPECIAL TO THE OBJECT. 657
three attributes assumed as distributing knowledge into differ.
ent heads of Logical Method.
_V..The attributes special to the Ossxcr, are as follows :—
(1) Hatension—This property is the fundamental circum-
stance of the object world, the one fact common to whatever
is not mind, or not subject. When we are in a purely subject
state, as a pleasure or a pain, we have no consciousness of ex-
tension or space. The distinction between extended matter
and the unextended mind, explicitly made in the 5th century,
A.D., was the commencement of correct views of mind and
matter.
Psychologically considered, Hxtension is a mode of our active
or moving energies, assisted by our senses. Motion is essen-
tial to the consciousness of things as extended. Extension is
a real property whether with or without matter; as scope for
motion, evenempty space is an actuality. The total of the
Hxtended World is sub-divided imto Extended Matter and
Extended Space without matter.
(2) Resistance, Inertia, Momentum, or Force.—This is the
characteristic property of Extended Matter, in its opposition
to an Extended void. The putting forth of our energies in
the peculiar mode called Resistance is perhaps the simplest
situation that we can be in, as regards the active side of our
being ; hence, resistance may be considered our fundamental
consciousness of the object world. Resistance is Matter; the
giving way of resistance, followed by movement, is Space. In
no subject state have we the peculiar sensibility called force,
energy, or resistance; where that feeling is present, we apply
the name matter.
fixtension and Inertia are the two generic facts entering into
the long known group of attributes called the primary qualities
of matter; the radical and identifying peculiarities of the
so-called external and material world. Still, these are in close
association with other properties, based on passive sensibility,
or sense proper, as colour, tactile feeling, &c. (secondary
qualities) ; which properties, of themselves, would not be
object properties, but become so by their dependence upon the
object class.
(3) Colour.—The pure and proper sensibility of the eye, the
susceptibility to mere light, is not properly an object fact.
The conjunction of the feeling with visual extension (the mus-
cular sensibility of the eye), and with locomotion, is necessary
to give objectivity to light and colour, Our notion ot the
extended or simultaneous in space is based on movements, but
658 ENUMERATION OF THINGS. ©
filled up and defined by our optical sensibility to (eden i.
light. Our feelings of illumination are definitely connected —
with definite movements and in that way comply with one ¢ of ;
the grand conditions of objectivity. a
(4) Touch.—The commonly recognized sense of Touch is a
compound of muscular energy with pure skin sensibility. —
This last, or touch proper, is scarcely ever separated from th 2
fundamental experience of Force or Resistance (we may make —
the separation by supporting the outstretched arm or leg).
Hence, touch is adopted and embodied among object properties. —
The tactile effects, called hard, soft, rough, smooth, are ‘eali= 2
ties of Matter.
Sight and Touch are the senses most completely i incorpora ed
with our activity, or with our object experience. The remain-
ing senses have a looser connexion with our energies, but, so
far as connected, we rank their indications among object,
qualities. i
(5) Sound.—Mere noise might be a form of simple subjec-
tivity. When related to movements, as when steadily increasing
or diminishing with our locomotion, it falls into a connexion”
with objectivity. So regularly is this connexion observed, th a
the fact is enrolled among properties of matter. zs
(6) Odour.— An exact parallel to Sound. The objectivity
of odour is established by its definite changes under ges is
movements on our part. m
(7) Taste.—There is here a compound ofa peculiar sensibili iy
—the proper gustatory feeling—with touch proper ; whence
Me comes readily into the object sphere.
(8) Heat and Cold.—This property needs no other comme ot
than the foregoing remarks on Sound and on Odour.
The various organic sensibilities of our body—Diges
Respiration, &c.—have a strongly subject character; yet,
contract object relationships whenever they are defin
changed with definite movements, as when we connect re
tion with taking food, or suffocation with impeded breathing.
But, in so far as they suggest no activities, or attitude
energy, they are pure subject states, modes of self-conscions!
These are the various sensible properties of the sp
‘matter’ in the genus ‘extended ;’ they are the mode
primitive sensibility that we call material. There are o
properties of a more subtle and abstruse kind, arrived
the help of our intellectual processes—such as we call A
tions, Repulsions, Molecular structure and arrangements-
which are necessary to completeness in the enumeration. — Bi
os.
=
seme p
=
ATTRIBUTES SPECIAL TO THE SUBJECT. 659
The Sciences of the so-called External world are occupied
with the various attributes now described. One portion of
Mathematics is occupied with quantity in Extension; Mechanics
embraces the essential fact of Matter, together with its other
incidents; Physics and Chemistry include Light, Sound, Odour,
Heat, &e.
VI. The attributes special to the Sunszcr are the defining
marks or essential attributes of Mind—Feeling, Will, and
Thought. All these are in full antithesis to the great object
facts, as above detailed.
Of Feelings, the greater part are pleasures and pains, which
are our most unequivocal types of subjectivity. We never
confound two such things as comfortable warmth, and lifting a
chair; the heterogeneous is at its utmost stretch in such a
contrast as this.
- Our states of Will, or Volitions, have a purely subject
origin, namely, our feelings, with outcomings in the object
sphere. The two departments are here, as often happens, in
close proximity, but are not therefore confused. Voluntary
action is always reckoned a special characteristic of mind.
For, although it is activity, directed often upon material things,
yet its origin in the pleasurable and painful modes of sensi-
bility gives it an indelible stamp of the subject.
Our Thoughts, Ideas, or Intellectual states, have in them a
considerable amount of object reference; still there is a broad
distinction between Sensations and Ideas, in the circumstance
that the one class is, and the other is not, connected with de-
finite bodily movements. The succession of our sensations is
in uniform accordance with our locomotive and other move-
ments; the succession of our thoughts is totally different.
Hence, although our ideas are the reflexion or repetition of our
sensations, yet their manner of occurrence assimilates them
with subject states.
In the complex fact called Sensation, we have incessant
_ shiftings of the scene, from the object to the subject. A sen-
sation, as cognisant of extension, resistance, colour, &c., is an
object fact; as a pleasure or a pain, it is subject. Now, un-
mistakeable as the contrast is, wide as is the chasm, we may
leap it a great many times in a minute; we flutter to and fro,
between the pleasurable consciousness of a sensation, and
the intellectual measure of it as a thing of size, form, or
colour.
The sciences of the Subject World have thus to deal with
our Feelings, Volitions, and Thoughts. They have, moreover,
660 ENUMERATION OF THINGS.
to draw the delicate boundary line between the two worl ds, |
to divide the spheres, where they become entangled. _ ie a
Sigs ada
If it were now asked what, in the final analpeuy is the :
nature of predication, we are able to affirm—Attributes of the
Object, and Attributes of the Subject, declared as related in
Quantity, as Co-ewisting or as Successive. a
VII. Sussrance is not the antithesis of all Atghiba tase ba 5
the antithesis between the fundamental, essential, or defining ~
attributes, and such as are variable or inconstant He wal} Bs
From the relative character of the word Attribute, the fancy
grew up that there must be a substratum, or something dif.
ferent from attributes, for all attributes to inhere in. Now
anything that can impress the human mind — Extensi
Resistance, &c., may be, and is, termed an attribute, we seem
driven entirely out of reality, if we would find a something that.
could not be called an attribute, and might stand as a sub- e
stance, +e
But ‘substance’ cannot be rendered by non-entity. T
antithesis that we are in search of is made up without
violent a supposition. Substance is not the absence of ¢
attributes, but the most fundamental, persisting, inerasible, or
essential attribute or attributes in each case. ‘The substance
of gold is its high density, colour, lustre, &c.—everything that
we consider necessary toits being gold. Withdraw these, a
gold itself would no longer exist: substance and oxpry ti ng
else would disappear. ive ee
The substance of Body or Matter, is the permanent, o
essential fact of Matter—Inertia or Resistance. This is
feature common to everything we call Body—whether §
Liquid, or Gas; the most generalized, and therefore the
ing property of Matter. The remaining attributes of m
vary in each separate kind; they make the kinds or spi
varieties—air, water, rock, iron &e. The real distinction
thus between the Essence and the Concomitants, the Invaria
and the Variable, the Genus and the Species. |
The substance of Mind is no other than the esrogate
three constituent powers— Feeling, Will, Thought. —
present, mind is present; these removed, mind is gone. —
three facts named do oe exhaust shi mind, there mu
some fourth fact; which should be produced and established
a distinct mode of our subjectivity. The substance would
be four-fold. But the supposition of an ‘ego’ or ‘self,
powers to inhere in, is a pure fiction, coined from non-¢
- MILL’S CLASSIFICATION, 661
by the illusion of supposing that because attribute applies to
something, there must be something that cannot be described
Mr. Mill, as the result of his analysis, gives the following as
an enumeration and classification of all Nameable Things :—
‘1st. Feelings, or States of Consciousness,
‘2nd. The Minds which experience those feelings.
‘3rd. The Bodies, or external objects, which excite certain
of those feelings, together with the powers or properties
whereby they excite them; these last being included rather in
compliance with common opinion, and because their existence
is taken for granted in the common language from which I
cannot prudently deviate, than because the recognition of such
powers or properties as real existences appears to be warranted
by a sound philosophy. —
‘4th; and last. The Successions and Co-existences, the
Likenesses and Unlikenesses, between feelings or states of
consciousness. Those relations, when considered as sub-
sisting between other things, exist in reality only between the
states of consciousness which those things, if bodies, excite, if
minds, either excite or experience.
‘This, until a better can be suggested, may serve as a sub-
stitute for tne abortive Classification of Hxistences, termed
the Categories of Aristotle. The practical application of it
will appear when we commence the inquiry into the Import of
Propositions ; in other words, when we inquire what it is
which the mind actually believes, when it gives what is called
its assent to a proposition.
‘These four classes comprising, if the classification be cor-
rect, all Nameable Things, these or some of them must of
course compose the signification of all names; and of these,
or some of them, is made up whatever we call a fact.’ (Logic
Book I., Chap. III).
The Categories of Aristotle.
We owe the Categories to the opposition made by Aristotle
to Plato’s Realism of Universals. Plato viewed Hns or Real
Being as belonging only to Universals separated from their
particulars; they only being permanent as contrasted with
the Generated and Perishable. Aristotle held, on the contrary,
that Real Being attached only to the Particulars ; that certain
varieties of Being might be predicated of an individual—Hoe
aliquid, That man, This horse, &c.—but that no Being had
662 ENUMERATION OF THINGS.
any reality apart from the individual. The varieties of E
that might thus be predicated of a particular individual,
enumerated in a schome known 48/the Categories («aty yop
Predicamenta). They are as follows :-—
1. Oveta—Substantia—Substance.
2. Tooov—Quantum— Quantity.
3. Tovev—Quale— Quality.
4. Tpos 1—Ad aliquid—Relation.
5. lod—Ubi—Location.
6. Tlore—Quando—Period of Time.
7. KetoOac—Jacere—Attitude, Posture. aga
8. "Exew—Habere—Hquipment, Appurtenance, Property. i
9. Tlovetv—F'acere—Active Occupation. tikes
10. [1doxew—Pati— Passive Occupation.
Mr. Mill points out the more obvious defects of the. Cat
gories considered as an enumeration of Things. aOR
‘The imperfections of this classification are too obvious t
require, and its merits are not sufficient to reward a minu ie ne
examination. It is a mere catalogue of the distintic
rudely marked out by the language of familiar life, w ao
little or no attempt to penetrate, by philosophical analgeie O-
the rationale even of those common distinctions. Such an
analysis, however superficially conducted, would have shown
the enumeration to be both redundant aad defective. ‘Som eo.
objects are omitted, and others repeated several times under
different heads. It is like a division of animals into men,
quadrupeds, horses, asses, and ponies.’ a
Hamilton endeavours to obviate this last obioonte by c
ing it into a scheme of successive grades of subordination. .-
elucidation is as follows :—‘ Being (70 ov, ens) is primal
divided into Being by itself, (ens per se), and Being by accid
(ens per accidens). Being by itself corresponds to the -
Category of Aristotle, equivalent to Substance: Being
accident comprehends the other nine, but is, I think, m
properly divided in the following manner :—Being by accid
is viewed either as absolute or as relative. As absolut
flows either from the matter, or from the form of tinge |
from the matter,—it is Quantity, Aristotle’s second category
If from the form, it is Quality, Aristotle’s third a
relative, it corresponds to Aristotle’s fourth category it
and to Relation all the other six may be reduced.
The arrangement would stand thus :— —
“an .
4 ai erry
cn
HAMILTON ON THE CATEGORIES, 663
L Substance (1)
. Quantity (2)
Il. Attribute <~ Quality (3)
Relation (4) /Place (5)
Time (6)
Posture (7)
Appurtenance (8)
Activity (9)
Passivity (10)
There is no evidence that Aristotle saw the division in this
light; if he had done so, he might have adverted to the mis-
placement of ‘ Relation,’ which, if it includes any of the others,
equally includes them all; Substance and Attribute, Quan-
tity, Quality—are all relationships. Still, the arrangement is
useful as showing how some of the worst defects may be
remedied, and as an aid to remembering the list. The four
first are easily remembered; the remaining six (under Relation)
may be cast into three couples—Place and Time, Activity and
-Passivity, Posture and Possession or Appurtenance.
The Categories do not seem to have been intended as a
classification of nameable things, in the sense of ‘‘ an enumera-
tion of all kinds of Things which are capable of being made
predicates, or of having anything predicated of them.” They
seem to have been rather intended as a generalization of pre-
dicates, an analysis of the final import of predication, including
Verbal as well as Real predication. Viewed in this light, they
are not open to the objections offered by Mr. Mill. The pro-
per question to ask is not—In what Category are we to place
sensations, or any other feelings or states of mind, but—Under
what categories can we predicate regarding states of mind P
Take, for example, Hope. When we say that it is a state of
mind, we predicate ‘substance :’ we may also describe how
great it is (‘ Quantity’), what is the quality of it, pleasurable
or painful (‘ Quality’), what it has reference to (‘ Relation’).
Aristotle seems to have framed the Categories on the plan—
Here is an individual: what is the final analysis of all that we
can predicate about him P
The proper comparison of the Categories is to the Predi-
cables, and to the Import of Propositions, or the Universal
Predicates. Comparing the Categories with the Predicables,
we see that through both runs the distinction between Funda-
mental and Concomitant, Essential and Accidental. The four
_ predicables, genus, species, differentia, proprium, are predications
of ‘substance :’ accidens,—concomilance (vp BeByxos) embraces
29
664 THE UNIVERSAL POSTULATE,
all the categories except substance. Other categories than "9
substance might be propria, or predications deduced from #l 10 %
ussence of the subject; but it is probable that Aristotle, in
speaking of ‘fundamental’ and ‘concomitant’ in connectialill .
with the categories, meant to include propria in the category —
of substance. Probably Aristotle’s list of propria had been —
smaller than the list that could be made out now. Secondly, —
if we compare the Categories with the Universal Predicates —
(Co-existence, Succession, Quantity), we see that the Categories
are more superficial and less ultimate than the later analysis. —
The category of ‘substance’ (if we do not include propria) —
belongs to the department of Verbal predication: the remain-
ing Categories are Real predicates, corresponding to the final —
analysis ‘of propositions. As such an analysis, they are open
to the objection of not being ultimate ; for example, the Pee
cations concerning ‘space’ and ‘ time’ may regard ‘co-exist- —
ence’ or they may regard ‘succession.’ More than this, they
are not adapted to any logical purpose; they cannot be gar) a
the basis of logical departments.
While these comparisons show the bearings of the, dates’ =
gories as regards Logic, it should be kept in mind that their
original purpose was simply to exhaust the possible predicates —
regarding an individual, and not either to exhibit a classification —
of nameable things, or to analyze the import of proponieeaay
with a view to the arrangement of logical Se ys
D.—THE UNIVERSAL POSTULATE. ag
The theory of Demonstration supposes that we come at as ;
to something that cannot be demonstrated. Dermonsttyeaeaa
the referring of a fact to a higher generality, already es
blished ; to demonstrate such higher generality would ‘be + jo
find some principle still more general; a few steps must lea
us to something that is absolutely final, something whose e i-
dence is not demonstrative, something believed in withou ot
extraneous support. i ee
The edifice of demonstration is not complete until we clea re
out these ultimate foundations, and state distinctly the natur
of the certainty attaching to them. Let us then ask what a
the facts to be received without proof, as underivable, unde
ducible, undemonstrable P ioe
In probing to the deepest foundations of id wld ae
certainty, there has often been a confusion of two classe
primary facts—the Logical and the Psychological. — oa
Logical primordia are meant the indemonstrable assumptions
TESTIMONY OF CONSCIOUSNESS, 665
at the foundation of all demonstrable truth; by the Psycho-
logical, are meant the elementary sensibilities of the mind,
whence our complex intellectual products are evolved by
growth, ag_ regation, or association. What the logical founda-
tions are, will be stated fully in this note; the Psychological
foundations are the primary sensibilities arrived at in an
ultimate analysis of the mind—such as Resistance, Motion,
Colour, Sound, &c. There may be a partial coincidence of the
two classes of ultimate data; but the coincidence is not neces-
sarily total; and each must stand on its own grounds, The
_ propriety of an Analysis of the mind needs to be established
by evidence; hence it must appeal to some first principles
different from itself; so that the priority belongs to the Logical
foundations of our knowledge.
‘The phrase ‘ Universal Postulate,’ proposed by Mr. Herbert
Spencer, to express the ultimate foundations of certainty, is
adopted from Huclid. While the subject-matter is quite differ-
ent in the two applications, there is this common feature, that
in both something has to be begged on one side and granted
on the other; one person cannot force another person into the
admission. The basis of all reasoning is something mutually
conceded between the different reasoners, When an opponent
accepts a certain first principle, and declares that he will
abide by all its consequences, we may compel him to accept
whatever we can show to be a consequence; but we have not
the same fulcrum with the first principle itself
In reviewing the modes of stating the primary assumptions,
we may commence with the so-called Laws of Thought—
Identity, Contradiction, and Excluded Middle. These, how-
ever, are too limited for our purpose. As explained in this
work, they are laws of Consistency and Equivalence ; the
Formal Logicians suppose them to include also Syllogism, or
Mediate Consistency ; by no one are they held as furnishing a
criterion of material truth.
Hamilton has put forward ‘the testimony of Consciousness ’
as the ultimate and infallible criterion of certainty. He ex-
presses the reference to consciousness in these three maxims
or precautions :— .
*(1) That we admit nothing, not either an original datum of
consciousness, or the legitimate consequence of such a datum.
* (2) That we embrace all the original data of consciousness,
and all their legitimate consequences ; and—
666 THE UNIVERSAL POSTULATE.
‘(3) That we exhibit each of these in its individual agen /
neither distorted nor mutilated, and in its relative er ‘a
whether of pre-eminence or subordination.’ eae Works, eo
747
Res in general terms, this criterion seems cnimpoachable,
But when we come to specific enquiries, we are aware of its
vagueness and uncertainty. Our present consciousness must —
be admitted to be our present consciousness; when we feel —
hungry, we have the fullest certainty that we are hungry.
The question, however, arises—what does consciousness say to
facts in the past, and to facts in the future. And strange as
the thing may appear, people may differ as to what things we
are actually conscious of, as will be seen presently. 4
Mr. Spencer expresses the Universal Postulate under ‘the —
form of the Inconceivability of the Opposite. The only reason —
assignable, he says, for our primary beliefs, is the fact of ‘ in-
variable existence tested by an abortive effort to cause non-
existence.’ When the opposite of an assertion is utterly 4
unthinkable by us, we can do nothing but receive that assertion |
as true. a
The difficulties attending the employment of this test are a
these :
First. The examples that are most in its favour are cases” ;
where the opposite is a self-contradiction. I cannot think that
I do not at present exist, because the two suppositions are in-
compatible ; the attempt is a violation of the law of consistency. —
So,—‘ Motion cannot be thought of without an object that
moves being at the same time thought of’ is an instance where
the two statements give the very same fact; ‘motion’ oN
‘a thing moving,’ are two slightly different " phrases for an-
identical conception. The opposite is pure self contradiction a
Now, for all such instances, a postulate of self-consistency
would answer the same end as a postulate of unthinkableness
of the negation. Eg
Secondly. In assertions where there is not mutual i implica-
tion but difference in things conjoined, the inconceivablene
of the disjunction has arisen from unremitted experience,
indissoluble association. This is the case with extension :
colour; we cannot think of an object as extended with
thinking it as of some colour; the visible form, althou
different fact from colour, has alw ays been embodied
optical impression of colour. Again, ice cannot, without
difficulty, be thought of but as cold; the visible appee
INCONCEIVABILITY OF THE OPPOSITE. 667
of ice and the sensation of warmth are repugnant because of
the strong opposing association. | |
The same remark applies to the (proper) Axioms of Mathe-
matics. The iteration of them in experience creates an almost
indissoluble link of thought in their favour. We are practi-
cally unable to think their opposites. So with the Logical
Axiom of Mediate Consistency.
Now, with regard to this class of beliefs, it is an open ques-
tion, whether the stress should be laid upon the acquired
inconceivableness of the negations, or upon the circumstance
that has brought about the inconceivableness, namely, the
unbroken iteration of the facts. Whether are we to lay hold
of the primary condition, or of its consequence or concomitant ?
There seems to be a presumption in favour of the primary
condition, namely, the unbroken experience.
Mr. Spencer himself attributes our inability to conceive the
opposites of axioms and other strong beliefs to the experience
of the race accumulated and transmitted to us. ‘ Objective
facts are ever impressing themselves upon us ; our experience
is a register of these objective facts ; and the inconceivableness
of a thing implies that it is wholly at variance with the re- |
gister.’
Thirdly, There are propositions admitted by us to be uni-
versally true, but whose opposites we can well conceive.
Such is the law of gravity. We can easily suppose that law
to be suspended. ‘The reason in this case is, that although the
greater number of unsupported bodies fall to the ground, some
do not; smoke and dust may be seen ascending. We learn to
regard these as exceptions, but they prevent us from having
an overpowering strength of association between the absence
of solid support and the descent of a body to the ground.
Fourthly. Some examples given as unquestionable applica-
tions of the principle of Inconceivableness are denied by a
whole school of thinkers. Both Sir W. Hamilton and Mr.
Spencer maintain that we are under the necessity of believing
the Persistence of Force; that we cannot conceive either
Matter or Force as absolutely created or absolutely destroyed.
It is under the first kind of inconceivableness (where the
opposite is a self-contradiction) that this case is brought; there
is no attempt to affirm it on unbroken experience. The
self-contradiction, however, is by no means apparent; Force is
one thing, and its commencement or termination is seemingly
a different thing. That aspect of Force whereby, in communi-
cating itself, it loses the numerical equivalent of what is
668 THE UNIVERSAL POSTULATE,
communicated, becomes familiar to us after we are educated in —
mechanical facts; and we are then prepared to receive the ~
doctrine of Persistence. But prior to this experience, which, —
to be sure, is requisite to a clear and precise cognition of —
Force, we can form a conception of force beginning we know ~
not how, and ending we know not how. We are not at first
struck with any self-contradiction in force arising out of no —
prior force; the contradiction that we discover at lastisa —
contradiction of our experience. '
A still more doubtful example is furnished by the question
of questions—Material Perception, which Mr. Spencer upholds _
* in its popularly received form, on the authority of the test of —
inconceivableness of the negative, Mysterious asis the con- —
sciousness of something out of consciousness, we are, he says, —
obliged to think it. ‘The current belief in objects as external
independent entities, has a higher guarantee than any other —
belief whatever.’ Yet thisis the belief that would have re-
mained undisturbed to this hour, but for its glaring self-contra-
diction, first exposed by Berkeley, and since by others. (See, —
in particular, Ferrier’s Review of Berkeley). Any test of
belief that guarantees this assumption must needs be repudi-
ated by the numerous believers in its self-contradictory —
character. There is an evident incongruity in laying down, —
as a universal postulate, what begs the very point in dispute, —
in a leading controversy. 4 ha
Fifthly. Mr. Spencer’s view, that inconceivableness (where —
there is no self-contradiction) represents ‘the net result of our
experience up to the present time,’ supposes a theory of the
sources of belief which is liable to great objections. He
considers that our habitual contact with actual things has —
engrained in our minds an intensity of connexion between the —
ideas of those things proportioned to the frequency of their
recurrence. For example, Space relations are the most iterated
of any, and, consequently, our minds are moulded to these with —
the highest possible tenacity. Next are Matter and Force | ,
relations. In this way, as already remarked, our repugnance —
to form even an idea of the opposites is a proof of the persis
ence of the corresponding facts. So that, experience and
inconceivability of the opposite are convertible statements, _
Now, it may be granted that the contact with actual thi
is one of the sources of belief; but it is not the only nor th
greatest source. Indeed, so considerable are the other sou
as to reduce this seemingly preponderating consideration to
comparative insignificance. The competing elements are
0
O
e
SOURCES OF BELIEF, 669
briefly the following :—(1) The innate impetuosity of believ-
ing that what is will continue; and (2) The influence of our
strong emotions and predilections. Both influences will be
illustrated afterwards as prevailing causes of error or Fallacy
(Book VI). There should also be taken into account the
circumstance that our strength of association does not represent
the comparative recurrence of the fact, unless our position is
such as to encounter the facts in proportion to their exact
frequency. What is most familiar to nature, may not be the
most familiar to us. We may not see the world from a
zentral or commanding point of view. The best example of
this is our excessive familiarity with one type of causation—
the human will; in consequence of which, we represent that
as the proper and natural type; whereas, it is an exceptional
and narrow instance of causal agency.
There still remains the effect of society in propagating and
iterating certain propositions in language; by which iteration,
no less than by confronting the facts in our own person, we
are moulded to belief in certain doctrines. On the whole,
therefore, when the various agencies operating to form our
convictions are taken together, the one circumstance assigned
by Mr. Spencer is so overborne as to render our strength of
belief no just criterion of the facts believed.
Sixthly. Nothing is gained by putting under one head, and
subjecting to a common test, two classes of beliefs so distinct,
as Self-Consistency and Consistency with Facts. Hitherto, in
philosophy, these two departments, under various names, have
been kept distinct. The one is known as Formal Truth,
Necessary Truth, the Laws of Thought; the other is Material
Truth, Contingent Truth, Inductive Certainty. Although the
most strongly iterated of the laws inductively arrived at tend
to indissoluble associations, and to a difficulty of thinking their
opposites—in that way approximating to the truths of consist-
ency, this is a mere incident belonging unequally to things
that are alike true. When the inconceivability occurs, a
reason can be given for it; and the reason not being always
the same, there is no propriety in disguising the deeper dif-
ferences by the superficial agreement. We are not obliged to
have only one Universal Postulate. Should there occur two
very different kinds of certainty, neither reposing on the other,
our proper course is to assign different postulates.
On these various grounds, we demur to the test of the
‘Inconceivableness of the Opposite’ as the basis of all cer-
tainty, or as the matter that cannot be proved, but must be
670 THE UNIVERSAL POSTULATE.
asked and granted, before demonstration can begin. We should
propose, instead of that test, at least two Postulates, accord- — q
ing to the distinction last noted ; perhaps more may be oo
uisite.
i First and foremost, we should place the Postulate of Consis-
TENCY, or Self- Consistency—the absence of self-contradiction. —
This is the basis of Immediate Inferences, or Equivalent Forms. —
It must be conceded as a prime condition of all reasoning,
discussion, and intelligent communication, Hnough has been —
said in regard to it.
Secondly, there must be some assumption or assumptions eS
the foundation of all inferences or conclusions from Experience — “4a
—some grounds of Material or Inductive certainty. There is
much more difficulty in deciding what the postulate should be —
for the department of real inference, or whether a single
postulate is enough. We here enter upon a totally new
sphere.
In order to guarantee the conclusions of our experience, ;
or to support us in such allegations as—‘ water quenches thirst,’ —
‘unsupported bodies fall’—there is clearly demanded, in the
first instance, a trust in present consciousness. We must assume |
that what we feel, we do feel; that our sensations and feelings —
occur as they are felt. Whether or not we call this an irresisti- —
ble belief, an assertion whose opposite is inconceivable or
unthinkable, we assume it and proceed upon it, in all that we
do. The calling the negation unthinkable does not constitute
any reason for assuming it; we can give no reason better than
that we do assume it.
‘The importance of stating this primary assumption is not
apparent, till we proceed beyond it. We are carried a very
little way into knowledge by the admission taken by itself’;
we must make some steps in advance, and assume thing
seemingly precarious in their character when compared with a
the decisive certainty of immediate consciousness.
It is requisite, in the second place, that we should believ 7 2
in past consciousness, or memory. Unless we trust our
lection, our knowledge is limited to what is now present ;
we cannot compare two successive experiences, or declare
facts to succeed one another. We have, one moment,
consciousness of thirst; the next moment, we have the |
sciousness of a certain act called drinking ; ; the next foll
ing moment, we have the farther consciousnees of relief
thirst. The succession of the three steps is a fact or ex]
ence; but we cannot believe it, unless we believe in
,
ee h® -
7 . ne
THE LEAP TO THE FUTURE. 671
recent fact, given in memory, as well as the present, given in
consciousness.
The belief in memory must therefore be postulated. It
may be asked, however, are we to believe our memory without
limits, or, if nitt, what are the limits to our belief? If there
be any circumstance qualifying or defining the belief, that
circumstance should be produced as something more funda-
mental, and therefore proper to take the place of the assump-
tion that it limits and qualifies. In short, memory must be
believed in; yet the postulate of the belief is not wholly
independent and isolated, but leans to some extent on another
and a different postulate.
Granting, however, that the belief in memory, as well as
the belief in present consciousness, is a primary assumption,
we next remark that it comes short of our needs. The most
authentic recollection gives only what has been; something
that has ceased, and can concern us no longer. A far more
perilous leap remains ; the leap to the future. All our interest
is concentrated on what has yet to be; the present and the
past are of value only as a clue to the events that are to
come. Now, it is far easier to satisfy us of what has been,
than of what is still to be.
The postulate that we are in quest of must carry us across
the gulph, from the experienced known, either present or
remembered, to the unexperienced and unknown—umust per-
form the leap of real inference. ‘ Water has quenched our
thirst in the past ;’ by what assumption do we aflirm that the
same will happen in the future? Experience does not teach
us this; experience is only what has actually been; and,
after never so many repetitions of a thing, there still remains
the peril of venturing upon the untrodden land of future
possibility.
The fact, generally expressed as Nature’s Uniformity, is the
guarantee, the ultimate major premise, of all Induction.
* What has been, will be,’ justifies the inference that water
will assuage thrist in after times. We can give no reason, or
_ evidence, for this uniformity ; and, therefore, the course seems
to be to adopt this as the finishing postulate. And, undoubtedly,
_ there is no other issue possible. We have a choice of modes of
expressing the assumption, but whatever be the expression, the
substance is what is conveyed by the fact of Uniformity.
As nature is not uniform in everything, we have to apply
a test to discriminate the uniformities from the varieties.
There is a uniformity in the manner of animal generation, but
672 THE UNIVERSAL. POSTULATE,
not an absolute sameness in the individuals born even of the —
same pair. Now experience will not establish uniformity, but
it will establish exceptions to uniformity ; it will sift the natural | ye
sequences and enable us to reject all that are not uniform. ae me)
does not prove that anything will always be in the future a
what it has been in the past, but it will prove that some things | a
have been uniform in the past, and others not uniform. oe
has at least a destructive certainty, og
Let us word the postulate thus :—What has uniformly been
in the past will be in the future. Otherwise, ‘ what has never —
been contradicted in any known instance (there being ample a
means and opportunities of search) will always be true.’ in aa
the course of our experience, we have seen a great many pro-
mising uniformities break down, Again, we have found in- —
stances that have never failed; on “such cases, we venture,
and it is a mere venture, to predict the future continuance of a
the same state of things. We go forward in blind faith, until a
we receive a check; our confidence grows with experience ; a:
yet experience has only a negative force, it shows us what has” i
never been contradicted ; and on that we run the risk of Ey Ss
ing forward in the same course, 7
This assumption is an ample justification of the poe
operation, as a ara of eM inference, Without it, we can
ie4
it other wise than as begged at the very outset. If there be a
reason, it is not theoretical, but practical. Without the as-
sumption, we could not take the smallest steps in practical
matters ; we could not pursue any object or end in life. Un-
less the future is to reproduce the past, it is an eni ma, &
labyrinth. Our natural prompting is to asswme such i entity ;
to believe it first, and prove it afterwards.
This third Postulate i is, properly speaking, the Postulate of m4
Experience. Not only does it involve a hazard peculiar 1 0 ;
itself, making a broad line between it and the postulates of
present consciousness and of memory, but it seems to remove —
all the doubts and ambiguities connected with these appar- .
ently more facile assumptions. Nothing can be better evidence
than present reality, provided we do not mistake an act ul
consciousness for an inference, or a recollection. This d
culty is got over by comparison of instances, and by the ap;
cation of general principles, which repose ultimately 1 upon
Great Postulate. a
So with Memory. We trust implicitly a recent recollee-
FALLACIES IN LANGUAGE, 673
tion ; but as the interval of time enlarges, our trust diminishes.
A limit has thus to be prescribed, through a comparison of
experiences, followed by an inference from the past to the
future, which brings us round again to the assumption of the
future from the past. Hence, whichever way we turn, we
find this to be the one resting place for the sole of our foot.
E.— ARISTOTELIAN AND SCHOLASTIC FALLACIES.
The Aristotelian is the basis of all subsequent classifications.
It proceeds upon the distinction between fallacies in Language,
and fallacies in Thought,
L ‘Pallacies arising in Language (In Dictione, of rapa tiv
hefiv). 1. Aequivocatio, Homonymia, opwrunia; ambiguity
ina single term. This is a very comprehensive class of fal-
lacy. One of the examples given by Aristotle illustrates an
ambiguity in the word ‘necessary.’ ‘ Hvil is good, for what is
necessary (ta deov7a) is good, and evil is necessary.’ What is
necessary aS a means to a desired end is good; but what
necessarily results from antecedent conditions may be evil.
Whately gives, in his Logic, an enumeration of words often
used ambiguously in discussion. This task belongs as much
at least to the lexicographer as to the logician. Thus: ‘ Ex-
pect’ is either what is possible, as that the sun will rise to-
morrow, or what is right, as ‘ England expects every man to
do his duty.’ ‘Old’ means either length of duration, or dis-
tance of time. As age gives experience, and experience often
teaches wisdom, there is a disposition to regard the ancients
as wiser than ourselves. To this Bacon replied, ‘we are the
ancients ;’ we inherit the wisdom of the old, and can add to it
more experience.
_ A chief cause of ambiguity is that the signification of words
is constantly shifting. The word ‘publish’ formerly meant
‘communicate’ or ‘show,’—‘ The unwearied sun publishes to
every land.’ This is now the legal meaning of publish: to
publish a libel is not necessarily to print it, any communica-
tion of written libellous matter to another is sufficient. The
law still speaks of ‘ uttering’ coin.
‘Some’ is of interest to the logician, in its two chief senses
‘some at least,’ and ‘someat most,’ or some = not none, and
some = not all.
The remedy for ambiguity is Definition.
2. Amphiboly, amphibolia, dug¢.Bodréa. A sentence may have
two grammatical renderings, but by preference suggest the one
intended to mislead. This was an occasional trick of the
O74 ARISTOTELIAN AND SCHOLASTIC FALLACIES.
ancient oracles. ‘Aio te, Avacida, Romanos vincere pos
reads as well whether the Romans are victors or vanquish
‘I hope that you the enemy may slay.’ iy
8. Fallacia compositionis et divisionis. Whately define th is
fallacy as the use of a term collectively in one premise, and
distributively in another. If the term is collective in
major premise, and distributive in the minor, it is a fallacy ae a
division ; if the collective is in the minor, and the distributive
in the major, it is a fallacy of composition.
Five is one number, i
Three and two are five, Fallacy of Division
Three and two are one number. (ae
Three and two are two numbers, ‘od HB ;
Fallacy of Composition. 2
bi ith ;
Aristotle gives a similar division,—ovv0eats, or the aa =
of wrong disjunction, and d:atpeors or the possibility of wrong
conjunction. His example of é:atpeors is :— Sa Fe
Five is two and three ;
Two and three are even and odd ;
Five is even and odd. th
This would be a fallacy of composition, according to Whate
and Mr. Poste observes that it is not easy to understand exactly
Aristotle’s distinction, and not worth the trouble. mm
4. Fallacia Prosodiae or Accentus, rpoowdia, This is
very trifling consequence, and chiefly noticeable because
the different meanings that may be given to a sentence
varying the emphasis. Mr, De Morgan remarks that
commandment, ‘ Thou shalt not bear false witness against
neighbour,’ is often read with the emphasis so placed as
suggest that subornation is not forbidden, or that anyth
false except evidence is permitted, or that it may be given
him, or that it is only against neighbours that false witness
may not be borne.’ Most of the old examples are mere puns. —
‘Tu es qui es; quies est requies ; ergo, tu es requies.”
5. Fallacta figurae dictionis, oxijua deEews. According t to
Aristotle's view, this fallacy is a species of grammati a
mistake, arising from the circumstance that unlike th
have names with a like inflexion. Thus, ailing and cuttong
have the same termination, but one applies to a state or
quality, the other to an action, dees.
IT. Fallacies in Thought (Hxtra Dictionem, ot é€w ths KeFews
l. Fallacia aceidentis, or a dicto simpliciter: add dict
Three and two are five,
Five is two numbers.
FALLACIES IN THOUGHT. 675
secundum quid, nupd 76 cuvpBeByxos, A fallacy assuming that
subject and predicate have all their attributes in common. It
is taking a predicate as co-extensive with a subject, when it
is not.
2. Fallacia a dicto secundum quid ad dictum simpliciter,
70 amos 7 fA) GrdBs adda TH i} Tod 7) Tore } pos te éyeaOas,
confusion of an absolute statement with a statement limited in
manner, place, time, or relation.
What you bought yesterday, you eat to-day;
You bought raw meat yesterday ;
You eat raw meat to-day.
This is the converse of the fallacia accidentis; many of the
examples of both are instances of erroneous conversion of an
universal affirmative.
3. Ignoratio clencht, ro mapa rv tod édéyxXov dyvov, an
inadequate notion of confutation. A debater undertakes to
contradict and overthrow a thesis, and proceeds to destroy
some different position. [tis the common error of arguing
beside the point, of proving what has only a superficial
resemblance to the conclusion, or of simply trying to distract
attention from the point at issue. Mr. de Morgan classifies,
along with this, any attempt to transfer the onus probandi to
the wrong side.
4, Fallacia consequentis, non sequitur, ro mapa 70 émopevoy.
To mistake gall for honey, because it is yellow, is a non
sequitur. Kain wets the ground, therefore wet ground implies
that it has rained. Every one in a fever is hot, but every
one that is hot is notina fever. In this case also, the ex-
amples are generally instances of wrong conversion of an
universal affirmative.
5. Petitio Principii, 70 rapa 76 év dpxG AanBaverw Aristotle
describes five forms of this fallacy. (1) When one begs the
very thing that ought to be demonstrated. (2) When one
begs universally, what ought to be demonstrated particularly.
(3) When one begs the particular to help to prove the uni-
versal. (4) When one begs all the particulars that compose
the universal. (5) When one begs something necessarily con-
nected with the conclusion.
Logicians discuss the question whether the syllogism itself
is a petitio principii.
6. Non causa pro causa, 70 py aitiov ws attiov 7Oévar, an
inductive fallacy, for which another name is, post hoc, ergo
proper hoc, which is the vice of the delusive induction called
per simplicem enumerationem. Whitfield attributed his being
676 ARISTOTELIAN AND SCHOLASTIC FALLACIES.
overtaken by a hailstorm on a certain occasion to his having in
not preached at the last town. ‘ ie ie
7. Fallacia pluriwm interrogationum, 70 74 metw peor ware Re
év oetv, is the fallacy of putting more questions than one as
one. Why did you strike your father? It is an easy snare
to ask a reason for a fact that has no existence. ‘The fir sb
members of the Royal Society were in this predicament, a
they tried to explain why a dead fish weighed more Af? |
living fish. The auswer was, it did not,
Hardly any addition has been made to Aristotle? s list of
Fallacies by modern writers on the Syllogism. Aristotle's _
principle of classification has been pronounced illogical, and —
new arrangements have been proposed; but his enumeration
has not been materially increased. aa
ce
The arrangement followed in most Manuals of Syllogistic
Logic, is that adopted by Whately. sh
Rejecting as indistinct the division of Fallacies into those
in the words (in dictione) and those not in the words (cotra
dictionem), Whately divides them into Logica and Non- Mrz
Loeican. The Logical include all cases of insufficient premise 3.
advanced as sufficient; all cases ‘where the conclusion does —
not follow from the premises.’ Such cases only, he contends, |
are logical in the strict sense: logic having to do only with
the sufficiency of the premises given for the conclusion based
upon them. As Non-Logical he reckons all cases where ;
premises are sufficient for the conclusion, ‘where the conclu-
sion does follow from the premises,’ but where either the
premises are unduly assumed, or the conclusion is irrelevant
to the point in dispute. To settle whether the premises are a
legitimate or whether the conclusion is in point, passes beyond
the proper sphere of Logic. ic
Such are Whately’s main divisions. The grouping of t
Aristotelian fallacies under them is as follows:—I. He: cube
divides Logical fallacies into the Purrty Locicat and the Sry I>
LOGICAL. The Purely Logical are Undistributed Middle, al |
Iilicit Process of the Major and of the Minor: two errors which
Aristotle did not enumerate in his list of Fallacies (sophisma
whether because he considered them too palpable to be fra
lently used by a sophist, or because he had sufficiently ex
them in treating of the syllogism. The Semz-logical em
all instances of ambiguous middle term. The ambiguit
be in the term itself, or may depend upon the context.
ambiguity being in bes term itself, we haye Fallacia a 41.00
WHATELY’S CLASSIFCATION, 677
cationis, and Fallacia Amphiboliae. Our author takes an
opportunity of remarking that a term may have two meanings
from accident (as the term ‘ light’); or from some connexion
of resemblance, analogy, cause and effect, &c., between the
different senses. The ambiguity arising from the context, we
have Fallacia Compositionis et Divisionis,and Fallacia Accidentis,
and a dicto secundum quid ad dictum simpliciter. In these
cases the middle term is not ambiguous in itself, but is used
with different adjuncts in the two premises.
II. In the Non-logical or Material group, the premises may
be unduly assumed, and the conclusion may be irrelevant. A
premise may be altogether false and unsupported. The only
guarantee against this is a knowledge of the conditions of In-
duction, The major premise may beg the conclusion (petitio
principti,; being either the very same as the conclusion, and
differing only in form, or not quite the same as the conclusion,
but unfairly implying it. So much for premises unduly
assumed. ‘Turning now to the other sub-division of the Non-
logical fallacies (ignoratio elenchi, or irrelevant conclusion), we
find various modes of shirking the question particularized.
One way is to lay great stress upon the objections, taking no
notice of what may be said in favour. Another way is to shift
ground, either to something wholly irrelevant, or from one
premise to another. A third way is to escape under cover of
vomplex and general terms. And a fourth way consists in
appeals to the passions and sentiments, ignoring altogether the
rational grounds of the point in question. (See Book VI).
THE AXIOM OF THE SYLLOGISM.
(Supplementary Note to the Second Edition.)
In pp. 18, 156, 226, 237, 247, 269, the Logical Axiom of
the Syllogism has been placed under the head of Inductive
truth. This has not been done without misgivings, as the
following remarks will show.
The drawing of a broad line between Immediate and
Mediate or Syllogistic Inference, and the laying down of a
Deductive Axiom founded on experience as the basis of the
Syllogism, will be seen to be attended with difficulties.
The first is the anomalous middle position of the Hypo-
678 SUPPLEMENTARY NOTE. —
thetical Syllogism. If we are bound to bring hy pothetic
inference under one or other of the two forms, we feel tha %
our decision is not satisfactory; the case passes somewhat
beyond Immediate Inference, and yet does not reach vg
Syllogism. "ye
There is the same unpleasant doubt about the cases di
cussed in p. 109, and p. 157, where a singular preposition
has to be treated as a Universal, We cannot, without con-
siderable straining, make these out either Equivalent a Si. 4
tions or Syllogisms. 4
The second difficulty is still greater. The question hagaih O-
be raised, whether syllogistic inference is or is not Self J
consistency. Is the conclusion the mere equivalent of the
premises, so that to deny it, while admitting the premises,
would be self-contradictory ? ae
That the conclusion of the Syllogism flows necessarily fi from.
the premises, is generally insisted on. To refuse the con-
clusion would be to contradict the premises. Indeed, the
self-contradiction would be as unequivocal as in the denial « of
an immediate inference—all A is B, some A is B. In what
then consists the distinction, as regards the logical foundation,
or the kind of certainty, between Mediate and Immedia te
inference P
In the Syllogism, the bond of necessary Sit vallonaal ‘ies
between one proposition and two others; in the immediate
inference, it lies between one proposition and one otl
This makes the case a degree more complicated, withou
apparently altering the generic character of the inference ;
it is an inference contained in the premises; it cannot | *
refused without contradiction in terms.
This circumstance of necessary, or self-consistent relatio
ship should appear in the axiom of the Syllogism. It ‘ae so
in the dictum de omni et nullo. That axiom seems to be 2
necessary truth ; we feel that to deny it would be not mer
to deny a fact, but to deny in one form of words what
have already affirmed in another ; which expresses wha’ 8
meant by ‘contradiction in terms,’ and by the denial « of a
‘necessary ’ truth.
The other form of the axiom—WNota note—‘ whatever |
mark has whatever that mark is a mark of, must al
necessary, if it is an exact equivalent. We cannot st
that the Syllogism under one form of axiom is an implies
or necessary inference—an analytic judgment ; and, 1 an
another form, an inductive or contingent inference—a
THE AXIOM OF THE SYLLOGISM. 679
thetic judgment; such a supposition could arise only from
_ some great confusion of ideas.
If, under the guise of nota note, the axiom is exactly equiva-
lent in substance, as it is in appearance, to the mathematical
axiom of mediate equality—-equals of the same are equal—
it would not be an axiom of self-consistency, or an analytic
judgment. That axiom may be very evident, may be styled
by courtesy self-evident, but it is a synthetic judgment ; the
subject and the predicate are not mutually implicated; its
denial is not a contradiction in terms. The subject is ‘ equals
of the same’—things severally compared to a common stan-
dard or measure; the predicate is—equal by ‘ coincidence,’ or
by being compared immediately—a totally distinct mode of
comparison. These two modes are said to concur; the trial
by the one mode is a test or mark of what would happen in a
trial by the other mode. We have an opportunity of comparing
two things with the same third; we have no opportunity of
applying the two things to each other; we are assured by the
axiom that the coincidence of the two with the common third
is proof that they would coincide if we could apply them to
each other. There would not be a contradiction im terns,
there would only be a contradiction of experienced facts, if we
denied that mediate coincidence infers immediate coinci-
dence.
Mr. Mill, in the new edition of his Logic, p. 208, states that
he regards Formal Logic as the logic of mere consistency, and
the dictum de omni as its axiom; he does not insist on apply-
ing to it the nota note, although he regards that form as the
proper axiom for the logic of the pursuit of truth by way of
Deduction ; the recognition of which can alone show how it
is possible that deductive reasoning can be a road to truth.
So viewed it is, not self-consistency, but an inductive, con-
tingent, or synthetic proposition, like the mathematical axiom
of mediate equals.
The difference between formal deduction and real deduction
is the difference between syllogism and inductive or experi-
mental truth. Real deduction is the following out of an
induction, and assumes the uniformity of nature. That the
men living and unborn will die is a necessary inference from
‘all men are mortal,’ but not a necessary inference from the
actual premise, which is confined to the men that have
actually died. The real deduction contains three steps :—
certain individuals possess the attributes called humanity, and
also the attribute mortality ; these two attributes have been
680 SUPPLEMENTARY NOTE, 9 ©
conjoined through all our past experience; hence the prese
of the one marks the presence of the other. Now, John Brown —
and William Smith possesses the first fact, humanity, therefo ro
they possess what it marks, that is the second fact, mortality. ye
This is the application of the nota note in its purity and sim
plicity ; the uniformity of nature being supposed in addition. — ;
For greater clearness, take another instance. ‘ All inert
substances gravitate ; ‘ ‘throughout all our experience, the
property ‘inertness’ is a mark of the property ‘ gravity.”
Now, the etherial medium in space has the mark inertia ( (by
resisting the comets); it therefore gravitates. >
But still the question recurs, might not the infonenbaals n
both these instances be given under the dictum de omni #
For, basing on the uniformity of nature, we at once convert —
the special observations into a general law; men in the past b
have died, men in the future will die; whee all men a A
mortal. Ghitis has the marks of man, is a man; Caius is
mortal. Inert matter gravitates; the ether is inert ; ¢ he eo
ether gravitates. a
It would thus seem that the attainment of new ta tia by.
the way of deduction, does not imperatively demand any
change of axiom. ‘The dictwm and the nota note are equally ly
suitable. If so, the inference must still be a case of necess
implied, or self-consistent truth. Of the dictwm and the
note alike, we must declare that their denial is a self-contra-
diction. ‘2
Necessary or self-consistent inference, instead of being con-
fined to the manipulation of the equivalent forms of
positions, takes a wider sweep and embraces the Syllog
which we should have to characterise as ‘ mediate self-c
sistency,’ ‘mediate necessity,’ ‘complex implication”
forms lying between immediate inference or propositi
equivalence, and mediate inference or syllogistic equiva
would be regarded as incidental varieties of Self-consistency ;
they need not be forced under either of the two principal
genera. ht whi hb
When we say ‘ Socrates was wise, ‘Socrates was poor ;
therefore ‘one man was wise and poor,’ we draw a nec
or self-consistent conclusion, but not by the way o
Syllogism, as representing deductive reasoning.
‘Socrates is wise,’ and ‘ Socrates is poor,’ we can Ct
‘Socrates is wise and poor;’ ‘wisdom and poverty ¢
joined in Socrates ;’ the axiom or assumption here is
properties can be affirmed of a subject separately, or in separate
THE AXIOM OF THE SYLLOGISM. 681
propositions, they may be affirmed conjunctly, or in a com
pound proposition. Again, to proceed to the farther variation
—one man was wise and poor—we perform the, process of sub-
stituting for ‘Socrates’ the designation ‘one man,’ which prop-
erly applies to him. ‘This is the mode of equivalence con-
stantly assumed in working algebraic equations; where, for any
expression, we insert at pleasure another equal to it. Neither
of these modes is the same as the dictum de omni, and, there-
fore, they need not be forced under the syllogism, although they
amount to something more than stating an equivalent form of a
single proposition.
F.—ANALYSIS AND SYNTHESIS.
The common idea—Analysis and Synthesis—is difficult to
express adequately, owing to the variety of its applications.
Chemical Analysis, Mathematical Analysis, Logical Analysis,
with the corresponding Syntheses, have a basis of agreement, but
with points of difference.
The general idea of Analysis is separation; of Synthesis,
composition or combination. Yet the contrast does not alto-
gether correspond to the distinction of Abstract and Concrete.
Analysis is Abstraction, but Synthesis is not the negative or
the absence of Abstraction; it is not the wn-abstracted Concrete.
While the scientific man is, by the law of his being, an analyst,
the poet or artist, who does not analyze but combines, is not a
synthesist. Synthesis in contrast with analysis, is combining
after analyzing.
The simplest exemplification of the two correlated processes
is seen in Cuemicat Analysis. The Chemist operates upon an
unknown mixture or combination of substances, as a strange pro-
duct from a furnace, or the stomach of a poisoned man. He.
separates and identifies the various ingredients of the compound.
The obverse Synthesis would consist in making up the given
compounds by means of the several elements in their proper
proportions. Thus, having ascertained the precise constituents
of a mineral water, it is then possible to form the water artifi-
cially. If the artificial water is exactly identical with the natural
water, both the analysis and the synthesis are successful and
complete. It is by the analysis, however, that the synthesis
has been possible. The analysis is the foundation of a new
means of production; it enables us not merely to imitate and
rival the spontaneous products of nature, but also, if need
682 ANALYSIS AND SYNTHESIS.
be, to vary those products on a definite plan or purpose. W To
may introduce beneficial variations into the ayathease bd
mineral waters, So, having analyzed some crude substance
medicinally valuable, we may artificially compound it, firs
literally (which proves the sufficiency of the analysis), | and
next with improved adaptations for the end.
The most notable application of Chemical synthesis is fo
the formation of organic compounds in the laboratory. By
foregone analysis, the chemist has discovered the constituen
elements of these compounds, and the peculiarities of their —
union ; he then uses his knowledge to re-produce by laboratory —
processes what has been produced in the course of living ~
growth. In this way, urea, acetic acid, and many other or-
ganic products have been obtained by laboratory 7
Such synthetic efforts are the trophies of analysis.
Our next example may be termed Loaican Analysis; it i:
the ordinary Scientific Analysis, the peculiar case of Mathe:
matics being reserved. Here, Analysis is substantially i iden-
tical with generalization, whether of the notion or of the pro-
position. What Synthesis is will appear presently. ath
The processes of assimilating, identifying, classing, general ale
izing, abstracting, defining, are the various sides, aspects or
stages, of one fundamental ‘operation. Now Analysis is merely
a farther aspect, another side, of the same proteus. To ident
classify, and abstract, is to separate or analyse, so far as the
case admits; the separation being no longer actual, as in
Chemistry, but mental or ideal. To identify and class y
transparent bodies, is to make abstractive separation, or ana-
lysis, of the property called transparency ; or to view its fu
tions, powers, or agencies alone and apart from all the ot
powers possessed by the individual transparent bodies. W.
is liquid, but this aspect is disregarded ; diamond has e:
ordinary refractive power but no notice is taken of it
two substances are studied merely in their agreement in w
we call transparency. Shia
Now the investigation of nature turns exclusively on this
abstractive separation. Bodies are constituted with a ch
of powers or properties inseparably combinated, yet
pursuing its independent course without any distur bance |
the others. Water, as transparent, has a power exaetly i
tical with diamond and rock er ystal, as transparent; the
peculiarities wherein the two bodies stand widely con
have no seen? exercise no interference, as regar
ANALYSIS MEANS ABSTRACTION AND INDUCTION. 683
of attention, and being easily impeded and thwarted by dis-
tracting circumstances, finds the advantage of neglecting all
allied properties, and concentrating its powers on the one
subject of study at the time.
Thus, Abstraction and Analysis, if not identical, are the
same fact viewed with a slight difference. Abstraction means
separately viewing one point of agreement, and leaving all
other accompaniments in the shade; the transparency is
studied by itself, the specific gravity and all other incorpo-
rated properties being left out of sight. Analysis means the
very same thing; only, proceeding a little farther, it supposes
that every one of the powers of a given concrete, as water,
may be abstracted by turns,—transparency, liquidity, specific
gravity ; so that water as a whole may be analyzed, or sepa-
rated (mentally) into a number of different powers, whose
enumeration is a full account of the agency of water.
The farther we push abstraction and generalization, the
farther we push Analysis. When, after generalizing all
mechanical movements, and forming an abstract idea, or
analytic separation of molar or mechanical force, we proceed
to identify mechanical momentum with molecular forces, we
make a new analysis; we separate the property of force from
its exclusive connexion with the movements of masses, and
view it as the movement of matter, whether in larger or in
smaller aggregates.
It is now requisite to assign a correlative meaning of Syn-
thesis. As Analysis is the ideal separation and separate exhi-
bition of all the functions of a concrete thing, as water, iron,
blood, Synthesis is the re-statement of the whole in their
ageregate. Its efficacy would be shown in supposing a new
aggregate, asa liquid diamond, a metal with all the properties
of lead except its corrosion. It would also be exemplified in
the act of communicating, by description, the knowledge of a
mineral, apart from a concrete specimen,
Another step is inevitable. As these abstractive properties,
or notions, are what enter into the inductive generalizations of
nature, each inductive law being two or more coupled together,
Analysis becomes applied to Inductive discovery. There can
be no wide induction without a correspondingly wide genera-
lization of at least two notions, that is, without an equivalent
analytic separation. The summit of generalization, in the
notions Quantity, Inertia, Gravity, Persistence, is the summit
of Analysis. The highest generalities of Mind are attained
through the most thorough Analysis of Mind.
684 ANALYSIS AND SYNTHESIS.
The employment of Analysis to signify Induction appears in
Aristotle, and pervades the logicians after him. (See Mansel’s
Aldrich, App. G., Hamilton’s Logic, II., 2). By an easy
transition, Synthesis would be applied to Deduction. The
deductive operation of following ont the law of gravity to
lunar perturbations, to the tides, to precession, &c., would be
called synthetical, as reuniting abstract elements into new
combinations. Having mastered the laws of central force,
and the composition of forces, Newton deduced or inferred the
orbits of bodies governed by other forces than gravity.
Synthesis, however, scarcely applies to simple Deduction,
the following out an induction to a new case, as when we infer
the death of the reigning pope from the mortality of the men
that have died. There is no element of combination in such
cases, there is but the filling up of the Induction, which is
only formally complete so long as any particulars are still
outstanding. The synthetic operation is best realized by the
complex deductions, or the union of several deductive laws to
a composite or concrete case—a secondary law. .
There is nothing gained by using the terms Analysis an
Synthesis to the Inductive and Deductive processes respec-
tively. We may show in what way the application is proper
or admissible, and that is all.
The use of the Syllogism may be expressed as analyzing or
separating, out of regard to our mental infirmity, the three
parts of a step of reasoning, so that they may be studied in _
separation. The premises, instead of being confused together,
- can be looked at apart, and each judged on its merits in its
isolated condition. ‘This is an advantage belonging to Method,
or Discovery. Wherever a separation of this kind can take
place, a great relief is given to the understanding, with a
corresponding enlargement of its powers. ons
An accountant separates his columns of debit and of credit,
and classifies under different heads payments that relate to
different subjects and follow different rules. i
Grammatical Analysis may be followed by Grammatical
Synthesis, as in constructing sentences upon new types sug-
gested by putting together the component elements in various e
WAYS. ae
Criticism is a species of analysis; and the composition of
an Oration or a Poem, by the guidance of critical and rheto-
rical rules, is a strictly synthetic operation; the previous —
analysis is the foundation of the method. Composition, with: —
1
Fy
out any rules, is not synthesis
i on hea
MATHEMATICAL ANALYSIS, 685
it is a weakness of the unscientific man to suppose that a
concrete thing, as, for example, a political institution, can be
viewed only as a whole—that its operations are an indivisible
totality. Thus, the obtaining of justice by the procedure in a
court of law is through a series of steps and processes—raising
the action, appearing by counsel, summoning a jury, and so
on. The effect of the whole being good, the un-analyzing mind
distributes the merit equally over all the parts, and is shocked
when a doubt is raised as to the utility of any one constituent,
as, for example, the jury.
To advert finally, to the special instance of Mathematical
Analysis and Synthesis. A new step in geometry may be
taken either by analysis or by synthesis. The various Geo-
metrical properties are said to have been first discovered, by
analysis, while in exposition they are in the form of synthesis ;
which is not strictly the fact ; we may proceed from the known
te the unknown in both ways; discovering new properties by
synthesis no less than by analysis.
Let us take Synthesis first, as suiting the case of a science
whose onward march is by the way of Deduction. Let us
assume that a certain proposition has been arrived at, ‘no
matter how, say, ‘ Parallelograms on the same base, and be-
tween the same parallels, are equal.’ Now any one consider-
ing this proposition might readily see, that the axiom of
mediate equality applied to it, would show that the same
thing might be predicated of equal bases ; such an inference
would be an effort of pure deduction, or the skilful combin-
ing of two already established propositions to yield a new
third proposition. So, by a repetition of the same apposite
union of truths possessed, one might also infer that ‘ Z7'7-
angles on the same base, or on equal bases, and between the
same parallels, are equal.’ By farther combinations, the rea-
soner might go on to deduce or infer the 47th, and so forth.
All which is a purely synthetic operation; and geometrical
truths may be evolved to any extent in this way. Corollaries
are usually deductive inferences, of short leap, from the main
proposition. The operation is seldom one of simple deduc-
tion, there is usually a certain concurrence of two or more
propositions to the new result; and the mental effort lies in
bringing these together. Geometrical synthesis and deduc-
tion are thus the same thing.
What then is Geometrical Analysis ? Is it Induction? We
are told that it proceeds from the unknown to the known. If
one were to suspect or surmise (without being sure) that the
686 ANALYSIS AND SYNTHESIS.
square of the hypothenuse of a triangle is equal to the sum of
the squares of the sides, and assuming it, were to endeavour
to connect it by a thread of geometrical reasoning with the
established propositions of geometry, the operation would be
called analytic or regressive, as compared with the synthetic
or progressive course above described. Yet in reality, the
mcntal operation is substantially the same in both; the two
differ only in superficial appearance, like the enquiry from
cause to effect, and from effect to cause. Assuming the truth
of the surmise first, we have to consider what prior proposi-
tions would be requisite to support it; and, again, what other
propositions would support these; until we come at last
upon admitted theorems. The real operation at each step is
a deductive one; we feign a proposition and try its conse-
quences ; if these coincide with the case, such proposition or
propositions are what we need; and if they are found among
the true propositions of geometry, we have made good our
point; we have proved our surmise, and put it in the train of
geometrical deductions.
The facilities for this inverted deduction are so greatly mvl-
tiplied by Algebra as to give to the algebraic processes the
designation ‘analytical’ by pre-eminence. In an Algebraic
equation, we work backward from the known to the unknown ;
yet it is by a series of properly deductive operations—the
application of axioms and theorems already established.
Algebraic Geometry is called ‘ Analytical ;’ the more recon-
dite processes of Algebra are called the Higher Analysis.
Thus, while Synthesis has throughout a reference to the
deductive and combining processes of science, Analysis relates
to generalization or inductiou, everywhere except in Mathe-
matics, in which it is merely the mode of deductive synthesis
adapted to the solution of special problems. The geometer,
when he has no special end in view, evolves new propositions
by direct or progressive synthesis ; when he has a problem to
work out, he confines his deductions to those that lie in the
approaches to the desired solution. The course of discovery
ina Deductive science can be only Deductive; it consists in
following out generalities in hand to new applications; usually
by combining several in one application. The art, the labour,
hes in the union of several propositions to a result. The
operation must be tentative ; it cannot be foretold; yet it is
amenable to a certain general method, which practice instils,
and which is not altogether beyond the reach of precept.
’
oe
BACON ON THE NECESSITY OF FACTS. 687
G.—GROWTH OF THE LOGIC OF INDUCTION,
Previous to Mr. Mill, the principal contributors to the Logie
of Induction were Bacon, Newton, Herschel, and Whewell.
Bacon.—The essential part of the service rendered by Bacon
to Science was his protest in favour of basing generalities on a
patient collection and accurate comparison of facts. It was
too much the custom, he complained, to ‘just glance at experi-
ments and particulars in passing ;’ in place of this, he proposed
to ‘dwell duly and orderly among them.’ With the whole
force of his eloquence he discouraged flighty speculation and
rash conjecture, and urged that generalities must be founded
upon a wide comparison of particulars.
Following up his emphatic enunciation that men must have
done with rash speculations and rashly abstracted notions, if
they desire to make progress in their knowledge of Nature, he
devised modes of elucidating truth by the comparison of
instances on a methodical plan. He directs the arrangement
of facts in three different tables. The first table is to contain
instances agreeing in the presence of the phenomenon to be
investigated; this he calls a Table of Essence and Presence
(Tabula Issentiae et Praesentiae). The second table is to con-
tain instances wanting in the phenomenon, but otherwise
allied to the instances where the phenomenon occurs, each
instance corresponding as far as possible to some one instance
in the first table; this he calls the Table of Deviation, or of
Absence in Allied Instances (Tabula Declinationis, sive Absen-
tiae in Proximo). The third table contains the phenomenon in
different degrees, and is called the Table of Degrees or Table
of Comparison (Tabula Graduum, sive Tabula Comparitiva).
The constitution of the three Tables is exemplified upon an
enquiry into the phenomenon of Heat; for the prosecution of
which are assembled no less than 27 instances agreeing in the
presence of heat, 32 allied instances agreeing in its absence,
- and 41 instances of heat manifested in different degrees.
The three Tables seem designed for the convenient applica-
tion of the three leading methods of Inductive elimination—
Agreement, Difference, and Concomitant Variations; but we
must not suppose that Bacon realized anything like the
precision of those methods. He did not conceive the idea of
choosing his instances so that they should differ in every point
but the phenomenon under investigation, agreeing only in that
—the fundamental idea of the method of Agreement. Nor did
he conceive the aces of the decisive method of Difference, the
688 GROWTH OF THE LOGIC OF INDUCTION.
choice of two instances agreeing in every point save the given
phenomenon. Having collected his Tables of Instances, he
went to work by excluding according to certain canons the
irrelevant instances, then making a hypothesis or guess at the
truth, and finally verifying this by farther enquiry.
Bacon takes especial credit for his process of Exclusion or
Rejection. He contrasts it with the popular method of pro-
ceeding by Simple Enumeration, that is, by counting only the
favourable instances, overlooking the unfavourable; and he
claims to be the first to make it prominent. The problem of
Induction being to ‘ find such a quality as is always present or
absent with the given quality, and always increases or
decreases with it,’ ‘the first work of true induction is the
rejection or exclusion of the several qualities which are not
found in some instance where the given quality is present, or
are found in some instance where the given quality is absent,
or are found to increase in some instance where the given
quality decreases, or to decrease when the given quality
increases.’
It will be observed that this process of exclusion, although —
a great advance upon generalizing without regard to contra-
dictory instances, is very rudimentary. Bacon does not dis-
tinguish between laws of simple’ Co-existence and laws of
Causation. The first of his principles of Rejection is suited
only to the establishment of co existences, and amounts to this,
that we are not to declare two qualities universally concomi-
_ tant, if in certain instances we find one absent when the other
is present. His other principle of rejection is the reverse of
the method of Concomitant variations, a disproving of causal
connexion on account of independent variation; and applies
to causation alone.
As to the modes of certifying the hypothesis allowed after
this process of collecting and sifting instances—the Logic of
Proof, Bacon has left us but a fragment. Of his nine divi-
sions of aids to Induction, he completed only the first, Prero-
gative Instances. Under this head, he dictates a farther
enquiry into particulars, and dwells upon instances of special
value to the inquirer, calling them Prerogative from that cir
cumstance. To call this division of his subject an aid te
induction is misleading; we expect to find an account of —
instances particularly suitable for founding inductions upon,
and find instead illustrations of various maxims applicable to
Definition, Observation, and even Experiment, as well as Sorte
specially adapted for Inductive Elimination,
BACON’S INDUCTIVE METHODS. 6389
It is among the Prerogative Instances, if anywhere, that we
are to look whether Bacon had conceived any practical device
for bringing the process of Exclusion or Elimination to a po-
sitive result, as is done in the modern methods of Agreement
and Difference. Under the heading of Solitary Instances, we
_ do find a crude approach to the selection of instances implied
in these methods. Solitary Instances are either instances
that exhibit a phenomenon without any of its usual accom-
paniments, as colour produced by the passage of light through
a prism; or instunces agreeing in everything except some
particular phenomenon, as different colours in the same piece
of marble. He says in a vague way that such instances
shorten very much the process of Hxclusion. They contain
really all that is demanded for the methods of Agreement and
Difference. Yet in Bacon’s hands they are comparatively
useless, and, as part of his method, could not even furnish a
suggestion for more perfect contrivances. The reasons are to
be found in his vague conception of the problem of Induction.
His methods of Exclusion are of avail only for problems of
Cause and Effect ; they are superfluous for problems of simple
concomitance, a single instance of disunion being sufficient to
disprove such a connexion; yet he speaks throughout as if
his elaborate comparison vf instances were designed only to
prove two properties co-existent. To this confusion he was
inevitably led by the subjects he proposed to investigate. He
seems to have thought principally of investigating abstract
qualities of bodies, such as density, weight, colour, volatility,
porosity, heat; his purpose being to establish their Form, by
which he seems to have vaguely understood something inva-
riably present with these qualities and endowing them with
their peculiar nature. Such an investigation gave ample
scope for numerous assemblages of instances ; but the methods
of sound knowledge were not likely to be perfected in a region
that can be approached only by hypothesis.
Under Migratory Instances, keeping still in view the same
class of subjects, he recommends attention to cases where
qualities are produced in bodies ; giving, as examples the pro-
duction of whiteness by pounding glass and by agitating water
into froth. From this’ we gather that he was sensible in a
measure of the advantage of studying the introduction of a
cause into known circumstances, although in his narrow field
of investigation it could lead to no result.
In these two first instances we see how far he anticipated
the Methods of Agreement and of Difference. Few of the other
690 GROWTH OF THE LOGIC OF INDUCTION.
twenty-five instances bear strictly on the Inductive Process.
With Migratory Instances, he compares Instances of Companion-
ship or Ennuty, such as the universal concurrence of heat with
flame, and the universal absence of consistency in air; just as
when a change is produced, we must seek the cause in some
- added influence, so when a quality is always present in a sub-—
stance, we must seek the cause in some property of that sub-
stance. In Striking or Shining Instances, and Clandestine
Instances, he urges the importance of the two extremes in a
variable phenomenon. His seventh and eighth Instances,
Singular Instances (as the magnet among stones, quicksilver
among metals), and Deviating Instances (individual monstro-
sities), are important for alike reason ; their novelty sharpens
investigation. His twelfth case, Instances of Ultimity or Linut,
is of the same nature. The five last go together ; the stimu-
lating efficacy ascribed to them is a favourite topic with
Bacon, and is the real characteristic of several other Instances.
Instances of Alliance or Union and Instances of Divorce, the
thirteenth and fourteenth, form a natural couple. The one
constitute instances reconciling apparent contradictions; the
heat of the Sun cherishes, the heat of Fire destroys; a con-
ciliatory instance is found in the growth of grapes in a house
heated by fire. The second constitute instances disproving
an alleged universal connection; it is asserted that Heat,
Brightness, Rarity, Mobility are always found together; we
point to air, which is rare and mobile but neither hot nor bright.
In exemplifying Instances Conformable or of Analogy, he
breaks clean away from Inductive caution; he gives as ana-
logous cases the gums of trees and most rock gems, and refers
the splendour and clearness of both products to the same
cause, fine and delicate filtering. Such fancies show how little
Bacon was removed from the rash speculation he condemned
in the works of his predecessors. on
His fourteenth case, the famous Instantia Orucis (Fingerpost
Instance), is mentioned in the Chapter on Hypotheses, § 7,
(p. 135), and is there placed in its true light as an instance
decisive of rival hypotheses, Such instances are otherwise
called Decisive and Judicial or Oracular and Commanding.
These are all the instances that have a direct bearing on
Induction. Of the remainder, two are of importance for Defi-
nition, the fifth and the ninth, Constitutive Instances, and
Bordering Instances. Constitutive instances give the constitu-
ents of a complex notion; Bordering instances make the
baffling transition border between two classes. i
- - PREROGATIVE INSTANCES OF BACON. 691
Five instances are classed together as Instances of the Lamp,
or of First Information; and relate to Observation, Under
Instances of the Door or Gate he comments on artificial aids to
the Senses—the Microscope, the Telescope, and measuring
rods. By Swmmoning or Hvoking Instances, he means indica-
tions of things not directly accessible to observation ; such
are the pulse and the urine, as symptoms of the condition of
the human body. Instances of the Road, otherwise called
Travelling and Articulate Instances, display stages of growth
and of other gradual changes :—the study of these is strongly
recommended. Supplementary Instances or Instances of Refuge
are said to supply us with information when the senses entirely
fail us ; when we cannot remove an agent altogether we may
vary its influence, and when a phenomenon defies observation
we may study analogous phenomena. Dissecting or Awakening
Instances are such as great effects produced by small causes;
they appeal to our wonder, and stimulate enquiry.
The seven concluding instances embody advice on the prac-
tical conduct of investigations. The four first of the seven
instruct us how to attain precision by definite determination
and measurement (Mathematical or Measuring Instances) ; the
three last how to economize our resouces (Propitious or Bene-
volent Instances). The Mathematical Instances are Jnstances
of the Rod or Rule, otherwise called of Range or of Limitation
(where measurement of Space is required) ; Instances of the
Course (measurement of Time) ; Instances of Quantity, or Doses
of Nature (where attention is called to the quantity of an
agent); and Jnstances of Strife or Predominance, under which
title he gives a confused enumeration of various ‘ Motions,’ or
tendencies to motion, and represents the movements of bodies
as determined by the victory of one or other of these conflict-
ing tendencies—for example, when water runs out of a crack,
the motion of Continuity is overcome by the motion of Greater
Congregation (the tendency of bodies to the ground). Nothing
could be more fanciful and illogical than this enumeration of
‘Motions.’ The Propitious Instances are—Jntimating In-
stances, which point out what is most useful to mankind;
Polychrest Instances or Instances of General Use, (contrivances
useful for a variety of purposes, as various modes of excluding
air from bodies to prevent decomposition) ; finally, Instances
of Magic, the use of small causes to produce great effects,
We have given no account of the tenth division, /nstances
of Power, otherwise Instances of the Wit or Hands of Man. It
is partly identical with awakening Instances: we have singled
692 GROWTH OF THE LOGIC OF INDUCTION, *
it out here as containing a homily against being led away by
admiration of skilful contrivances from better ways of accom.
plishing the same end.
In concluding this brief account of the Baconian method
we may reiterate that the merit of Bacon lay neither in the
machinery he provided nor in the example he set, but in the
grand impulse he gave to the study of facts. .
Nuwron. Newton cannot be said, any more than Bacon,
to have made a direct contribution to the methods either of
Discovery or of Proof; but he set an example of rigorously
cautious enquiry that did more than all the precepts of Bacon
to raise the standard of Proof, and to purify science of fanciful
hypotheses. He even went to an extreme and was over-
rigorous in his requirements of proof; such was his dislike to
making hypotheses (in the sense of assuming causes not
known to exist), that he wished to banish them from science
altogether. |
The Rules of Philosophizing (Regule Philosophandi) pre-
fixed to his Principia were long quoted «as authoritative.
Although worded with an express view to the establishment
of Gravitation, they are necessarily applicable to other induc-
tive generalizations.
The Frst rule is twofold, and may be thus explicated.
(1) “ Only real causes’’ (vere cause, actually existing causes)
“are to be admitted in explanation of phenomena.” We have
stated the limits to this under Hypotheses (p. 131), (2) “No
more causes are to be admitted than such as suffice to explain
‘the phenomena.” This is an echo of the maxim known as
‘Occam’s razor’ (‘ Entia non sunt multiplicanda preter neces-
sitatem’), and means that when one cause is proved to be
present in sufficient amount for the effect, we are not at
liberty to suppose the presence of other causes. From a few
words of explanation affixed to the rule, we should gather that
he meant also to suggest that there was a presumption in
favour of an explanation accounting for the phenomena by the
fewest agencies—a special pleading for his theory of gravita-
tion: ‘Nature does nothing in vain, and a thing is done in
vain by several agents when it can be done by a smaller
number.’
The Second rule is—‘‘ In as far as possible, the same causes.
are to be assigned for the same kind of natural effects,”” For
example, respiration in man and in beasts; the fall of stones
in Kurope and in America. An aspect of the Uniformity of
Nature designed to favour his view of Solar attraction as the
NEWTON’S RULES OF PHILOSOPHIZING. 693
sume kind of effect with the attraction of the Earth for the
Moon or for terrestrial bodies.
The Third—“ Qualities of bodies that can neither oe increased
nor diminished in intensity, and that obtain in all bodies
accessible to experiment, must be considered qualities of all
bodies whatsoever.” Another aspect of the Uniformity of
Nature, also specially adapted to his extension of Gravity to
the heavenly bodies.
The Fourth‘ In philosophical experiment, propositions
collected from phenomena by induction, are to be held, not-
withstanding contrary hypotheses, as either exactly or ap-
proximately true, until other phenomena occur whereby they
are either rendered more exact or are proved liable to excep-
tions.’ This is indirectly aimed at the Cartesian explanation of
the celestial movements by Vortices, the word hypothesis being
used in an opprobrious sense, as involving an element of fancy
operating upon imperfectly known materials. The rule may
be held to imply that the test of a theory is its accordance
with facts, which is not altogether correct.
Herscuer. Sir John Herschel devotes a considerable por-
tion of his Discourse on the Study of Natural Philosophy to an
account of ‘the principles on which Physical Science relies
for its successful prosecution, and the rules by which a syste-
matic examination of Nature should be conducted, with illus-
trations of their influence as exemplified in the history of its
progress.’ His introductory chapters on this head reiterate
with greater clearness the admonitions of Bacon; enforcing
recourse to experience as the sole fountain of knowledge,
illustrating the dangers of prejudice, and urging the import-
ance of recording observations with numerical precision.
Farther, he dwells upon the value of Classification and
Nomenclature ; although he suggests no leading principles for
either process. In these preliminary remarks we recognize
the sagacity of the practised experimenter; but it is when he
comes to analyze what is involved in the notion of Cause, and
to state his rules of philosophizing, that we become fully aware
of the advance made in the investigation of Nature since
Bacon and Newton, and of the advantage possessed by the
expounder of scientific method in having a large body of
successful observations and experiments to generalize from.
From the characters implied in the connexion between
cause and effect, he derives nine ‘ propositions readily appli-
cable to particular cases, or rules of philosophizing.’ Four of
them, the second, seventh, eighth, and ninth, are the four
694. GROWTH OF THE LOGIC OF INDUCTION.
Experimental Methods ; which are stated with snfficient pre-
cision, although not exalted into the prominence given them by
Mr. Mill as the sufficing and only methods of Proof. By
Herschel in fact, the four rules are regarded solely as aids to
Discovery ; the ‘idea of Proof. does not seem to have crossed
his mind. His other rules are more purely suited for Dis-
covery. The first is a more precise statement of Bacon’s main
principle of Exclusion, the foundation of the methods of Agree-
ment and of Difference :—‘ that if in our group of facts there
be one in which any assigned peculiarity or attendant circum-
stance is wanting or opposite, such peculiarity cannot be the
cause we seek.’ The third is ‘we are not to deny the exist-
ence of a cause in favour of which we have a unanimous
agreement of strong analogies, though it may not be apparent
how such a cause can produce the effect, or even though it
may be difficult to conceive its existence under the circum-
stances of the case ’:—a maxim identical with the principle of
analogy, that we may sometimes infer the presence of one
phenomenon from the presence of another, although no causal
connection has been established between them. As an example
he states that though we do not know how heat can produce
light, we yet conclude that the sun is intensely hot because it
is vividly luminous. The fourth rnle is that ‘contrary or
opposing facts are equally instructive for the discovery of
causes with favourable ones.’ The fifth recommends the —
tabulation of facts ‘in the order of intensity in which some
peculiar quality subsists,—perhaps the most valuable art of
Discovery. To this precept Herschel very properly appends
that the value of the device may be frustrated by the interfer-
ence of counteracting or modifying causes. The sixth rule
reminds the enquirer ‘ that such counteracting or modifying
causes may subsist unperceived,’ and urges attention to them
as a means of explaining exceptions.
In some general remarks following the enunications of his
rules, he illustrates the necessity of combining Deduction with
Induction in complicated enquiries, and explains the nature
of Empirical Laws, glancing at the fact that they are limited
in their application to new cases, without stating more pre-
cisely what their limits are.
The concluding chapter treats ‘ of the higher degrees of
Inductive Generalization, and of the formation and verification
of theories.’ He insists that the assumed agents must be
vere causm, ‘such as we have good inductive grounds to
believe do exist in nature.” The value and the test ofa hypo-
Pe
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WHEWELL’S FACTS AND IDEAS. 695
thesis he places in its accordance with the facts, and its enabling
us ‘ to predict facts before trial.’
Wuewett. The scheme of the late Dr. Whewell’s Novum
Organum Renovatum commends itself as strikingly thorough
and exhaustive. It professes to be ‘a revision and improve-
ment of the methods by which Science must rise and grow,’
founded upon a comprehensive History of Scientific Discovery
and a History of *cientific Ideas. Now, theoretically, there
could be no more perfect way of elaborating a body of maxims
for the aid of the discoverer, than to pass in review, chronolo-
gically or otherwise, the great physical discoveries that have
been made, and to study the essentials of the process in each
case.
The distinguishing feature of Whewell’s scientific writings
is his persistent driving at an antithesis that he conceives to
be fundamental, between Ideas or Conceptions and Facts.
This antithesis is the shaping principle of his system and
meets us at every point. It regulates the division of his
history into two parts: the History of Scientific Ideas tracing
the gradual development of the so-called ideas, such as Cause
Affinity, Life, that form the subject-matter of various depart-
ments of science ; and the History of Scientific Discovery, illus-
trating how by the instrumentality of Ideas (the highest
generalities), and of Conceptions (the lower generalities), the
particular facts of Nature are united and bound together.
The same antithesis divides scientific method into two pro-
cesses. Generalization consisting not in evolving notions from
a comparison of facts, but in superinducing upon facts con-
ceptions supplied by the mind. There are two requisites to
satisfy before this operation can be perfected, namely, that the
Conceptions be clear and distinct, and that they be ‘ appro-
priate’ to the Facts, capable of being ‘applied to them so as
to produce an exact and universal accordance:’ whence there
are two scientific processes, the Explication of Conceptions and
the Oolligation of Facts.
The grand problem of Science is to superinduce Ideas or
Conceptions upon Facts. The business of the discoverer after
familiarizing himself with facts, is to compare them with con-
ception after conception, in the view of finding out aftera
tonger or shorter process of trial and rejection, what concep-
tion is exactly ‘appropriate’ to the facts under his consider-
ation. When the investigator has at length, by a happy gues.
hit upon the appropriate conception, he is said to ‘colligate’
the facts, to ‘bind them into a unity.’ No distinction is
696 GROWTH OF THE LOGIC OF INDUCTION.
drawn in this operation between the generalization of Notions
and the generalization of Propositions ; the difference between |
them is merged in the one grand purpose of procuring for
facts clear and appropriate conceptions.
It is difficult to understand what he supposes to have been
the origin of the conceptions thus superinduced upon facts.
He speaks of them as being struck out in the gradual march
of Science by the discussions and reflections of successive
thinkers, a view not inconsistent with their derivation from
the comparison of particulars and the gradual evolution of
decp and pervading agreements. But he says also that they
are supplied by the mind, while facts are supplied by sense;
and the language he holds regarding the suiting of facts with
their ‘appropriate’ conceptions, is consistent only with the
assumption that the mind is a repository of conceptions accu-
mulated there independently of the experience of particulars.
By this initial severance of generalities from the particulars
they repose upon, he excluded from his method definitions
formed by the comparison of facts and the precise statement
of common features. He rather decries the value of Definition,
and allows it no place of hononr in his Lxplication of Conceptions.
The meaning of a conception is, he thinks, oftener apprehended
from an axiom than a definition—another instance of his total
neglect of the distinction between notions and propositions.
His ‘methods employed in the formation of Science,’ the
title of the third Book of the Novum Organon, are three in
number, Methods of Observation, Methods of obtaining clear
_ Ideas, and Methods of Induction. As a preliminary to Obser-
vation, he recognises an Analysis or Decomposition of Facts.
Under Observation, he discusses chiefly the modes of obtaining
precise measurement; he speaks also of the education of the
senses, but does not attempt to lay down any definite precepts
farther than recommending the study of Natural History and
the practice of Experimental manipulation. His Methods of ac-
quiring clear scientific ideas, are neither more nor less than
the study of the various departments of science where the
ideas occur ; the very method that would be recommended by
a preceptor believing in the evolution of general notions from —
particulars. An aid to the acquisition of clear ideas is Discus-
sion.
We find no trace of the three leading Experimental Methods
in his Methods of Induction, nor indeed of any methods of
Proof. He conceived that his province was to furnish arts of
Discovery, in so far as anything was of avail beyond natural
mw
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WHEWELL’S METHODS OF INDUCTION, 697.
sagacity; and he seems to have thought slightingly of the
efficacy of the Three Methods as a means to the attainment of
new laws. His principal arts of Discovery are given under
the title of ‘Special Methods of Induction applicable to Quan-
tity.” The Method of Curves isa device for making apparent
to the eye the result of observations on the concomitant varia-
tion of two phenomena. It ‘consists in drawing a curve of
which the observed quantities are the Ordinutes, the quantity
on which the change of these quantities depends being the
Abeissa,’ The Method of Means is the familiar device of
eliminating the effects of a constant cause from the conjoined
effects of accidental accompaniments by striking an average of
several observations. The Method of Least Squares is a some-
what complicated supplement to the Method of Means. When
more than one mean is proposed, they are each compared with
the series of actual observations; the deviations from each
case in the series are squared, and the mean is affirmed to be
most probable, the sum of whose squares is lowest in amount.
The Method of Residues is the method we described under that
name.
Under the title of ‘Methods of Induction depending on
Resemblance,’ he illustrates the Law of Continuity (‘that a
quantity cannot pass from one amount to another by any
change of conditions, without passing through all intermediate
magnitudes according to the intermediate conditions’); the
Method of Gradation, a name given to the process of proving
that things differ not in kind but in degree); and, in the
Method of Natural Classification, enforces the importance of.
grouping objects according to their most important resem-
blances.
Perhaps the most valuable part of the Organon is the con-
eluding Book on the Language of Science. Of this subject
Whewell had made a special study ; his aphorisms on the
requisites of philosophical language contain nearly all the
important points.
H.—ART OF DISCOVERY.
It was the distinction of Mr. Mill’s handling of Logic to
draw a clear and broad line between the Art and Science of
Proof and the Art of Discovery. The main business of Logic,
according to him, is the proving of propositions; only in an
incidental way does it aid in suggesting them.
There is, in the laws of evidence well understood, a power-
ful indirect incitement to original discovery. A thorough
698 ART OF DISCOVERY.
means of testing whatever is propounded for acceptance leads
to the rejection of the false, and, consequently to a renewed
search, ending at last in the true. For this reason alone —
would discovery be more rapid in the Mathematical and
Physical sciences, where verification is easy, than in the
Mental, Moral, and Political sciences, where the facts are
wanting in the requisite precision. Kepler was not left in any
doubts as to whether he had arrived at the true law of the
periodic times of the planets; psychologists could not so
easily satisfy themselves as to the thorough-going concomitance
of mind and body.
The Arts and methods of Discovery embrace (1) the Facts,
that is, Observation ; and (2) the Reasonings on Facts, namely,
Deduction, Induction, and Definition; which are all compre-
hended in the one process, generalization.
As regards the accumulation of Facts, there is little to be
said, and that little is apparent at a glance. Facts are ob-
tained by active search, enquiry, adventure, exploration. For
some, we must travel far, and visit many countries ; for others
we have to lie in wait till occasions arise. For a third class,
we have to institute experiments, involving contrivance and
devices, and the creative ingenuity of the practical mind ; all
which is itself a department of discovery, the least of any
amenable to rules.
The arts of Observing were remarked on, in the Introduc-
tion, as being special for each department, and not a fit sub-
ject for general logic. The precautions common to all kinds
of observation, in regard to accuracy and evidence, would be
worthy of being recited, provided there could be given a sufli-
ciency of illustrative instances to make the desired impression.
From the limitation of the human faculties, the highest
powers of observation are not usually accompanied with high
speculative force. Hence, among other consequences, a not
unusual misdirection of the energies of great observers. .
Passing from the region of fact, we come to the region of
Generality. A number of individual observations being sup-
posed, the next thing is to discover agreements among them—
to strike out identities wherever there are points to be identi-
fied; these identities ending either in Notions or in General
Principles. It may seem a work of vast labour to exhaust
all the facts of the material and of the mental world; it is nota
less labour, although of a different kind, to exhaust all the
identities among the facts.
Although the main condition of success, in bringing about
: : ad
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PSYCHOLOGICAL AIDS TO DISCOVERY. 699
identities, is a peculiar intellectual aptitude, belonging to some
men in a pre-eminent degree; yet there are aids, methods,
and precautions, for increasing the power. Some of these
aids are suggested by intellectual psychology, others grow out
of the methods unfolded in logic.
The methods growing out of the psychology of the intellec-
tual powers are briefly these :—to possess the mind of a large
store of the related facts; often to refresh the recollection of
them ; to come into frequent contact with subjects that seem
likely to afford comparisons and analogies; not to stand too
near any one set of facts so as to be overpowered by their
specialities ; not to be engrossed with the work of observing
the facts ; and in general, as to matters of great difficulty, to
keep the mind free from attitudes and pursuits antagonistic
to the end in view.
Newton alternately devoted himself to mathematics and to
the observation and collection of facts in the various subjects
of natural philosophy; and this alternation doubtless makes
the perfect physical enquirer.
Frequently an identification has to be embedded in some
conception apart from the facts ; as Kepler’s laws in numerical
and geometrical statements, the law of sines, &c. In such
cases, proximity to the sources of the conceptions will help to
bring about the coalition. If mathematical relations, the
mathematical knowledge should be kept fresh, and so with
other subjects. These constructing instances alone give any
meaning to Wheweil’s much iterated antithesis of Fact and
Idea. The identification and generalization of facts often
happens without any ‘idea,’ any central form, or representa-
tive beyond the facts themselves; there is no idea for a circle
but round things, abstractedly viewed ; and no idea for gravity,
but gravitating bodies compared and regarded in their points
of agreement. In certain other cases, a conception is obtained
(not from any intuitive source, but) from some already existing
generalization, either in the same department, or in another
department. The ‘idea’ for embracing water waves, and
sound vibrations, was found by Newton in the ‘ Pendulum;’
and apart from the facts themselves, no better ‘idea’ has yet
been given.
The connexion of Body and Mind has its ‘idea’ yet to seek.
There has hitherto prevailed the bad idea of External and In-
ternal. Inshort, the most suitable comparison wherein to em-
brace therelation has not been obtained from any source, intuitive
or other. One approximation is a ‘ union of distinct states.’
700. ART OF DISCOVERY.
The arriving at difficult identifications, that is, the tracing
of similarities shrouded in diversity, by such devices as have
been advanced in logic with a more special eye to proof, may
be viewed in the first place with regard to generalizution as
such; not distinguishing the notion from the principle or
proposition: What pertains specially to the induction of the
general proposition, namely, the conconwtance of distinct pro-
perties, is best considered apart.
_ Under the Deductive Method (p. 96) attention was called
to three helps to the discovery of generalities—multiplication .
of instances, close individual scrutiny of instances, and selec-
tion of the least complicated instances. A wider view of the
available resources must now be taken. We have to see how
far the thorough explication of the reasoning processes, and of
all the adjuncts to reasoning, called forth by the comprehen-
sive Logic of Proof, can be brought to bear also in the striking
out of suggestions to be submitted to proof or disproof.
The first great practical lesson derivable from Logic, and
applicable in a much wider sphere than proof, is to impress us
with Generality as the central fact of science and of all know-
ledge transcending individuals. After we have gained posses-
sion of a certain range of facts, the next great aim is to
generalize them to the uttermost. This is not all. In pro-
portion to the compass of any agreement, ought to be the
pains taken with it, and the prominence given to it. We
have urged, under the Logic of Medicine, the prime import-
ance of generalizing the Diseased Processes and General Thera-
peutics, because of the wider compass of their application. In
everything else, the rule holds. The biologist should take no
rest until he has exhaustively accumulated instances of the
great fact of Assimilation, under every possible variation of
circumstances’. In like manner, the physical concomitants of
mental processes need to be searched out in all their innumer-
able modes, in order to rise to the generalities of the connexion.
The severest etiquette of the most punctilious system of
ranks and dignities in society is as nothing compared with the
graduation of estimate and of respect to be shown to generali-
ties of different grades. It is a grave logical misdemeanour
ever to give an inferior generality precedence over a superior,
or to treat the two as of equal consequence, or even for a
moment to be unaware of their relative standing. We may
give all due consideration to the phenomenon of falling bodies
as a wide fact co-extensive with the surface of the earth; but —
in presence of the superior sway of the law of gravity through-
VALUE OF ORDER AND METHOD. TO1
out the solar system, the terrestrial fact must sink into a
second place in our esteem.
The next great application of Method, as an aid to discovery,
consists in the use of the various Forms or Formalities, ela-
borated with a view to proof. This is the largest part of the
present subject.
« Logicians have always striven to set forth the value of Order,
method, and explicitness, in complicated statements. Hamil-
ton’s dictum—making explicit in the statement what is implicit
in the thought—has been received as a happy enunciation of
one function of logic. Mr. Mill remarks,—‘ One of the great
uses of a discipline in Formal Lggic, is to make us aware when
something that claims to be a single proposition, really con-
sists of several, which, not being necessarily involved one in
another, require to be separated, and to be considered each by
itself, before we admit the compound assertion.’ This is the
disentangling or analyzing function of the syllogism, and is
deservedly extolled as perhaps its highest utility. It is a
direct remedy for the weakness of the mind formerly adverted
to (p.398).
We may, however, go farther back than the exposition of
- Syllogism for valuable aids growing out of the logical formali-
ties. All the Equivalent Propositional Forms are instrumental
as means of suggestion. They enlarge the compass of any
given proposition, by unfolding all its implications; many of
these not being disposed to rise to view of themselves, or
without the stimulus of the formal enunciation. Of all the
modes of Hquivalence, probably the Obverse is the most fruit-
ful and suggestive ; this has become apparent on many occa-
sions, in the course of the present work; we may instance
especially negative defining. Next in value is Conversion ; the
converting of A by its legitimate form is.a check to the blunder
of supposing the subject and predicate co-extensive in uni-
versal affirmations ; and the arresting of the mind on the road
to impending error seldom ends there, but is also a start in
the search for truth. Even the immediate inference from the
Universal to the Particular is suggestive of facts not previously
in the view.
Much could be said as to the unsystematic but wide-ranging
mode of Equivalence by Synomyous terms, or by varying the
ways of expressing the same proposition. Although some-
what ensnaring, this is a fruitful and suggestive operation.
Its power consists in resuscitating from the stores of the past
all the various known examples of the proposition ; to which
702 ART OF DISCOVERY,
also may be added even illustrations and analogies. We know
from many celebrated instances, how mere opulence of phrase-
ology gives the semblance, and occasionally the reality, of
superior insight. The Shakespearian wisdom, the stirring
apothegms of Pope, have their source, not in the scientific
process of the intellect, but in the suggestiveness of exuberant
phraseology.
The Methods of Inpuctive Elimination, both directly and
indirectly assist in Discovery. The collection and comparison
of instances, to comply with the method of Agreement as a
method of proof, will in many cases lead to new and improved »
generalizations. A man can scarcely go through the labour
requisite for establishing a law of high generality upon ade-
quate evidence, without adding to his knowledge of the law.
Hspecially is this likely to happen in working the Method of
Agreement, whose exigencies are exactly those of inductive
discovery.
The same remark applies to the union of Agreement in
Absence with Agreement in Presence ; and there is the addi-
tional force and incisiveness that always belongs to the working
of the negative side.
The method of Residues, to which Sir John Herschel called
special attention, was by him expressly commended as an aid
to Discovery.
The importance of Concomitant Variations has already been
signalized, and will be again referred to.
Without dwelling farther on the specific virtues of the
‘several methods, we would call attention to the value of a
complete scheme of Inductive Proof, in urging a search for
instances to fill up all its requirements. He that has thoroughly
mastered the experimental methods, desires to bring up in
favour of every important principle a series of particulars
under each one of them separately ; an operation as fertile for
discovery as it is thorough-going for proof or disproof.
The remark is not confined to the methods of experimental
elimination. The greater number of propositions or laws may
derive evidence through the Deductive Method, and through
Chance and Probability also. The wish to satisfy all possible
methods of establishing a law is a wholesome stimulus to
enquire after the very facts that improve the character and
extend the application of the law. The consilience of Indac-
tion and Deduction is the very highest art that the human
intellect can command, not merely for proving difficult propo-
sitions, but for getting hold of propositions to be proved.
INDUCTIVE ELIMINATION, 703
All this is to repeat in another shape, and in a grander
sphere, the function of the Syllogism in insisting that there
should be produced an explicit major and an explicit minor
premise in any pretended ratiocination. Every inductive in-
stance should be viewed in its proper character, by reference
to the method that it subserves. An instance of Agreement
should be given as such; a Deductive proof should be quoted
under that description. If the Logical rules are not arbitrary,
but founded on a correct analysis of the scientific processes,
the conscious reference to them, on all different occasions,
must be a relief and a comfort to the perplexed enquirer.
_ The Deductive operation, understood not formally as in the
syllogism, but really and materially, as in finding new appli-
cations and extensions of inductions, is a pure generalizing
process. It consists in identifying particulars with other par-
ticulars, exactly as in the properly inductive operation. It is
the same march of mind continued and prolonged. An induc-
tion so called is merely a certain collection of particulars, with
a generalized expression superadded ; deduction is the bring-
ing in of new particulars. The difference of the two is not in
the mental operation; it is in the end thatis served. The
inductive particulars are those necessary for giving the gen-
eralized expression, and for proving it as a law of nature ; the
subsequent deduced particulars, not being required for esta-
blishing the generality, receive illumination from the other
class. In both cases the effort of discovery is identical ; it is
the bringing together in the mind by the force of resemblance
a host of particular facts from all times, places, and subjects.
Before the induction is gained, the particulars contribute to
its establishment; after it is gained, the new particulars are
receivers and not givers of benefit.
The processes included under Derinitron—the canons for
Defining, General Naming, and Classification—are processes
of Discovery directly, and of Proof indirectly. Mr. Mill calls
them subsidiary to Induction, meaning Inductive Proof.
Every step indicated under those several heads has an imme-
diate efficacy either in suggesting generalities, or in purifying
them from ambiguity, perplexity, and confusion. It is impos-
sible to make a single well concerted move in any of the paths
marked out in these several departments without gaining an
enlargement of views, or the means of some future enlarge-
ment.
Everything of the nature of an antidote to inadvertent and
confused tainking, everything that reduces information to the
TO4 ART OF DISCOVERY.
shape best suited for recollection and reference, everything
that facilitates the comparison of resembling facts—must be
enrolled among the means of Discovery. These various ends
are explicitly aimed at by the prescriptions contained under
Definition, Naming, and Classification. To substantiate the
allegation would be to rehearse the methods explained
under those heads. The amassing of particulars, positive and
negative, with a view to Definition, is the express act of gen-
eralization, and brings with it discoveries of concomitance, as
well as generalizes notions. All the devices of Naming are
intended primarily to ease and assist the understanding in
arriving at new truths. The machinery of Classification is stall
more strikingly the economizing of the faculties in amassing
and in manipulating knowledge. |
When the generalizing process has expressly in view the
discovery of laws, or concurring properties, a most material
help (as formerly seen) is afforded by Tabulation, espe-
cially according to a scale of degree. Failing this, great stress
is always laid upon extreme instances. These are the glaring
and striking instances of Bacon and Herschel (see the Re-
search on Dew, p. 68). The method of exhibiting gradation
by Curves is considered one of the best ways of suggesting
numerical laws.
Mr. Darwin has given an account of the steps that Jed him
to propound the doctrine of Development under Natural
Selection. It affords an interesting commentary on the fore-
going enumeration of the causes that prompt original sugges-
_ tions.
‘When I visited, during the voyage of H.M.S. Beagle, the
Galapagos Archipelago, situated in the Pacific Ocean about
500 miles from the shore of South America, I.found myself
surrounded by peculiar species of birds, reptiles, and plants,
existing nowhere else in the world. Yet they nearly all bore
an American stamp. In the song of the mocking-thrush, in
the harsh cry of the carrion-hawk, in the great candlestick-
like opuntias, I clearly perceived the neighbourhood of
America, though the islands were separated by so many miles
of ocean from the mainland, and differed from it in their
geological constitution and climate. Still more surprising was
the fact that most of the inhabitants of each separate island
in this small archipelago were specifically different, though most
closely related to each other. ‘The archipelago, with its imnu-
merable craters and bare streams of lava, appeared to be of
recent origin ; and thus I fancied myself brought near to the
ate ie
a Saal oe Ne he akg 8b A i iy
CONSTRUCTIVE INVENTION, 705
very act of creation. I often asked myself how these many
peculiar animals and plants have been produced: the simplest
answer seemed to be that the inhabitants of the several islands
had deseended from each other, undergoing modification in
the course of their descent; and that all the inhabitants of
the archipelago had descended from those of the nearest land,
namely America, whence colonists would naturally have been
derived. But it long remained to me an inexplicable problem
how the necessary degree of modification could have been
effected, and it would have thus remained for ever, had I not
studied domestic productions, and thus acquired a just idea
of the power of Selection. As soon asI had fully realized this
idea, 1 saw, on reading Malthus on Population, that Natural
Selection was the inevitable result of the rapid increase of all
organic beings; for I was prepared to appreciate the struggle
for existence by having long studied the habits of animals. ’
(Domestication, vol. I., p. 9).
Throughout the entire logical scheme, the analytic separation
already insisted on, is an invaluable help to the faculties under
the complications of natural phenomena. Toenable us to view
separately whatever can be separately viewed is the motive
for such artificial divisions as Structure and Function in
biology, Physical Side and Mental Side in psychology, Order
and Progress, Theory and Practice in politics, Conservation
and Collocations in cause and effect, Description and Explana-
tion every where.
The process of Invention in the Arts and business of life, is
amenable to the general rule of keeping the mind fresh upon
the most likely sources. The mere cogitating process in prac-
tical constructions is exactly the same as in the solving of
geometrical gp other problems. Certain data are given, a
certain construction is required ; there is an intervening chasm
that has to be bridged. The habit of analytical separation is
of avail in this instance also. The mind should steadily view
one poiut at a time, drawing out connexions with each by
turns. Thus, to t..ke a simple geometrical construction : given
the vertical angle, the base, and the altitude of a triangle to
construct it. Now the base is given, and we have to follow
out the deductions and implications of the two other data—
altitude and vertical angle—with a view to arrive at some
known process that will construct the triangle. Let us con-
sider separately what the altitude will suggest. Now, a
certain fixed altitude implies that the apex of the triangle will
lie somewhere in a line parallel to the base; consequently, if
706 ART OF DISCOVERY.
we draw such a parallel, we limit the place of the apex to that
line. Turn next to the given angle. Considering how to
erect upon a given base a triangle with a given vertical angle,
we are reminded that upon the given base may be constructed
an arc of a circle, such as will contain that angle. The next
step is to find a means of constructing the proper arc; the
operation of discovery is exactly the same; and brings us at
length to some construction that we can perform. We then
unite our two threads hitherto followed out in separation.
The parallel line first suggested, and the arc next found out,
give by their intersection an apex to the desired triangle. It
is our previous knowledge that must forge the links of con-
nexion between what is given and what is required; but the
analytic habit concentrates the attention by turns on each
datum, and each outgoing from it; and this is probably the
utmost that mere art or method can do for us in constructive
inventions. .
The uncertainty as to where to look, for the next opening in
discovery, brings the pain of conflict and the debility of
indecision. This is a case fit to be met by the collective
wisdom of a generation. There might at intervals be held a
congress on the condition-of-science question, to decide, accord-
ing to all the appearances, what problems should be next
taken up.
Lessons may be drawn from the history of Hrrors, as well
as of Truths. All the Fallacies are beacons both in discovery
and in proof. Every source of confusion is an incubus on in-
- vention. More particularly, the excessive devotion to the con-
crete, and to the artistic interests nourished by it, may amount
to a total disqualification for scientific originality, whose very
existence is in the domain of abstraction.
Certain widely prevailing tendencies of natural phenomena
have been indicated as of value in prompting discovery. Such
are the Law of Continuity, and the maxim that Nature works
by the Simplest Means. Both these principles are uncertain
in their scope ; which, however, does not prevent them from
being used to give suggestions ; it only disqualifies them from
being conclusive evidence. If we are careful to verify our
hypotheses, we are at liberty to obtain them from any source.
Still, the mind that has become largely conversant with the
ways of nature will find many more fruitful sources of suggese
tion than either of those principles. -
RECITAL OF FACTS, [07
I.— HISTORICAL EVIDENCE.
Two leading branches of Evidence, applied in practical life,
are Legal Hyidence and Historical Evidence. The two depart-
ments have much in common. The evidence both in courts of
law and in matters of history is probable, and approaches to
certainty by the summation of probabilities.
The following abstract of Historical Evidence represents
the maxims in use among historians at the present day, as
summarized by Sir G. C. Lewis.
_ The object of History is the recital of facts—of events that
have actually occurred.
In the case of contemporary history, the writer may be able
_to rely upon his own observations, or upon original documents
obtained from authentic sources. Personal knowledge was
the basis of much of Xenophon’s Anabasis, Polybius’ History,
Cexsar’s Gaelic War, and Lord Clarendon’s History of the
Rebellion. But the greater part even of contemporary history
must repose on the evidence of witnesses.
To a historian, not himself cognizant of the events he nar-
rates, the sources of information fall under one or other of
two classes :—(1) Monuments, ruins, coins, and generally all
ancient remains; and (2) the evidence of Witnesses. From
the former exclusively is derived whatever we know of the
pre-historic age; in the same way as geology is built on in-
ferences drawn from fossils and the nature and position of
rocks. It is only with regard to history resting upon the tes-
timony of witnesses that rules of historical evidence apply.
Two points demand the notice of one seeking to verify any
alleged historical fact. (1) Does the evidence of the witness
exist in an authentic shape? and (2) Is it true? The first
regards the accuracy wherewith the evidence has been trans-
mitted to us; the second, the worth of the evidence itself.
The means of knowledge of the witnesses, the goodness of
their memory, their judgment, their general veracity, their
special interests,—are all to be considered. This the historian
has in common with a jury or a judge, except that he has to
deal with men long since dead, and whose character there is
more or less difficulty in ascertaining. What forms the pecu-
liar subject-matter of rules of historical evidence is not there- -
fore the worth of the evidence, but the accuracy of its trans-
mission. |
The supreme canon of historical evidence is that all testi-
708 HISTORICAL EVIDENCE.
mony must be contemporary, or received directly or through
trustworthy tradition, from contemporar.es. ‘ Whenever any
event is related in histories written after the time, and not
avowedly founded on contemporary testimony, the proper
mode of testing its historical credibility is to enquire whether
it can be traced up to a contemporary source. If this cannot
be done, we must be able to raise a presumption that those
who transmitted it to us in writing received it, directly or
through a trustworthy tradition, from contemporary testi-
mony. If neither of these conditions can be fulfilled, the
event must be considered as incurably uncertain, and beyond
the reach of our actual knowledge.’ (Lewis’s Methods of
Politics, I. 270.)
This rule is universally recognized as inclusive; whatever
is established by such testimony is credible. There is not,
however, the same unanimity, in admitting it as exclusive; or that
whatever is not authenticated by external evidence is uncer-
tain. 7 Sis ‘
ee pares Se! We
TRANSMISSION OF WRITTEN EVIDENCE. 709
and fact; from the Secession of the Plebs io the war with
Pyrrhus (213 years) is solid history. It would perhaps be
too much to condemn Niebuhr’s efforts on a priori grounds.
To what extent a license of guessing may be permitted will
best be seen when it has been tried by different men. If the
result should be a general concordance of opinion, we might
reasonably infer that the ancient narratives, although they.
conceal, nevertheless betray the truth. If, however, this
method lead to irreconcileable and endless diversity of opinion,
it must cease to be regarded as valuable or trustworthy.
Evidence may be transmitted in two ways, by writing or by
oral tradition. These may be considered separately.
The value of a written memorial consists generally in this,
that its credibility is not impaired by the mere action of time.
An English mathematician named Craig held that all testi-
mony was enfeebled by mere lapse of time, and thus the evi-
dence of Christianity would at length be reduced to zero.
Assuming that that event would coincide with the end of the
world, he calculated when the end would come. Laplace
adopts the same view, and says that even in spite of printing,
the events that are now most certain, will, in the course of
ages, become doubtful. But this must be regarded as an error.
The only deterioration that a document can suffer from mere
lapse of time is the increased difficulty of weighing the credi-
bility of the writer. A written memorial has none of the
disadvantage of a statement handed down orally from one
person to another, and losing value at each transmission.
Yet the evils of transmission are not wholly overcome even
with written records. Two doubts may arise, (1) whether the
writing is ascribed to its real author, and (2) whether it is free
from interpolation and mutilation.
‘In many cases the original memorial is preserved; as in
ancient inscriptions upon stone, brass, or other durable ma-
terial. Such are the inscriptions, in the arrow-headed cha-
racter, on the Babylonian bricks, and on other Assyrian
monuments ; the hieroglyphics engraved on the remains of
Egyptian architecture; and the numerous Greek and Latin
inscriptions found in different parts of Asia Minor, Africa, and
Europe, and belonging to different ages. Ancient coins, with
their legends, are another original record of the same kind, as
well as historical sculptures or paintings, such as the bas-reliefs
on the column of Trajan, or the Bayeux tapestry. Ancient
documents, likewise, containing the authentic records of many
important events and public acts, are preserved in the original
710 HISTORICAL EVIDENCE.
in national archives. Such, for instance, is Domesday-book, the
rolls of Parliament, court records, charters, and other official
registers and documents kept in public depositories.’ (Lewis,
I. 201).
In authenticating books and documents, whose safe-keeping
is not specially provided for, great difficulty is often expert-
_enced. A mere tradition regarding the origin of a document
would be exposed to nearly all the doubts that attach to oral
tradition. ‘Hence the importance of archives, chartularies,
public libraries, and other safe places of deposit, which are
under the care of trustworthy guardians, appointed and con-
trolled by public authority.’ The law of England requires
that written documents, before they can be tendered as evid-
ence, be produced from the proper place of custody.
The difficulty of ascertaining the genuineness of ancient
books, is forcibly illustrated by the controversy regarding the
Platonic Dialogues. Until the close of last century, thirty-six
dialogues were attributed to Plato on the authority of Thra-
syllus, whose list dates from about the commencement of the
Christian era. As, however, Plato died more than three
hundred years before, the canon of Thrasyllus stands in need
of corroboration and support. Most of the German Critics
allow it very little weight, and test each dialogue upon
own evidence, external or internal, but chiefly internal. This
unavoidably gives rise to great diversity of opinion, and there
is little agreement as to what ought to be rejected or retained.
Ast, the least sparing critic, leaves only fourteen out of thirty-
six. Mr. Grote, on the other hand, discards the German
criticism, and putting little stress upon the indications of
authorship contained in any reputed dialogue of Plato, searches
for more decisive evidence, so far as it can be got, in the
history of the books mentioned by Thrasyllus.
Plato died B.C. 347, and left his works to the care of the schoal
continued under Xenophanes and Speusippus. We do not
possess any list of their master’s works resting on their autho-
rity, and the first solid ground we reach (apart from the few
incidentally mentioned or alluded to by Aristotle) is an extract
from the works of the Grammaticus Aristophanes, who lived
at Alexandria from B.C. 260 to B.C. 184. He comes thus a
century after Plato, and nearly two centuries before Thra-
syllus. He divided the dialogues into trilogies, and several
of these are mentioned by Diogenes Laertius. They are re-
markable as containing the names of some of the compositions —
that are least acceptable to the critics, and that would be hard
EXAMPLE OF PLATO’S DIALOGUES. 711
to vindicate on internal evidence. These are Leges, Epinomis,
Minos, Epistolae, Sophistes, Politicus. It would be interest-
ing to know what means Aristophanes had of distinguishing
the genuine from the spurious works, if any such then existed.
For two centuries after the death of Plato, the Academy
was kept up as a philosophical school, with an unbroken suc-
cession of presidents. The chief treasure of the school was .
the works of the master. It cannot be too much to assume
that there was provided a safe custody for the MSS. of Plato,
and a ready means of verifying any alleged works. Plato is
better off in this respect than any of his great contemporaries,
. Socrates, Demosthenes, Euripides, or Aristophanes.
Aristophanes, the Grammaticus, was head of the Alexan-
drian Library. He was taught by Callimachus, who preceded
him in the office of Chief Librarian. Callimachus is the author
of the ‘Museum,’ a general description of the Alexandrian
Library ; and less important authors than Plato, as e.g. Demo-
critus, are mentioned by him. It is then highly probable that
such a library as that of Alexandria would contain copies of
oue of the foremost Greek philosophers. And, considering
the ease of verification, it is most likely that the Librarian
would assure himself that his copies were authentic.
There were, in the time of Thrasyllus, spurious dialogues. .
Whence came these, and by what criterion did he discard
them? If Aristophanes and Thrasyllus (who appears also to
have been connected with Alexandria) depended upon the lib-
rary there, they must be allowed to speak with great weight ;
but if'they proceeded wholly or partially upon internal evidence,
they have less claims on our attention than the better-equipped
modern critics. Mr. Grote supposes that the spurious works
were made for the demand in Greece and Asia Minor, and
for the library started by the Kings of Pergamus as a rival to
the Alexandrian.
So much for the difficulty of settling the real authorship.
The other point to be determined is the freedom of existing
copies from spurious additions or omissions, accidental or
intentional.
In the first place, errors will accidentally creep in, by the
mere act of copying. It is impossible to guarantee strict
accuracy in transcription. This is recognised in jurisprudence,
and the English law refuses to admit any copy where the
original can be produced. But the reason of the law does not
apply with the same force in history. A very slight alteration
in a deed might sometimes alter the meaning of it; and, more-
3]
712 HISTORICAL EVIDENCE.
over, there is often an exceedingly powerful temptation to
tamper with deeds. Now, the value of a copy of MS.
depends on its accuracy, and the motives for falsifying history
are far weaker. It is therefore considered that the works of
classical authors are preserved to us substantially as they were
when published. Such variations as there are do not affect
the general accuracy of the copies that have reached us. _
In the second place, changes may be made intentionally, to
suit a purpose. We are told that Solon inserted a verse in
the Iliad with a view to confirm the title of the Athenians to
the possession of Salamis. At an early period, authentic lists
or canons of authors and their works were prepared to guard
against deception. Short writings are most easily forged, and
hence there are numberless forgeries of letters; but we find
examples of falsification at greater length in the poems of
Ossian. Ecclesiastical writings contain many forgeries, made for
the purpose of propagating or confirming opinion. The motive
for executing forgeries is often to make money by arousing
curiosity ; but in such cases as Ossian, it is merely the pleasure
of deceiving the world. Literary forgeries. are generally
detected by internal evidence—by inconsistencies, anachron-
isms, imitations of subsequent writers, and other, maria of
recent composition.
When we have sufficient assurance that a work is both
authentic and genuine, written by its reputed author, and not
tampered with in the course of transmission, we have still to
consider the worth of the testimony. Besides examining our
- author’s means of information—whether he writes as an eye-
witness or at second hand, or at what other remove from eye-
witnesses—we must enquire into his character for versaiigiend
his motives to depart from the truth. sine
There is often intentional perversion or enppression of the
truth, especially in Autobiography, as Ceesar’s Gallic Wars,
and Napoleon’s Memoirs of his Campaigns. Vanity, a love of
the marvellous, and party spirit, operate in the same direction.
There are Catholic and Protestant histories of the Reforma-
tion; Whig and Tory histories of England. The accounts of
modern campaigns and military operations differ very much
according to the side the writer belongs to. Many inaccuracies
arise from not taking the trouble to investigate the truth.
History may be blended with fiction for a didactic or moral
purpose, as in Xenophon’s Cyropeedia.
The ancient historians departed from strict truth, by intone,
ducing into their works speeches composed by themselves.
it ia ie re. a
MYTHICAL HISTORY. 713
One fourth of the history of Thucydides is composed of such
speeches. Lucian thought it a sufficient excuse for introduc-
ing fictitious speeches, that they were suitable to the charac-
ter of the speaker, and appropriate to the subject. Polybius
is the only writer of antiquity who condemns the practice, for,
he says, the object of the historian is not to astonish the reader,
but to record what was actually done or said.. This opinion
has been followed by modern historians, and the manufacture
of speeches has therefore ceased. The same thing, however,
in substance, is still done, although introduced as part of the
history, namely, interpreting acts and suggesting motives.
It is a great, though perhaps not uncommon, error, to treat as
history what thus owes its origin to conjecture.
Another perversion of history is mythical history. ‘The
original author of such a legend must, no doubt, be at first
conscious that it is the spontaneous product of his own inven-
tion, unattested by any external evidence. But the fiction is
suggested by prevailing ideas and feelings; it interweaves
existing facts and customs into its texture; it furnishes an
apparent support to institutions or practices for which the
ular mind seeks an explanation; it fills a void which is
sensibly felt, and supplies food for an appetite whose demands
are at once urgent and general. The inventor of such a legend,
therefore, differs altogether from the author of a novel or
romance, who lays before the public a tale avowedly fictitious,
and which they accept as such.’ Hxamples may be found in
Greek mythology, in the fabulous heroes of medieval chivalry,
and in the lives of medieval saints. Such legends havea use,
not as describing events, but as throwing a reflected light on the
circumstances and character of those who invented, believed,and
circulated them. The most difficult case to the historian
is not pure mythology, but the blending of myth and history,
which lures men on to search for fact, but leaves them un-
able to distinguish it from fiction. The history of Greece,
from the first Olympiad to the Persian war, and of Rome,
from Tullus Hostilius tothe Punic wars, illustrates this inter-
mediate period of twilight and uncertainty.
The second mode of transmitting evidence— Ora TRADITION,
loses credit very rapidly with the lapse of time. An account
of an event, diminishing in evidentiary value at each remove
from the original eye-witness, very soon ceases to have any
value at all, This has always been more or less recognized.
Polybius confined himself to what he learned from eye-
witnesses of the preceding generation, and thus begins his
714 HISTORICAL &VIDENCE,
consecutive history about twenty years before his birth.
Newton thought that oral tradition might be trusted for 80
or 100 years; and Volney remarks that the Red Indians had
no accurate tradition of facts a century old, .
The average value of oral tradition may be enhanced in
various ways. During the panic caused by the mutilation of
the Mercuries, and the fear of treasonable attempts to esta-
blish a despotism, the Athenians recurred to the government
of Pisistratus and his sons, which had begun nearly 150 years
and ended 100 years before that time. Thucydides describes
the Athenians as referring, entirely by oral tradition, to the
attempt by Cylon—a fact at the time 180 years old. That
event had however created a hereditary curse in the powerful
family of the Aicmaeonidae, and the memory of it was revived
at different times by public acts. The Dies Alliensis, the
anniversary of the fatal battle of the Allia, was doubtless kept
up by uninterrupted usage from B.C. 390. Festivals, emblems,
antiquated offices, serve to fix tradition, and keep alive the
recollection of events. The Interrex, in Rome, who continued to
be appointed during the Republic in the vacancy of the consul-
ship, was a reminiscence of a period of elective kings. The
King of the Sacrifices, like the King Archon at Athens, is also
a decided indication of the regal period. There were, more-
over, many buildings, monuments, and public places in Rome
associated with the names of kings. The existence of laws,
like the Twelve Tables, inscribed on metal or stone, may serve
to perpetuate a correct oral tradition.
Rubino, the author of a work on the early Roman Constitu-
tion, has laid down some rules on this subject. He divides
oral tradition into two classes, one referring to the constitution,
and the religious and civil institutions connected with it, the
other embracing the more common material of history, wars,
negotiations, and the striking events that give interest to the
history of Rome. This last alone was committed to the ex-
clusive keeping of oral tradition, and was much more liable
to error and uncertainty than the traditions relating to the
constitution. ‘T'o some extent, constitutional usage implies a
knowledge of precedents. Such information in all probability
existed at the beginning of the Second Punic war; but it
might not reach far back without the help of documents,
There is no reason to suppose that accurate knowledge would
have gone back beyonda century. It is not possible to draw
any broad line between constitutional history, and the common
events of history ; we could not discuss the changes in the
ARGUMENT.-—CATEGOREMATIC.—DICTUM. 715
English Constitution during the seventeenth century, without
a knowledge of the events that gave birth to them.
There is one case where oral transmission makes an approach
to the value of transmission by writing. This happeus when
the memory is assisted and checked by a set form of words,
especially if the form be metrical. Czsar tells us that the
secrets of the Druidical religion were contained in a great
number of verses, in committing which to memory a druid
would spend twenty years of his life. In like manner, the
Iliad and Odyssey were perpetuated by a race of professional
reciters and rhapsodists.
K.—EXPLANATION OF SOME LOGICAL TERMS.
The following terms, not being deemed essential to any of
the important doctrines of Logic, may not have been made
fully understood in the previous exposition. As they occasion-
ally occur in logical discussions, short explanations of them
are here appended.
ARGUMENT is used in severa! different senses. Apart from
its more popular significations, a disputation, a chain of rea-
soning, and even a chain of events (the argument of a play),
its meaning is not fixed and uniform among logicians. Some
apply it to an entire syllogism, premises and conclusion, some
to the premises only as the grounds of the conclusion, while
Hamilton maintains that its proper meaning is the middle
notion in a reasoning,—‘ what is assumed to argue something.’
So Mansel holds that the word should be applied only to
the Middle Term.
CaTeGcoREMatic.—A distinction is drawn between words that
can stand alone as subject or predicate of a proposition, as
man, stone (Categorematic) ; and words that can stand only
in company with other words, as all, none (Syncategorematic),
DictoM DE OMNI ET NULLO.—This applies directly to the First
Figure alone. It is usual to give similar principles for the
other Figures, and among these we may notice the dicta given
by Mr. Mansel in his notes on Aldrich (p. 86).
‘Principle of second figure. Dictum de Diverso. If a cer-
tain attribute can be predicated (aflirmatively or negatively)
of every member of a class, any subject of which it cannot be
so predicated, does not belong to the class,
* Principles of third figure. I. Dictum de exemplo. Ifa
certain attribute can be affirmed of any portion of the members
716 EXPLANATION ON SOME LOGICAL TERMS,
of a class, it is not incompatible with the distinctive attributes
of that class. Il. Dictum de excepto. If a certain attribute
can be denied of any portion of the members of a class, it is
not inseparable from the distinctive attributes of that class.’
EnrHyMEME.—A syllogism with one of its premises sup-
pressed in the enunciation. Hamilton argues against the
prominence given to Enthymeme as a division of syllogisms,
on the ground that they are not a special form of reasoning,
but only an elliptical mode of expression. He also shows
(what is done more elaborately by Mr. Mansel) that Aristotle
understood by Enthymeme not an elliptical syllogism, but
‘a syllogism from signs and likelihoods,’ or a syllogism with
the major premise only probable.
Tanava Ratio or Sophisma pigrum is the master fallacy of
Fatalism. It might be classed with fallacies of Non-observa-
tion. The Fatalist argues that, if a thing must happen, it
will happen whether he interfere or no; overlooking oe his
own agency is one of the co-operating causes.
InruitIve—SyMBOLICcAL.— We often employ words itd sym-
bols without fully realizing their meaning. This Leibnitz
called Symbolical as distinguished from Intuitive, Knowledge,
ideas and sensations fully realized in consciousness. We can
conceive a yard, a mile, or even ten or twenty miles, in
the full reality of the extent; but of the distance between the
earth and the moon, the sun, or one of the fixed stars, we have
no proper conception; we may, however, express such dis-
_ tances in figures, which are intelligible as such. This would
be a symbolical conception. | |
Mopvats.—(See Part I, p. 99). The opposition of Pro-
positions has been applied to Modals, in the following state-
ments,
If the matter be necessary, all affirmatives must be true, and
all negatives false,
If the matter be impossible, all negatives must be true, and
all affirmatives must be false.
If the matter be contingent, all particulars must be true, and
all wniversals false,
Here the meaning of ‘ necessary’ is no more than univer-
sally true, as all men are mortal, all matter gravitates. ‘* Im-
possible ° is universally false ; all men are gods. ‘ Contin-
gent’ means partly true and partly false; Some men are wise.
Porpuyry’s TreE.—This is a tabular arrangement showing
different grades of generality. The example chosen ranges
from the summum genus Substance, to the infima species Man,
PROPHYRY’S TREE. 717
ending with two individuals. It may be exhibited thus, in a
form better described by the Greek name, Porphyry’s Ladder
(jue) —
ie | Substance
Corporeal Incorporea]
(Body)
Animate Inanimate
(Living Body)
Sensitive Insensitive
(Animal)
Rational Irrational
(Man)
Socrates Plato
PREDESIGNATE is a term applied by Hamilton to propositions,
laying their quantity expressed by one of the signs of quan-
tity, Ail, None, &. The contrasting term is Preindesignate.
The terms commonly used in logic are Definite, Indefinite.
SmpLe APPREHENSION is defined by Whately as ‘ the opera-
tion of the mind by which we mentally perceive or forma
notion of any object.’ It is the same as Perception, whereby
we know things in the actual or concrete—a house, a tree.
By another faculty, designated Abstraction, we conceive things
in the general.
Surricient Reason.—Under this title Leibnitz stated the
law of Causality. Everything that exists must have a ‘ suffi-
cient reason ’ for its existence. The attempt has been made to
prove certain truths, such as the law of perseverance of uni-
form motion in a straight line, on the ground that no suffi-
cient reason can be given why a body should either lose its
velocity or deviate to one side or the other. The same line of
remark has been used with the principle of virtual velocities.
Sopuisma PoLyzerescos and SopuisMA HEev1eROZETESEOS are
two ingenious Greek Sophisms. ‘The first was alluded to
under Definition. Choosing a word having a doubtful margin
of application, the sophist asks whether it applies to such and
such a case, and goes on putting the question to one contiguous
case after another, until he has drawn the respondent palpably
_ beyond the range of the word, when he demands the difference
between the last case admitted and the first refused. Such
words as heap, calf, &c., are suitable: the sophist asks—Was
it a calf to-day, will it be a calf to-morrow, next day, and so
on ; the respondent cannot say on what day it ceases to be a
calf, and becomes a heifer. The Heterozeteseos (Soplism of
718 EXPLANATION ON SOME LOGICAL TERMS,
Irrelevant Question) decoys a person into committing himself
by a categorical answer—‘ Have you cast your horns ?—If
you answer, I have; it is rejoined, Then you have had l.orns:
if you answer, I have not, it is rejoined, Then you have them
stall.’
he Niel) Bp Xt
ApstRAcTIoN, allied to Analysis, 683.
Abstract Ideas, dispute regarding, 5.
Abstract name, completion of gener-
. alizing process, 52.
value and abuse of, 53.
Accidens, 76.
Accidentis, fallacia, 674.
Activity, a source of fallacies, 607.
Adjectives, connotative, being gener-
alized names, 49.
Aiquivocatio, 673.
A dicto secundum quid ad dictum
simpliciter, 602, 624, 675.
Assthetic emotions, a source of fal-
lacy, 6138.
A dicto simpliciter ad dictum secun-
dum quid, 674.
Affinity, chemical, defined, 473.
maximum of, 417.
in Mineralogy, 524.
in Botany, 532.
in Zoology, 540.
in diseases, 596.
A fortiori, 164.
Agreement, intellectual property of,
3
the basis of Reasoning, 8.
basis of Definition, 385.
defines the limits of Explanation,
351.
stated in classification, 422.
in the arrangement of chemical
elements, 476.
statement of, in Mineralogy, 529.
in Botany, 535.
in Zoology, 548.
in diseases, 596.
Method of, 279.
fundamental maxim of, 278.
in Biology, 500.
Agreement, Method of, in Politics,
565.
in Medicine, 590.
frustrated by plurality of causes,
308.
protected against plurality of
causes, 309.
an aid to Discovery, 702.
in Absence, basis of, 279.
Universal, the sole evidence for
Inductive truths, 2377.
the test of uniform co-existence,
244,
proof of concomitant properties
in Natural kinds, 245.
the sole Inductive Method, 277.
fundamental mode of Proof, 344.
Algebra, notions of, 4382.
account of, 443.
highest operation of, 445.
Algebraic Geometry, notions of, 432.
account of, 448.
All, two meanings distinguished by
De Morgan, 187.
Ambiguity of terms, 602, 616.
Amphibolia, 678.
‘Analysis, Chemical, 627.
Logical, 628.
allied to Abstraction, 39, 629.
applied to Induction, 684.
Grammatical, 684.
Critical, 684.
Mathematical, 685.
preliminary to elimination, 272.
in Psychology, 511,
in Society, 570.
conformed to rules of division,
427.
an aid to Discovery, 705.
Analytic judgment, 76.
720
Analogy, as a form of Inference,
373
does not amount to Proof, 373.
examples of, 375.
Analogies, false, 372, 624.
Analogical Hypotheses, 377.
Animals and Plants contrasted, 495.
Antecedence, invariable, not causa-
tion, 268.
causal usually complicated, 271.
Apprehension, simple, 717.
Approximate Generalizations, 365.
probability of, stated in numbers,
366.
how brought nearer certainty, 368.
open to sophistry, 369.
A priori, applied to knowledge, 10.
Argument, 715.
Aristotelian contrasted with Bacon-
ian logic, 642.
Arithmetic, definitions of, 433.
ultimate notions of, 434.
account of, 442.
proof in, 443.
Associations, a source of fallacy,
615.
Astronomy, its place among the
Sciences, 630, 636.
Averages, 321.
Axiom of Syllogism, various forms
discussed, 155.
proof of, in experience, 159.
Hamilton’s forms, 160.
as given by Thompson, 161.
as given by De Morgan, 162.
not derivable from the “ Laws of
Thought,” 162.
Axioms, nature of, 224,
requisites of, 294,
only two Mathematical, 224,
of Inductive origin, 225,
Bacon, contributions to inductive
methods, 687.
Belief, the nature of, 12.
inherently excessive, 607.
law of, explains intense convic-
tions, 225.
Biology, scope of, 488.
divisions of, 492.
notions of, 494,
propositions of, 496,
INDEX.
Biology, conservation of Force in,
498.
Empirical laws in, 498.
logical methods of, 500.
Hypotheses of, 502.
as basis of Medicine, 577.
Body, substance of, 660.
Body and Mind, 357, 376, 505.
Botany, arrangement of characters
in, 531,
maximum of affinity in, 532.
grades in, 534.
agreement and difference in, 535.
peculiarity in exhibition of differ.
ences, 586.
index in, 538.
CaLcuLts, notions of, 432.
account of, 448.
Canons of Syllogism, 149.
according to Hamilton, 151.
special for each Figure, 152.
Canons, special, derived from Axiom,
163.
Categorematic, 715.
Categories, of Aristotle, 661.
Categorical Imperative, meaningless,
376.
Causation, law of, 20, 226.
uniformities of, as a branch of
Logic, 239.
law of, expressed, 245,
obverse denied, 246,
three aspects of, 247.
practically viewed, 24/7.
scientific, 249.
fallacy of, 250.
as Conservation of Force, 251.
as an instrument of elimination,
276,
unfolded in three maxims of elimi-
nation, 277.
induction of, 843.
rests on Agreement alone, 845.
as an Empirical law, 845.
discriminated from’ Co-existence,
381.
not distinguished from Co-exist
ence, 688.
propositions of, in Biology, 497.
in Polities, 556, 564.
contradiction of, incredible, 379,
A”) Para
INDEX.
Cause, an alleged intuition, 11.
to be sought ameng the antece-
dent circumstances, 267.
not proved by invariable antece-
dence, 268.
the unconditional invariable ante-
cedent, 268.
material, formal, efficient, final,
248. :
Causes, composition of, 268.
combination of, 327.
real, 359. .
_ Chance, computation of, a resource
under Intermixture of Effects,
313.
coincidence explained, 315.
principle of computation, 316.
applicable where other methods
fail, 316.
combined with law, 319.
submerging a small uniformity,
319.
in Biology, 501.
in Psychology, 516.
in Medicine, 592.
elimination of, an aid to Discov-
ery, 702.
Character, Science of, based on Psy-
chology, 516.
elements of, 518.
as affected by Conservation, 518.
influences on, 519.
not classified like Natural History,
520.
peculiarities of, 521.
human, in Politics, 556.
Characters, descriptive, sequence of,
414,
in Chemistry, 478.
in Mineralogy, 528.
in Botany, 531.
in Zoology, 588.
Chemical force, conservation of, 355.
combination, not a union of forces,
370.
defined by contrast, 398.
Chemistry, fundamental fact of, 472.
propositions of, 473.
arrangement and methods of, 474.
elements of, classified, 474.
descriptive method of, 478.
agreement and difference in, 483.
721
Chemistry, empirical laws in, 484.
law of Conservation in, 484.
hypotheses in, 485.
nomenclature of, 486.
notation of, 487.
Class, two meanings of, definite and
indefinite, 280.
Classification, golden rule of, 383,
Methods of, 414.
descriptive characters in, 414.
grades of, 418.
terminates with Species, 420.
statement of agreements and dif-
ferences in, 422.
Index, 424.
of Characters, 520.
Sciences of, 522.
an aid to Discovery, 704.
Co-existence one of the three Uni-
versal Predicates, 108.
as Order in Place, 103.
as Co-inherence of Attributes,
104,
uniformities of, as a branch of
Logie, 289, 248.
induction of, 241.
proof of, by Universal Agreement,
244,
propositions of, in Biology, 296.
in politics, 556.
and Succession, common to sub-
ject and object experience,
656.
Collective names, singular or gener
al, 48.
Colligation of Facts, 695.
Collocation of Circumstances, 251.
degrees of complexity, 260.
elliptically spoken of as the Cause,
262.
as Potential Energy, 264.
the effect of expended force, 265.
in Politics, 564.
Colony, example of positive defini-
tion, 388.
Colour, not intrinsically objective,
657.
Complex Propositions, how far mat-
ter of Logic, 85.
Complications of Cause and Effect,
271.
722
Compositionis et Divisionis, fallacia,
674.
Comprehension, 50.
practically more important than
extension, 333.
Hamilton’s syllogism in, criticized,
Conceptualism, 6.
Concept, formation of, 383.
Conception, formal, 473.
Concomitance, discovery of laws of,
419.
in Zoology, 539.
Concomitant, a predicable, 76.
separable and inseparable, 77.
Variations, 292.
fundamental maxims of, 278.
interrupted by critical points,
294,
as a means of suggestion, 294.
tables of, for Discovery, 295.
under intermixture of effects,
403.
in Biology, 500.
in Politics, 567.
in Medicine, 591.
Concrete names, 54.
Conditional Propositions, 85.
Syllogism, involves no inference,
117,
Confusion, fallacies of, 602, 616.
Consciousness, 507.
testimony of, 665.
Connotation, of General Names, 49.
Conservation of Force, law stated,
251.
proved ae universal agreement,
23
explained, 250, 252.
evidence of, 844,
has same proof as Causation, 266.
not an @ priori conception, 267.
in Chemistry, 484.
in Biology, 498.
in Medicine, 589.
under re-distribution, 460,
in Character, 518.
Consistency, Principle of, 14, 108,
645, 670.
Contiguity, extension
through, 403.
Jontinuity, law of, empirical, 338,
of names
INDEX.
Continuity, a help to Discovery, 697,
706.
Continuous Comparison, 295.
Contradiction, principle of, 16.
Contradictory, propositions, 93.
misapplication of the name, 94,
Contraries, expression of, made pre-
cise by De Morgan, 56.
basis of De Morgan’s additions to
syllogism, 184,
Contrary propositions, 92.
Contrast, in defining, 385.
animals with plants, 495.
exhibition of, in Chemistry, 483.
Conversion, Simple, 113,
Fallacies of, 114.
by Limitation, per accidens, 114.
obverted, or by Negation, or Con-
traposition, 116.
Copula, 44.
meanings of, 182.
Correlative names, 55.
Correlation of Forces, see Conserva-
tion,
Credibility, consistency with proved
inductions, 379.
Crystallization, an example of Agree-
ment, 284,
explanation of, confirmed by Joint
Method, 291.
Curves, method of, 697, 704.
Depvcrtiov, first principles of, 17.
explained, 40.
why placed before Induction and
-Definition, 41.
laws of, 645.
as general presumption, 284,
involves observation of facts,
825.
two stages of complexity, 32'7.
simple, extension of a law, 327.
combination of causes, 329.
fallacies of, 625.
Deductive Method, three requisites
of, 325.
in Psychology, 513.
in Politics, 567.
in Medicine, 592.
me insufficient in Politics,
572
Sciences, how constituted, 216.
INDEX.
Definition, as verbal predication, 71.
exhaustive and unexhaustive, 71,
72.
explained, 38, 384.
fundamentals of, 385.
Positive Method of, 386.
margin of transition, 890.
Negative Method of, 392.
deductive, 395.
the language of, 395.
by synonyms, 396.
per genus et differentiam, 74, 396.
by Analysis, 396.
notions not susceptible of, 398.
mixed with Real predication, 582,
587.
fallacies of, 626,
neglected by Whewell, 696.
an aid to Discovery, 706.
De Morgan, divisions of Terms, 51.
on Positive and Negative names,
56.
enumeration of Propositions, 90.
additions to syllogism, 182.
Demonstration, based on Induction,
219.
Denotation, of General Names, 49.
Derivative laws, 334.
various kinds of, 334.
limited application of, 336.
of wider application than Em-
pirical, 342,
in Politics, 568.
Description, of chemical bodies, 478.
not to be mixed with explanation,
483, 584.
Descriptive terminology, 407.
characters, sequence of, 414.
Development hypothesis, 502.
Dew, research on, an example of
elimination, 298,
Dictum de omni et Nullo, 155.
Difference, Method of, fundamental
maxims of, 278.
explained, 287.
where indecisive, 289.
in Politics, 566.
in Medicine, 591.
exhibition of, in Chemistry, 483.
Differences, statement of, in Classi-
fication, 422, 529,
in Botany, 535.
723
Differences, statement of, difficult in
Botany, 536.
in Zoology, 543.
in Diseases, 596.
Differentia, 73.
Dignity, a source of fallacies, 613.
Dilemma, 121.
Discovery, Art of, 697.
distinguished from Proof by Mill,
697.
three aids to, 326.
secondary in Logic, 327.
Disease, definition of, 575.
Disjunctive Propositions, 85.
Disjunctive Syllogism, involves no
inference, 119.
Division, an aspect of classification,
425,
rules of, 426.
a mode of grades, 427.
fails with undefined classes, 428.
Documents, invalidated by two
doubts, 709.
Erricient Cause, 248.
Electricity, Conservation of Force in,
257.
characters and branches of, 468.
Elimination, of Cause and Effect,
271.
weapons of, 276.
is Proof, 279.
of chance, 314.
Empirical laws, explained, 333.
various kinds of, 334.
criteria of, 335.
limited application of, 336.
established by Universal Agree-
ment, 237.
more precarious than derivative,
842.
in Chemistry, 484.
in Biology, 498.
in Psychology, 514.
in Politics, 568.
Enthymeme, 716.
Equality, uniformities of, as a branch
of Logic, 239.
Equality and inequality, one of the
three Universal Predicates,
103.
Equivalence of propositions, 107.
724
Equivalent terms, as an aid to Dis-
covery, 702.
Essential attributes, 74.
predication, in Psychology, 509.
Excluded Middle, principle of, 17.
Exclusion, Bacon’s process of, 688,
Existence, has no real opposite, 59.
propositions of elliptical, 107.
means Object and Subject indis-
criminately, 620.
Experience, the source of knowl-
edge, 9.
the proof of the Axiom of the Syl-
logism, 159, 226.
the proof of Causation, 226.
Hxperiment, advantages of, 278.
in Biology, 500.
in Politics, 563.
Experimental Methods, apply only to
Cause and Effect, 240.
deductive, in character, 277,
345.
explained, 279.
examples of, 297.
frustration of, 306, 312, 3138.
in Psychology, 512.
in Politics, 565, 572.
in Medicine, 590.
how far anticipated by Bacon,
687, 689.
given by Herschel, 694.
neglected by Whewell, 696.
Fixperimentum crucis, 865.
Explanation of Nature, a joint effect,
347.
intermediate links, 348.
subsumption of laws, 349.
limits of, 351.
fallacious, 354.
Extension, 50.
fundamental property of the Ob-
ject, 657.
Evidence, assertions beyond reach
of, incredible, 382.
Historical, 423.
supreme canon of, 707.
internal and external, 708.
two modes of external, 709.
transmitted by writing, 709.
transmitted orally, 7138.
Facts anp Ipmas, 695, 699.
INDEX.
Fallacies, Aristotelian and Scholastic,
673.
Whately’s division, 676.
Mill’s classification of, 599.
a priori, 599.
of observation, 600.
of generalization, 601.
of ratiocination, 601.
of confusion, 602, 616. ©
position of, 603.
extralogical, 605.
tendencies to, 606.
logical, 624, .
knowledge of, = Discovery,
707.
in Politics, 572.
Fear, a source of fallacy, 612.
Feeling, two-sided, 2.
Feelings, a source ‘of fallacy, 609.
Fever, definition of, 581.
Figures, 136.
relative value of, 146.
reasons for different, 146.
Figure dictionis, fallacia, 674,
Fina] Cause, 248.
Food, an example of positive defini-
tion, 388.
Force, definition of, 251.
chief predicates of, 251.
Conservation of, 21.
Form and Matter, 639.
Formal Logic, too narrow, 645.
Cause, 248.
thinking explained, 640.
requires inductive verification,
648.
Freedom of the will, 844, 621.
Functions of living bodies, 491.
Function and Structure viewed
separately, 493.
GENERAL Name, explained, 48.
Generality, Names classed according
to, 47.
higher and lower, 54.
degrees of, in Notions, 64.
fixed grades of, in Botany, and i in
Zoology, 65.
degrees of, in Propositions, 78.
of Proposition follows Notion, 78.
as classifying Propositions, 78.
as a basis of Definition, 385,
— 7
INDEX.
Generalization, identical with Expla-
nation, 446.
the highest ambition of Science,
456.
approximate, 465.
fallacies of, 601.
' excessive tendency to, 608.
as an art of Discovery, 279, 698.
Genus and species, movable names,
except in Natural History, 65.
a predicable, 73.
Geometry, notions of, 432.
definitions of, 434.
ultimate notions of, 436.
axioms of, 438. »
postulates of, 439.
order of topics in, 446.
proof of Euclid’s fourth proposi-
tion in, 447.
Glaring instances, 690, 704.
Government, forms of, 549, 553.
definition of, 551.
functions of, 552.
local and central, 554.
defines Public and Private, 554.
Grades of generality, great import-
ance of, 700.
in classification, 418,
Statement of, suited to discovery
of concomitance, 419.
in Mineralogy, 528.
in Botany, 534.
in Zoology, 542.
in Diseases, 596.
Gravity, an example of Hypothesis,
460.
contraction of, incredible, 379.
Hamintoy, additions to syllogism,
Quantification of Predicate, 178.
syllogism in Comprehension criti-
cized, 180.
Health-Disease, indefinable, 264.
Heat, generated by collision, 253.
conservation of, 254.
unprofitable dissipation of, 255.
definition of, 467,
heads of the science of, 467,
propositions of, 470.
structural, should be stated in
chemical formula, 487,
725
Herschel, contributions to Induc-
tion, 693.
History, Philosophy of, 548.
basis of Politics, 561.
perversions of, 712.
Homonymia, 505.
Hypothesis, various meanings of, 358.
of known agencies desirable, 359.
of a new agent permissible, 361.
as a representative fiction, 362.
differs from geometrical abstrac
tions, 364.
analogical, 377.
in Chemistry, 485,
in Biology, 502.
in Psychology, 515.
in Politics, 569.
in Medicine, 593.
Hypothetical Inference, 116.
IDEA AND Facts, 695, 699.
Identification of a Minor, when dif
ficult, 218.
not an induction, 235, 328.
Identity, principle of, 16,
Idola, Bacon’s, 609.
Ignava Ratio, '71'7.
Ignoratio elenchi, 602, 628, 675.
Immediate Inference, 107.
by Added Determinants, 109.
fallacies of, 625.
Import of Propositions, 100.
Hobbes’s view, 100.
not the reference of something
to a class, 101.
Inconceivability of the opposite, ex-
plained, 223.
rejected as ultimate test of truth,
665.
Incredibility, inconsistency with
proved inductions, 379.
Index, to a classification, 424.
in Mineralogy, 530.
in Botany, 538.
in Zoology, 544.
in Diseases, 597.
Individual, our idea of, a conflux
of generalities, 7.
Induction, first principles of, 19.
explained, 40, 231.
would furnish Formal processes
650.
726
Induction, a branch of Logic, 651.
improperly so called, 233, 235.
cannot be brought under the syl-
logism, 233.
a prerequisite of deduction, 325,
in difference of subject, 371.
postulate of, 502.
fallacies of, 625.
growth of, 687.
Inductive, Discovery, 326.
Methods an aid to Discovery, 702.
Syllogism, 233.
Infime species, 63,
Inflammation, definition of, 583.
Intermixture of Effects, 310.
in Politics, 565.
in Medicine, 591.
International law, 548.
Intuition, an alleged source of knowl-
edge, 10.
Intuitive—symbolical, 716.
Invention, how assisted, 705,
Joint Mernop of Agreement and
Difference, 291.
counteractive to plurality of
causes, 310.
in Politics, 566.
in Medicine, 591.
an aid to Discovery, 703.
Judgment, formal, 641,
as a synonym for proposition,
80
its significance with Aristotle, 80.
Jurisprudence, 548,
KNOWLEDGE, the act of, includes al-
ways two things, 3.
conjoins Agreement and Differ-
ence, 4.
of two kinds, called Object and
Subject, 5.
Individual or Concrete, and Gen-
eral or Absiract, 5, 22.
origin of, in Experience, 9.
limited by our sensibilities, 13.
nature and classification of, 21.
should be true, 22.
conveyed in propositions, 44.
relativity of, appears in language,
54
Kinds, 63.
INDEX.
Kinds, exemplify co-inhering attri.
butes, 241.
LanauaGeE, truths expressed in, 42,
fallacies of, 616.
Law, confused meanings of, 643, 617.
metaphorical use in “ Laws of Na-
ture,” 239.
involved in Government, 552.
combined with Chance, 319.
Laws of Nature, by preéminence,
239.
Liberty, 550.
Life, definition of, 488.
Light, undulatorg theory of, 361.
commutation of, not established,
258.
production of, an example of
Agreement, 286.
definition and subsidiary notions
of, 468.
Likeness and Unlikeness, common
to subject and object expe-
rience, 655.
Love, a source of fallacy, 612.
Marain, doubtful, in definition, 390.
Mathematics, Logic of, 429.
the best example of a Deductive
Science, 429, 647.
notions of, 430.
propositions of, 482.
definitions of, 433.
axioms of, 437,
leading branches of, 442.
Materia Medica, 581.
Method, expresses part of the func-
tion of Logic, 35.
an aid to Discovery, 701. —
Mind, substance of, 660.
definition of, 505.
difficult to estimate quantity in,
517.
Mind and Body, 357, 876, 505.
Mineralogy, scope of, 522.
relations to Chemistry, 522.
arrangement of characters in, 523,
maximum of affinity in, 524,
grades in, 528.
agreement and difference in, 529, —
index for, 530.
Material Cause, 248.
INDEX.
Material, names of, singular, 48.
Matter, as Resistance, 657.
defined by positive method, 391.
by negative method, 393.
constitution of, a hypothesis, 363.
Force, Inertia the same fact, 455.
‘physical properties of, 464.
Mechanics, 462.
Medicine, scope of, 575.
based on Biology, 577.
definitions of diseases in, 581
general diseases in, 579, 581.
specific diseases in, 586.
propositions of, 588.
_ experimental methods in, 590,
elimination of chance in, 592.
the deductive method in, 592.
hypotheses in, 593.
classification in, 595.
Minor, identification of, not an in-
duction, 235.
Mnemonics, 147.
Modals, 99, 717.
Molar forces, conservation of, 252.
Molecular attractions, 464.
Molecular forces, enumerated, 254.
Motion, laws of, reduced to one,
458.
Monarchy, example of positive defini-
tion, 887.
Moods, 138,
_ usual enumerations justified, 153.
Muscular Irritability and Putrefac-
tion, an induction, 303.
Mystery, 356.
Names, why considered at beginning
of Logic, 45.
defined, 46.
denote things, not ideas of things,
46.
variously classified, 4’7.
De Morgan’s divisions of, 51,
go in couples, 54.
meaning of, increases with oppo-
site, 60.
loosely extended, 402.
transitive application of, 408.
class, 409.
of generalities should be short,
410
new, 410.
127
Names, precautions in appropriating
old, 412.
expressive, 414,
different, held to imply different
things, 418.
improper use of, 420.
Naming, general, value of, 401.
first requisite of, 402.
second requisite of, 407.
Nature, explanation of, 346,
ambiguity of the word, 616.
Negation, variously expressed, 58.
Negative names, 55.
singular or plural, 57.
of a real property, also real, 58.
Necessary Truth, 14.
Necessity, meanings of—certainty,
220.
implication, 221.
inconceivahility of the oppo-
site, 223.
Nerve force, conservation of, 258.
Newton, contributions to Induction,
693.
Nomenclature, 412, 414.
of Chemistry, 486.
Non causa pro causa, 675.
Non sequitur, 675.
North-east wind, an example of
Agreement, 283.
Nota note est nota rei ipsius, 156.
Notation, of Chemistry, 487.
Notion and Proposition, not distin.
guished by Whewell, 696.
Notions, contrasted with Proposi-
tions, 61.
disguised as Propositions, 66.
of singular or plural constitution,
63.
indefinable, ultimate, 398.
Ossect, analysis of, 486.
attributes special to, 657.
Dhyecksmuiees highest real couple,
opie of all antitheses, 653.
attributes common to, 655.
Observation, why not a department
of Logic, 36.
the basis of Induction, 234.
compared with Experiment, 278.
in Biology, 500.
728
Observation, in Politics, 561.
erroneous, causes of, 562.
fallacies of, 600.
as an art of Discovery, 698.
Opposition, of propositions, 92.
error in common square, 94.
amended square, 97.
Aristotle’s square, 98.
Obversion, formal, 109.
material, 111.
Order, valuable aid to Discovery, 701.
Order and Progress, 555, 570.
Oxygen, exemplary description of,
479.
Parity of Reasoning, 235.
Pathology, general, 579.
Per genus et differentiam, 885, 396.
Persistence of Force, see Conserva-
tion.
Petitio Principii, 602, 6238, 675.
Physics, Molar, divisions of, abstract,
and concrete, 452.
notions of, 452.
propositions of, 454.
definitions of, 455.
axioms of (laws of motion), 458,
concatenation and method of,
462.
Physics, Molecular, departments of,
463.
notions of, 464.
propositions of, 469.
predominant methods of, 472.
Plants and Animals contrasted, 495.
' Plato’s dialogues, how authenticated,
710.
Plurality of Causes, 246.
how far subject to uniformity, 246.
bearing of, on the Experimental
Methods, 307.
in. Politics, 565.
in Medicine, 591.
Plurium Interrogationum, 6'76.
Political Economy, 648.
Politics, two divisions of, 547.
embraces several sciences, 549.
province of, 549.
Descriptive, 550.
Theoretical, defined, 556.
propositions of, 558.
universal propositions of, 559.
INDEX.
Politics, Theoretical, limited proposi-
tions of, 560.
methods of, 561.
experiment in, 563.
causation in, 564.
method of agreement in, 565.
other experimental methods in,
566.
deductive method in, 567.
hypotheses in, 569.
simplifying of, 570.
fallacious methods in, 572.
Practical, End in, 573.
based on Theoretical Politics,
574,
origin of political devices in,
575.
Porphyry’s tree, 716.
Positive names, 55.
Post hoc ergo proplter hoc, 675.
Postulate, the universal, 664.
Potential energy, 259.
an aspect of Collocation, 264.
Practice, logic of, 545...
maxims of, in Politics, 575.
Predesignate, 717.
Predicables, 73.
Predication, verbal, 76.
confounded with real, 68.
in plural notions, 69.
in Natural Kinds, 69.
verbal not tautological, 70.
final analysis of, 660.
Predicates, three universal, 102.
Mr. Mill’s scheme of, 106.
Premises, 135.
Prerogative Instances of Bacon, 688.
Presentative and Representative, 7,
640
Primary qualities of matter, 657.
Probable Inference, explained, 365.
may be estimated, 366. ~
how made more precise, 368,
Probability, 320,
explained, 321.
principle of, 321,
rules of, 322. n
applied to Causation, 824.
an approximate generalization,
366. aeons .
comparison of, 381.
in Biology, 501.
bs vA
INDEX.
Probability, in Psychology, 516.
ambiguity of the word, 618.
Progress and Order, 555, 570.
Proof or Evidence, the scope of Logic,
34, 279.
Proposition, a, contains two names,
and two notions, 274, 292.
verbal, 67.
Propositions, 78,
Proprium, 74,
exemplified in Mathematics, 432.
Psychology, scope of, 505.
subordinate notions of, 507.
propositions of, 509.
logical methods of, 511.
empirical and derivative laws in,
514.
hypotheses in, 515.
chance and probability in, 516.
suggesting arts of Discovery, 699,
oncrete Science ? 636.
Quatity, of Propositions, Affirma-
tive or Negative, 83.
an ineradicable distinction, 83.
designations of, 84.
Quantification of ‘Predicate, 86.
makes two propositions in one,
88.
cack a to syllogism, basis of,
178.
Quantity, of Propositions, Total or
Partial, 81.
Universal and Particular, inapt
names, 82.
Indefinite, 82.
one of the three universal Predi-
cates, 333.
common to Object and Subject ex-
perience, 655.
subject-matter of Mathematics,
429,
designations of, 81.
sciences of, Deductive, 103.
uniformities of, as a branch of
Logic, 239.
RATIOCINATION, fallacies of, 601.
Realism, 5.
fallacy of, 619.
Reasoning, ‘used in defining Logic,
30,
729
Reasoning, founded on Similarity, 8,
370
from particulars to particulars,
209.
chain of, reducible to a series of
syllogisms, 215.
causes of}, complicated, 217.
formal, 641,
Reductio ad impossibile, 141,
Reduction, 147.
Relativity, law of, 2.
Names classed according to, 54.
universal, 61.
as affecting Notions, 66.
as classifying Propositions, 78.
as a basis of Definition, 385.
basis of an enumeration of things,
485.
fallacies of, 621.
of Proposition follows Notion, 79.
Relative. terms, for special relation-
ships, 60.
names, 55.
Representative Fictions, 362.
in Medicine, 594.
Residues, Method of, 279, 295.
in Politics, 569.
an aid to Discovery, 702.
Resistance, 657.
SANGUINE TEMPERAMENT, & source
of fallacy, 611.
Science, the perfect form of Knowl-
edge, 23.
characteristics of, 23.
problem of, as conceived by
Whewell, 695.
Sciences, classified, 25.
Abstract and Concrete, 25.
Abstract, 25.
Concrete, 28.
Practical, 28.
defined, 545.
Classification of, Bacon, 6217.
D’Alembert, 628.
Engyclopedia Metropolitana,
628.
Neill Arnott, 629.
Comte, 629.
Herbert Spencer, 630,
criticism of Spencer’s scheme,
634.
730 INDEX,
Secondary qualities of matter, 657.
Laws, importance of, 332.
Self-interest, a source of fallacy, 620.
Series, Classification by, 295.
Serial order, in classification, 417.
Similarity, law of, 3.
the foundation of Reasoning, 8
370.
basis of scientific explanation, 346.
extension of names through, 402,
405.
Singular Name explained, 48.
Propositions, syllogism of, 159.
Smelling, due to oxidation, induc-
tively proved, 297.
Society, notion of, 547.
structure of, 550.
Solid defined by positive method,
390.
by negative method, 393.
Sophisma Heterozeteseos, 717.
Pigrum, 15.
Polyzeteseos, 716.
Sorites, or heap, 390, 717.
face, an abstraction, 11.
characterized, 657.
Species, a predicable, 73.
Species, importance of in classifica-
tion, 420.
-infima, 421.
in Mineralogy, 528.
in Botany, 535.
in Zoology, 542.
Statistics, Political, 549, 562.
Medical, 592.
Structure of Living Bodies, 490.
and Function viewed separately,
463.
Subject, explained, 655.
attributes special to, 659.
Teter i highest real couple,
reas of all antithesis, 653.
attributes, common to, 655.
Substance, a supposed intuition, 11.
fundamental attribute, 660.
Succession, one of the three Uni-
versal Predicates, 105.
as Order in Time, 105.
as Cause and Effect, the chief
part of Induction, 106.
Sufficient Reason, 600, 717.
Sumption and Subsumption, 146.
Syllogism, defined, 138.
examples of, 165.
additions to, by Hamilton, 178.
by De Morgan, 182.
by Boole, 190.
Numerically Definite, 188.
functions and value of, 207.
how far a material process, 211.
axiom of, reposes on experience,
226,
an aid to Discovery, 703.
of the Will, meaningless, 376.
Sympathy, a source of fallacies, 610.
Symbolical—Intuitive, 716.
Symbols, of Propositions, 86.
Synonymous Propositions, 123.
Synonyms, definition by, 396.
as an aid to Discovery, 701.
Synthesis, Chemical, 681.
Logical, 683.
does not apply to Simple Deduce-
tion, 684.
Grammatical, 684.
Mathematical, 685.
Synthetic judgment, 76.
TABULATION, as an Index Classifica-
tion, 580, 597.
as an aid to Discovery, 704.
Tabular arrangement, Bacon’s, 687.
Terminology, descriptive, 407.
Terms, of syllogism, 364.
Therapeutics, general, 580.
Things, enumeration of, 652.
Mr. Mill’s enumeration of, 661.
Thought, Laws of, 16, 641.
definition of Logie, 30.
too limited to make a Universal
Postulate, 664.
Time, an abstraction, 240.
Tradition, oral, value of, 7138.
approaching to written evidence,
715.
Truths, known immediately, 32.
known by the mediation of other
truths, 32.
Uttimate Laws or Narurg, pei
in number, 353.
Uniformity of Nature, supposed’ in
Deduction, 19.
See eee
INDEX. 731
Nature, enters into | Verification, in Politics, 567. — -
tt etical Logic, 645. Vere Cause, 359.
te major premise of all
tion, 671. WHEWELL, contributions to Induc.
nat a unity, 238, tion, 695.
Wonder, a source of fallacy, 612.
S “among effects of same
eeu 335. Zooioey, difficulties of, 588.
ited in application, 341, 342. arrangement of characters in,
oon connection, 334. 538.
laws of Concomitance in, 539.
‘ maximum of affinity in, 54¢.
, souree of fallacies, 603. grades in, 542.
of circumstances, 278. agreement and difference in, 548.
ion, } index in, 544.
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