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SYMBOLISM AND TRUTH 
 
LONDON : HUMPHREY MILFORD 
 
 OXFORD UNIVERSITY PRESS 
 

 
 
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 Ley, OGIGAL § aewine 
 
 SYMBOLISM AND TRUT 
 
 AN INTRODUCTION TO 
 THE THEORY OF KNOWLEDGE 
 
 
 
 
 
 BY 
 
 RALPH MONROE iene ibe. D: 
 
 INSTRUCTOR AND TUTOR IN PHILOSOPHY 
 HARVARD UNIVERSITY 
 
 
 
 CAMBRIDGE 
 HARVARD UNIVERSITY PRESS 
 
 1925 
 
COPYRIGHT, 1925 
 
 BY HARVARD UNIVERSITY PRESS 
 
 PRINTED AT THE HARVARD UNIVERSITY PRESS 
 
 CAMBRIDGE, MASS., U.S. A. 
 
TO 
 
 . B. €. 
 
 IN GRATITUDE FOR 
 FAITH AND WORKS 
 
When I heard the learn’d astronomer; 
 
 When the proofs, the figures, were ranged in columns before me; 
 
 When I was shown the charts and the diagrams, to add, divide, 
 and measure them; 
 
 When I, sitting, heard the astronomer, where he lectured with 
 much applause in the lecture-room, 
 
 How soon, unaccountable, I became tired and sick; 
 
 Till rising and gliding out, I wander’d off by myself, 
 
 In the mystical moist night-air, and from time to time, 
 
 Look’d up in perfect silence at the stars. 
 
 Wait Wuitman, Drum Taps, 1865 
 
PREFACE 
 
 Tue theory of knowledge, occupying as it does the borderland 
 between psychology, logic, and metaphysics, is a peculiarly diffi- 
 cult subject to isolate and study in itself. The materials are 
 widely scattered through philosophical literature, discussions of 
 the problems appear in works of the most diverse character, and 
 any one who attempts to single out the essential questions will 
 be sure to omit some that are important in the eyes of many 
 people and to include others that might be omitted. He will 
 place his emphasis somewhere, with the result that he will fail to 
 stress points that perhaps equally deserve emphasis. By way of 
 remedy therefore he ought to indicate his angle of approach and 
 call attention to what he believes are the major gaps in his treat- 
 ment. 
 
 The method of the present work is mainly critical and ana- 
 lytic, rather than speculative.’ A single line of attack, which 
 goes at once to the heart of the problem, is chosen—namely, the 
 réle of symbols in knowledge; and about this the entire analysis 
 is organized. Knowledge is inseparable from its expressions; a 
 study of these expressions should therefore throw light on the 
 theory of knowledge as a whole. With this conviction, I begin by 
 examining meaning. But unfortunately the psychology of mean- 
 ing is still in a fluid state, and the most that one who is not a 
 psychologist can do is to point out in a rough way that to which, 
 in his own experience, he gives the name “meaning.” The con- 
 sideration of the logical forms of meanings leads to a discussion 
 of the nature of facts, relations, qualities, universals and indi- 
 
 1 See Mr. C. D. Broad’s interesting statement of the difference between 
 critical and speculative philosophy in Contemporary British Philosophy, edited 
 by Professor J. H. Muirhead (1924), pp. 63 ff.; also, Broad’s Scientific Thought, 
 (1923), introduction. 
 
Vill PREFACE 
 
 viduals, classes, description, synthesis and analysis, possibility, 
 and finally to the definition and tests of truth. The question of 
 truth is naturally linked to that of belief, judgment, and nega- 
 tion; and since logical form stands out most clearly in quasi- 
 mathematical deductive systems, a chapter is given to the study 
 of these systems. 
 
 Metaphysical ideas are kept as far as possible in the back- 
 ground. Speculations concerning the relation of knowledge to an 
 ultimate reality, that is, the issues of idealism and realism, of 
 gnosticism and agnosticism, of monism and pluralism, of the 
 final validity of intuition as opposed to reason, are postponed 
 until the last chapter; for a theory of the relation of knowledge 
 to reality can be successfully held only after the ground has been 
 cleared by an analysis of knowledge as a phenomenon. By exam- 
 ining in detail the elements that make up the complex process, 
 knowledge, I hope to introduce the reader to the wider specu- 
 lative aspects of the subject; but in this direction the line of 
 further thought is merely sketched. 
 
 Discussions of the theory of knowledge often begin by classi- 
 fying different types of views and proceed to compare these in 
 the effort to distill some truth from each. This method is useful; 
 it sets in order, for one unfamiliar with philosophy, a large 
 amount of material; but it tends to become a study of conflict- 
 ing schools of opinion on the problem of knowledge rather than 
 of the problem itself. No systematic classification of epistemo- 
 logical theories is given here, though an acquaintance with such 
 classifications, and with the history of philosophy, will be help- 
 ful to the reader. 
 
 The central place of the concept of logical form gives to cer- 
 tain parts of the book a superficial resemblance to Mr. L. Witt- 
 genstein’s recent T'ractatus Logico-Philosophicus. How deep this 
 resemblance goes I am unable to say, but the language is similar. 
 “We make to ourselves (in thought) pictures of facts,” says Mr. 
 
PREFACE IX 
 
 Wittgenstein. ‘‘In the picture and the pictured there must be 
 something identical in order that the one can be a picture of the 
 other at all. What the picture must have in common with the 
 reality in order to be able to represent it after its manner — 
 rightly or falsely —is its form of representation.”’ And Mr. 
 Bertrand Russell adds to this the comment, “‘We speak of a 
 logical picture of a reality when we wish to imply only so much 
 resemblance as is essential to its being a picture in any sense, 
 that is to say, when we wish to imply no more than an identity 
 of logical form.” 4 
 
 The positive or descriptive theory of knowledge of the first 
 seven chapters, which attempts cautiously to thread its way be- 
 tween psychology and metaphysics, is no doubt allied to the 
 type of philosophy known in Germany as phénomenologie. But 
 it leans much more heavily towards psychology than does the 
 phinomenologie of E. Husserl’s Logische Untersuchungen. Simi- 
 larly, A. Meinong’s theory of the objective, set forth in his Unter- 
 suchungen zur Gegenstandstheorte und Psychologie, in his studies 
 of Hume and other works, appears to me to remove meaning too 
 completely from its psychological setting and to view as simple 
 what is in reality complex. However, I am at one with the phe- 
 nomenological school in wishing to treat the theory of knowl- 
 edge as an autonomous subject, that is, in desiring to assure it 
 as much autonomy as belongs to any other branch of philosophy 
 or to psychology. It is clear that knowledge cannot be wholly 
 described in psychological terms. Hume attempted this and 
 failed. But it is clear also that nothing is gained by trying to 
 banish from knowledge all concrete psychological factors. 
 
 Among the topics that might be included in such a critical 
 study of knowledge but that are omitted or only lightly touched 
 here, are the following: the knowledge of other minds and of the 
 
 1L. Wittgenstein, Tractatus Logico-Philosophicus (1922), introduction, 
 p. 10. 
 
x PREFACE 
 
 self; the knowledge of values and the relations of theories of 
 truth to theories of moral and aesthetic value; the validity of in- 
 ductive inferences; the nature of scientific hypotheses, especially 
 the place of elegance, economy, and completeness in scientific 
 theories; the knowledge of space and time. (The allusions to 
 space and time made in connection with the discussion of the in- 
 dividual in Chapter III need to be supplemented by a detailed 
 treatment, such as that of Mr. A. N. Whitehead’s The Principles 
 of Natural Knowledge and Mr. C. D. Broad’s Scientific Thought. 
 Particularly is this so at the present time, in view of the theory 
 of relativity.) But what is said here of the fundamental factors 
 in knowledge may suggest ways of approach to these more 
 tangled problems. 
 
 For the use of the student, a list of selected readings bearing 
 on the subjects discussed in each chapter is given. This makes 
 ‘available for study along with the text some of the widely scat- 
 tered literature of the theory of knowledge, and will aid the stu- 
 dent in obtaining a complete and systematic grasp of this branch 
 
 of philosophy. 
 R. M. E. 
 
 CAMBRIDGE, Mass. 
 January, 1925. 
 
CONTENTS 
 
 INTRODUCTION Sods daybed ia SO AIO Og cle 
 1. The point of view of the theory of knowledge. —2. The positive 
 theory of knowledge distinguished from the metaphysics of knowledge. 
 
 CHAPTER I 
 
 1. Two senses of the term idea: idea and image. Images not the only ele- 
 ments of knowledge. — 2. Images do not mean by resemblance alone. Sym- 
 bols may mean any kind of objects; not restricted to meaning images or the 
 present content of the mind. — 3. Mediate and immediate knowledge. Im- 
 mediate knowledge the presentation of objects, mediate knowledge represen- 
 tation through symbols. — 4. Presentation as a union of sensation and 
 conception: sensations as signs. The passage from presentation to represen- 
 tation. —5. Pure awareness: not the apprehension of sense data. A non-con- 
 ceptual cognition of the real. — 6. Meaning a function of psychical activity: 
 not the association of ideas. —'7. The meaning activity as preparation for 
 an object. Overt action as a sign of belief. Belief and understanding. — 8. 
 The behavioristic analysis of meaning inadequate: does not distinguish 
 habits of meaning from other habits. The meaning activity a suspension of 
 outward action, and hence observable only in introspection. — 9. Summary 
 of the description of meaning. The nature of thought in general. — 10. Syn- 
 tactical meaning: a complex meaning is a synthesis of meanings in a single 
 meaning and represents an object or fact analytically, that is, as a unity of 
 elements. — 11. Simple symbols: unless their meanings are defined they 
 have significance only through reference to experienced objects. Simple 
 symbols an integral part of presentations. — 12. Syntactical meanings 
 built on simple meanings. A group of symbols may be significant when there 
 is no object to which it refers. — 13. Summary. 
 
 CHAPTER II 
 
 AMMEN Sey Te ae aan Vax Se) Dama ERR eae oi 
 
 1. Symbolic groups as copies of the logical form of complex objects: their 
 likeness to maps. — 2. Logical form determined by characters and relations 
 which belong to objects as such. Symbols being objects share these with the 
 things they mean. — 3. The concept of growping: the same as the concept 
 of function. Demands that the whole be uniquely determined by its parts, 
 and the meaning of a symbolic whole by the meanings of its parts. Symbols 
 reproduce factual groups by symbolic groups. — 4. Numerical identity and 
 diversity as formal characters of objects. These together with grouping de- 
 termine the form of symbols and of facts. Simple symbols not formally dis- 
 tinct; they set the scale of representation. Groups differ formally in multi- 
 
xii 
 
 CONTENTS 
 
 plicity, or type, or both. — 5. Signs of syntax: symbols of symbolism. A gen- 
 eral schematism for presenting logical forms. Comparisons of form effected 
 by one-to-one correlations. — 6. Alternative analyses of identical objects. 
 Statements of identity not trivial. — 7. The principle of identity: two in- 
 terpretations — as a principle of symbolism and as a statement of fact. 
 Equivalences by definition. — 8. The third distinguishing feature of logical 
 form: the distribution of tautologous symbols or identical elements within 
 groups. — 9. Summary. 
 
 CHAPTER III 
 
 UNIVERSALS AND INDIVIDUALS: ORDER 
 
 1. The objects of knowledge are of double aspect: iniveal Aa; individual. 
 — 2. The antinomy of the universal and the individual: no description 
 reaches the specific essence of the individual. — 3. Spatial and temporal 
 relations do not determine individuals. — 4. The postulate of the identity 
 of indiscernibles: leaves the antinomy of the universal and individual un- 
 solved for finite knowledge. — 5. Representation of the individual through 
 a variable: the variability of proper names. — 6. Universals determinately 
 known: as identities in changing and diverse instances. —7. The struc- 
 tural function of universals: elements of unity in facts. The distinction be- 
 tween terms and elements of unity. The unity of fact indefinable. — 8. The 
 structural function of individuals: they appear only as terms. — 9. Uni- 
 versals as terms: abstraction, beginning in perception and completed in con- 
 ception. — 10. The objectivity of universals: arguments against nominal- 
 ism. — 11. A grammar of symbolism based on the distinction between terms 
 and elements of unity. — 12. Plans of syntax in symbolic systems as deter- 
 mining possibilities for knowledge. Deductive and non-deductive systems. 
 — 13. Nonsense: distinguished from fantasy, absurdity, and contradiction. 
 — 14. Order described in terms of group structure. Asymmetry. — 15. 
 Symmetry: symmetrical relations as relations without sense. — 16. Repre- 
 sentations of order through spatially and temporally ordered symbols am- 
 biguous. — 17. Complex elements of unity. — 18. Summary. 
 
 CHAPTER IV 
 
 DESCRIPTION AND ANALYSIS 
 
 1. General nature of descriptions: Votes euiee to terms through predicates of 
 these terms. — 2. Descriptions mean complex wholes: in this respect they 
 are like propositions. — 3. Descriptions distinguished from other complex 
 expressions by their form: through a variable they signify a term as modi- 
 fied by a predicate; the term takes a central, rather than a subordinate 
 place, in the structure. — 4. The variable: variable meaning a distinct kind 
 of significance attaching to an uninterpreted element in a whole. A minimal 
 context of logical structure necessary to variables. — 5. The ambiguity of 
 the variable: distinguished from equivocation. Variable meanings must 
 follow the principle of identity. “The,” “a,” “any,” and “‘some,”’ as signs 
 of interpretation. — 6. Descriptions of universals. —7. Examination of 
 Messrs. Russell and Whitehead’s argument, from the triviality or falsity of 
 “Scott is the Author of Waverley,” to prove that descriptions are incomplete 
 
 66 
 
 108 
 
CONTENTS xiil 
 
 symbols. Such statements neither trivial nor false. —8. Judgments of 
 analytic form and synthetic effect: they analyze unanalyzed concepts or en- 
 large the meanings of concepts. — 9. Indeterminateness of proper names. — 
 10. Judgments of synthetic form and analytic effect. — 11. Knowledge in 
 universal terms determinate. The tendency of science to become analytic in 
 form: a completely interpreted science rests on some synthetic judgments.— 
 12. Descriptions of the non-existent: the significant use of symbols when 
 they refer to no objects. The theory of descriptions as incomplete symbols 
 rests on a narrow conception of meaning. —13. Classes: not the same type 
 of objects as facts. Defined through the primitive idea of totality. — 14. 
 Summary. 
 
 CHAPTER V 
 
 LECPaPANDMOALSIT Ly hl chch ae em enue Uae kU TAQ 
 1. Truth and falsity as properties of symbols. Meaning both necessary and 
 sufficient to truth. Truth and reality. — 2. Examination of the theory that 
 truth is a property of subsistent entities or propositions. The proposition as 
 a tertium quid. — 3. The objective reference of meanings independent of the 
 existence or subsistence of a referent. — 4. Subsistent entities not necessary 
 to the analysis of meaning. Propositions as symbols. — 5. Perception as a 
 criterion of existence. Conceptual constituents in perception. Dreams, 
 illusions, hallucinations. Bare existence alone guaranteed by givenness in 
 perception. — 6. Sensationalism and empiricism contrasted: sense data 
 not the only data. Presentational thinking as a means of knowing the real. 
 The tabula rasa view of mind. —7. Consistency with the whole of knowl- 
 edge as a criterion of existence. Rationalism and irrationalism: limited 
 rationalism. — 8. The empirical categories. Theory and perception as 
 mutually corrective. —9. Tests of truth: distinguished from truth. — 
 10. The coherence theory. Truth as correspondence implies the distinct- 
 ness of knowledge and reality. Identity of logical form the medium of corre- 
 spondence. — 11. Belief, judgment, and assertion. Belief continuous with 
 understanding. The interest in truth as the motive of belief. Pure specula- 
 tion. — 12. Belief not the addition of the concept of existence: the onto- 
 logical argument. Single words and incomplete phrases as propositions. — 
 13. Disbelief as belief in negative propositions. Incredulity or scepticism 
 the true opposite of belief. — 14. Signs of belief: the copula. — 15. Rela- 
 tivism and scepticism. The need for belief. The concept of truth as an ap- 
 proach to metaphysics. — 16. Summary. 
 
 CHAPTER VI 
 
 NEGATION AND CONTRADICTION .............. 197 
 
 1. The paradox of negative truth: negative facts. The negative as a vari- 
 able. — 2. Ambiguity essential to negation: the possible values of a nega- 
 tive as its possible grounds. Incompatibility of propositions not a part of 
 the definition of the most elementary sort of negation. Formal and material 
 simplicity of concepts. — 3. Purely conceptual negation: the possible values 
 of the negative determined by distinctness of meaning irrespective of ob- 
 
X1V 
 
 Format DEDUCTION ..... 
 
 CONTENTS 
 
 jects meant. “Determination is negation.” — 4. The principles of identity 
 and contradiction as general rules of symbolism, and as general conditions 
 of the being of objects. — 5. The law of the excluded middle: the inferential 
 negative. — 6. The conditions of the truth and falsity of negatives. Am- 
 biguous truth. The implications of the law of the excluded middle. — 
 7. Negative judgments: bare denial contrasted with specific denial. — 8. 
 Conceptual validity and truth: formal and material consistency. — 9. Sum- 
 mary. 
 
 CHAPTER VII 
 
 1. The study of pure form through uninterpreted symbols: sets of postu- 
 lates as plans of syntax. — 2. The general principles of symbolism: assumed 
 in all deductive systems. — 3. Substitution as the modus operandi of formal 
 deduction. The rule of completeness of substitution. Equations of struc- 
 ture. Implicational substitutions. — 4. An uninterpreted Boolean Algebra 
 as an illustration of formal deduction. — 5. The class interpretation of the 
 Boolean Algebra. — 6. The meaning of rules of substitution: ranges of 
 variability : functional constants and functional variables. — 7. Operations 
 distinguished from relations. A set of postulates for serial order. — 8. In- 
 ference: its relation to belief and assertion. Completely interpreted deduc- 
 tive systems completely inferential. — 9. Incompletely inferential systems: 
 analogy between the manipulations of a formal deductive system and the 
 thought process in words and images. Reason and imagination. — 10. Sum- 
 mary. 
 
 CHAPTER VIII 
 
 THe METAPHYSICS OF KNOWLEDGE .. 
 
 1. Metaphysical basis of criticisms of knowledge. Scepticism and meta- 
 physics. — 2. Critical agnosticism. Kant and Locke. — 3. The theory of 
 mind-isolation in Kant and Locke. — 4. Positive conclusions from the re- 
 jection of agnosticism. — 5. Appearance and reality: how this distinction 
 must be interpreted. — 6. The relation of the mind to real objects in cog- 
 nition: activity and passivity in knowledge. Idealism. — 7. Critique of 
 idealism. Materialism. — 8. Neutralism. The mental and the physical as 
 aspects of reality. —9. The mental and the physical discovered within a 
 single field of experience. Mind and non-mental objects continuous in cog- 
 nition; specific nature of this continuity. — 10. The problem of the cogni- 
 tion of physical objects distinguished from the mind-body problem. The 
 relevance of perceptual objects to the psycho-physical situation. — 11. The 
 role of thought-activity in knowledge: the general as fulfilling the intentions 
 of thought. Innate ideas. — 12. Is reality logical in form? Intuition and ir- 
 rationalism. — 13. Metaphysical insight. The relation between the form 
 and the detail of reality. A final truth in a growing experience. — 14. Con- 
 clusion. 
 
 SUPPLEMENTARY READINGS 
 
 INDEX 
 
 . 222 
 
 266 
 
 317 
 323 
 
SYMBOLISM AND TRUTH 
 

 
 
 
 
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INTRODUCTION 
 
 I 
 
 As the various sciences have branched off from the common 
 stem of philosophy, which was in the beginning the pursuit of 
 truth wherever it might be found, the philosophers have been 
 left with certain problems preéminently their own, and among 
 these is the theory of knowledge. It is not probable that the 
 theory of knowledge will ever be a science in the sense in which 
 mathematics, physics, and biology are sciences. There is too 
 much room for difference of opinion, not only in the solution of 
 its problems, but in their statement. Yet progress in this field of 
 thought, as in any other, comes only with the attempt to define 
 the subject-matter more clearly, to cut it off from neighboring 
 fields which threaten it with incursions of irrelevant questions, 
 and to find some ideas that bind the whole together. 
 
 Just as a physical theory takes its rise from physical facts, so 
 a theory of knowledge is built on the facts of knowledge; but 
 though these facts are before us when we make the simplest 
 statement or perform the most elementary process of reasoning, 
 they are by no means so apt to strike the mind as are the facts of 
 physics or of any other special science. We are mentally far- 
 sighted and tend to neglect that which is closest to us. 
 
 Everything that can be mentioned is known in some sense. If 
 I deny the existence of two-headed lions or red elephants, I 
 know what I mean by these denials, and therefore these imagi- 
 nary creatures are somehow objects of my knowledge. If I open 
 my eyes on the world about me, I see trees and houses, and 
 people passing in the street; and these are obviously known in 
 some other way than the red elephants and the two-headed 
 lions. The geometer sketches a rough triangle on a bit of note- 
 
4 SYMBOLISM AND TRUTH 
 
 paper, and on this diagram demonstrates that the sum of the 
 three interior angles of the triangle is equal to a straight angle. 
 This exact geometrical proposition is not true of the imperfect 
 penciled triangle; it is true of an ideal Platonic triangle, which is 
 only suggested by the rough figure and is apprehended through 
 the eye of reason rather than the eye of sense. The ideal triangle 
 belongs thus to another class of objects of knowledge, just as do 
 the ideal gas, the frictionless motion, the perfectly rigid and 
 elastic body, of the physicists. Again, what is one to say of 
 dream objects? The events and people of dreams are for the 
 time as intensely real as the events and people in the street out- 
 side at the present moment. What is the reason for our prejudice 
 in favor of the reality of the things of waking life, which fill at 
 best only three-quarters of our experience? Certainly the dream 
 is a form of knowledge. 
 
 There are evidently many different senses of the term ‘‘knowl- 
 edge.’ We dwell in the medium of the known, which surrounds 
 us as an atmosphere. This very ubiquity makes it difficult to 
 stand off from knowledge and analyze it. Perhaps the simplest 
 way of marking out the subject-matter of the theory of knowl- 
 edge is this: Anything of which it can be said that it is known in 
 any sense is a proper subject of our investigation. The theory of 
 knowledge is interested in these things not as physical, psycho- 
 logical, mathematical, or any other particular sort of objects, 
 but as things known. Although mathematical equations, physi- 
 cal, chemical, and biological laws, historical facts, and a multi- 
 tude of other data which belong to the special sciences are also 
 data of the theory of knowledge, this theory looks on them in a 
 different light from any of the special sciences. What common 
 factors, laws, uniformities, relations, belong to things merely as 
 objects of knowledge? This is the question that must be asked. 
 
 Thus the theory comprehends in its subject-matter all the 
 special sciences. These are particular cases of knowledge from 
 
 —— 
 
INTRODUCTION 5 
 
 which the general principles are to be induced. But it attacks 
 problems that none of these sciences can meet. With Bacon it 
 “takes all knowledge to be its province” and views this province 
 from an angle of its own. It includes much of what is often classi- 
 fied as philosophy of science or logic, for it considers such ques- 
 tions as what is a proposition, what is a scientific law, what are 
 truth, error, assertion, belief, conception, meaning? In short, 
 wherever there are principles of the known qua known, these 
 principles are a part of the theory of knowledge. 
 
 Meaning, for example, is present in all knowledge, from the 
 simplest perception to the most complex mathematical expres- 
 sion. Any knowledge that does not make use of meaning is an 
 immediate awareness, an intuition, which can give no rational 
 account of itself. Just what meaning is is a thorny question. But 
 if a satisfactory answer can be given, the description of knowl- 
 edge will have been pushed forward some distance. Moreover, 
 one of the most notable facts about knowledge — and this is 
 plainly connected with the presence of meaning — is that it can 
 be expressed. Knowledge can be shut in between the covers of 
 books and passed on from generation to generation; it can be 
 transmitted from mind to mind by word of mouth; it can be em- 
 bodied in the intricate formulae of the exact sciences. The sym- 
 bols which are the outward instruments of this expression must 
 have a close and necessary relation to the thought they convey, 
 and the analysis of these instruments should aid us in bringing 
 the true nature of knowledge into view. It is from this angle that 
 we propose to attack the problem. 
 
 II 
 
 The most troublesome intruder in the field of the theory of 
 knowledge is metaphysics, for the questions that usually first 
 suggest themselves to the student of the subject are these: How 
 is knowledge related to reality? Is reality independent of or de- 
 
6 SYMBOLISM AND TRUTH 
 
 pendent on knowledge? Is it genuinely given in knowledge, and 
 if so how? These questions turn on the distinction of subject and 
 object, of a knowing-being with ideas, perceptions, and sensa- 
 tions, and an external world of existences alien to this being. Is 
 this alienation complete? Or is there a rapprochement between 
 reality and the mind in which it makes its appearance? Many 
 philosophers believe that before a theory of knowledge can be 
 stated these problems must be solved. 
 
 But if this were so, it would be as if the physicist insisted that 
 a theory of the ultimate nature of mass is essential to a state- 
 ment of the laws of mechanics, or as if the biologist refused to 
 examine the laws of heredity without an adequate definition of 
 life. Human knowledge is a fact just as mass, motion, and life 
 are facts. The study of its principles, its elements, its structure, 
 does not presuppose an answer to the more ultimate questions, 
 how is this fact possible? — what is the relation of knowledge to 
 reality? These queries carry one beyond the analysis of knowl- 
 edge itself to a theory of reality, and no one can hope to discover 
 whether or not reality is reached through knowledge until he 
 knows what knowledge is. 
 
 Though none of these metaphysical questions is prior to the 
 descriptive study of knowledge, no theory would be complete 
 unless it attempted to answer them. A good theory — of any- 
 thing — must consider all the intelligible questions its data sug- 
 gest; and so a complete theory of knowledge will fall into two 
 parts: it will be both a positive analysis and a metaphysics of 
 knowledge, it will both describe knowledge and explain its rela- 
 tion to reality. But the metaphysics of knowledge demands a 
 final concept of reality, and it naturally supervenes on a more 
 restricted inquiry which makes use of a provisional, working 
 concept of the real. Let us call this the posttwe theory of knowl- 
 edge, epistemology proper, which is an examination of knowledge 
 undertaken in the spirit of the laboratory. We must begin by 
 
 
 
INTRODUCTION 7 
 
 viewing knowledge as a natural phenomenon if we are to deter- 
 mine its place in reality. We must proceed inductively and “‘rise 
 by gradual steps to that which is prior and better known in the 
 order of nature,” instead of ‘‘beginning at once by establishing 
 certain abstract generalities.” ! 
 
 From the point of view of the positive theory of knowledge 
 one can set out without being a realist, an idealist, a monist, a 
 pluralist, a nominalist — without attaching himself to any sys- 
 tem of metaphysics. Metaphysics comes later; it is the coping- 
 stone of the theory and it cannot be securely placed without a 
 careful survey of the facts. 
 
 The confusion of metaphysics with the positive analysis of 
 knowledge can be traced, in modern thought, to Locke. Locke’s 
 Essay, though it deals with the structure and laws of knowledge, 
 especially with the manner in which ideas are built up from sim- 
 ple impressions into complex systems, is nevertheless shot 
 through with the conception of an unknowable substance which 
 lies beyond ideas. This conception colors the whole work. For 
 Berkeley and Kant, metaphysics is still intertwined with the 
 descriptive treatment of knowledge, though the Critique of Pure 
 Reason in distinguishing the transcendental aesthetic and analytic 
 from the dialectic makes a division that corresponds roughly to 
 these two aspects of the subject. Yet the whole Critique is 
 haunted by a metaphysical ghost — the thing-in-itself. The 
 first modern philosopher who severely restricts himself to the 
 analysis of knowledge without metaphysics is Hume, and this is 
 accidental, the result of his scepticism. Since he believed in no 
 theory of reality, he advanced no theory of the relation of 
 knowledge to reality, but he fell on the contrary into the trap of 
 the purely psychological point of view. 
 
 The phdénomenologie which has become prominent in recent 
 German philosophy, especially through the writings of A. 
 
 1 F. Bacon, Novum Organum, Bk. I, Aphorism 22. 
 
8 SYMBOLISM AND TRUTH 
 
 Meinong and E. Husserl, pursues the analysis of knowledge in 
 the positive spirit; and the same tendency, if not the same mat- 
 ter, is to be found in England in the work of Mr. Bertrand 
 Russell, Mr. A. N. Whitehead, Mr. G. E. Moore, and Mr. C. D. 
 Broad. 
 
 Yet metaphysics always lurks in the background, even for 
 those who attempt to avoid this type of speculation. The ques- 
 tion of the ultimate validity of knowledge remains to be an- 
 swered; the notion of truth points inevitably to a final concept 
 of the real. A definition of truth cannot fail to invite metaphysi- 
 cal criticism, and it can be defended in the last resort only by 
 arguments that rest on metaphysical premises. Therefore, un- 
 less we are to persist in a partial scepticism such as Hume’s, the 
 separation of the positive theory of knowledge from metaphys- 
 ics cannot be maintained to the end; but it is of immense value 
 as a working distinction in the study of epistemology. 
 
 
 
 
 
CHAPTER I 
 
 MEANING 
 I 
 
 Wuavr are the facts that a theory of knowledge needs to organ- 
 ize and explain? 
 
 It is customary to say that knowledge is built up from ideas. 
 Locke defined knowledge as “‘nothing but the perception of the 
 connection of and agreement, or disagreement and repugnancy, 
 of any of our ideas,”’ and he gave as his reason for this definition 
 that “‘the mind, in all its thoughts and reasonings, hath no 
 other immediate object but its own ideas, which it alone does or 
 can contemplate.” ! If we ask what ideas are, we learn nothing 
 more definite than that they are the mind’s objects. Thus 
 Locke’s statement that “‘our knowledge is conversant only with 
 ideas” affirms that knowledge is conversant only with the 
 mind’s objects — a truism which no one will deny. The term 
 “idea” is robbed of its force by being extended to all the ele- 
 ments of knowledge. 
 
 There is a narrower and more profitable sense of this term, 
 which makes ideas one class of the ingredients of knowledge, but 
 not the only class. This is the sense in which “idea” is used by 
 the psychologist. An idea is an image, a psychical event, and 
 it must be distinguished from other psychical events, namely 
 sensations and perceptions. The ground of this distinction is 
 difficult to establish. Intrinsically an image and a sensation or 
 perception are much the same. The difference is not, as Hume 
 supposed, one of vividness or intensity. But the things of sen- 
 sation and perception have a type of coherence with one another 
 
 1 J. Locke, Essay Concerning Human Understanding, Bk. IV, ch. i, secs. 1, 2. 
 
10 SYMBOLISM AND TRUTH 
 
 which those of the imagination do not have. Sensory and per- 
 ceptual objects obey, not merely “psychical” laws, but also the 
 laws of physics; and so in most cases images can be set apart 
 from sensations and perceptions. 
 
 The striking thing about ideas in this narrower sense is that 
 they usually refer beyond themselves to other things. They are 
 not as a rule self-contained, but reach out with tentacles of sig- 
 nificance toward other ideas or toward the things of sensation 
 and perception. Locke found this to be characteristic of all 
 ideas in his sense of the term, that is, of all the mind’s objects. 
 They are all symbolic of that which lies beyond the mind’s 
 grasp, says Locke. But since the realities which these ideas sig- 
 nify are not themselves ideas, Locke is at a loss to interpret the 
 meaning of knowledge in terms of these extra-mental realities. 
 He is clear however on one point, that ideas in so far as they are 
 vehicles of knowledge are symbolic; that the area of knowledge 
 is coextensive with the area of significance. 
 
 In the more restricted sense of “‘idea,”’ it is not necessary to 
 attempt the impossible, to seek beyond knowledge for the mean- 
 ing of ideas. They are to be interpreted as referring to objects 
 sensed or perceived, and often as referring to other ideas or psy- 
 chical states. But as mere meaningless successions of psychical 
 phenomena following the laws of association, ideas (images) are 
 of no special importance in knowledge; they are not conveyors 
 of knowledge. They make their appearance before the mind and 
 pass away, and this is all that can be said about them. However, 
 as mediators between the mind and objects in perception or ob- 
 jects beyond the immediate circle of the mind—in other words, 
 as significant symbols— images are the first instruments of 
 meaning and hence of knowledge. Instead of saying as Locke 
 does that “knowledge is of ideas,” one ought rather to say that 
 knowledge comes through ideas. It would be of slight value to 
 have knowledge of ideas if we did not know through ideas. 
 
MEANING 1] 
 
 Images, then, pass by the easiest possible transition to a 
 second level of knowledge, the level of significance. Without 
 perceptible effort, the mind takes them to refer to something 
 other than themselves, and thus endows them with a function 
 which attaches much less readily to other elements of knowledge 
 — the function of meaning. 
 
 II 
 
 What do images signify? The simplest answer is that they sig- 
 nify things they resemble. Though this is true in many in- 
 stances, and is indeed the reason why they are such ready 
 vehicles of meaning, images are not restricted in their signifi- 
 cance to the objects of which they seem to be faint and partial 
 copies. The vagaries of individual processes of imagery are with- 
 out limit, and therefore naive copy theories of the significance of 
 ideas are faulty. The subtlety of the threads that bind ideas to 
 their objects must be recognized. Any image may come to mean 
 any object. 
 
 The fact that images resemble the experiences which pro- 
 duced them, and that the image of a part of an experience tends 
 to recall the whole, so that they take on meaning with a mini- 
 mum of effort on our part, makes images the primal instruments 
 of knowledge. But they are not the only instruments. Man adds 
 to them and improves on them. He adds speech and writing, and 
 finally the complex symbols of mathematics and logic. Ideas 
 take their place as one among many classes of symbols. 
 
 It is no doubt possible completely to supplant images as vehi- 
 cles of thought by words or other conventional signs. Yet, when 
 the major burden of significance is carried by symbols other 
 than images, the latter usually arise in the process. In most 
 minds significant imagery is never wholly absent. The traces of 
 our intellectual childhood, when to think of things is to see them 
 vividly in imagination, remain with us in the most abstract 
 
12 SYMBOLISM AND TRUTH 
 
 kinds of thought. Witness the many attempts to visualize Ein- 
 stein’s “spherical universe.” And this is so much the case that 
 we tend to believe that the meanings of words or other written 
 or spoken signs are nothing more than images in the mind, 
 either in our own or another mind. Being in the habit of discov- 
 ering the significance of most signs via the route of imagery, we 
 fail to observe that what is meant by words or other signs is not, 
 as a rule, a set of images, but the things for which these images 
 stand. If I say, “The sun is shining brightly outside my win- 
 dow,” the reader may believe that when he has called up a pic- 
 ture of sunlight streaming through a window he has before him 
 the meaning of this sentence. But the sentence means neither an 
 image in my mind nor in his. It means through these mental 
 events to something else. (This does not deny that some words 
 and sentences mean images only; ¢.g., “my mental picture of 
 China” refers only to ideas in the narrower sense of this term.) 
 
 It cannot be maintained that all meanings terminate in 
 images and that when this type of symbol is absent there is no 
 meaning. Images as well as other symbols are not confined in 
 their significance to any class of objects. They may stand for my 
 own or another person’s psychical states, for the content of a 
 perception, for other symbols, for objects that have never en- 
 tered any one’s experience; and not only may symbols stand for 
 any kind of object, they may, as will presently be shown, stand 
 for no object and still be significant. 
 
 Some objects are, to be sure, more accessible than others. I 
 have a closer knowledge of my own feelings and perceptions 
 than of another person’s. The paper on which I write is open to 
 inspection in a way that the other side of the moon is not. But 
 symbols can refer to the inaccessible as well as the accessible; 
 and if there are any objects which symbols cannot mean, these 
 will appear only when we have thoroughly examined the ob- 
 jects they can mean. 
 
 
 
MEANING 13 
 
 The observation that symbols may mean any kind of object 
 frees us from the presupposition that all meanings terminate in 
 the present content of the mind, and at the same time leaves 
 open the question as to the metaphysical status of the objects 
 meant. 
 
 III 
 
 We have said that images pass readily to a second level of 
 knowledge, that of significance; and that other objects, spoken 
 sounds, written marks, gestures, also take on significance, 
 though somewhat less easily than images. 
 
 Below this level of significance (at least of pure significance) 
 is a primary level of acquaintance, and all objects which are sig- 
 nificant are also objects with which we are acquainted. Whether 
 the symbol be a sensation, an image, a perception, whether it be 
 believed to belong to the physical or mental world, this symbol 
 will be something presented, and will belong to the primary as 
 well as the secondary level of knowledge. This immediate way of 
 knowing, by direct presentation, is the basic form of knowledge, 
 and it has been frequently distinguished from a less direct way 
 — knowing of or about objects. I am, for example, presented 
 with the groups of letters and words on this page and through 
 them I know about the subject under discussion; when I say 
 that I know the whiteness of this paper, it is clear that I do not 
 use the verb “‘know”’ in the same sense as when I say that I 
 know Marcus Aurelius was a Roman Emperor. I am acquainted 
 with the one object but not with the other. 
 
 Knowledge about things springs from acquaintance with 
 them or with other things in terms of which they can be de- 
 scribed; and though it is difficult to explain what it is to be 
 known in the sense of being immediately presented to a mind, 
 without this sort of knowledge we should probably know 
 nothing. We are here in contact with a fundamental concept of 
 our theory, the concept of the presentation of objects. 
 
14 SYMBOLISM AND TRUTH 
 
 Among the objects presented, some take on meaning and be- 
 come symbols, while others remain merely presented. What is 
 given to the mind becomes an instrument by means of which 
 things not given are represented, and thus we begin to pass from 
 immediate to purely mediate knowledge. To know about things 
 is to refer to them through symbols when they are not presented, 
 while to know things immediately is to have them before the 
 mind, not simply as something referred to, but as something 
 given, in which symbolic references terminate. My knowledge 
 that Marcus Aurelius was a Roman Emperor is exhausted by 
 statements I can make or ideas I can entertain. I can speak sig- 
 nificantly of him, I can think about him, but I cannot be pre- 
 sented with him. And this is true of all events in the past and 
 future, of distant places, and probably of other minds. I can, at 
 the moment, reach these only through symbols. On the other 
 hand, my knowledge of the object I call “‘the whiteness of this 
 paper” is not exhausted by what I can say or think about it. 
 This knowledge is more than a significant idea or statement; it 
 is an immediate presentation. 
 
 The most striking fact in knowledge is that it falls into these 
 two divisions, mediate and immediate; that mediate knowledge 
 is wholly symbolic, a reference to objects through objects, while 
 immediate knowledge, even though it may be partially medi- 
 ated by symbols, is more than reference to objects. It is a unique 
 seizure of objects by the mind. Yet this distinction between 
 mediate and immediate knowledge is not so sharply marked 
 as many contemporary schools of philosophy, especially those 
 which maintain that knowledge is constructed from sense data, 
 would have us believe. 
 
 IV 
 
 Objects which are presented are not merely sensed. The unit 
 of cognition is not a sensation but something much richer. Sen- 
 
 ; 
 : 
 
 
 
 Ce 
 
 ee ae 
 
MEANING 15 
 
 sations are discovered as elements in larger wholes, and these 
 larger wholes are perceptions or objective presentations. The 
 datum of the theory of knowledge is much nearer to William 
 James’s stream of thought than to pure sensation. 
 
 “Most books (of psychology), says James, “‘start with sen- 
 sations, as the simplest mental facts, and proceed synthetically, 
 constructing each higher stage from those below it. But this is 
 abandoning the empirical method of investigation. No one ever 
 had a simple sensation by itself. Consciousness, from our natal 
 day, is of a teeming multiplicity of objects and relations, and 
 what we call simple sensations are results of discriminative at- 
 tention, pushed often to a very high degree.” ! 
 
 Empiricists rarely mean by “‘experience”’ that which is given 
 wholly through the senses at the moment of experiencing. We 
 experience objects, relations, qualities; we perceive things of cer- 
 tain sorts rather than of no sort in particular; we are presented 
 with situations and facts, rather than with bare sense data. 
 From this full experience certain irreducible elements that come 
 from the senses can be analyzed out; these are elements such as 
 white, hard, smooth; but these elements are not the whole of the 
 experience. They are always bound up with other elements. 
 
 The cognitive unit, a presentation, is therefore complex. It in- 
 cludes a concept (and often a belief) as well as sensations. If I 
 gaze from my window at the trees bending in the wind, there is 
 much more in my mind than impressions of color, movement, 
 shape, and relative position. I see the trees. My mind leaps be- 
 yond sensations to concepts — concepts of solid three-dimen- 
 sional objects of a certain nature. The fusion of concepts and 
 sensations is the presentation of the object, and neither con- 
 cepts nor sensations by themselves would give the peculiar kind 
 of cognition I call “presentation.” The simplest experience, e.g., 
 that of the color white which is now before me, is more than a 
 
 1 W. James, The Principles of Psychology, vol. i, ch. ix, p. 224. 
 
16 SYMBOLISM AND TRUTH 
 
 pure sensation. I recognize something as white, and in doing so 
 bring it under a concept. 
 
 Thomas Reid, the leader of the Scottish school of common- 
 sense philosophy, which succeeded Hume, adds that belief also 
 is a constituent of perception. We believe “irresistibly,” he says, 
 in the existence of the object perceived. But this is not always 
 the case. An illusion may be present, actually perceived, but not 
 believed; we often doubt our perceptions; seeing is believing 
 only to credulous minds. Though there is a strong tendency to 
 believe our perceptions, this tendency cannot be a constituent 
 of the perception, since perceptions persist when they are 
 doubted or disbelieved. A concept, on the other hand, is a neces- 
 sary part of a presentation. 
 
 The concepts which enter in perception may function explic- 
 itly, as when I judge that “this is white,” or they may function 
 silently, without conscious judgment, as when I perceive the 
 whiteness. But one knows that he is presented with an object 
 only when he brings it, in some way, under a concept. The fact 
 that immediate knowledge can deceive, that we are as vividly 
 presented with objects in dreams and hallucinations as in other 
 states, bears witness to the presence of concepts in immediate 
 knowledge. It is only because the stuff of perceptions is largely 
 manufactured or elaborated by thought that we can be thus led 
 astray. If there were such things as pure sensations, it could be 
 readily granted that they would not deceive. They could be 
 what they were known to be, and nothing else. But since there 
 are no pure sensations, we must admit that any presentation 
 can be deceptive. The very perception that something is white or 
 hot or hard is subject to error. 
 
 “Sensation, then,” says James, “so long as we take the ana- 
 lytic point of view, differs from perception only in the extreme 
 simplicity of its object or content. ...A pure sensation is an 
 
 abstraction.” ! 
 1 W. James, op. cit., ii, 1 ff. 
 
 — 
 
 
 
MEANING 17 
 
 It is evident that the presence of concepts in perception blurs 
 the distinction between mediate and immediate knowledge, and 
 especially is this so when we see what a concept is. We shall find 
 that a concept is a symbol taken with the mental attitude that 
 gives it significance. When we conceive of an object we mean it 
 or refer to it, we entertain the idea or symbol of it; and thus the 
 mechanism of conception is the mechanism of symbolism. Im- 
 mediate knowledge, no less than mediate knowledge, presup- 
 poses therefore the functioning of symbols in a mind. 
 
 A mind enters on perception with predispositions or inten- 
 tions, which determine to a large extent what is perceived; and 
 these predispositions are aroused by symbols — ideas, incipient 
 vocal utterances, word imagery — which are at work in the per- 
 ception.! The sensory elements also operate as signs. When I 
 open my eyes on the room in which I now write, the stimuli 
 present to my senses awaken (through sensations) concepts in 
 my mind; indeed these sensations themselves play the part of 
 
 1 The psychologists of the Wiirzburg school, in recording their experiments 
 on the thought-process, speak of these predispositions as determined by the 
 Aufgabe, that is, the problem to be solved in any given case. Something very 
 like an Aufgabe is, I believe, present in any mind engaged in perceiving, and 
 plays an essential part in determining what is perceived. The following passage 
 is quoted from a paper by Dr. C. C. Pratt, entitled “The Present Status of In- 
 trospective Technique,” in The Journal of Philosophy, vol. xxi, no. 9, April 24, 
 1924: “‘ At the congress for experimental psychology at Giessen in 1904 Kiilpe 
 made a brief report on some experiments of his own on abstraction in which 
 geometrical symbols, the components of which differed with respect to form, 
 color, and arrangement, were used as stimuli. By means of instructions the ob- 
 servers were determined now in the direction of form, now of color, and now of 
 - arrangement. And it turned out that when an observer was under the Aufgabe 
 for color, e.g., he could make at best only a very inadequate report on form 
 and arrangement — in some cases he reported that form and arrangement 
 were not present to consciousness at all. The implications of such a state of af- 
 fairs is far reaching. ... As far as accurate observation and unequivocal report 
 are concerned, an observer is adequate only to those aspects of a given experi- 
 ence which the determining tendency brings clearly into line with the particu- 
 lar Aufgabe of the moment; other aspects of that experience fall at various dis- 
 tances outside of the sphere of immediate observation and hence cannot be 
 made the objects of scientific description.” See O. Kiilpe, “‘Versuche iiber Ab- 
 straktion,” in Bericht ti. den I. Kongress f. exper. Psychol., 1904, pp. 56-69. 
 
18 SYMBOLISM AND TRUTH 
 
 concepts, that is, of symbols. They arouse unuttered judg- 
 ments which are carried by images or fleeting and unspoken 
 words. Through the whole process, I am aware in immediate 
 presentation, not of the sensations alone, but of the objects I 
 thus conceive. I see the desk and the rows of books because 
 these are what the passing sensations mean. 
 
 If the presence of concepts in immediate knowledge blurs the 
 distinction between the mediately and the immediately known, 
 still it does not obliterate it. As we travel up the scale from pres- 
 entation to representation, we come finally to a kind of knowl- 
 edge in which the object conceived or meant is no longer given 
 along with the symbols through which it is conceived. This is the 
 kind of knowledge embodied in a mathematical expression or a 
 scientific theory; or, more simply still, in a judgment as to the 
 past or future. It is purely symbolic. Between presentation and 
 representation there is a twilight zone in which oné cannot be 
 sure whether the object intended is given or merely conceived. 
 Here most of the errors of perception occur. But the ends of the 
 scale are distinct. At the one end is a direct acquaintance with 
 objects such as is not possible through concepts (or symbols) 
 alone: this is a cognition in which what is meant is grasped in a 
 union of sensation and conception, often attended by belief. At 
 the other end is pure conception, knowledge which is significant 
 reference and nothing more. 
 
 Vi 
 
 The statement that concepts (symbols) are always to be ) 
 
 found in immediate knowledge must be modified if there is any 
 such cognition as M. Henri Bergson’s intuition of the flux of 
 reality. The Bergsonian intuition is a pure awareness more im- 
 mediate than the perception we have described; it does not give 
 presentational knowledge in our sense of the term; it is not an 
 acquaintance with objects, not even with simple qualities. 
 
 
 
 — 
 
 { 
 ‘| 
 | 
 
MEANING 19 
 
 One cannot adequately explain what this intuition gives him. 
 He must search for it in his experience and if he finds it must 
 admit his inability to express it. He will be unable to bring it un- 
 der any concept, but must remain content to gesticulate in its 
 direction with words and metaphors. I cannot, in Bergson’s 
 sense, have an intuition of an object, for this would require the 
 concept of an object — the content of the intuition would be con- 
 ceptualized in this general and vague way as “something-or- 
 other.”’ Thus if we grant the existence of such a non-conceptual 
 form of cognition, it will give us neither objects, qualities, rela- 
 tions, things, or events, but will fall into a category of its own, 
 beyond all rational categories. 
 
 Now there does seem to be a background of pure awareness 
 not unlike the Bergsonian intuition in all presentations. Beyond 
 the objects which are clearly given, beyond what is singled out 
 and conceptualized as “‘experience,”’ there is something which 
 cannot be singled out and conceptualized. This is an amorphous 
 datum which transforms itself, under the working of concepts, 
 into the articulated data of perception. 
 
 Perceptual knowledge, the knowledge of objects, persons, 
 events, places, relations, qualities, sense data, has a structure. 
 Only after we have examined this structure will the distinction 
 between pure awareness and rational presentation become 
 clear. Pure awareness must be the complete antithesis of con- 
 ceptual knowledge; it must be knowledge in which all symbols 
 have been transcended, knowledge wholly deconceptualized; 
 and yet it must be continuous with perception, and through per- 
 ception, with conception. The presentation of objects must arise 
 from this pure awareness and return to it with no perceptible 
 break. 
 
 Theories of knowledge which find pure immediacy in sense 
 data do not carry their analysis far enough. The sense datum is 
 something discrete, fixed and referred to by a concept, and be- 
 
20 SYMBOLISM AND TRUTH 
 
 hind the sense datum is the vaguely apprehended whole from 
 which it is discriminated. Even so fluid a datum as Mr. A. N. 
 Whitehead’s event ! is not known in pure immediacy; the event 
 is picked out from a background, and certainly the perception 
 of relations between events demands more than a purely im- 
 mediate knowledge. 
 
 The attempt to discover the purely immediate leads thus be- 
 yond perception and sensation to what can be described only as 
 the unarticulated awareness of a whole. (And even this descrip- 
 tion is faulty since it makes use of concepts.) But this pure 
 awareness is not a form of knowing which can stand on its own 
 feet. It issues from the whole cognitive act as the final aroma 
 of knowledge, as a sense of oneness with the object known; and 
 the attempt to isolate pure awareness meets with no better suc- 
 cess than the attempt to grasp a pure sensation. Though this 
 intuition passes beyond what can be clearly compressed into 
 concepts, it does not contradict but supplements conceptual 
 knowledge. We must leave till later the discussion of this pure 
 awareness and its relations to other forms of knowledge.? 
 
 VI 
 
 From the basic units of presentational knowledge, purely 
 symbolic or conceptual knowledge is constructed. Through sym- 
 bols, themselves presented and significantly linked to objects 
 (and sometimes to no object), we move from the realm of pres- 
 entations to that of representations. It is here that the sciences 
 appear, that logic enters, that the common knowledge of every- 
 day speech comes into being. The world of the purely concep- 
 tual is superimposed on or abstracted from the world of the im- 
 mediately known. The mind reaches out from its data. Words, 
 ideas, and other signs carry it beyond things that are given to 
 
 1 A, N. Whitehead, The Principles of Natural Knowledge (1919), ch. vi. 
 2 See below, ch. VIII, sec. xii. 
 
 
 
MEANING 21 
 
 the imaginary and even to the non-existent, the fantastic, and 
 the impossible. And this brings us to the central problem of the 
 present chapter, the nature of meaning. 
 
 A symbol, briefly described, is an object which stands for an- 
 other object or is still significant if it stands for no object. This 
 is no definition, and serves merely to raise the question of how a 
 symbol is related to the thing it means and how it can be signifi- 
 cant when it means no existing object. 
 
 In the first place, the symbol stands in a mind for an object; 
 it takes on significance through psychical activity, and if there 
 were no minds there would be no symbols. Since the symbolic 
 relation is not something given in the external world, any signifi- 
 cance discovered in the events about us is read into these events; 
 and quite apart from the metaphysical question as to whether 
 these events could be if there were no minds, they certainly 
 could not be significant unless they were so interpreted. When 
 one says that clouds mean rain, that a low temperature means 
 ice and snow, he refers to a causal connection between these 
 things, but this relation alone does not make the one a sign of 
 the other. It is because the cause is interpreted as a symbol that 
 the antecedent event takes on significance. Aside from the con- 
 nections of meaning established in a mind, things in the order of 
 nature simply are; they are bound together by laws, but not 
 bound so that any one by its own nature means any other. 
 Berkeley, who interpreted all sense impressions as signs, found 
 it necessary to postulate a Divine Mind communicating with 
 man through this language of natural events. 
 
 Written marks and spoken sounds are not different in this 
 respect from other objects: without a mind which uses them to 
 refer to things, they would be nothing more than physical occur- 
 rences; and the same is true of images or ideas—unless we took 
 them to be significant, they would pass through the mind as 
 psychical events, conforming to the laws of association but bear- 
 ing no meanings with them. 
 
22 SYMBOLISM AND TRUTH 
 
 Meaning then is something superadded to things by a mind. 
 What is the nature of this activity which adds significance? 
 
 The commonest answer to this question, familiar especially in 
 English philosophy from Hobbes onward, is that the meaning 
 activity is the association of ideas; and this reappears in James, 
 who says that the meaning of an idea is to be found in its “‘psy- 
 chical fringe.”’ Locke sees the weakness of this view when he 
 speaks of association as a distemper of the mind which leads 
 thought away from its objects rather than toward them. In de- 
 termining the meaning of a word or image, we must rule out ir- 
 relevant associations; much of the “‘psychical fringe”’ must be 
 overlooked; and this being the case, meaning must be something 
 other than association. Though associations sometimes conduct 
 one to the things he means, they more often conduct him away 
 from them, and he can never be sure that the paths of associa- 
 tion are not by-ways rather than high-roads of thought. The 
 associations that play a part in carrying meanings are con- 
 trolled, that is to say, their direction is prescribed by what the 
 psychologists know as a “determining tendency ”’ or an Aufgabe. 
 The word ‘New York” may arouse by association the image of 
 the Statue of Liberty, which may lead to a picture of the guil- 
 lotine and the red flag, but none of these associated ideas is the 
 meaning of ““New York”’; they must be dismissed as irrelevant 
 associations. Images of canyon-like streets and suspended 
 bridges bring the meaning nearer, since they fit the attitude or 
 set of mind the word induces. 
 
 There is a still more damaging objection to the view that 
 meaning is the association of ideas. Association is a link between 
 images and carries the mind no further than ideas in the nar- 
 rower sense of the term; and yet what is meant by a symbol need 
 not be an idea. ““New York” means the city on the banks of the 
 Hudson, rather than the representation of this city in images, 
 and these images themselves mean something other than images. 
 
 
 
MEANING 23 
 
 They stand for a perceptual object, and the word means what 
 the images mean. The activity of meaning is, more frequently 
 than not, directed beyond ideas, and so it cannot be described in 
 terms of association, which is restricted to ideas. 
 
 VII 
 
 The simplest solution for the purposes of the theory of knowl- 
 edge is to accept as unique a meaning activity. This does not im- 
 ply that from the point of view of psychology this activity is 
 unanalyzable; it may well be that it can be reduced to more ele- 
 mentary activities, but it is not necessary for our present 
 purposes to do so. We must confine ourselves to a general 
 description, which is intended to direct the reader to the point in 
 experience where the meaning activity is to be found. Having 
 discovered meaning in its primitive form, we can show how 
 more complex meanings are constructed, and this will lead to the 
 logical and strictly epistemological, rather than psychological, 
 aspects of the subject. 
 
 To reach out with the mind toward objects, as one does when 
 _ he means them, is to be in a state of preparation for these ob- 
 jects. The meaning activity is one of vague anticipation: the 
 mind is poised expectantly, awaiting something other than the 
 thing, the symbol, which is immediately before it; and this an- 
 ticipation is vague because it is not accompanied by a belief that 
 the object meant will appear or that it exists. When I mean an 
 object I do, in some sense, prepare my mind for a presentation 
 of this object. Though I cannot be said to turn my attention 
 toward the thing I mean, since one cannot attend to something 
 not presented to him, there is no doubt that I do more than at- 
 tend to a symbol or an image. Indeed, I turn my attention away 
 from the symbol or the image, and this constitutes the first step 
 in preparation for the thing meant. 
 
 Toward every object certain activities are appropriate. I can 
 
24 SYMBOLISM AND TRUTH 
 
 eat bread; I can throw a stone; I can sit on a chair. These 
 activities are appropriate to the object for many reasons, the 
 most important of which are biological reasons: the appropriate 
 activities are those which enable me to adapt myself to the 
 thing; and for any single thing there are many such activities. 
 When a symbol is before the mind, it sets in motion the activ- 
 ities appropriate to an object and this object is then what the 
 symbol means; but it sets these activities in motion only par- 
 tially, it touches nothing more than their psychical roots, so 
 that if the effect of the symbol appears in consciousness, it is as 
 a barely noticeable feeling of tendency. 
 
 Physiologically, a symbol probably stirs the central part of a 
 chain of nervous connections which constitute a tendency to act 
 in a certain way. The process of understanding a symbol ter- 
 minates in the brain, and for this reason the activities it arouses 
 are implicit, so implicit as to diminish almost to the zero-point 
 both for outward and inward observation. And yet they are ade- 
 quate to carry the reference, the outward reach of the mind, 
 which is significance. 
 
 Ideas, as well as written and spoken words, set up these cen- 
 tral tendencies to action. Every idea, in James’s opinion, has its 
 motor side; and not only do ideas arouse tendencies to action, 
 they spring from these tendencies, so that the set of the mind in 
 a certain direction determines what images appear and causes 
 irrelevant images to be disregarded. It is this set rather than the 
 image itself which fixes the meaning, and this is why ideas do 
 not mean by resemblance alone. 
 
 But what if the activities brought into play by a symbol be- 
 come overt? What if they push out beyond the central nervous 
 system and terminate in completed acts? 
 
 In this case the mind has gone further than merely under- 
 standing the symbol. Understanding has passed into belief, that 
 is, one has begun to behave as if the thing meant were present, 
 
 
 
MEANING 25 
 
 as if the activity which is fitted to it could be successfully per- 
 formed here and now. Understanding and belief being of the 
 same genus, the line which separates them cannot be sharply 
 drawn. Belief is willingness to act on what is understood, while 
 understanding is preparation for activities appropriate to an ob- 
 ject, though these activities are checked far short of perform- 
 ance. 
 
 If you tell me that it is a good day for a walk in the hills, I 
 understand by putting myself in an attitude of mind suited to a 
 walk in the hills, but this attitude does not amount to belief. 
 Though I need not actually set out on the expedition if I believe 
 the statement, I must nevertheless be more fully prepared to do 
 so than if I merely understand it. I must feel that the walk could 
 be successfully undertaken. Belief is a more complete prepara- 
 tion for activity than understanding: it is understanding with an 
 added psychical pressure in the direction of performance. There- 
 fore, if the effect of a symbol on a mind is to produce overt acts, 
 we can conclude that the symbol is not only understood but also 
 believed. 
 
 VIII 
 
 This is not the only possible conclusion, and here the inade- 
 quacy of the behavioristic treatment of meaning comes into 
 view. 
 
 The extreme behaviorist assumes that there is only one way in 
 which psychical processes can be studied, namely through out- 
 ward action. Now an object that is immediately presented may 
 produce outward activity without either understanding or be- 
 lief. Certainly if one is to believe, he must begin by understand- 
 ing, for he cannot believe what he does not understand even in a 
 vague sense; and so if overt activity does not testify to under- 
 standing, it cannot prove the presence of belief. The crucial 
 question in the behavioristic account of thought is, then, does 
 overt activity indicate understanding? 
 
26 SYMBOLISM AND TRUTH 
 
 Let us suppose that our dog comes for his food when the 
 
 dinner-bell is rung. The bell has aroused an activity appropriate 
 to an object, and we can assume that the bell means dinner to 
 the dog; and yet we cannot be sure of this. The dog’s act is not 
 different, so far as we can know, from many other habitual acts. 
 He will go to a certain corner each night to sleep, he will bark at 
 certain persons and not at others, he will howl when the moon 
 is full. Are we to say that all of these acts are acts of under- 
 standing? . 
 _ The weakness of the behavioristic theory of meaning is that it 
 affords no criterion by which acts of understanding can be dis- 
 tinguished from other habitual acts, yet no one would be willing 
 to say that all such acts are cases of understanding. The theory 
 leads us to the conclusion that any stimulus to which we react in 
 an habitual way is a symbol. 
 
 It is true that most signs acquire significance through habit. 
 The connection between the sign and its meaning is based on a 
 conditioned reflex. The object A, food, for example, stirs the 
 activity B, hunger and eating; and if X, the sound of the dinner- 
 bell, accompanies A for a sufficient number of times, X alone 
 will become an adequate stimulus for these activities. This is the 
 pattern of all habits. But there is a distinction between habits 
 which carry meaning and those which do not. Though we should 
 have no speech and writing were it not for our ability to form 
 habits, the formation of a habit does not argue a connection of 
 meaning; there are many habits in our behavior that are not 
 vehicles of significance. 
 
 Habits of meaning belong to a special class. They are abbrevi- 
 ated habits, habits purely of the mind, not extending beyond the 
 central nervous system. When we understand a word or an idea, 
 we perform no observable acts, unless it be silently to repeat the 
 word. The actions appropriate to the object are confined to the 
 brain, or nearly so; and it is just this mental or inner character 
 
MEANING Q7 
 
 of habits of meaning which differentiates them from meaning- 
 less habits. A sign causes us to think rather than to go off into a 
 series of immediate and unreflective acts, as do other habit- 
 stimuli. Deliberation, abbreviated action, understanding, rather 
 than overt activity, are the effects produced by symbols. 
 
 The behaviorists explain that meaning is based on language 
 habits and that meaningless vocal acts or habits develop into 
 language habits, which carry significance when they become 
 associated with “arm, hand, and leg activities and substitutable 
 for them.” ! This is an attempt to formulate a criterion of signifi- 
 cant as opposed to meaningless habits. The substitution of a sign 
 for an object indicates that the sign is understood, that is, that 
 it has become a sign. But substituted how? Substituted where? 
 And here the whole problem of meaning is concealed. The only 
 intelligible answer is, substituted in an internal experience not 
 open to external observation. 
 
 It is impossible without introspection to say when this substi- 
 tution has taken place. Mr. J. B. Watson’s example of such a 
 substitution is inconclusive: the fact that sounds are uttered in 
 conjunction with arm, hand, and leg activities,— in conjunction 
 with an infant’s reaching for an object held out toward him,— 
 and that the sounds alone are uttered at a later time, either 
 when the object appears or when it is absent, does not show that 
 the sound has been substituted for these activities, that the 
 child has passed from unreflective action to deliberation, and 
 that the sound has come to mean the object. The substitution of 
 a symbol for an object, which is its “‘standing for the object,” is 
 essentially a fact for introspective observation and only secon- 
 darily a fact of behavior. 
 
 Meaning is an activity that can be described only in intro- 
 spective terms, and even in introspection it is difficult to grasp. 
 
 1 J. B. Watson, Psychology from the Standpoint of a Behaviorist (1919), 
 pp. 319 ff. 
 
28 SYMBOLISM AND TRUTH 
 
 Thought is distinguished from action simply on the ground that 
 it is activity which does not work itself out in behavior. If 
 thought is behavior, it is behavior inhibited and yet fully aware 
 of its directions and intentions. The habits on which it is built 
 are private. Though it may be true that the dog genuinely thinks 
 dinner at the sound of the bell, we are not justified in inferring 
 that he does from his behavior alone; and if our own reactions to 
 dinner-bells and to words or images were always overt and fully 
 carried out, if we could not pause to deliberate and so check, 
 short of performance, the tendencies to action aroused by sym- 
 bols, we could not be said to understand language or ideas, but 
 only to react to them as we might to a bright light or a loud 
 noise. The moment of suspension of mind between the immedi- 
 ate stimulus and the activities that follow would be shortened to 
 exclude understanding, and none of the stimuli of habitual ac- 
 tions would become symbols. They would remain merely ob- 
 jects which set in motion conditioned reflexes, and their capacity 
 to mean other objects would be as yet unrealized. 
 
 No doubt there is an insensible gradation between habits that 
 do not carry meaning and habits that do, and by this gradation 
 an organism passes from action to thought. As the capacity to 
 retain the effect of a stimulus in the mind without overt activity 
 increases, the ability to understand is gained, and the objects to 
 which the organism has before reacted habitually without un- 
 derstanding become symbols of the things toward which these 
 activities are directed. Unless this capacity to suspend reactions 
 and to anticipate an object rather than to behave as if it were 
 present were developed, we should not be able to think but only 
 to act. 
 
 IX 
 
 The psychological aspects of meaning can be summarized as 
 follows. A significant reference to an object with an object is ac- 
 complished through a suspension of activity, known in intro- 
 
MEANING 29 
 
 spection as an intention. A symbol touches a train of psychical 
 connections which, if followed out, lead to activities appropriate 
 to an object. In understanding alone, this train of connections 
 is remotely stirred and is not pushed to its terminal point, but 
 when the suspension of mind breaks over into the actions suited 
 to the object, understanding passes into belief. Belief must be 
 preceded by understanding, and overt activity is not necessarily 
 a sign of belief or of understanding. In this suspension of activ- 
 ity the mind reaches out beyond its immediate field, and the 
 stimulus of this outward reach, whether it be an image, a word, 
 a mark, or a gesture, is a symbol. 
 
 A general conception of what it is to think can now be framed. 
 Without symbols there is no thought. Thinking is activity, or 
 rather the suspension of activity, through symbols. It is the sub- 
 stitution of symbols, which are in the field of presentation, for 
 the things intended by the symbols, which may be beyond this 
 field; and sometimes thought is carried by symbols that stand 
 for no objects. Thought is not to be classified with sensations, 
 images, feelings, conations, as an element of consciousness. It is 
 built up from these elements, and it may be from others; it is the 
 use of these elements for the purpose of recording and conveying 
 significant references. 
 
 If psychologists have discovered an imageless thought, they 
 have not discovered a thought which does not rest on the use of 
 symbols. Symbols are the universal instruments of knowledge, 
 and the ancient logicians who defined man as a “rational ani- 
 mal” might well have given another definition, ‘employer of 
 signs,” for man’s rationality consists in his ability to use signs. 
 Without the semi-artificial media of language, writing, and the 
 numerical system, human knowledge as we know it could not 
 have come into existence; and beneath these systems of semi- 
 artificial signs lies a still more primitive system, that of images. 
 
 To indulge in pure thought is to put in the place of the things 
 
30 SYMBOLISM AND TRUTH 
 
 found in experience a set of substitutes, secondary realities such 
 as marks on a page, vocal noises, psychological images, and to 
 move in this world in a way corresponding to that in which one 
 might have moved among the primary realities. And thought is 
 more than this: it is the extension of the references of symbols 
 beyond the experienced, it is the significant use of signs when 
 there are neither presented nor existent objects for which they 
 stand. These more complex types of meaning remain to be con- 
 sidered. 
 
 xX 
 
 It is not difficult to see how things such as colors, shapes, 
 sounds, simple states of mind — anger, fear, pleasure, pain — 
 can be referred to; but one speaks significantly also of “‘the uni- 
 verse,” “‘the world,” “the solar system,” and yet none of these 
 objects has entered experience in its wholeness, nor is there any 
 single activity or set of activities appropriate to it. This is true 
 also of more restricted objects such as ““New York City” or 
 “the British Empire.”’ We cannot mean these things merely by 
 taking a single symbol to stand for them. The mind must reach 
 out toward them in some immensely more complex fashion than 
 it does toward simpler objects. 
 
 All of our most complex ideas, says Locke, even to the idea of 
 God, are constructed from simpler ideas which are the founda- 
 tions of knowledge; and Locke’s distinction between simple and 
 complex ideas can be extended to all symbols. Objects such as 
 the universe, the other side of the moon, the continent of Europe, 
 are referred to by means of complexes of references to simpler 
 objects. 
 
 Most of the things with which we are familiar are easily seen 
 to be composed of other things, they can be separated into ele- 
 ments; and if an object as a whole cannot enter experience to be- 
 come the terminus of a meaning, some or all of its components 
 usually can. Though we cannot directly form habits of speech or 
 
MEANING 31 
 
 thought appropriate to the universe or to New York City, we 
 can come in direct contact with parts or aspects of these objects. 
 These objects can be analyzed and thus can be represented in 
 thought; the whole can be grasped through its elements. 
 
 The symbolic systems of language, mathematics, and the 
 imagination are peculiarly adapted to this analytical representa- 
 tion of objects. Men think not by means of isolated words, signs 
 or ideas, but by joining these into groups, into propositions, 
 phrases, and sentences, which have a meaning as a whole. This 
 is syntactical meaning. Syntax is literally “taking together,” and 
 symbols taken together are significant, as symbols by themselves 
 cannot be: any phrase, sentence, or complex idea — any group 
 of symbols — has a meaning other than the meanings of its ele- 
 ments but determined by these, and these alone. This gives us 
 the first principle of symbolism, the principle of syntactical sig- 
 nificance: the significance of any group of symbols is a function of 
 the significance of its members. To the elements of a symbolic 
 group correspond elements of the object which might be meant 
 by the group as a whole, and thus, through a symbol that can be 
 analyzed into parts, an object that can be likewise analyzed is 
 represented. The sentence, “‘the sun is shining outside my win- 
 dow,” means a fact composed of the objects meant by “‘sun,”’ 
 
 99 66 99 66 
 
 “shining,” “outside,” “my,” and “‘window.”’ The fact is these 
 elements, built up according to a definite plan, taken in a certain 
 order, and the meaning of the sentence is a synthesis of separate 
 
 meanings in a single meaning. 
 
 XI 
 
 Before we can employ groups of symbols to represent objects 
 analytically, we must be equipped with simpler instruments of 
 thought. These are simple symbols, whose significance is of the 
 direct sort described above. 
 
 Simple symbols have no syntactical meaning. Their signifi- 
 
32 SYMBOLISM AND TRUTH 
 
 cance is not a function of that of their parts, if they have sym- 
 bolic parts, but rather a function of the presentation of objects 
 and of a mind which establishes connections of meaning between 
 presented objects. The significance of “Shakespeare”’ is not de- 
 termined by the meanings of “shake” and “‘speare”’: it arises 
 from the direct use of this name for a person. (A simple symbol 
 may have meaning, however, through definition only, that is, it 
 may be defined as equivalent to a symbolic group, e.g., “nectar” 
 is “the food of the gods”’; and in this case the meaning will not 
 be a function of the presentation of an object for which the sym- 
 bol is taken to stand.) The conditions under which simple sym- 
 bols acquire meaning are such that they cannot mean objects 
 which have not appeared in perception, unless they are expressly 
 defined through symbolic groups which mean such objects. 
 Knowledge is built on experience, on presentation, because it is 
 only in experience that these first instruments of knowledge are 
 of use. In order that (undefined) simple symbols may take on 
 meaning for us, we must have performed acts directed toward 
 the things they mean. We must have experienced the symbol 
 with the object, and a conditioned reflex must have been estab- 
 lished, so that when the symbol appears the appropriate activ- 
 ities and the intention directed toward the object will be set up. 
 
 It was said above that without concepts, that is, significant 
 symbols, there are no presentations of objects, and it should be 
 added that without presentations of objects there are no con- 
 cepts. Simple symbols, that is, single words or ideas and the 
 psychical attitudes which accompany them, play a necessary 
 part in determining the cognitions of their objects, and at the 
 same time the cognitions of these objects play a necessary part 
 in determining the meanings of the simple symbols: they are 
 functions of one another, and it is impossible to say that the 
 presentation of objects precedes in time the use of symbols. 
 Perception is born through the significant use of symbols, and 
 the significant use of symbols, through perception. 
 
 a i 
 
MEANING 33 
 
 The significance of a simple symbol, unless it is defined 
 through a symbolic group, rests on three necessary factors: first, 
 the symbolic object proper, the mark, the image, the sound; 
 then the attitude of preparation, the intention or psychical set; 
 and finally the presentation of the object meant. To say that a 
 concept enters in every perception of an object means simply 
 that these three factors are always present in perception. I am 
 never presented with a thing unless I am also presented with a 
 sign appropriate to the thing. Significance of this simplest sort 
 is a part of every experience. Symbols and the mental attitudes 
 which accompany them pick out things, relations, qualities, 
 sense data, from the background of pure awareness and make 
 them objects of knowledge. Signs are a genuine part of presenta- 
 tions, and we come originally to know their meanings apart from 
 presentations by separating them out, rather than by artificially 
 creating and applying them. The artificially created sign is a late 
 product in the evolution of thought. Having been sifted out 
 from the presentation of which it was in the beginning a part, 
 the sign can mean when the object meant is not presented, but 
 it could not mean this object unless the latter had been pre- 
 sented. 
 
 It is less evident that words are integral parts of presenta- 
 tions than that images are. Words probably appear later than 
 images as carriers of cognitive attitudes. But theories of the de- 
 velopment of language assume that words were originally bound 
 up with perceptions. Those who believe that language arose, in 
 part at least, from ejaculations say that a noun such as “‘ache”’ 
 comes from the ejaculation “‘ach!”’ the cry of pain; the pronoun 
 
 +>? 
 
 “me” from the ejaculation “ahem!” by which the speaker in- 
 voluntarily calls attention to his own presence.! Cries and vocal 
 expressions, once parts of an experience, were thus cut off from 
 the whole and became significant in their own right. Certainly 
 
 1G. Willis, The Philosophy of Speech (1920), p. 9. 
 
34 SYMBOLISM AND TRUTH 
 
 in our adult perceptions we are often conscious of the passage of 
 words through the mind as a means by which we adjust our- 
 selves to the object perceived. 
 
 There can be little doubt that all perceptions include a psychi- 
 cal set toward the object. The mind is not purely passive in per- 
 ception, as Locke supposed — not a tabula rasa on which experi- 
 ence writes. Perception is an activity, and mental activity is 
 always directed toward something; it always intends something. 
 This active attitude of intending, which is the second essential 
 of simple meaning, is more prominent in perception than the 
 first, that is, the symbol proper, to which this attitude is at- 
 tached. But the first is nevertheless present. The symbol proper 
 arises somewhere in the course of the perception, and the three 
 elements, symbol, attitude, and object, are united in a whole 
 which is the presentation of the object. 
 
 Thus, as far back as we can trace our articulated experience, 
 simple concepts are present in it, and these have meaning only 
 through experience because they are of the very stuff of experi- 
 ence. 
 
 These elementary symbols (concepts) stand for data. When a 
 single word, gesture, or sound has once been taken as significant 
 without definition, a datum has been accepted; and though sub- 
 sequent use of the symbol may lead one to observe that the ob- 
 ject it refers to is complex and can be analyzed into new data 
 signified by other symbols, still no analysis can be pushed so far 
 that all data disappear. But it must not be forgotten that many 
 simple symbols have meaning only through definition. “Santa 
 Claus”? means the same as “the good saint who fills up our 
 
 b 
 
 stockings at Christmas”; “the universe” is a name for “the 
 
 totality of objects, known and unknown”’; “matter” a name for 
 “objects that obey physical laws.” Such defined symbols are 
 abbreviated forms of more complex meanings. They are derived 
 
 concepts whose objects are not data. 
 
MEANING 35 
 
 XIT 
 
 Having once at our command a stock of the simpler instru- 
 ments of meaning given in our commerce with the immediate 
 environment, we can construct new meanings determined by the 
 old. Through these the imagination takes wings and the world 
 of speculation is opened. 
 
 A symbolic group, if it stands for anything, will stand for a 
 complex object, which may be the kind of object signified by a 
 descriptive phrase such as “‘the center of gravity of the solar 
 system,” or the kind signified by a completed sentence either 
 asserted or unasserted, e.g., “knowledge is power.” The latter 
 type of symbolic group is ordinarily termed a proposition. The 
 peculiarity of a descriptive phrase is that through a complex of 
 predicates or relations it signifies a term, while the meaning of a 
 proposition, on the other hand, is not focussed on a single term.! 
 
 The constituents of the complex object meant by a symbolic 
 group are signified by simple symbols, and it is clear that these 
 constituents must have been given in experience or must be de- 
 finable through symbolic groups whose simple symbols refer to 
 elements given in experience. ““New York” means “the city at 
 the mouth of the Hudson,” and if the objects meant by “‘city,”’ 
 “at,” “‘mouth,” “of,” and “Hudson” cannot be known di- 
 rectly, they must be defined in terms of objects that can be 
 known directly; that is to say, every symbol (simple or complex) 
 must signify a datum or be reducible to symbols which signify 
 data. And yet a descriptive phrase or proposition whose simple 
 symbols refer to data or are defined in terms of references to 
 data, may as a whole stand for no object; it may state no fact, 
 describe nothing, and still be significant. Thus the phrase, “the 
 hereditary monarchs of the United States,”’ has meaning though 
 it describes no one; the proposition, “‘the gods live on nectar and 
 ambrosia,” states no fact, yet it is significant. 
 
 1 See below, ch. IV, for a discussion of this distinction. 
 
36 SYMBOLISM AND TRUTH 
 
 Both reason and imagination rest on this possibility of using 
 symbols significantly when there is nothing to which they refer 
 — a possibility which arises through joining simple symbols into 
 groups. The meaning of the group is a function of nothing but 
 its subordinate meanings and — what is more important still — 
 of its logical form. No object meant need be presented; the 
 being, either in or out of experience, of an object to which the 
 group as a whole refers is irrelevant to the meaning, for group- 
 meanings are determined by meanings alone. 
 
 Many writers dismiss the possibility of thinking or speaking 
 significantly when there is no object thought or spoken of, by a 
 simple argument. To think when there is nothing thought of is 
 not to think; to mean when there is no object meant is not to 
 mean.! It is denied that symbols can be used significantly when 
 they do not refer to existing objects. This is indeed true of unde- 
 fined simple symbols but it is not true of symbolic groups. The 
 argument rests on the assumption that all meaning is simple 
 reference to an object with an object, and the more subtle type 
 of reference through groups is neglected. 
 
 Syntactical or group-meaning is, like all meaning, an outward 
 reach of the mind, but it takes an indirect course and may never 
 terminate in an object. A phrase sets up all the anticipations or 
 intentions its single words arouse; when I understand the signifi- 
 cance of “‘a sunny day in spring,” I am stirred psychologically 
 as I would be by “‘sunny,” “day,” and “spring”; I take an atti- 
 tude appropriate to the things meant by each of these words; 
 
 1 Plato puts this argument in The Sophist, Jowett’s translation, marginal 
 page 237: 
 
 Stranger. You mean by assenting to imply that he who says something 
 must say some one thing? 
 
 Theaetetus. Yes. 
 
 Stranger. Then he who says “not something”? must absolutely say 
 nothing. 
 
 Theaetetus. Most assuredly. 
 
 Stranger. And he who says “‘nothing,”’ is not to be described as speaking; 
 and therefore he who says “‘not-being”’ does not speak at all. 
 
MEANING 37 
 
 but my attitude is at the same time a unity. I anticipate these 
 elements as forming a whole, and if no such whole exists the atti- 
 tude of mind will still carry the meaning. Through the many 
 references of its members (and its logical form) the symbolic 
 group, as a unity, has a reference, that is, a direction toward 
 something; and even though there is (or has been) in experience 
 no object for which the expression as a whole stands, there will 
 nevertheless be a locus in experience toward which this unitary 
 reference is directed. This is the locus of the objects meant by 
 the elements of the group. There is no “present king of France”’; 
 and yet this phrase tells me where to seek for the object it 
 might mean. A symbolic group means through a complex inten- 
 tion constructed from simpler intentions, and so performs the 
 function of referring, which is the essence of meaning, when as a 
 whole it refers to nothing. 
 
 Syntactical meaning — a meaning of the whole determined 
 solely by that of the parts and their plan of unity — can be 
 found in any phrase, sentence, mathematical expression; in 
 short, in any group of symbols. Its requisites are: (1) a number 
 of simple symbols referring directly to objects, or defined in 
 terms of such references, and (2) a unity of these symbols and 
 the intentions which attach to them in a single intention. It is 
 not necessary that this complex intention should arise from or 
 terminate in any single object. 
 
 The manner in which the simple symbols are joined into a 
 unity gives the expression a structure, and it is in the analysis of 
 this structure that the central problems of the theory of knowl- 
 edge appear. It may seem to the reader that the structure of 
 symbolic groups is merely a matter of grammar. What possible 
 light can the study of grammatical forms throw on knowledge? 
 The fact is that grammatical forms are reflections of logical 
 forms; and if the study of the structure of symbolic expressions 
 is grammar, it is what has been called “philosophical grammar” 
 
38 SYMBOLISM AND TRUTH 
 
 —an analysis of the structure of thought. In order to under- 
 stand what is meant by the form of a symbolic complex, it is 
 necessary to probe deep into the nature of knowledge and its 
 objects. But before we turn to this topic, let us put together the 
 facts of knowledge which are now before us. 
 
 XIII 
 
 The objects of knowledge are not ideas, unless “idea” be 
 taken in the broad sense of any known object. Ideas in the sense 
 of “images”’ can be distinguished from sensory and perceptual 
 objects, and the objects of knowledge may be either images or 
 sensations and perceptions. Ideas in the narrower sense occupy 
 a special place in thought: they are the most primitive type of 
 symbols, the primary carriers of meaning. Ideas need not signify 
 merely the sensory or perceptual objects they resemble: any 
 idea may mean any thing. Moreover, semi-artificial signs such 
 as those of speech and writing supplement images, and in some 
 cases completely supplant them. It is important to observe that 
 no symbols are restricted to meaning a particular class of ob- 
 jects, least of all to meaning ideas in the narrower sense. 
 
 The study of the principles of symbolism, which is also the 
 study of the mechanism of conception (for a concept is nothing 
 more nor less than a significant symbol), provides a single point 
 of view from which to approach knowledge. 
 
 Knowledge as a whole falls into two great divisions: mediate 
 and immediate, knowledge about and acquaintance with objects. 
 The former rests on symbols alone; the latter is a union of sym- 
 bolic knowledge and direct apprehension. The presentation of 
 objects, that is, experience, is always attended by the functioning 
 of symbols (of concepts) in the mind, and intending or meaning 
 an object is a part of every experience. The mind is not a tabula 
 rasa but an active agent in perception, and so the line between 
 mediate and immediate knowledge cannot be sharply drawn. 
 
MEANING 39 
 
 But immediate knowledge is not sensation, for sensations do not 
 appear by themselves but only as elements in larger cognitive 
 units, in which they usually play the part of signs. All so-called 
 “immediate” knowledge is partly mediated by concepts, with 
 the exception of pure awareness, which is the complete antithesis 
 of conceptual knowledge and the only form of pure immediacy. 
 Pure awareness is not the cognition of objects, relations, qual- 
 ities, or sense data: it is the apprehension of an unarticulated 
 datum. Pure awareness cannot be dissociated from the act of 
 knowledge as a whole. 
 
 Signs have meaning only through the activity of minds. Nat- 
 ural objects, even images, are not significant unless they are 
 taken to be so by a mind. The meaning activity is a preparation 
 for the object meant, but a preparation which goes no further 
 than the central nervous system, and which appears in con- 
 sciousness as an intention. Belief, which is of the same genus as 
 understanding, is a completer preparation for an object: it is 
 willingness to act as if the object were in existence. Understand- 
 ing arises only when the mind is able to suspend the activities 
 appropriate to a thing, and to deliberate rather than act; and 
 though meaning rests on habit, it is not the association of ideas, 
 nor is it the type of habitual response which leads at once to 
 outward action. Thus it is impossible to describe meaning wholly 
 in terms of behavior. 
 
 There are two types of meaning, one of which is built on the 
 other: (1) simple and (2) syntactical meaning. Simple symbols 
 are objects taken by a mind to stand for other objects: their sig- 
 nificance is not a function of their parts and, unless their mean- 
 ing is defined, they have meaning only through direct reference 
 to things which are (or have been) experienced. The significance 
 of these undefined simple symbols rests on direct experience be- 
 cause they are an integral part of the presentation of the object 
 to which they refer. 
 
40 SYMBOLISM AND TRUTH 
 
 Complex or syntactical meanings (so called because they are 
 created by taking together simple meanings) are functions of 
 
 other meanings; and this sort of significance, which attaches to 
 
 any phrase, sentence, or mathematical expression, rests on the 
 general principle of symbolism, that the meaning of a symbolic 
 group as a whole is determined by the meanings of its elements. 
 A symbolic group represents an object analytically, that is, as a 
 unity of elements with a form; but a symbolic expression may be 
 significant when it stands for no object, for its meaning is a func- 
 tion of meanings only and not, as in the case of an undefined 
 simple symbol, of the presentation of an object. 
 
 Now that we have a general notion of what meaning is we can 
 enter on a wider problem — that of showing how the structure 
 of symbolic expressions points beyond itself to the structure of 
 the world of fact. The garments in which knowledge is clothed, 
 loose and ill-cut as they often appear, reveal the outlines of the 
 form beneath them; syntax and grammar, which seem to be 
 conventions of human intercourse, spring from the adaptation 
 of the mind to an order which pervades its environment. 
 
CHAPTER II 
 
 LOGICAL FORM 
 
 I 
 
 Menrsztx to place a number of symbols together at random 
 does not make them a symbolic group. The phrases of language 
 are not chance combinations of words; they have a structure, 
 and certain word-structures are significant while others are not. 
 The same words in one combination mean one thing, and in an- 
 other combination, another thing. The problem of the structure 
 of significant phrases cannot be solved by showing that any 
 group of words which conforms to the rules of syntax in lan- 
 guage is significant, for this leaves the rules of syntax to be ex- 
 plained. 
 
 Every symbolic system, whether it be speech, mathematics, 
 logic, or the system of mental images, has its own rules of syn- 
 tax. Within the system some combinations of symbols are signif- 
 icant and others are nonsensical. Some of these principles are 
 arbitrary: they have grown up through usage, as have the mean- 
 ings of the individual signs, and usage can alter them; but they 
 are not all arbitrary. The structure of every symbolic system is 
 the same in general outline; it is modeled on the structure of 
 fact, for every symbolic system, if it represents anything, will 
 represent facts. 
 
 The meaning of a symbolic group is, for this reason, not 
 purely a matter of choice, as is the meaning of a simple symbol. 
 There are certain objects that the group can signify, and other 
 objects that it cannot signify. The structure of the group fur- 
 nishes a criterion which enables us to determine its possible 
 meanings. At first sight it might seem that groups of symbols 
 
42 SYMBOLISM AND TRUTH 
 
 could represent anything, as can simple symbols. Simple sym- 
 bols are attached to their objects only accidentally, through 
 habit or definition. We can change our conventions for their use 
 as we please. Why is this not also true of symbolic groups? Are 
 not all symbols arbitrary and accidental in their meaning? 
 
 If this were so, the problem of how symbols represent objects 
 would be speedily solved: we could say merely that we are in the 
 habit of using such and such signs for such and such things, 
 (though we should have difficulty in saying this), and the study 
 of the principles of symbolism would be reduced to the compil- 
 ing of dictionaries. But this is not all. 
 
 When a group of symbols takes on a meaning through the 
 meanings of its constituents, it becomes in a far-reaching sense 
 a representative of an object, if it stands for an object. The re- 
 lation between a group of symbols and the fact it signifies can be 
 likened to the correspondence of a map to a region of which it is 
 a partial picture. Each element of the map means a feature of 
 the landscape, which is related to other features as the map- 
 elements are related to one another. So, each symbol of a group 
 means a part of the whole fact signified, a part which is related 
 to other parts of the fact as the symbols are related in the group. 
 A phrase, a sentence, a mathematical expression, or a complex 
 idea is as much a picture of a fact as a map is of a country. The 
 difference is that the portraiture is infinitely more subtle. The 
 map reproduces the spatial relations of the country by spatial 
 relations on a smaller scale. The phrase or sentence reproduces 
 the logical relations of the elements in the fact by similar logical 
 relations among the symbols. 
 
 A phrase or sentence cannot, then, be arbitrary in meaning. 
 It can mean only a fact logically constructed as it is constructed. 
 Its form must be the form of the fact for which it stands. 
 
 It is not difficult to discover in what respects a photograph 
 or a map resembles its original. The correspondence of the copy 
 
LOGICAL FORM 43 
 
 with the original is written on the face of both. But the evasive 
 features of logical form are not readily made out. What can 
 there be in common between the sentence, “‘the sun is shining 
 outside my window,” and the fact which the sentence means? 
 
 II 
 
 Symbols, whether they be words, gestures, or ideas, are ob- 
 jects. In their rdle as instruments of meaning they are still 
 things. A spoken word is a combination of noises distinct from 
 other noises. A spoken sentence is a collection of combinations 
 of noises with pauses and inflections to indicate its grouping into 
 phrases. A written sentence is a collection of marks on a page, 
 distinct from other marks and other collections. 
 
 The nature of symbols as objects is not in the foreground of 
 perception when they are used to convey meanings. We are only 
 dimly conscious of the print when we read; we pierce through it, 
 as through a luminous medium, to the meaning. The quality of 
 a voice, the sound of a spoken word, fade into the background 
 of the mind when we attend to a speaker; we hear only what the 
 speaker intends to say. And yet the nature of symbols as ob- 
 jects is not completely forgotten in interpreting them, for it is 
 this that causes them to be recognized as having a structure. 
 There are characters and relations which belong to all objects 
 alike and are the most abstract features of their being, and it is 
 these characters and relations which the symbols — being also 
 objects — reproduce. 
 
 Logical form is the least common factor of all objects. Any 
 entity which is presented or thought exhibits logical form, and a 
 thing without logical form (if it could be a “‘thing”’) could not be 
 brought within the circle of reason. Where logical form ends, the 
 presentation of objects, analysis, representation, the rational 
 processes, also end; and if any knowledge could remain, it would 
 be knowledge by intuition — the pure awareness which gives us 
 no objects. 
 
44 SYMBOLISM AND TRUTH 
 
 The characters and relations that determine logical form ap- 
 pear when we ask what it means to be an object or a fact. ““Ob- 
 ject”? is the most general of all terms. It applies to everything, 
 whether simple or complex; and a definition of “‘object”’ is im- 
 possible, since it could not be framed without making use of this 
 term. A person, a landscape, a mental state, a quality, a relation, 
 an operation — all are objects. The very statement of the fact 
 that everything is an object is a tautology. 
 
 “Object” is more inclusive than Aristotle’s “substance” 
 (that is, his “first substance’’). By “substance” Aristotle meant 
 an individual, which could be a subject of predication or could 
 stand in relations to other substances. Objects include not only 
 subjects of predication and terms of relations, but also the predi- 
 cates and relations which can be attached to subjects and terms. 
 Several kinds of objects go together to make up the thing meant 
 by “Caesar was the noblest Roman of them all.” Caesar is an in- 
 dividual subject; Roman is a predicate; noblest of them all is a re- 
 lation — a different kind of object from either of the first two. 
 Each of these, as well as the whole fact, is an entity with a dis- 
 tinct being; each is an object. 
 
 To assert that a thing is an object is to make the minimum 
 statement about it; it is to affirm merely that z is x. But trivial 
 as this assertion appears, it is implicit in all knowledge of ob- 
 jects; for it informs us that something is singled out, fastened on 
 by the attention, and referred to through symbols. 
 
 A fact, which could be represented analytically in a symbolic 
 group, is not a bare “this,” an x with no character in particular 
 and no relations to other objects. A fact is a complex of different 
 kinds of objects: it is a thing with characters, or a number of 
 terms in relation; it is a concretion of objects. The whole for 
 which “Brutus killed Caesar” stands is a fact. “Rome was not 
 built in a day,” stands for another fact. “‘ Fairies have wings,” if 
 it stood for anything, would stand for a fact. Taken as wholes, 
 
 
 
LOGICAL FORM 45 
 
 as clusters of objects, facts are themselves objects of an articu- 
 lated sort. Unanalyzed objects are the atoms of thought and 
 facts the molecules; but molecules can play a part not unlike 
 that of atoms, and any given fact can become the foundation of 
 more complex facts. 
 
 III 
 
 The first element of structure in a fact is that it is a group — a 
 group whose character as a whole is determined by the nature 
 and relations of its parts. This concept is fundamental in the 
 description of logical form. 
 
 A group, as the term is used here, is any object constituted of 
 other objects. The fact meant by (2 + 2) is a group, because the 
 whole is a function of the objects meant by 2 and (+). The ob- 
 ject signified by “‘the blue sky” is a group determined by the 
 objects meant by “blue” and “sky.” (‘‘The” does not stand for 
 a constituent of the fact.) ! Similarly, “a precedes b” means a 
 group — a fact constituted of the objects a and 6 and the rela- 
 tion precedes. Some groups are subjects qualified by predicates, 
 others are terms in relation, and still others, terms joined by 
 mathematical or logical operations. In short, any object deter- 
 mined by other objects is a group. 
 
 The concept of grouping is the same as that of function. To 
 say that a whole is a function of its parts is to call attention to 
 the fact that it is a group. Every whole is a group and every 
 group is a whole; and not only is every fact a group, but every 
 collection of symbols with syntactical meaning is also a group, 
 whose character as a whole is determined by the nature and re- 
 lation of the parts, and whose significance as a whole is a func- 
 tion of the significance of the parts. 
 
 It must not be supposed that a disunified plurality of ob- 
 jects or symbols is a group in the true sense. There must be a 
 determination of the whole by the parts. The relations between 
 
 1 See below, ch. IV, sec. v. 
 
46 SYMBOLISM AND TRUTH 
 
 the parts, if there are relations other than the general unity of 
 the group, are themselves parts or members of the group. Thus 
 a between b and ¢ is determined not only by a, b, and c, but also 
 by the relation between. This determination of the whole by the 
 parts is essential: without this, the plurality of objects is not a 
 group. A factual group must be a single fact and a symbolic 
 group a single symbol. 
 
 The concept of grouping then presupposes, (1) a plurality of 
 objects (members), which may be terms, or characters and rela- 
 tions, or both; and (2) the union of these so that the members 
 uniquely determine a whole; and in the case of symbolic groups, 
 (3) a union of the meanings of the parts so that they uniquely 
 determine the meaning of the whole. 
 
 What there is in common between a phrase, a mathematical 
 expression, or a complex idea, and the fact it might represent, 
 now begins to emerge. Both the symbol and the fact are groups. 
 Symbols reproduce groups by groups, as the map reproduces 
 spatial relations by spatial relations. But this gives only the 
 frame-work of the picture. There are an infinite number of dif- 
 ferent symbolic groups and different factual groups, each of 
 which can be distinguished by its logical form alone. The possi- 
 bilities of reproducing different structures of fact by formally 
 distinct symbolic structures are without limit. 
 
 IV 
 
 Every entity, simple or complex, is identical with itself and 
 distinct from other entities. Numerical identity and diversity, 
 together with grouping, determine logical form because they are 
 the most abstract, that is to say the “formal,” characters of 
 objects. Differences in logical structure are numerical in nature; 
 they are differences in the number of constituents in groups, and 
 in the number of groups which are members of groups within a 
 whole. Form is in a literal sense number, as the Pythagoreans be- 
 
LOGICAL FORM 47 
 
 lieved. If, in the apprehension of a fact, everything is disregarded 
 excepting the numerical identity and diversity of its elements, and 
 their grouping into wholes, what remains will be the logical form. 
 
 Since a simple symbol is not a group, it is not distinguished 
 from other simple symbols by its form, though it is distinguished 
 formally from any complex symbol. These most elementary of 
 signs differ only materially in meaning from one another, that is, 
 through the concrete characters of the intentions which attach 
 to them or of the objects they mean. At the lowest stage of anal- 
 ysis formal distinctions of significance do not appear, €.9.5 
 proper names are all of the same form. 
 
 Any analytical representation of an object carries its analysis 
 to the limit of the things meant by the simple symbols, and if 
 any further analysis is possible, this analysis is not contained in 
 the representation. When it is said that the fact meant by “the 
 sunshine on the ocean” is composed of the simple elements, swn- 
 shine, on, and ocean, these elements are not affirmed to be abso- 
 lutely simple, to be irreducible. They are the elementary com- 
 ponents of the fact as it is here expressed; the representation 
 goes no further in analysis. 
 
 It is evident that the constituents of most facts, as they are 
 expressed in symbols, can be further analyzed. If there is a final 
 limit of analysis, if some data are absolutely simple, most repre- 
 sentations stop short of this limit. A simple symbol represents an 
 object with the smallest possible amount of analysis — with a 
 zero analysis. These symbols set the scale of reproduction. Just 
 as the map may employ one inch for ten miles, so a symbolic ex- 
 pression may use a simple symbol for something which is in real- 
 ity complex; just as another map may depict the same region on 
 a larger scale, so another symbolic group may represent as com- 
 plex what is elsewhere represented as simple. But through 
 simple symbols alone objects cannot be represented as of differ- 
 ent forms. 
 
48 SYMBOLISM AND TRUTH 
 
 When symbols or objects are grouped, the groups will be 
 formally alike or different in several ways: in multiplicity, in 
 type, and in the distribution of identical elements (or tautologous 
 symbols) within the constituent groups. (These terms are arbi- 
 trarily chosen to suggest the concepts they mean.) 
 
 The multvplicity of a group is determined by the number of 
 major members. 
 
 However simple or complex the elements of a fact may be, 
 these elements, as they are seen through a symbolic expression, 
 are of a definite number; and the elements of the fact are corre- 
 lated with the constituents of the symbolic group so that for 
 each symbol, simple or complex, in the expression there is a cor- 
 responding part of the fact, and so that the expression as a whole 
 means the fact as a whole. The first layer of facts will be those 
 represented by symbolic groups whose elements are all simple 
 symbols. “The sunshine on the ocean”’ is such a fact; (2 +8) is 
 another such fact. Clearly, neither of these symbolic expressions 
 could mean a fact which could not be analyzed into at least three 
 elements. The major members of these facts (but only of this 
 simplest type of facts) are the unanalyzed objects signified by 
 the simple symbols. The number of these objects determines the 
 multiplicity of the fact, and the number of simple symbols, the 
 multiplicity of the symbolic group.' But the major members are 
 not always simple symbols or the objects meant by simple sym- 
 bols; the major members may be complex, and the multiplicity 
 of the expression or the fact will not then be fixed by the number 
 of simple components. 
 
 Primary facts, facts of the lowest layer, may enter as wholes 
 with other constituents to form new facts; and these will belong 
 to a second layer. At least some of their constituents will be 
 
 1 The article, “‘the,”’ does not represent a constituent of the fact. With it 
 must be classed “a,” “any,” “some,” “every,” “each,” and “‘all.”’ See below, 
 ch. IV, sec. v. Similarly, “‘not” does not stand for a constituent of a fact. See 
 
 below, ch. VI. 
 
 
 
LOGICAL FORM 49 
 
 themselves complex, and will be signified by groups within 
 groups. This gives the second dimension of logical form — the 
 type of the group. Horizontally, so to speak, a form is deter- 
 mined by the number of its major members; vertically, by the 
 number of groups included within groups. 
 
 The sentence, “‘the sunshine on the ocean pleases me,’’ repre- 
 sents a fact whose constituents are not unanalyzed objects signi- 
 fied by simple symbols. One of the constituents of this fact is 
 itself an analyzed fact reproduced by a symbolic group. The 
 whole includes a subordinate group, “the sunshine on the 
 ocean,” and this is combined with the things meant by “pleases” 
 and “‘me” to form a fact of higher type. The secondary fact 
 therefore contains a primary fact as one of its constituents. 
 
 Now the sentence, “‘I am happy because the sunshine on the 
 ocean pleases me,’”’ means a fact of a still higher type. The 
 secondary fact, “the sunshine on the ocean,” has become an 
 element in a new whole through its union with the things meant 
 by “I,” and by “‘happy,” and “because.” (The copula, “is” 
 and its variants, is a sign of assertion; its function is unlike that 
 of any other sign.)} 
 
 Facts combine and recombine in this way, reaching higher 
 and higher levels of complexity. The result is a multitude of new 
 logical forms — new combinations of symbols with symbols and 
 objects with objects. 
 
 The major constituents of such facts and symbolic groups are 
 the facts and groups which enter immediately into the whole 
 without being constituents of sub-facts or sub-groups. All the 
 other elements are minor constituents. The fact, ““I am happy 
 because the sunshine on the ocean pleases me,” contains as 
 major constituents the two subordinate facts, “I am happy” 
 and ‘‘the sunshine on the ocean pleases me,” and these are 
 joined by the major relation “because.” These subordinate 
 
 1 See below, ch. V, sec. xiii. 
 
50 SYMBOLISM AND TRUTH 
 
 facts in turn contain their major constituents, which are the 
 minor constituents of the larger fact. The analysis proceeds as 
 far as the facts composed of elements meant by the single words, 
 and these facts contain only major constituents. Their elements 
 are the basic materials of the structure. 
 
 The type of an expression or fact is therefore determined by 
 the number of groups within groups. An expression or fact of the 
 first type has no members which are groups. (2 + 2), (a — b), 
 France fears Germany, are of the first type. An expression or fact 
 of the second type will include as a major member at least one 
 (or more than one) group of the first type; e.g. (a (b—c)), France 
 fears a new war. The other major members of such a fact may, 
 as in these cases, be things meant by simple symbols, or things 
 meant by groups of the first type, e.g. ((a + b) — (e+ d)). 
 In general, an expression or fact of the nth type will include as a 
 major member at least one (though it may include more than 
 one) group of the n — Ist type; and as a consequence, it will in- 
 clude as minor members groups down to the {st type. 
 
 In determining the multiplicity of a group, its type must be 
 taken into consideration, for it is the number of major constitu- 
 ents (the members entering immediately into the whole without 
 being constituents of sub-groups) which establish the multiplic- 
 ity, and these may be of a higher type than the first. Thus 
 ((a — b) — (b— ¢)) has only three major members, that is, the 
 operation (— ), and the complex terms (a — 6) and (b — c). Its 
 multiplicity is not determined by the number of simple symbols 
 or unanalyzed elements. 
 
 If facts of a secondary, tertiary, or higher type are alike both 
 in their horizontal and vertical dimensions, they will be of the 
 same form. This means that they must have the same number of 
 major constituents, and that each of these constituents in the 
 one must be constructed of groups within groups exactly as is a 
 corresponding constituent in the other, and vice versa. 
 
LOGICAL FORM 51 
 
 vi 
 
 Language exhibits the form of the facts it signifies much less 
 clearly than do some other kinds of expressions. This is because 
 the grouping of words into phrases and sentences is brought 
 about by grammatical rules, which are felt rather than made 
 evident in the group. Nevertheless, every phrase or sentence of 
 any complexity is organized into groups within groups, as is also 
 the fact for which it might stand. The major verb or connec- 
 tive shows the major lines of cleavage; it connects the major 
 symbolic members. These in their turn are composed of minor 
 groups, joined by minor verbs and connectives. Punctuation 
 plays a part here; commas, semicolons, dashes, brackets, peri- 
 ods, etc., indicate what symbols are to be taken together. These 
 are signs of syntax. 
 
 Signs of syntax are secondary signs — signs of symbolism 
 rather than signs of objects. They do not refer to elements in the 
 fact for which the symbolic group might stand. They refer 
 merely to the symbols. They mean that the symbols with which 
 they are placed are to be treated as a group; that these symbols 
 constitute a significant whole. 
 
 Mere juxtaposition of symbols, although it is usually a sign 
 that they are a group — and is the only sign of syntax in the 
 system of mental images — is not a sufficient sign in most sys- 
 tems. There must be additional ways of indicating the grouping. 
 In language there are at least four signs of syntax: classification 
 of words and expressions as parts of speech; inflections, case 
 endings, genders, etc.; position; and punctuation. The signs 
 of syntax in algebra, arithmetic, and all quasi-mathematical 
 groups, having been invented for convenience, are simpler than 
 those of language. The form of an algebraic expression is indi- 
 cated by parentheses; thus ( (a + 5) X c) is plainly similar in 
 grouping to ( (d — e) X f). These expressions are of the same 
 logical form — a form which can be described as a group of 
 
52 SYMBOLISM AND TRUTH 
 
 three major members, one of which is a group of three unana- 
 lyzed major members. The parentheses are the signs of syntax, 
 that is, the punctuation of these mathematical expressions. 
 
 In Messrs. Whitehead and Russell’s Principia Mathematica, 
 the signs of syntax are dots; the larger numbers of dots indicate 
 the more inclusive groups, the smaller numbers, the minor 
 groups. Any signs of syntax must be such that they preserve the 
 integrity of the groups and show what groups are members of 
 other groups. 
 
 As the forms of facts and the symbols which represent them 
 grow more complex, verbal descriptions become more lengthy. 
 There is a simpler manner of exhibiting forms. If letters are 
 taken to stand for the elements of a fact (or a symbolic group) 
 and parentheses as signs of grouping, any logical form can be 
 presented in a general schematism. ((a R 6b) S c) exhibits the 
 
 form of the two algebraic expressions given above, ((a + 6) Xc) - 
 
 and ((d — e) X f), and of the facts for which they might stand. 
 It also exhibits the form of the sentence, “‘Brutus was the friend 
 of Caesar,” and of the fact which this signifies. This sentence, 
 and the fact, fall into major and minor groups as follows: (Bru- 
 tus was (the friend of Caesar) ), and except for spatial order, 
 which can be disregarded here, the symbols are grouped exactly 
 as is the expression ((a Rb) S c). 
 
 The use in this general schematism of capital letters for some 
 of the group-elements should be noted. Wherever there is a com- 
 bination of elements, the terms combined must be distinguished 
 from the relation or operation which unites the terms. Qualities, 
 relations, and operations enter into, modify, and give unity to 
 groups of terms in a peculiar way, and they can be classed to- 
 gether as elements of unity, which are distinguishable from the 
 terms they unify. A quality is a modifier (or element of unity) 
 in a group of one term, ¢.g., “‘the white knight,” which is of the 
 form (fa). A relation appears in a group of several terms, e.g., 
 
LOGICAL FORM 53 
 
 “‘a between 6 and c,” and an operation may enter in a group of 
 any number of terms. The capital letters in this general repre- 
 sentation of logical forms stand for symbols or elements of 
 unity, while the small letters stand for terms. 
 
 Similarity of form between groups, whether it be between 
 facts, between symbols, or between symbols and facts, can be 
 shown by correlating them as follows: Each major constituent 
 of the one must be made to correspond with one and only one 
 major constituent of the other, and vice versa; and if these con- 
 stituents are groups, each of their major members must be made 
 to correspond uniquely, and so on, down to the elements signi- 
 fied by the simple symbols. This correlation will give a perfect 
 parallelism of members, both horizontally and vertically. (Pos- 
 sible complexities in the element or symbol of unity are neg- 
 lected. There will be at least one element or symbol of unity in 
 every group, and although this may be complex, it can be 
 treated as one — as the element of unity.) ! 
 
 When a symbolic group stands for a fact, such a correlation of 
 the group with the fact is set up by the relation of meaning. 
 
 This parallelism of groups, of terms and elements of unity, of 
 complex and simple constituents, makes possible a comparison 
 of the structure of groups without counting the number of the 
 members or the layers of superimposed groups. We do not need 
 the concept of the number-series in order to apprehend similar- 
 ities and differences of form, but merely the concept of one-to- 
 one correspondence, on which the number-series is based. The 
 eye effects such a correlation in observing that ((Rab) Sc) and 
 ((Qde) Mf) are of the same form. 
 
 VI 
 Symbolic groups thus constructed could not have a wholly 
 arbitrary meaning; the principle of syntactical meaning makes it 
 
 1 See below, ch. III, sec. xvii, for the additional differences of form intro- 
 duced by the complexity of the element of unity. 
 
54 SYMBOLISM AND TRUTH 
 
 necessary that in form at least they must reproduce the objects 
 they might signify. Given significant simple symbols and a logi- 
 cal form, and the meaning of the whole will be determined by 
 the meanings of the simple symbols and by the logical form. It 
 will be possible to analyze the fact meant (if there is a fact) into 
 groups and simple elements parallel to those of the symbolic ex- 
 pression. 
 
 Any fact can be analyzed in a number of different ways. Its 
 lines of division and grouping run in different directions, de- 
 pending on the elements chosen as the basis of the analysis. All 
 the possible ways of stating the same fact will represent the dif- 
 ferent lines of structure, the different analyses. The fact, “‘a is 
 
 > 
 
 between b and ec,” is the same (if a, b, and c mean the same 
 things in both cases) as “a is to the right of b and ¢ is to the 
 right of a.’ ““Caesar conquered Gaul” and “the first Emperor 
 of Rome triumphed over the region which is modern France and 
 Germany,” are different analyses of the same fact. No fact and 
 no object is exhausted by a single analysis. The analysis directs 
 our attention to certain aspects of the fact, but other aspects of 
 it remain untouched. There is no single logical form which is 
 peculiarly the form of any one fact. 
 
 Statements of the type, “a is y,”’ where “‘is”” means “‘is identi- 
 cal with,” tell us that a single fact permits different analyses; a 
 large part of our knowledge is embodied in observations of dif- 
 ferences of structure in the same fact. “2 + 3 is 5,” for example, 
 informs us that the object which we signify by “5” can be de- 
 composed into the constituents meant by “2” and “3” and 
 **plus.”’ And if statements of identity were trivial, as they are 
 sometimes said to be, much of our knowledge would be trivial. 
 It is doubtless of no interest, excepting as a case of a general 
 logical principle, to know that “a is a,” and only of slight inter- 
 est to know that “a is b”’; but it is of great interest to know that 
 the same fact can be stated in different ways, that a single ob- 
 ject exhibits a variety of logical forms. 
 
LOGICAL FORM 55 
 
 VII 
 
 We have yet to consider the third element of form — the dis- 
 tribution of identical members, or tautologous symbols, among 
 the constituent groups of a fact or a symbolic expression. 
 
 Meanings must have a certain fixity and continuity. If sym- 
 bols were fluid and capricious in their references they would be 
 of no use, for we should never know exactly to what they re- 
 ferred. In any discourse symbols recur, they appear again and 
 again, and on each recurrence they are given the same interpre- 
 tation. 
 
 Now, strictly speaking, a repeated symbol is not the same ob- 
 ject. The sound “bird” uttered to-day is not identically the 
 sound “‘bird”’ uttered to-morrow. The image of my friend which 
 is in my mind now is not identical with the image of him which 
 was in my mind an hour ago. Therefore a symbol is something 
 more than a single object which comes before the mind, takes on 
 meaning, and disappears. Recurrence is of the essence of sym- 
 bols. The same word may enter many times in one sentence and 
 many more times in a paragraph. A number or letter may reap- 
 pear in different parts of a single mathematical or logical ex- 
 pression. We cannot say that the word, the number, or the 
 letter is the very same in each instance, but all the instances are 
 like enough to be classified together, though each is a distinct 
 object. The symbol is all the cases of its own recurrence. 
 
 A symbol then is not a single object, but a class of objects. 
 Symbols are the same symbol only if they exhibit a generic sim- 
 ilarity as objects, and they are distinct symbols if they exhibit 
 a generic difference. Thus a and 6 are distinct symbols because 
 their contours as marks on a page are different, while a and a (if 
 they are not ambiguous) are the same symbol because their con- 
 tours are alike. When we select an object as a symbol, we fasten 
 on one or more of its concrete characters, and only objects with 
 these characters are treated as the same symbol, while objects 
 
56 SYMBOLISM AND TRUTH 
 
 of different characters are treated as distinct symbols. The char- 
 acters that give generic similarity or difference to symbols may 
 be any characters whatsoever. In European languages, for ex- 
 ample, differences of pitch do not differentiate spoken signs, 
 while in Chinese they do. 
 
 Apart from ambiguity, which must be dealt with as a special 
 factor, a recurrent symbol always means the same object. Re- 
 current symbols are tautologous; they are not symbolically dis- 
 tinct and yet they are not identical as objects. But when it is 
 said that tautologous symbols mean the same object, this 
 “‘sameness”’ is not the sameness of similarity. The object is 
 identically the same. Identity is that which makes an object one 
 and unique. No two objects which are alike can be identical, for 
 they are two and must therefore be at least numerically distinct. 
 The recurrent instances of a symbol, though they are alike, do 
 not signify objects which are merely alike. They mean an identi- 
 cal object. 
 
 The principle which gives rigidity to the meanings of symbols, 
 that is, that the same symbol, if it stands for an object, stands for an 
 identical object, is the principle of identity. Not only is a symbol 
 a class of objects; it is a class of objects whose meaning is unique. 
 Symbols which have different meanings are different symbols; 
 it is impossible that the same symbol should have more than one 
 meaning. 
 
 The attempt to interpret a symbol in more than one way 
 gives rise to psychological ambiguity or equivocation; and this 
 must be distinguished from the logical ambiguity of a phrase 
 such as “a man” or “some man.” Logical ambiguity is useful in 
 thought, but equivocation makes precision of conception or 
 statement impossible.! Equivocation is eliminated only when 
 
 1 It is true, however, of logically ambiguous symbols, as of all symbols, 
 that they follow the principle of identity. They can have only one meaning. 
 The variable, ‘a man,” if it is given a value, can be given one and only one 
 value. 
 
LOGICAL FORM 57 
 
 the equivocal symbols are treated as distinct. Though the 
 spoken words “read” and “red” do not differ in their character 
 as objects, they are different symbols in the sentence, “I read 
 a red book,” and they cannot be construed as the same without 
 a distortion of the meaning. Needless to say, images are even 
 more open to ambiguous interpretations than words. 
 
 Every symbol, then, presupposes the uniqueness of its own 
 meaning, and this is what the principle of identity, a is a, tells 
 us. It states that a, wherever it occurs, is to be interpreted by 
 one and only one object; and if a is significant, but stands for no 
 object, the principle tells us that if a represented an object it 
 could be one and only one. 
 
 This principle is therefore a general rule of symbolism. 
 Phrases such as “the round square” and names such as “ Phoe- 
 bus Apollo,” which refer to no existent objects, follow the law of 
 identity no less than do phrases such as “the present king of 
 England” or names such as “‘ Julius Caesar.” “A round square” 
 as ““a round square,” “Phoebus Apollo” is “Phoebus Apollo,” 
 in the sense that each of these symbols is to be interpreted in 
 one and only one way, in the sense that each has a meaning of its 
 own different from that of all other symbols not expressly de- 
 fined to have the same meaning. “Round square” plays the 
 same part in the symbolism, wherever it appears, as “round 
 square’; instances of this symbol can replace one another in any 
 expression without altering the meaning of the whole. In short, 
 as a general rule of symbolism, a is a, states that a is the same 
 symbol as a. It declares an intention to interpret a uniquely. 
 The very conception of a symbol as distinct from other symbols 
 and the same in all its instances demands that its meaning be 
 unique. 
 
 The principle of identity can also be interpreted in another 
 way, that is, as a statement of fact about objects; but this sec- 
 ond interpretation presupposes the first—the interpretation as 
 
58 SYMBOLISM AND TRUTH 
 
 a rule of symbolism. When a stands for an object, a 7s a asserts, 
 not merely that a and a are the same symbol, but that the ob- 
 ject meant has an identity, that it is an object. This is the 
 existential as distinguished from the symbolic interpretation of 
 the principle of identity. And if a is a variable, so that it means 
 any object, a is a affirms that “any object is identical with 
 itself.” 
 
 Clearly, such a statement of identity is false if it refers to no 
 object; it is not true that “a round square is a round square” in 
 the sense that round squares have identity. However, “a 2s a,” 
 man 7s man,” could not be asserted as 
 
 99 66 
 
 “Caesar is Caesar, 
 
 99 «66 > 
 
 a,” “Caesar,” “‘man,”’ were 
 
 “«¢ 
 
 existential propositions unless 
 construed as the same symbols in each case. It must be assumed 
 that the meaning of a symbol is unique if any object is affirmed 
 to be identical with itself; but it is not necessary to assume that 
 the symbol stands for an object in order to assert that it can 
 have one and only one meaning, for this latter rule is a condition 
 of its use, whether or not it stands for an object. 
 
 Distinct symbols, symbols whose characters as objects are 
 dissimilar, may be equivalent in meaning; they may stand for 
 an identical object, or if they stand for no object, they may be 
 treated as indistinct in meaning. This treatment will not make 
 them the same symbol, for symbols must be alike as objects to 
 be the same. Thus “red” and “vermilion” are distinct symbols 
 with the same meaning; but they are not tautologous or recur- 
 rent instances of one symbol. Such equivalences may be equiva- 
 lences by definition only, and they will then be statements of 
 special intentions in the use of symbols: the equivalence “a is 
 b” tells us that a and b can be substituted for one another 
 wherever each occurs. This equivalence is a valid definition, but 
 as an assertion of fact it may be false. Thus “Titania” is “the 
 queen of the fairies’; but there are no fairies and no Titania. 
 Definitions do not require the existence of an object defined, for 
 
 
 
LOGICAL FORM 59 
 
 they are primarily concerned with the use of symbols, and a 
 valid definition may be false as a statement of fact. 
 
 VIII 
 
 The proposition, a ts a, when it means that any object is iden- 
 tical with itself, is true without exception. There is nothing of 
 which we can speak that is not self-identical. 
 
 The concept of the identity of an object is said by Hume to be 
 a fiction. Objects weave themselves in and out of experience as 
 do threads in a tapestry, and it is difficult, if not impossible, to 
 know that a thing which appears the same is really the same. 
 But the entire fabric of thought would fall apart if we did not 
 assume that an object fixed as a thing meant can remain identi- 
 cal with itself. 
 
 Putting aside the question of the reality of these self-identical 
 objects, we must suppose that objects — for knowledge at least 
 — stand still long enough to be referred to and re-referred to, 
 for if this were not so nothing could be represented. All objects, 
 including symbols themselves, would flow together; there would 
 be no differentiation in knowledge. Nothing would remain itself 
 to be an instrument of significance or a thing signified. We could 
 not relocate anything we had previously known, and we should 
 be helplessly blown about by the winds of change. Thought must 
 view the world as if it were made up of points and lines of iden- 
 tity, which combine with and intersect other points and lines, 
 but which do not cease to be themselves. 
 
 The nearest approximation to a definition of an object 
 (though it is not a definition) is this: that an object is anything 
 with the twin characters of identity and diversity; and this 
 statement is equally true of subjects, predicates, terms, rela- 
 tions, and complex wholes. A universal such as whiteness has its 
 identity ; it is something because it is identical with itself and dis- 
 tinct from other things — from other universals and from each 
 
60 SYMBOLISM AND TRUTH 
 
 of its own instances. A particular, referred to by “this white ob- 
 ject,” for instance, is more obviously self-identical and diverse 
 from other objects. These two formal characters are the sources 
 of unity and plurality in the world. Wherever there is an object 
 it must be a unity — one and identical with itself — and there 
 must be other such unities from which it is distinct. 
 
 It would be natural to suppose that the identity and diversity 
 of objects arise through special qualities or predicates, or 
 through sets of relations, which attach to objects. But if we at- 
 tempted to carry this idea forward, we should then have to ex- 
 plain why these predicates or sets of relations are unique, why 
 they are themselves and not something else; and we should have 
 made no advance. Identity and diversity are irreducible con- 
 cepts, and the argument which shows most convincingly that 
 they are indefinable is that the characters and relations in terms 
 of which they could be defined (if at all) must themselves be 
 assumed to be self-identical and diverse from all other characters 
 and relations. 
 
 When symbols copy the forms of objects, they reproduce the 
 identities and diversities among objects, together with the 
 grouping of these identical and diverse elements into wholes. A 
 symbolic group is a black and white portrait of a fact; it leaves 
 out everything but the identities, diversities, and groupings of 
 the original. But the representation of the identities is a projec- 
 tion, rather than a copy; for an identical element, entering and 
 reéntering in several places in a fact, is signified not by an iden- 
 tical symbol but by a recurrent symbol. The identical element is 
 projected into the medium of time (or space) in the representa- 
 tion. What is a single thing in the fact is reproduced by a series 
 of similar things in the significant expression, that is, by a num- 
 ber of instances of the same symbol, and the convention by 
 which this projection is effected is the principle of identity. For 
 this principle affirms that if the instances of a symbol stand for 
 
 
 
LOGICAL FORM 61 
 
 an object, this will be a single object. Tautologous symbols in 
 the representation stand for identities in the fact. 
 
 An identical element may enter in many different ways in a 
 fact. Many different complexes may be centered about the same 
 object to constitute a whole, and this identical component need 
 not be recurrent in a spatial or temporal sense. ‘‘ Hamlet’s father 
 was Hamlet’s Nemesis,” states a fact in which the same object 
 enters in two different ways: the whole fact is composed of two 
 major groups with an identical constituent in each. It is of the 
 form ((a 8 b) Q (aS c)). Such a fact is like a number of inter- 
 secting lines; it is made up of groups with common members. 
 
 Still other facts are reflexive they; arise through relations 
 which hold between a term and itself. The identical element in a 
 reflexive fact enters as a major constituent at least twice in the 
 same group. “‘Hamlet feared himself”’ stands for a reflexive fact, 
 for the fact “‘Hamlet feared Hamlet,”’ which is of the form 
 (a R a). Strictly speaking, we ought not to say in such a case 
 that the fact is reflexive; rather, it is the symbolic expression 
 which is reflexive, for here again the expression does not exactly 
 copy the fact. The fact has only one term, while the symbolic 
 group has two, though these two are not distinct. The fact is 
 really of the form (Sa); and it is through the tautologous re- 
 currence of a symbol that we can represent it as of the form 
 (a R a). Thus what is in fact a quality (for a quality is an ele- 
 ment of unity attached to a single term) is symbolized as a rela- 
 tion. “Napoleon loved Napoleon” means the same thing as 
 “Napoleon was egotistical’’; and the possibility of representing 
 an identical term through a recurrent symbol enables us to treat 
 this quality as a relation — a relation between a term and itself. 
 
 In determining the multiplicity of such reflexive expressions, 
 the different instances of the same symbol must be reckoned as 
 separate terms or members. Thus (a R a) has two terms and is 
 the same in multiplicity as (a R 6). (Qaab), which is the form of 
 
62 SYMBOLISM AND TRUTH 
 
 “*a gives b to a,” where “gives to”’ is a single relation, has three 
 terms and is the same in multiplicity as (Qabc), which is the 
 form of “a gives b to c.” It is clear that the multiplicity of the 
 fact meant by these reflexive groups is not that of the symbolic 
 group; a fact of a lesser multiplicity is represented, through 
 tautologous symbols, as of a greater multiplicity. 
 
 The manner in which an identical object appears and reap- 
 pears as a component in a single fact is the third distinctive fea- 
 ture of logical form; and facts or symbols of the same form must 
 correspond not only in the number of their constituents, but 
 also in the distribution of identical elements or tautologous sym- 
 bols among the groups. Thus (a R a) and (0 S 6) will represent 
 facts of the same form, which is that of “Napoleon loved Na- 
 poleon” or “Hamlet feared Hamlet.” The symbols ((a R b) S 
 (a Rc)) and ((eQf) L (e Q g)) will stand for facts of the same 
 form — facts such as that signified by “Juliet’s love caused 
 Juliet’s doom.” It is easily seen that the appearance of an identi- 
 cal element in different ways in a fact leads to many new vari- 
 eties of form. 
 
 These identical elements may also be represented by distinct 
 but equivalent symbols; and here too the symbolic group does 
 not exactly portray the fact, but contains more distinct mem- 
 bers than there are distinct elements in the original. “‘Hamlet 
 mistrusted himself” is composed of three distinct symbolic 
 members, (“‘Hamlet”’ and “‘himself”’ are symbolically distinct), 
 while the fact to which this expression refers contains only two. 
 The expression is redundant in form. Such a group can always 
 be reduced to a more exact copy, or projection, of the form of 
 the fact by replacing the equivalent symbols by instances of the 
 same symbol; and this is what is done in interpreting the expres- 
 sion. Its meaning is the same as that of ‘‘Hamlet mistrusted 
 Hamlet.” 
 
 The distribution of tautologous symbols or identical elements 
 
 
 
LOGICAL FORM 63 
 
 in the constituent groups of a symbolic expression or a fact 
 takes a place of equal prominence with multiplicity and type in 
 the determination of logical forms. For the distinction between 
 a reflexive and a non-reflexive group, or between a group whose 
 sub-groups contain common members and one whose sub-groups 
 contain no common members (or differently distributed ones), 
 is a formal and not a material distinction. 
 
 IX 
 
 Among the more important differences of form which have 
 not been mentioned are those of order — the difference between 
 ““a precedes b” and “‘b precedes a.’’ Order requires no new con- 
 cepts; it is determined by grouping alone.! 
 
 In the present chapter we have shown how logical form arises 
 from the grouping of self-identical and diverse objects into facts, 
 and of tautologous and distinct symbols into significant wholes. 
 The structure of a symbolic expression copies the structure of 
 the fact which it means, or might mean, through its grouping. 
 
 The three chief features of logical form are: (1) multiplicity, 
 (2) type, and (3) the distribution of tautologous symbols or 
 identical elements within groups. The multiplicity of a group is 
 determined by the number of major constituents, recurrent sym- 
 bols being counted as separate constituents; the type by the 
 number of groups within groups down to the elementary con- 
 stituents. The major members of any group are those which en- 
 ter immediately into the whole and are not members of minor 
 groups. These major members may be simple or complex. 
 
 The distribution of identical elements in a fact is not exactly 
 reproduced in the symbolic group; these identical elements, 
 which may not themselves be recurrent, are represented by re- 
 current symbols. Groups of like form must correspond with one 
 another in this respect, as well as in multiplicity and type, and in 
 
 1 See below, ch. III, sec. xiv. 
 
64 SYMBOLISM AND TRUTH 
 
 the multiplicities and types of their sub-groups, down to the 
 simple constituents. The principle which permits us to represent 
 identical elements in a fact by recurrent or tautologous symbols 
 is the principle of identity. A symbol is not a single object but a 
 class of like objects, and in any or all of its instances its meaning 
 is unique. The principle of identity tells us that a symbol can 
 have one and only one meaning; and this is the case whether or 
 not the symbol stands for an object. The principle of identity is 
 therefore primarily a general rule of symbolism, but it can also 
 be interpreted as stating a fact — the fact that “any object is 
 identical with itself.” Its use in this sense presupposes its valid- 
 ity as a rule of symbolism; but a statement of identity which is 
 false as an affirmation of the existence of a self-identical object 
 is valid as an affirmation that the same symbol is always used in 
 the same sense. Distinct symbols may be defined as equivalent 
 in meaning, regardless of their reference to existent objects. 
 Identity and diversity are indefinable. 
 
 Equivocally interpreted symbols are distinct, for a single 
 symbol can (by the principle of identity) have one and only one 
 meaning. 
 
 Simple symbols are not distinguished from one another by 
 their form, for they are not groups. They represent objects with 
 a zero analysis; they set the scale of reproduction; but the ob- 
 jects which they represent as simple may be in reality complex. 
 These objects are taken as simple merely for the purposes of 
 representation. Any single fact permits many alternative analy- 
 ses; it may have many different forms; and no analysis exhausts 
 a fact. 
 
 The concept of a group, on which the notion of structure rests, 
 is the same as the concept of function. A group is (1) a plurality 
 of objects and (2) a whole determined by its parts, and the rela- 
 tions between them; and (3) in the case of symbolic groups, 
 the meaning of the whole is determined by the meanings of the 
 
 
 
LOGICAL FORM 65 
 
 parts. Signs of syntax—punctuation, parentheses, etc.— indicate 
 what symbols are to be taken together as significant groups. 
 
 Logical forms can be represented in a general schematism 
 through letters grouped in parentheses. Thus (Rab) and (Sabc) 
 differ in multiplicity but not in type; ((Sab) Q (Ldf)) and 
 (Rab) differ in type but not in multiplicity; ((Sab) Q (Zdf)) and 
 (Sabc) differ both in multiplicity and in type; and ( (Raab) Sa) 
 and ((Qabc) Sd), though they are alike in every other respect, 
 differ in the distribution of identical (or tautologous) elements. 
 Comparisons of form, since form is numerical in nature, can be 
 effected by a one-to-one correlation of groups without the use of 
 the concept of the number-series. 
 
 The capital letters in this schematism signify elements which 
 perform a unique function in each group, elements of unity, that 
 is, relations, operations, qualities; and these must be distin- 
 guished from the terms related, qualified, or operated on. 
 
 Logical form is so woven into speech, and even into the play 
 of the imagination, that it is impossible to utter a phrase or call 
 to mind the images of a past or future experience without throw- 
 ing them into the forms we have described. To say that a fact is 
 not of logical form is to say that no significant assertion can be 
 made about it; it is to say that it is not a fact. Such a “‘fact”’ is 
 placed beyond the reach of thought or rational experience. 
 
CHAPTER III 
 
 UNIVERSALS AND INDIVIDUALS: ORDER 
 
 I 
 
 Every presented object has two aspects: it is both universal 
 and individual, a “‘what” and a “‘this,’’ an essence and that in 
 which an essence is embodied; and we have not completely de- 
 scribed logical form until we have considered this cleavage of 
 the objects of knowledge into universals and individuals. 
 
 Objects are not perceived without their natures and their re- 
 lations to other objects being also perceived. Each is a “this” of 
 some quality, or a “this” related to something which is diverse 
 from it; and the minimal cognition of objects — a perception of 
 the distinctness of “this” and “‘that”’ — contains a universal, 
 for distinctness is a universal. If one attempts to grasp the 
 “this” without its qualities or relations, it is no longer a “‘this”’; 
 it becomes so vague as not to be known even as “‘something-or- 
 other.’’ We lose it in the pure awareness where there is neither 
 “this” nor “‘that.’’ And yet no object is perceived as a pure 
 quality or relation. I am not presented with sheer whiteness or 
 betweenness or beforeness. A perceived universal is perceived in 
 something, as qualifying a subject or as relating terms; and this 
 subject or these terms are not themselves merely qualities or re- 
 lations. There is something in perception to which the universal 
 is united. The universal is perceived as individualized. 
 
 No distinction has given rise to wider divergence of opinion. 
 Plato dismisses the imponderable something in perception which 
 is not universal as an element of imperfection; but this indeter- 
 minate something reappears as the unintelligible “matter” or 
 absolute non-being of his cosmology. In Aristotle’s metaphysics 
 
 
 
UNIVERSALS AND INDIVIDUALS 67 
 
 the same imponderable, far from taking the form of absolute 
 non-being, becomes infinite potentiality, infinite possibility of 
 being; but Aristotle finds no actual being which is not also uni- 
 versal. The nominalist, on the one hand, affirms that only the 
 individual is real; and the realist — the extreme realist — that 
 only the universal is real. But if with the Platonic realists we 
 turn our minds away from the things of perception and deny the 
 reality of individuals, we are still confronted with the facts of 
 perception; and though these facts are proclaimed to be “‘opin- 
 ion”’ or “illusion,” the duality of universal and individual, in a 
 very persistent form, continues in knowledge. Nor does the 
 denial of the reality of universals make them any the less im- 
 portant as phenomena of knowledge. 
 
 The distinction between the “‘ what” and the “this” is omni- 
 present in knowledge whether or not it is in reality. 
 
 II 
 
 One of the paradoxes of knowledge is that having made the 
 distinction we attempt to escape from it by describing the in- 
 dividual in universal terms. 
 
 My house is built of brick and stands on a hill. I return to it 
 after a day’s absence to find that the red walls still top the hill; 
 but what I recognize are the characters and relations, and not 
 the individual thing—my house. If I try to describe its individ- 
 uality, I find that this dissolves into new characters and rela- 
 tions; it continually recedes from my grasp. I have embarked on 
 an apparently endless process of distinction and characteriza- 
 tion. Predicates split off from the individual and leave it intact. 
 The very name of an individual takes on universal significance; 
 
 1 This distinction between the universal and the individual is not the same 
 as the distinction between essence and existence, which Mr. F. H. Bradley 
 describes as the separation of the “‘what” from the “‘that.”’ (See F. H. Brad- 
 ley, Appearance and Reality (1893), ch. xv.) An individual, a “this,” may or 
 may not be in existence, yet its individuality, its “this,” will be distinct from 
 its nature, its ‘‘ what.” 
 
68 SYMBOLISM AND TRUTH 
 
 we speak of ‘‘a Solon” or “a Solomon.”’ From “Caesar”’ is de- 
 rived “Caesarian’’; and we refer to “Caesarian pomp” or 
 “‘Caesarian power.” What was “Caesarian” in Caesar was not 
 then the individual himself, but a quality of the individual. A 
 distinction of the “what” from the “this”? always leaves a 
 “this” in which a new “what” can be distinguished. 
 
 The problem of whether the individual is completely de- 
 scribable in universal terms is one form of the general problem 
 of determinism. Laws are descriptions of phenomena; and de- 
 terminism in one sense means that all phenomena follow laws — 
 that they can be described in universal terms. And if the task of 
 knowledge is completely to describe its objects through laws — 
 to reach a “specific essence”’’ of everything — then knowledge 
 defeats its own purpose by admitting the distinction between 
 universals and individuals, unless it can finally abolish the dis- 
 tinction and identify an individual by its predicates and rela- 
 tions. 
 
 The pursuit of the “specific essences”’ of individuals makes it 
 equally plausible to assume either that individuals are not iden- 
 tified by their predicates and relations, or that they are. The 
 question raises a genuine antinomy. The fact that every individ- 
 ual can be more and more fully characterized, that the margin 
 of confusion with other individuals is narrowed as more and 
 more predicates are affirmed of it, seems to be evidence that a 
 sufficient number of predicates — perhaps an infinity — would 
 exhaust the individual; but it is equally good evidence that no 
 predicates exhaust it. If I say of the tree beside my window that 
 it is a pine with bark of grayish green, that it stands six feet from 
 the house and thirty feet high, that its branches are covered 
 with moss—if I describe it by these and a thousand other pred- 
 icates, it is still that to which the predicates attach, and I can 
 find more predicates. The universals are like intersecting lines at 
 a focus, excepting that the lines determine a point, while the in- 
 
 
 
UNIVERSALS AND INDIVIDUALS 69 
 
 dividual seems to lie outside all intersecting universals; and 
 there is no contradiction in assuming that another individual 
 might have all the same predicates and relations. 
 
 iI 
 
 But is an individual not determined by its spatial and tem- 
 poral relations? Is it not impossible that two individuals should 
 be in the same place at the same time? And if we can know where 
 and when an individual is, have we not described it beyond all 
 confusion with other individuals? 
 
 There is in perception a direct apprehension of the numerical 
 diversity of individuals — of the “this” of one object and the 
 “that” of another — and this perception, taken together with 
 the perception of change, is the basis of the concepts of space 
 and time. This is the sole manner in which an individual is 
 known as distinct from other individuals. Of two peas which are 
 exactly alike in every respect the only difference I can perceive 
 is a bare numerical diversity, which is not a diversity of char- 
 acters and relations, but a pure difference of individuality. To be 
 thus perceived as distinct, individuals must be copresent, and 
 they must neither change nor be in motion. The “this” and the 
 “that”? must form a changeless whole of perception. This nu- 
 merical diversity may, moreover, be given as a relation between 
 several terms; the distinctness may be one of three or four, or 
 possibly half a dozen, individuals. 
 
 If, along with this perception of numerical diversity, goes a 
 perception of change, the phenomenon is ambiguous; there is a 
 question as to whether a “this” which is present at a later stage 
 of the change is the same as the “this” of an earlier stage. The 
 two individuals are not perceived as distinct, since they are not 
 copresent; and yet they are not perceived as the same. Imagine 
 a uniform field of gray before the eyes and suppose that this be- 
 comes green and then red. Is the “this” of the object the same 
 
70 SYMBOLISM AND TRUTH 
 
 beneath its changing aspects, or is each perceptible difference of 
 quality joined to a different “this’’? Is the individual momen- 
 tary, or does it persist through time? 
 
 Change, introducing as it does the element of time, is open to 
 two interpretations: it may be that the qualities and relations 
 alone are different, while the individual remains the same; or 
 that both are different. The change may be like the flow of a 
 river, a continuous displacement of one individual by another, 
 or like the approach of two moving bodies, an alteration of 
 qualities and relations without the entrance of new individuals. 
 From one point of view it seems that in each moment of time 
 individuals are destroyed and replaced by new individuals, 
 while from another point of view it seems that the individual 
 must persist, at least for a brief period of time. How are we to 
 recognize either the destruction or the persistence of an individ- 
 ual? How are we to know that the “‘this”’ of one situation is the 
 same as the “this” of another? We can interpret our memory of 
 the historical continuity of our own selves as the perception of 
 an individual persisting through time; but if this is what we 
 mean by the perception of a persisting individual, certainly we 
 know only one individual in this way. Whenever we believe that 
 we are perceiving in the outer world an historically continuous 
 individual, whose qualities and relations alone are changing, it 
 is always possible that Descartes’s playful demon is at work, 
 substituting distinct individuals along with the different quali- 
 ties and relations; and if a changing object is viewed at remote 
 times, it becomes increasingly difficult to believe that the indi- 
 vidual persists through change. 
 
 Individual objects can be perceived to be distinct and self- 
 identical only if they are held together in a single whole of per- 
 ception. But this does not amount to the scholastic principle of 
 individuation — that the place of an individual at a certain 
 time determines its individuality. This principle reverses the 
 
 
 
UNIVERSALS AND INDIVIDUALS 71 
 
 true order-of the concepts of spatio-temporal position and in- 
 dividuality. The reason why individuals cannot be in the same 
 place at the same time is that their numerical diversity and 
 self-identity as individuals — apprehended in a single whole of 
 perception — gives us the meaning of “the same or different 
 places at the same time.” 
 
 If there were any such thing as an independent space-time, it 
 would probably be true that position in space and time would 
 identify individuals. But it is impossible to view space and time 
 as independent entities with reference to which objects take 
 positions. Space and time are functions of objects; there are 
 “places” in space and “moments” in time because individuals 
 are self-identical and distinct. If I wish to show where and when 
 an individual is, I must do so by referring it to other individuals 
 from which it is numerically diverse, and so on, ad infinitum. 
 The spatio-temporal relations of individuals are not describable 
 without the use of other individuals as a frame of reference, and 
 since the individuals which constitute this frame of reference 
 are not themselves identifiable by their spatial and temporal 
 codrdinates, no individuals are identifiable in this way. Space 
 and time are not peculiarly privileged universals. Like all other 
 universals, they appear only as individualized; and spatial and 
 temporal predicates have no more claim to define the individual- 
 ity of a “this” with which they appear than do other predi- 
 cates. 
 
 1V 
 
 To solve the antinomy of the determination of the individual 
 by the universal, Leibniz makes use of the postulate of “the 
 identity of indiscernibles”’: no individual can share all its pred- 
 icates and relations with another, that is, only that which is dis- 
 tinguishable by predicates is distinct. But this postulate takes 
 advantage of the weakness of our powers of knowledge; it may 
 be that we fail to make distinctions where distinctions exist. 
 
72 SYMBOLISM AND TRUTH 
 
 The postulate needs to be reénforced by another, “the principle 
 of sufficient reason,” from which it follows. This principle as- 
 serts that everything has a reason, and since reasons are univer- 
 sal, that everything (including the individual) is describable in 
 universal terms. Thus the individual is connected logically, 
 deductively, with the universal. 
 
 But if an individual is determined by its predicates, so that no 
 individuals can have all their characters and relations in com- 
 mon, the process of distinguishing characters and relations in 
 individuals should sometime come to an end. The “specific es- 
 sence”’ of an individual should sometime be reached, unless it 
 takes an infinity of universals to determine an individual. Faced 
 with the apparently endless exfoliation of the “‘what”’ from the 
 ‘this,’ Leibniz added that the number of universals which de- 
 termines an individual is infinite; and this leaves finite knowl- 
 edge no better off, so far as the determination of individuals 
 by universals is concerned, than if the individual were not so 
 determined. 
 
 If the assumption of the identity of indiscernibles is true for 
 reality, it is nevertheless useless for finite knowledge. The dis- 
 tinction between the universal and the individual persists in its 
 original form for perception and thought. The metaphysical pos- 
 tulate leaves the epistemological difficulty as it was. 
 
 V; 
 
 It is possible for knowledge to proceed — and it does as a 
 matter of fact proceed — without answering the question as to 
 whether the individual is describable in terms of universals. The 
 assumption of determinism (or indeterminism), even in this 
 most abstract form, is not essential to thought. 
 
 It may or may not be true that a sufficient number of predi- 
 cates determines the unique “this” of an object; the individual 
 can still be thought of, it can still be referred to through sym- 
 
 
 
UNIVERSALS AND INDIVIDUALS 73 
 
 bols. The individual appears in conceptual knowledge as an 2, 
 as something represented by a variable symbol which we as- 
 sume to have a meaning, though what this meaning is we can- 
 not say. We cannot even assert that this x might not stand for 
 an aggregation of universals, for it is always possible that Leib- 
 niz’s infinity of predicates might be its value. But if we could not 
 employ variables, which are symbols whose meaning is undeter- 
 mined, we could not bring the individual into thought.! Thus 
 knowledge of the individual always takes the form (xR), where 
 x is a variable term and R is a quality of that term, or the form 
 (xy . . . S), where z, y, etc. are variable terms and S is a rela- 
 tion between them. (S or R might also be a mathematical or log- 
 ical operation.) If one asks what it is to which the relation or 
 quality attaches, he is driven to descriptions in terms of other 
 qualities and relations; the term is lost behind essences which 
 are of it but which are never it. In short, the value of the varia- 
 ble continues undetermined. 
 
 The representation of an individual through a variable elimi- 
 nates a possible confusion between the individuality of a thing 
 and its reality or existence; it makes clear the point that individ- 
 uality may be purely conceptual. If the “this” of an object — 
 the ultimate subject of all its predicates or the final term of all 
 its relations — is simply the real or the existent, the individual 
 is destroyed; it is absorbed in reality. This ultimate subject or 
 term is represented by a variable as distinct from other subjects 
 or terms — as one ofa plurality. The x which gives individuality 
 to one essence is thought of as other than the y which gives in- 
 dividuality to another; the indeterminateness of the z or y is the 
 counterpart in thought of the inexhaustibility of the individual. 
 Thus things of the imagination, which have not been presented 
 and which may or may not exist, are individualized. Witness 
 the characters of one’s favorite novel who, if they live in the 
 
 1 See below, ch. IV, sec. iv, for a general discussion of the variable. 
 
74 SYMBOLISM AND TRUTH 
 
 mind, are as inaccessible to complete description as any real 
 persons. 
 
 It might be thought that a proper name stands definitely for 
 an individual, that the variability which is present in the repre- 
 sentation of individuals is thus eliminated. But if proper names 
 are more closely examined, they are found to be subject to the 
 same indeterminateness which infects all references to individ- 
 uals. The name “Napoleon” or the name “Stratford-on-Avon”’ 
 stands for one and only one individual, but which individual we 
 can know only through description (or else as a mere “this” 
 numerically diverse from a “‘that’’). Napoleon is “the conqueror 
 of Europe,” “the exile of St. Helena,” “‘the defeated general of 
 the Battle of Waterloo”’; Stratford-on-Avon is “the birthplace 
 of Shakespeare.”’ Each is an a to which characters and relations 
 attach, and the proper name no more determines what z this is 
 than does the description; indeed, the meaning of the proper 
 name is equivalent to the meaning of one or more of these de- 
 scriptions of the individual named, and the variability present 
 in the description is not absent in the name. The “this” of an 
 object for which a proper name stands is as elusive as the “this” 
 of any other thing.! 
 
 Since knowledge presupposes the distinction between the uni- 
 versal and the individual, and since the individual is always (for 
 knowledge) something other than its predicates and relations — 
 represerited in no other way than through a variable x to which 
 these predicates and relations attach — knowledge presupposes 
 its own indeterminateness. Leibniz’s metaphysical principles of 
 “the identity of indiscernibles” and of “sufficient reason” pos- 
 tulate that this indeterminateness would disappear in an infinite 
 knowledge; such a knowledge could assign a value to the x which 
 represents the individual. But for finite thought, only proposi- 
 tions which make no reference to the individual can be free from 
 
 1 See below, ch. IV, sec. ix, for a discussion of proper names. 
 
 
 
UNIVERSALS AND INDIVIDUALS 75 
 
 this indeterminateness — only propositions which are stated in 
 universal terms can have an invariable meaning. For we can 
 know what we mean by a symbol which stands for a universal, 
 but we can never know what we mean by a symbol which stands 
 for an individual; or rather, we can know only that we mean a 
 “this” which is distinct from a “that.” 
 
 VI 
 
 The universal is determinately known, it can be represented 
 in thought by a symbol whose meaning is invariable, because it 
 is presented as self-identical in different ‘“‘thises”’ and “thats,” 
 in different individuals. And when change renders the identity 
 of the individual ambiguous, the universal — or at least some 
 universal — remains what it was. Universals are strands of 
 identity which spread themselves out through time and space; 
 it is of the essence of universals to be recognized as the same in 
 changing and diverse instances. 
 
 There is also a perception of the distinctness of universals, 
 which is perhaps more primitive than the perception of their 
 identity in different instances. Cutting across the numerical di- 
 versity of individuals, when they are copresent as “this”? and 
 “that,” is a second (numerical) diversity — that of qualities 
 and relations. The “this” is apprehended as distinct from the 
 “that” in some other respect than its individuality. It is a “this 
 of the sort X”’ as distinguished from a ‘‘that of the sort Y.” And 
 if there are several “‘thises” and “thats,” two or more of them 
 taken together may be distinct in some other respect than in- 
 dividuality from two or more others taken together. This will be 
 a perceived difference of relations, ¢.g., if four circles are pre- 
 sented, two including one another and two excluding one an- 
 other, the inclusion and exclusion are aspects in which the 
 groups of two differ. “Inclusion’’ is the “what” of one group, and 
 “exclusion” the “what”’ of the other. 
 
76 SYMBOLISM AND TRUTH 
 
 Such diversities of qualities and relations are numerical, no 
 less than are those of individuals; the universals are “‘two”’ or 
 more. But this second numerical diversity is additional to the 
 first; it is a numerical diversity in numerical diversity. As with 
 individuals, so with universals — they need to be copresent to 
 be known as distinct. But despite the fact that the distinctness 
 of universals is of the same general sort as the distinctness of in- 
 dividuals, the one is not reducible to the other, for the universal 
 is always merely an aspect of the individual, the “what” and 
 the ‘‘this” are always held apart. If I am presented with a 
 white object and a black object, the perception contains two 
 numerical diversities on different levels, the diversity of “this 
 object” and “‘that object” and of “blackness”? and “white- 
 ness.” 
 
 Along with this perception of differences of qualities and rela- 
 tions may go that of the identity of a quality or relation in dif- 
 ferent individuals. The ‘“‘this” and the “‘that” may be per- 
 ceived as the same in some aspect. When two white objects and 
 a black object are given together there will be, beside the 
 numerical diversity of the three individuals, a diversity of two 
 qualities; but a single quality will be shared by two of these 
 individuals. A self-identical universal will be recognized in dif- 
 ferent instances. 
 
 Mr. G. E. Moore discards this possibility of a universal being 
 an “‘identity in diversity’ because a self-identical object can be 
 one and one only; and he believes, as a corollary of this, that a 
 self-identical universal could not be split between several in- 
 dividuals and remain self-identical. The individual ‘‘ whiteness” 
 of one white object, he argues, is not identically the “white- 
 ness’’ of another white object. 
 
 The difficulty arises from a confusion of identity with in- 
 
 1 G. E. Moore, “Identity,” in Proc. Arist. Soc. (1900-1901), p. 103; espe- 
 cially pp. 1165 ff. 
 
 
 
 | 
 : 
 
UNIVERSALS AND INDIVIDUALS ri 
 
 dividuality. By a self-identical “whiteness”? one does not mean 
 an individual white; and if there is an individual white, this is 
 not a universal but the same thing as is meant by “‘a white ob- 
 ject.”’ Now a white object is obviously not identical with an- 
 other white object, but the “whiteness,” as a universal, is the 
 same in both cases. The fact that a universal occurs with individ- 
 uals which are not identical does not rob it of its own identity. 
 Since identity and individuality are not the same, a single iden- 
 tity can be individualized in many different cases. Each dis- 
 tinct quality or relation is something in itself; it has an identity 
 which makes it what it is, and if it had none it would be a non- 
 entity. But to say that a universal is an identity is not to say 
 that it is an individual. 
 
 The perception of the numerical diversity of individuals, then, 
 is accompanied by a perception of the diversity or identity of 
 qualities and relations in these different individuals. 
 
 What of the perception of diverse universals in a single indi- 
 vidual? Obviously, a white object can be both white and round; 
 it can be included in or excluded from another object; univer- 
 sals, themselves static, can be grouped about a static “‘this,”’ so 
 long as no ambiguity concerning the identity of the individual is 
 introduced by changes in the situation. Just as we perceive (in a 
 single whole of experience) the self-same universal as qualifying 
 or relating many different individuals, so we perceive the self- 
 same individual as entering into many different relations and as 
 qualified by many different predicates. 
 
 But every whole of experience gives way to new wholes; 
 change is of the essence of experience. 
 
 The self-identity and distinctness of the individual slips away 
 behind what seem to be its changing aspects, and the universal 
 alone continues to be known as the same. The waxing and wan- 
 ing of a light is always light; the approach of two moving bodies, 
 always motion; the alteration of colors in the field of vision, al- 
 
78 SYMBOLISM AND TRUTH 
 
 ways color; the drops of water which displace one another in the 
 flowing river are always of the same chemical composition. It is 
 impossible to determine whether the individual persists, but a 
 changeless universal is the background of the change; and the 
 identity of this universal does not become ambiguous, as does 
 that of the individual. 
 
 All perceptual distinctions, therefore, excepting an immedi- 
 ately apprehended difference of the “this” of one object and the 
 “that” of another, are distinctions of universals; and all per- 
 ceived identities, excepting the identity of a momentary “this,” 
 are identities of universals. 
 
 VII 
 
 What has been said so far of universals and individuals is pre- 
 liminary to another point — to a further characterization of 
 logical form. The idea of the structure of groups is not complete 
 without the concept of a universal and of the part it plays in 
 groups. From the point of view of logical form, universals and 
 individuals are distinguished by their structural functions. 
 
 A universal is an aspect of a group as a whole. It is that which 
 distinguishes the group from another whose constituents, apart 
 from the universal, are indistinguishable from those of the for- 
 mer except by their bare numerical diversity. The group as a 
 whole is an instance of this universal, which is itself an element 
 in the group, but not an element codrdinate with the others. 
 The universal is an element of unity, while the others are 
 terms. 
 
 Group-unity is the universal of universals, it is the “what” of 
 every group; and different universals are different kinds of 
 group-unities. To recognize anything as a group is to recognize 
 it as a unity of a specific sort, that is, an instance of a quality, a 
 relation, or an operation. 
 
 Consider the unity of a simple qualitative fact such as “Iago 
 
 
 
UNIVERSALS AND INDIVIDUALS 79 
 
 was wicked.”” Here the predicate and the subject are knit 
 together. The expression does not mean “Jago” and “ wicked- 
 ness”? as a mere plurality, but “ Tago-as-qualified-by-wicked- 
 ness.” And if the fact were a number of terms joined by a rela- 
 tion or a mathematical operation, the relation or operation 
 would be attached to the terms in the same general manner as 
 the quality to the thing qualified. The quality, relation, or oper- 
 ation is not related to its terms, for this would involve an infinite 
 series of relations; we can say only that the terms enter into the 
 peculiar unity which makes them a group or a fact. The fact 
 “clouds precede rain,” for example, is not made up of the ele- 
 ments, clouds, rain, and the relation precedes related to one an- 
 other; for if this were so, there would need to be a third relation 
 which unites the second relation to the original terms and rela- 
 tion, and so on. If the unity of a fact depended on the knowledge 
 of such an endless series of relations, the fact would not be pre- 
 sented as a whole. The unity is given immediately. A relation 
 relates its terms and a quality qualifies its subject once and for 
 all; and this is true of the simplest fact — of a fact, for instance, 
 constituted of the meagre relation of conjunction or the mathe- 
 matical operation of addition. “‘A plus B” cannot mean A and 
 B and plus added together, for this would demand an infinity of 
 new pluses, and the fact would remain incomplete. A plus Bisa 
 new entity, something other than the entities A and B and plus; 
 and it is given when the terms and the operation are given in the 
 unity which makes the whole an instance of addition. 
 
 That a quality, when it modifies a subject, is of the subject in 
 the sense in which an operation or relation is of its terms, is 
 borne out by our habits of speech. Relations or operations are 
 predicated of their terms as qualities are predicated of their sub- 
 jects. One says “‘x 1s between y and z”’ as readily as “‘x ts white”; 
 x, y, and 2 as a group have betweenness as z alone has whiteness. 
 Thus qualities, relations, and operations, despite their differ- 
 
80 SYMBOLISM AND TRUTH 
 
 ences, are alike in their structural functions.! They can be 
 distinguished from the terms they unite or the subjects they 
 qualify, but at the same time they are cemented to these terms 
 and subjects. 
 
 The ability to enter with other elements in a group so that the 
 plurality of members becomes a whole is characteristic of uni- 
 versals; and each group contains a universal which performs 
 this function in it. If a fact (a complex object) is presented, the 
 determination of the group by the elements attests the presence 
 of a universal. The form of a fact is a blank into which the con- 
 stituents must fit, and at least one of the places in the blank is 
 for a universal, while the others are for terms. And even the per- 
 ception of bare numerical diversity, either of individuals or uni- 
 versals, is an analysis of a whole into parts which are diverse 
 from one another but have unity through the relation of diver- 
 sity. 
 
 A fact is therefore something more than a union of any ele- 
 ments whatsoever; it is a union of elements so that a universal 
 enters into terms or subjects. The notion of a group involves not 
 only the concept of members united into a whole, but also the 
 concept of an element (itself a member) which determines the 
 members to be a whole. But the universal is distinct from the 
 terms because it fulfills a different office in the fact; it stands 
 above the terms, pervading the whole and lending to it a distinc- 
 
 1 Operations and relations, though they are like qualities in that they unite 
 with terms in the same fashion, are not qualities. From the point of view of 
 form, a quality modifies only one term; it is of the form (Ra). A relation has at 
 least two terms; it is of the form (Sab); and if these terms are not distinct, as 
 in (Saa), the relation still has two terms, so far as the representation goes 
 (though these are not distinct), but the fact has only one. Such reflexive “re- 
 lations”’’ are qualities represented as relations between a term and itself. It is 
 the symbolic group rather than the fact which is relational in form. Opera- 
 tions, on the other hand, may appear with one or more terms. They may be of 
 the form of qualities or of the form of relations. But operational groups are 
 distinguished from qualitative and relational groups by the way in which they 
 are used in symbolic systems; they permit uses which these others do not per- 
 mit. See below, ch. VII, sec. vii, for this distinction. 
 
 
 
UNIVERSALS AND INDIVIDUALS 81 
 
 tive coloring. The concept of the unity of a universal and the 
 terms on which it rests must be placed with the concepts of ob- 
 ject, and of identity and diversity, among our indefinables. 
 The Platonic description, “participation,” as nearly charac- 
 terizes this unity as any we know. If one were to revise Kant’s 
 list of the categories, leaving aside the question as to whether 
 they are of the object or of the mind, he would find it necessary 
 to include among the presuppositions of knowledge, not only 
 the notion of the identity and diversity of objects, but also that 
 of the peculiar unity of groups which springs from the presence 
 of a “participating”’ universal. 
 
 VIII 
 
 If a universal is any object which can assume the réle of ele- 
 ment of unity in a group, an individual must be an object which 
 can take no other part than that of a term. 
 
 Individuals alone do not constitute facts; there are no purely 
 individual facts. Through universals we describe and relate in- 
 dividuals, but through individuals nothing is described or 
 brought into relation. ‘‘The table,” “the chair,” “the book,” 
 cannot in themselves unite into a group; by their nature they 
 are capable of playing the part of terms and nothing else; and 
 only when they are related or qualified in some way do they be- 
 come elements in a fact. (Indeed, an individual referred to as “‘a 
 table,” “a chair,”’ or “‘a book,”’ is already an x qualified by a 
 predicate, and has already become an element in a fact.) “The 
 table with the book on it and the chair beside it” is a fact; but 
 “the table the chair the book” is no fact. Words and phrases 
 that signify individuals do not, by themselves, go together to 
 form significant expressions, and here again language reflects 
 the structure of objects. 
 
 Without predicates, relations, or operations to bring them 
 into groups, individuals (if they are thought of) continue in iso- 
 
82 SYMBOLISM AND TRUTH 
 
 lation, cut off by their individuality from other objects. Such 
 isolated individuals are never known concretely; it is only by 
 the most violent act of abstraction that we can conceive of 
 them. 
 
 The search for a relation between a universal and the individ- 
 ual which is an instance of it results, therefore, in the discovery 
 that “being an instance of”’ is not a relation. The unity of a uni- 
 versal with individuals is a wholeness within which relations are 
 distinguished; a relation is a species of group-unity; but this 
 unity is not itself related to its terms, and the statement that it 
 is “in” or “of” or “with” its terms serves only to point to it as 
 an indefinable. The minimal object of knowledge is a universal 
 in its instance; the universal, the individual, and their unity are 
 given at once. 
 
 IX 
 
 The distinction between terms and elements of unity is not 
 the same, however, as that between individuals and universals; 
 for the terms as well as the element of unity in a fact may be uni- 
 versals, as in “truth is beauty,” “dishonor is worse than death,” 
 ‘the course of true love never did run smooth.” 
 
 A fact whose terms are universal is not the same kind of fact 
 as one whose terms are individual. The latter is concrete; the 
 former, abstract; but both are nevertheless facts. An abstract 
 fact is an aspect of a concrete fact; or rather, it is an aspect of 
 many such facts. But in perception, facts come to us as individ- 
 ualized, and not as abstract. 
 
 The ability of universals to fulfill a double function in groups 
 — both as terms and elements of unity — divests them of the 
 separateness which belongs by nature to individuals. In an ab- 
 stract fact such as ‘‘dishonor is worse than death,”’ a universal 
 which might qualify or relate in some instance is referred to 
 apart from its qualifying or relating function, and it becomes a 
 term in a new fact; but the universal remains a universal be- 
 
UNIVERSALS AND INDIVIDUALS 83 
 
 cause it can appear as a qualifying or relating element, rather 
 than as something qualified or related. Thus when I say “‘this 
 paper is white,” I refer by the word “white” to the same object 
 as that to which I refer by “whiteness” when I say “whiteness 
 is the symbol of purity.” The difference is not in the identity 
 of the object meant, but in its function. In the one case it is a 
 term in an abstract fact; in the other, an element of unity ina 
 concrete fact. 
 
 We tend to speak of facts whose terms are individuals as 
 “particular,” but the word “particular”? is misleading. Every 
 object or fact is in a sense particular, for it has an identity of its 
 own; it is a ““somewhat”’ distinct from other objects, and it can 
 be referred to as “this” object, “this” quality or relation, 
 “this” fact. Particularity in the sense of identity is found 
 everywhere; not only in individuals, but in universals and in 
 facts whose terms are universal. “Dishonor is worse than 
 death” is a particular case of the relation “worse than,” and 
 everything is a particular case of the logical character of “ob- 
 jectivity.”’ If one means by the particularity of an object or fact 
 simply its identity, he ought to speak of particulars of higher 
 and lower orders, for the world is composed of identities of 
 higher and lower orders. A fact that contains as a term some ob- 
 ject that enters as an element of unity in another fact is of a 
 higher order of particularity than this second fact. “Dishonor is 
 worse than death” is not of the same order of particularity as 
 “Judas was dishonorable”’; the latter is the kind of fact from 
 which the former is abstracted. The quality which appears as a 
 qualifying element in the latter is itself a subject of description 
 in the former; ‘‘dishonor”’ is taken now as a substantive instead 
 of as an adjective. 
 
 In this manner, facts are overlaid, the one on the other, the 
 less particular on the more particular, the terms of those of 
 higher orders of abstraction being separated out from those of 
 
84 SYMBOLISM AND TRUTH 
 
 lower orders of abstraction, till we reach the facts whose terms 
 are the most abstract of all — the facts of logical structure. But 
 any fact at any stage is particular in some sense. 
 
 The relation between these different orders is like the Aristo- 
 telian relation of matter to form. The lower orders of particulars 
 are the matter of the higher orders; a fact which is particular in 
 relation to one fact is general in relation to another; and the 
 lowest members in the scale are those whose terms are finally 
 and irreducibly particular. That is, they are facts whose terms 
 are capable of being terms and nothing else — whose terms are 
 individuals. These terms are like Aristotle’s prime matter; they 
 are cases of universals, they have form in the Aristotelian sense, 
 but there is nothing in relation to which they are form. Nothing 
 is an instance of them. They are that upon which universals 
 rest, but which themselves rest on nothing. 
 
 Though the individual which is an instance of a universal is 
 one with the universal in the instance, the process of abstraction 
 — of separating the two for thought — has begun when the uni- 
 versal is distinguished in its instance. To abstract is to disregard 
 an aspect of a presented object; and since all presented objects 
 are of double aspect, both universal and individual, we can dis- 
 
 regard the latter and refer only to the former. Not only can we. 
 
 abstract from the individuality of an object; we can also ab- 
 stract from any of its more specific qualities or relations. Thus a 
 green object is a colored object; when I am presented with the 
 relation before, I am also presented with an asymmetrical rela- 
 tion; and I can refer to the color apart from the greenness, or to 
 the asymmetry apart from the beforeness. The very presentation 
 of objects — for they are only presented when they are known 
 both as universal and individual — is the beginning of abstrac- 
 tion. 
 
 The abstraction which begins in distinguishing a universal in 
 a perceived instance is completed in the realm of conception; 
 
 ~~ 
 
UNIVERSALS AND INDIVIDUALS 85 
 
 the instruments of conception (symbols) are also the instru- 
 ments of complete abstraction. In perception the sense of the 
 oneness of the object — as an individual in which many univer- 
 sals join — cannot be shut out; but through symbols any of 
 these universals, or for that matter, the individual, can be re- 
 ferred to alone. We can abstract the individual, as an indeter- 
 minate x, from the universal, or the universal from the individ- 
 ual. The abstracted universal is not referred to as it occurs in 
 any special one or in all of its instances; it is meant apart from 
 instances, as an object with an identity of its own. 
 
 Needless to say, the symbol which carries an abstract refer- 
 ence is not itself abstract; it is a presented object with its own 
 individuality and general nature. And yet the once heated con- 
 troversy over “abstract ideas” turned on a confusion between 
 the abstractness of the symbol and the abstractness of its refer- 
 ence. It is indeed absurd to hold, as Berkeley accuses Locke of 
 holding, that ideas as images (as psychical events) are ab- 
 stract; they are obviously as concrete as any other presented 
 objects. But there is no absurdity in their having an abstract 
 meaning. The problem of abstraction, so far as it touches uni- 
 versals, comes in the end to this: Can we refer to universals as 
 single, self-identical objects distinct from individuals? And this 
 is the problem of the objectivity of universals. 
 
 X 
 
 There is no reason to suppose that a universal is any the less 
 an object than the subject it qualifies or the terms it relates. If I 
 say that “the afternoon is warm,” or that “Chicago is between 
 New York and San Francisco,” the warmth is as objective as the 
 afternoon, and the relation between as genuine a constituent of 
 the fact as Chicago, New York, or San Francisco. Unless the 
 concept of an object is taken in a much narrower sense than we 
 have given it, universals cannot be distinguished from individ- 
 
86 SYMBOLISM AND TRUTH 
 
 ual subjects and terms on the ground that the latter are objects 
 while the former are not. Both are in knowledge; both are given 
 as constituents of facts, though neither is given alone. 
 
 When it is said that universals are not objective, what is 
 meant is that they are not in reality the same kind of object as 
 their terms when these are individuals; universals do not belong 
 in the same metaphysical category as individuals. The nominal- 
 ist views the world as being really a collection of individuals; 
 what are called universals are to him ideas, mental addenda, 
 created by an act of comparing individuals. He believes that 
 white objects exist, but that whiteness does not exist — at least 
 that whiteness exists only in a mind. It is a name for a number 
 of things which are closely alike, that is, for an artificial con- 
 struction, “‘the class of white objects.” 
 
 In answer to the nominalist, it must first be observed that the 
 question as to whether a universal exists in a mind or in reality 
 (assuming that reality and “‘a mind” are different), is a meta- 
 physical and not an epistemological question. Universals are 
 known in some manner, whether it be as elements in an external 
 or an internal world. They appear in the simplest units of cogni- 
 tion; and whether or not they are contributed by the perceiving 
 subject, they are objects of knowledge in the broadest sense of 
 the term. For the purposes of the positive theory of knowledge, 
 this is enough. We need not ask if reality is a concourse of indi- 
 viduals, or if it is a network of universals without individuals, or 
 if it is a fusion of both. 
 
 There are, however, many considerations that cast doubt on 
 a metaphysics which affirms that individuals are real and that 
 universals are unreal. First among these is the indeterminate- 
 ness of our knowledge of the individual. If the x which is quali- 
 fied or related by universals is the sole known reality, knowl- 
 edge touches reality only at the tiniest point — only through 
 the fleeting “this” of perception, which can be described in no 
 
UNIVERSALS AND INDIVIDUALS 87 
 
 way. Secondly, it appears beyond question that when one per- 
 ceives a colored object he is presented with the color as well as 
 the colored object. Color is given in the field of vision, and the 
 fact that it might be found elsewhere is no evidence that it is not 
 here. 
 
 The nominalist will doubtless reply to this by asking how one 
 can perceive an abstraction. The answer is that the color of an 
 object is no more an abstraction than its individuality; the 
 “what”? of an object is no less of the object than its “this.” The 
 very act of perception is the beginning of abstraction; for a pre- 
 sented object is both broken in two for thought (that is, ab- 
 stract) and knit into a unity for perception (that is, concrete). 
 
 Thirdly, to say as the nominalist does that an object belongs 
 to a class is to notice its similarity to another object, and al- 
 though the discovery of the qualities or the relations of the ob- 
 ject comes through comparison, the result of the comparison is 
 the perception of the universal in the object, that is, as an ele- 
 ment of the whole. And if objects are similar, this similarity is a 
 universal; the likeness of objects, no matter how remote, rests 
 therefore on a universal. In order that the nominalist may main- 
 tain his point that classification is artificial, he must either be- 
 lieve that it is wholly a matter of caprice (and then it is not 
 classification), or that there is some basis for it; and unless he 
 wishes to negate his own view, he must show in the latter case 
 that classification rests on something other than universals. 
 This he does not show. 
 
 It can be further urged, in favor of the equal right to reality of 
 the universal, that objects which are known as bare identities, 
 as mere “‘thises” and “thats,” still have the property of being 
 objects. The very entrance of a thing on the stage of thought im- 
 plies that it has a minimum of characters and relations — that 
 it is identical with itself and diverse from other things. The con- 
 cept of the individual itself gives rise to a universal — individu- 
 
88 SYMBOLISM AND TRUTH 
 
 ality. Therefore, if universals are unreal, it ought to be added 
 that all objects of thought, including individuals, are unreal; 
 and the distinction between the reality of universals and in- 
 dividuals falls to the ground. 
 
 The nominalist will then ask, granting that one is presented 
 with whiteness, hardness, and other sensory qualities, is one 
 also presented with relations and operations? These seem to be 
 much less “presentable” than qualities. But if the whole con- 
 tent of the perception were a, b, c, when a is perceived to be be- 
 tween b and c, this mere plurality would not be a perceived fact. 
 Some sort of unity pervades and characterizes the whole; in this 
 case, the relation “‘between.” But perhaps it is less difficult to 
 understand how one can perceive a specific relation than how he 
 can perceive this general unity. Is there a perception of the 
 unity of objects? The only answer to this is that every percep- 
 tion is one of the unity of objects; without a presentation of 
 unity, which is not unlike Kant’s “unity of the manifold,”’ there 
 is no presentation of objects. One is no more aware of objects as 
 dis-unified than he is of a white object without its whiteness. 
 The two cases are exactly parallel. They are cases of the appre- 
 hension of the universal in its union with the individual. 
 
 As for operations, such as (2 + 2) — they also are kinds of 
 group-unity. If two objects are before me, ““twoness”’ is before 
 me; and when I perceive four objects as a group of “two and 
 two,” I am presented with something which approximates to a 
 case of the operation plus. 
 
 It is quite as accurate to describe the growth of knowledge by 
 pointing out that the individual is abstracted from the univer- 
 sal, as it is to describe it as an abstraction of the universal from 
 the individual. Knowledge of the individual is not prior to 
 knowledge of the universal; to discover the individual requires 
 an effort of thought. And if universals are “‘ideal,”’ if they enter 
 knowledge only through the working of the mind in sifting ex- 
 
 
 
UNIVERSALS AND INDIVIDUALS 89 
 
 perience, the same is true of individuals. As a matter of fact, 
 neither of these descriptions is true. The “this” and the “‘ what”’ 
 blend in the pure awareness which underlies and completes clear 
 cognition; they emerge as distinct in the perception of objects, 
 but the one does not thereby become less objective than the 
 other. 
 
 To hold, with M. Bergson and Mr. Bradley, that neither qual- 
 ities or relations, or the individual things qualified or related, 
 are real — that all are “‘ideal’’ — is to gain at least the merit of 
 consistency. Nothing short of this will do if one sets out to at- 
 tack the reality of universals. But it is not necessary to prove 
 that universals or individuals, or both, are real in order to vindi- 
 cate their objectivity. If either, or both, are appearances, they 
 are still objects; for an appearance is an object. 
 
 General propositions, laws, and principles which ignore the 
 individual have a meaning that is as much a part of the world 
 of fact as the meaning of propositions whose terms are bare 
 particulars. Abstraction is possible because universals are self- 
 identical objects which can be singled out and referred to 
 through symbols. 
 
 XI 
 
 The analysis of facts into terms and unifying universals is the 
 basis of a general “grammar” of symbolism. Substantive sym- 
 bols (symbols of terms) cannot be taken together to form signif- 
 icant wholes; they must be grouped with adjectival symbols — 
 with symbols of unity. Nor can adjectival symbols alone make 
 up significant expressions; some of the symbols of a group must 
 signify terms, whether these be universal or individual terms. 
 An expression without a symbol of unity, or without terms, 
 would violate a fundamental principle of the structure of fact, 
 and could not possibly have a meaning among facts. 
 
 This grammar of symbolism is the source of all special gram- 
 mars. Every language, if it contains no other distinctions of 
 
90 SYMBOLISM AND TRUTH 
 
 function among its words, will differentiate substantives from 
 adjectives — “‘adjective”’ being taken to include all modifying 
 or connecting words, that is, adverbs, verbs, conjunctions, etc., 
 as well as adjectives proper. Substantives or adjectives alone will 
 not, in any language, enter into significant unions with one an- 
 other. Thus “‘chair table book,” “large brown on,” are intrinsi- 
 cally without meaning, for they do not conform to the first prin- 
 ciple of symbolic grammar. On the other hand, “book on table” 
 or “large brown chair” are significant phrases (whether or not 
 they stand for objects) because they are properly constructed. 
 Language recognizes not only the distinction between terms and 
 elements of unity, substantives and adjectives, but it recognizes 
 also that the same object, if it is a universal, can play the part of 
 both. A root-word assumes a different form when it enters as a 
 term from the form it assumes as an element of unity. This is 
 the difference between the words “‘nearness” and “‘near,”’ 
 “beauty” and “beautiful,” “run” and “‘running.” These dis- 
 tinct forms of words signify the same object, but they represent 
 this object in different structural relations to other objects, that 
 is, in its adjectival and its substantive functions. 
 
 The signs of addition, multiplication, subtraction, and divi- 
 sion are the “adjectives” — the symbols of unity — in arith- 
 metic and algebra; the signs for numbers cannot by themselves 
 constitute significant arithmetical or algebraic expressions. They 
 must be joined by operational symbols, for an arithmetical or 
 algebraic fact is made up of numbers operated on in some way. 
 And a similar “‘grammar” is present in symbolic logic. (p-q) or 
 (p vq) is a group in which the dot, in the one case, or the sign 
 (v), in the other, stands for the unifying element, while the let- 
 ters stand for the terms — for propositions united by the rela- 
 tion “‘and” or “‘or.”’ 
 
 There are many special rules for the construction of signifi- 
 cant symbolic groups, but the general rule — that symbols for 
 
UNIVERSALS AND INDIVIDUALS 91 
 
 terms must be grouped with symbols of unity and that symbols 
 for terms or symbols of unity alone cannot have meaning, if 
 they are grouped — lies beneath all systems of symbols. Any 
 possible symbolic group in any possible system must follow this 
 principle, since any possible fact will be a unity of terms and 
 qualifying or relating universals; the most general rule of sym- 
 bolic syntax rests on a “‘syntax”’ of fact — on the most general 
 way in which objects fit together to form wholes. 
 
 XII 
 
 Each symbolic system will have its own special plan of syn- 
 tax; and this plan, if it assumes no very large proportions, can 
 be set forth merely by enumerating the significant groups per- 
 mitted in the system. There may be no special rules for con- 
 structing the groups, though none of the groups can violate the 
 general principle which has just been stated. More extended and 
 useful systems, such as language and arithmetic, are built on 
 syntactical plans which can be embodied in rules. These rules 
 state how the symbols can be taken together as significant 
 wholes and how groups can be derived from one another. 
 
 Once the syntactical plan of a system is given as a set of rules, 
 expressions of many different forms can be constructed within 
 it, and none of these expressions will be without syntactical 
 meaning so long as it conforms to the plan. The significance of 
 the groups will be a function of the meanings of their elements 
 and of their form; it is necessary only that the elementary sym- 
 bols of the system should stand for existing objects; the groups 
 may or may not represent existing objects. 
 
 Some systems, notably languages, contain an endless number 
 of groups which fulfill the conditions of syntactical significance 
 but stand for no objects. These systems are non-deductive (or 
 incompletely inferential). If we follow their syntactical rules, we 
 are as apt to be led away from fact (and truth) as to be led to 
 
92 SYMBOLISM AND TRUTH 
 
 fact (and truth). In these systems, there is a discrepancy be- 
 tween significance and truth. But in a deductive system which 
 is completely interpreted there is no such discrepancy. Any 
 group that can be properly derived from the original groups by 
 the rules of syntax will stand for an object, that is, it will be true 
 as well as significant. The conditions of significance and of truth 
 are the same in a completely interpreted deductive system, and 
 the rules of syntax are the rules of deduction.+ 
 
 But in any case, the syntactical plan of a symbolic system de- 
 termines its range of significance. It determines not what ob- 
 jects actually are represented in the system, but how the sym- 
 bols can be used significantly regardless of whether they stand 
 for objects. It determines an area of concepts. 
 
 This gives us a criterion of possibility for knowledge. A “pos- 
 sibility for knowledge” in the widest sense need not be a refer- 
 ence to an object; it is any meaning that is conceivable. And any 
 group of symbols — of words, mathematical signs, or ideas — 
 which follows the rules of syntax in a system has a conceivable 
 meaning; the group is a possible concept. Possibility for knowl- 
 edge belongs only to concepts, and if one says that a non-exist- 
 ent object is a possible object of knowledge, this is only a man- 
 ner of speaking. He does not mean that there is any such object 
 to have the predicate “possible”’; he means merely that a signif- 
 icant concept which refers to no object can be framed. “The 
 immortality of the soul’ is conceivable and therefore a possi- 
 bility for knowledge; but the possibility resides not in an actual 
 fact for which this expression stands, but in the fact that the ex- 
 pression has meaning. Aside from this “possibility as an object 
 of knowledge,”’ the test of which is conceivability, there may or 
 may not be an absolute metaphysical possibility, such as that of 
 Leibniz’s infinity of possible worlds. But with this we are not 
 concerned. 
 
 1 This is an anticipation of what is more fully set forth in ch. VII. 
 
 
 
UNIVERSALS AND INDIVIDUALS 93 
 
 The rules of syntax in a symbolic system therefore mark the 
 limits of possibility for that system. (And in completely inter- 
 preted deductive systems, every possible concept is also true.) 
 But what is conceivable in one system may have no counterpart 
 in another. The general rule of symbolic syntax — that symbols 
 of terms alone or symbols of unity alone cannot form significant 
 wholes — tells us how fact in general must be conceived; it 
 marks the most general limits of possible concepts. 
 
 XIl 
 
 The two symbolic systems whose application to fact is at once 
 most sweeping and most familiar are the systems of the imagi- 
 nation (of mental images) and of language. 
 
 The habits of correct and ordered speech become the habits of 
 correct and ordered thought, so that if a thing can be thought 
 clearly it can be said clearly. We grow unconsciously to accept 
 certain combinations of words as significant, and to reject others 
 as nonsensical because they do not conform to the rules of syn- 
 tax. And yet the possibilities of significant combinations in lan- 
 guage are so wide that almost any chance grouping of words has 
 syntactical meaning. If words are thrown together at random it 
 is more than likely that a significant phrase will be achieved, for 
 no phrase that follows the rules of syntax in language is without 
 meaning. 
 
 When expressions such as “the round square,” ‘the moon is 
 made of green cheese,” “Socrates is a triangle,” etc., are rejected 
 as meaningless, they are not strictly speaking rejected as non- 
 sense, unless we have passed over the thin line that separates 
 nonsense from falsity and contradiction — that divides the 
 meaningless from the fantastic. It is true that there are no ob- 
 jects which correspond to these expressions, yet the expressions 
 are not totally without meaning. The very fact that we say “a 
 round square is a geometrical contradiction,” that ‘Socrates is 
 
94 SYMBOLISM AND TRUTH 
 
 a triangle” or “the moon is made of green cheese” are fantastic 
 notions, shows that we grasp these expressions as concepts; 
 otherwise we could attribute neither contradiction nor absurd- 
 ity to them. A nonsensical expression, an utterly meaningless 
 collection of symbols, could be neither false, fantastic, or con- 
 tradictory. 
 
 And yet nonsense cannot be without a semblance of sense. 
 There must be vestiges of significance in the symbols, or else 
 they would not be symbols but mere collections of presented ob- 
 jects. In the pseudo-phrases, “large brown on ” and “chair table 
 book,” for example, the elements are significant but the wholes 
 are without meaning. They present the semblance of wholes but 
 they conform to no rules of syntax. In direct contrast to this 
 type of nonsense stand pseudo-phrases that have a seeming in- 
 telligibility as wholes since they follow syntactical rules, but 
 that are meaningless through the presence of meaningless ele- 
 ments. The lines from Lewis Carroll’s Jabberwocky, a classic of 
 nonsense, exhibit just the proper distribution of significant ele- 
 ments along with meaningless elements to give the whole a 
 structure: “O frabjous day! Callooh! Callay! He chortled in his 
 joy.” So powerful is the sense of significance as a whole that the 
 parts tend to derive meaning through their places in the whole. 
 
 The interpretation of words — or any symbols other than 
 images — usually takes the route of the imagination, and for 
 this reason it has been maintained that what cannot be imag- 
 ined cannot be thought, that conceivability in images is the 
 only conceivability. 
 
 The syntax of the imagination is extremely simple. Any 
 images that can be held together before the mind form a signifi- 
 cant group. The distinction between terms and elements of 
 unity is not made explicit, though one never imagines an object 
 composed of parts which are unrelated or unqualified. There are 
 no signs of grouping other than the mere juxtaposition of 
 
UNIVERSALS AND INDIVIDUALS 95 
 
 images, and no juxtapositions of images are excluded as mean- 
 ingless, though many are fantastic and absurd. Yet some images 
 refuse to go together before the mind; there are no counterparts 
 
 99 66 
 
 in the imagination for “a round square,” “a curved straight 
 line,” etc.; the images corresponding to these words exclude one 
 another’s presence. It is difficult to give any reason for this ex- 
 clusion; but this fact shows that the syntax of the imagination 
 has its limits, and that there are possible concepts in other sys- 
 tems which cannot be translated into the imagination. 
 
 What is fantastic or absurd, or even contradictory, is not then 
 utterly nonsensical. No properly constructed symbolic expres- 
 sion is void of meaning. The general grammar of symbolism 
 marks out the most general limits of possibility for thought, fol- 
 lowing the most general lines of the structure of objects, while 
 special plans in special systems mark out narrower limits of con- 
 ceptual possibility. What is an impossibility for thought in one 
 set of symbols may not be an impossibility in another set. It is 
 not strange, therefore, that we can “imagine” much less than 
 we can mean. 
 
 XIV 
 
 One class of syntactical rules must be especially noticed, that 
 is, the rules of order. The sentence, “Brutus killed Caesar,”’ has 
 a different significance from, “‘Caesar killed Brutus,” and the 
 pseudo-group, “killed Brutus Caesar,”’ has no significance. The 
 spatial or temporal arrangement of the symbols enters here as a 
 factor in the meaning; the order in the symbols mirrors an order 
 in the fact signified. Must we then include the spatial or tem- 
 poral arrangement of symbols as a feature of their logical form? 
 
 It is less difficult to illustrate than to describe what is meant 
 by the order of a group. Facts of identical constituents may be 
 wholly different in order, they may be of opposite orders. The 
 fact ‘A precedes B” is different and opposite in order to the 
 fact ““B precedes A”’; the facts “A between B and C,” “B 
 
96 SYMBOLISM AND TRUTH 
 
 between A and C,” and ‘‘C between A and B” are distinguished 
 by their orders. Most active verbs and prepositions, if they enter 
 in groups, give us phrases or sentences representing ordered 
 facts. “Hamlet killed Polonius” does not mean the same thing 
 as “‘Polonius killed Hamlet”’; ‘grace before meat”’ is something 
 other than ‘“‘meat before grace.”’ 
 
 The simplest manner of describing order is to say that all re- 
 lations have a direction, and that a fact whose elements are re- 
 lated in one direction is different (for some relations) from a fact 
 of the same elements related by the same relation in another 
 direction. And the usual manner of representing order in lan- 
 guage and mathematics bears out this description. The symbols 
 of speech and writing themselves have a direction in space and 
 time, and it is through this that the order in the fact is signified. 
 This manner of representing order is a convenient device of sym- 
 bolism, but it does not analyze order; if the order in the fact is 
 not spatial or temporal, it merely represents one kind of order 
 by another. 
 
 Order is something common to groups which have a direction 
 in space and time and to other groups which are non-spatial and 
 non-temporal, and can only metaphorically be said to have a 
 “direction.” “‘Hamlet believed the ghost” is an ordered fact, 
 but “believing” is not a temporal or spatial relation, though the 
 order it gives to the fact is reflected by the spatial order of the 
 symbols. What is the common structural feature that makes 
 this reflection possible? 
 
 An asymmetrical (or ordering) relation not only unites its 
 terms, but in uniting them, distinguishes them; it lends to each 
 a distinctive mark, so that the whole is not of the simple form, 
 (Rab), but of the form, (R(Sa)( Qb)). The whole is a group of 
 groups, and the order is the manner in which the terms are dis- 
 tributed in the sub-groups. Thus (R(Sa) (Qb)) and (R(Sb) (Qa)) 
 
 represent different orders of the same elements. There are as 
 
UNIVERSALS AND INDIVIDUALS 97 
 
 many possible orders as there are possible distributions — in 
 this case, only two. 
 
 Consider, for example, any fact in which the constitutive re- 
 lation is a transitive verb, ¢.g., ““A knows B.” The relation re- 
 lates the terms, but at the same time distinguishes one as “‘ac- 
 tive” and the other as “passive’’; and the fact is more fully 
 stated as, “A, active, knows B, passive.”’ This is plainly of the 
 form, (R(Sa) (Qb)), where R is the relation “knowing,” and S 
 and Q, respectively, the qualities “activity” and “passivity.” 
 The relation both relates and “qualifies” its terms; though this 
 must not be construed to mean that the relation is reducible to 
 qualities of its terms. It is always a relation; but each term, 
 through being in the relation, assumes a special character — a 
 character that attaches to it only when it is in the relation. Lan- 
 guage generalizes this distinction of quality which an ordering 
 relation imparts to its terms into the distinction of “‘subject”’ 
 and “‘object.”’ Thus in “‘a before b” or “a in b,” a is the subject 
 and b the object; and in apprehending the fact as ordered, we 
 grasp this distinction of relational quality in the terms. It is ap- 
 prehended as of the form, (before (a, subject) (b, object) ); and this 
 is different from the form, (before (b, subject) (a, object)).! 
 
 The reason why there is a “direction” from one term to an- 
 other in an ordered fact is, therefore, that these terms are mem- 
 bers of distinct groups; the terms are distinct not merely as 
 terms, but through their places in the whole. If they take differ- 
 ent places, though the constituents of the fact remain the same, 
 the fact will be different. Direction in space or time is a special 
 case of this general structural feature of groups. This description 
 of order applies, moreover, not only to complexes of two terms, 
 
 1 It follows from this description of order that a fact such as “A walks and 
 B runs” has order; for the terms are united by a relation, and at the same time 
 distinguished by predicates. The difference between this fact and ‘‘a before b” 
 is not that the former is without order, but that the distinguishing predicates 
 of the terms are independent of the relating relation; they are not relational 
 qualities. 
 
98 SYMBOLISM AND TRUTH 
 
 but to polyadic complexes of any number of terms, in which 
 there is no single direction or “‘sense”’ but a number of interre- 
 lated directions. The relation ‘“‘trusteeship,” for example, dis- 
 tinguishes the ‘“trustor” from the “‘trustee,”’ both from the 
 thing intrusted, and all three from the “beneficiary”’ of the 
 trust.) This tetradic relation gives an order to its terms by mak- 
 ing each a member of a distinctive group; it is of the form, 
 (R (Sa) (Qb) (Lc) (Md)). But not every term in a polyadic com- 
 plex need be distinguished by an order, from the other terms: each 
 between b and c,” makes no distinction of order between 6 and 
 c, though it distinguishes a from both. There are in this complex 
 two objects and one subject; and obviously the objects are not 
 distinct from one another through the relation. Its form can be 
 represented as, (Ra(Sb) (Sc)), which has only three possible 
 variations of order, viz., (Rb(Sa) (Sc)), (Re(Sa) (Sb)), and 
 (Ra (Sb) (Se)). 
 
 When order is seen to be a matter of grouping alone, it can be 
 represented by symbols whose spatial order is irrelevant to the 
 meaning — whose group relations alone are significant. (Ra(Sb) 
 (Se)), which might mean “a between b and c,” can be written 
 ((Sb)Ra(Sc)), or ((Se) (Sb)Ra), or ((Sb) (Sc)Ra), etc.; and all 
 of these different spatial arrangements will signify the same 
 order of the fact. Language finds in the passive form of expres- 
 sion that order can be indicated by grouping alone. “ Polonius 
 was killed by Hamlet” is equivalent to “Hamlet killed Polo- 
 nius’’; and here the group of the agent (or subject) ? is distin- 
 
 1 The other distinctions of case in language, which are additional to the 
 nominative and accusative (subject and object), are generalized forms of these 
 distinctions of order in polyadic complexes. 
 
 2 Expressions in the passive form show us, further, that the distinction be- 
 tween subject and object as the active and passive terms, respectively, of a re- 
 lation (or as the referent and relatum) does not always correspond to the dis- 
 tinction between the grammatical subject and predicate of the sentence. Only 
 in the active form is the subject of the relation — or relational subject — also 
 the grammatical subject; e.g., in “Hamlet killed Polonius,” ‘‘ Hamlet” is both 
 the relational and grammatical subject, while in “‘Polonius was killed by 
 Hamlet,” “Polonius” is the relational object but the grammatical subject. 
 
UNIVERSALS AND INDIVIDUALS 99 
 
 guished by the preposition “by.” The expression has the form, 
 (Polonius killed (by Hamlet)), that is, (Ra(Sb)), where R is the 
 relation “killing” and S the preposition “‘ by’ — the mark of the 
 agent. (Rb(Sa)) would be the alternative order. It is clear that 
 in the passive form the spatial order of the words does not affect 
 the significance, so long as the integrity of the groups is pre- 
 served. The sentence might read, “By Hamlet Polonius was 
 killed,” or “Polonius was by Hamlet killed,” or ‘‘By Hamlet was 
 Polonius killed,” or even “Killed was Polonius by Hamlet.’’ In 
 any of these spatial arrangements, the meaning will be the same; 
 and a different order can be signified only by interchanging the 
 terms in the groups. 
 
 It is therefore only accidental, and not essential — though it 
 is a useful accident — that the spatial or temporal order of sym- 
 bols should be significant. 
 
 XV 
 
 If an asymmetrical (or ordered) fact is one in which the terms 
 are distinguished by being members of different subordinate 
 groups within the whole, a symmetrical fact is one in which 
 there is no such distinction of terms through their membership 
 in subordinate groups. Consider “A with B.” The relation 
 “with” imparts no distinctive qualities to its terms; each term 
 is with the other and nothing more. The fact has the form (Rab) 
 and could be symbolized by this group where the spatial and 
 temporal orders of FR, a, and 6 are irrelevant to the meaning. 
 There are no subordinate groups here in which the terms could 
 be differently distributed. 
 
 We are in the habit, however, of representing symmetrical 
 facts as if they had an order. Since the spatial order of words and 
 mathematical signs is usually significant, we assume that ‘‘ A 
 with B”’ means something other than “B with A” until the 
 contrary is asserted. For this reason, the symmetry of such ex- 
 pressions as “‘ A with B” or “a X b” is commonly described by 
 
100 SYMBOLISM AND TRUTH 
 
 saying that alternative orders of the symbols have the same 
 meaning, that is, that ““A with B”’ is equivalent to ‘‘B with A,” 
 that “a X 6” is equivalent to “b X a.” But this is necessary 
 only because the fact, which is without order, is represented by 
 symbols with an order. If the fact were originally represented 
 by a group such as (Rab), in which the order of the symbols is 
 irrelevant, its symmetry would be apparent. Therefore, the 
 commutative law in algebra and logic — that (aRb) = (bRa)— 
 says nothing more than that the spatial order of the symbols is 
 irrelevant to their meaning. 
 
 The distinction between subject and object (and between 
 agent and patient) is also carried over to expressions which 
 stand for symmetrical facts; they are represented as if such a 
 distinction were present in them. Thus “‘a is accompanied by b” 
 states a symmetrical fact in asymmetrical form; but it is the 
 same fact as “‘b is accompanied by a,” and to recognize this is to 
 see that no distinction of subject and object (of agent and pa- 
 tient) exists in the fact. The order, which is in this case a certain 
 grouping of the symbols (rather than a spatial order), belongs 
 only to the symbols; the fact is without order. 
 
 Mr. Bertrand Russell describes all relations as having “sense” 
 or direction; no relation, he says, is without a referent and a re- 
 latum.1 This is certainly true for asymmetrical relations; the re- 
 ferent and relatum are what language recognizes as the subject 
 and object. But the assumption that all relations — symmetri- 
 cal and asymmetrical — differentiate their terms as referent and 
 relatum has no foundation in the data of perception. It rests only 
 on the custom of representing all relational complexes by sym- 
 bols with an order; and it obscures the true nature of symmetri- 
 cal relations, for it makes them a special case of asymmetrical 
 ones. The mere fact that a and b are related does not distin- 
 
 1 See B. Russell, The Principles of Mathematics (1903), ch. 9; also, A. N. 
 Whitehead and B. Russell, Principia Mathematica (1910), i, 34. 
 
UNIVERSALS AND INDIVIDUALS 101 
 
 guish 6 from a in any way. Why we should say that a is the rela- 
 tum any more than 6, or b the referent any more than a, is impos- 
 sible to see. A relation is a kind of unity of two terms (or more), 
 and only some relations distinguish, as well as relate, their 
 terms. If it is assumed that all relations have *“sense,”’ it is of 
 course impossible to define a symmetrical relation in any other 
 way than as one which is identical in both of its senses; and this 
 amounts to saying that the distinction of sense (for this sort of 
 relation) is merely symbolic. The more direct way is to represent 
 the fact in the first place by symbols in which there is no distinc- 
 tion of sense, for this makes it clear that symmetrical relations 
 are of a different genus from asymmetrical ones. 
 
 XVI 
 
 The representation of order in a fact through the spatial and 
 temporal order of symbols is open to an ambiguity which is not 
 present when the order is reproduced by the grouping of the 
 symbols. ‘There is no mistaking the meaning of “A is preceded 
 by B” or of “Romeo was loved by Juliet.” One knows that the 
 first of these expressions means the order in which B is the re- 
 ferent and A, the relatum; and that the second means the order 
 in which Juliet is the agent and Romeo is the patient. But the 
 expressions, “‘B precedes A” and “Juliet loved Romeo,” lack 
 this explicitness of meaning; and if we could express the order of 
 the fact in no other way than the latter, we should not know 
 which of the alternative orders was meant. 
 
 The symbols permit two possible spatial arrangements — 
 (aRb) and (bRa) — and the fact, two possible orders; but the 
 question remains, which represents which? The meaning of 
 these groups must therefore be further defined. 
 
 It is understood that “‘B precedes A” has the same meaning 
 as “A is preceded by B;” that “Juliet loved Romeo” has the 
 same meaning as “Romeo was loved by Juliet.” Thus a unique 
 
102 “SYMBOLISM AND TRUTH 
 
 correlation is established, so that one spatial order of the sym- 
 bols means one order of the fact, while the other means the al- 
 ternative order. Without this further definition of the meaning, 
 we should know that “Juliet loved Romeo” stands for a fact 
 composed of Juliet, loved, and Romeo, taken in one of two possi- 
 ble orders — taken in the order opposite to that of the fact 
 meant by “‘Romeo loved Juliet.’’ But neither order of the sym- 
 bols could be attached uniquely to either order of the fact. 
 
 A complete and unambiguous interpretation of the meaning 
 of symbolic expressions requires that the spatial and temporal 
 order of symbols be supplemented, as a means of representing 
 order, by the more accurate and general kind of representation 
 through grouping. (This appears in language as the syntactical 
 rule that the relational subject of a phrase or sentence precedes 
 the relational object, excepting where the subject and object 
 are represented by case endings, or where the sentence is in the 
 passive form.) 
 
 Order then is not an independent factor of logical form which 
 refuses to be assimilated to group structure. The distribution of 
 terms in distinct major or minor groups which make up a whole 
 is their order. A symmetrical relation is one that groups its 
 terms without distinguishing any of them through their mem- 
 bership in sub-groups; and an asymmetrical relation is one that 
 groups its terms so that some of them are distinct not only as 
 terms, but through their membership in sub-groups. The form, 
 (Rabed), is a symmetrical form (the spatial order of the letters 
 being irrelevant), and can be written indifferently, (abcRd) or 
 (aRbcd), etc. Similarly, the form, ((Sa)R(Sb)) is a symmetrical 
 form, and can be written indifferently ((Sb) (Sa)R), ((Sa) (Sb) R), 
 etc. On the other hand, (R(Sa) (Qb)) is an asymmetrical form, 
 and permits the alternative order, (R(Sb) (Qa)), though it can 
 be written indifferently ((Sa)R(Qb)) or ((Sa) (Qb)R), ete., in 
 the one order, and ((Sb)R(Qa)) or ((Sb) (Qa)R), ete., in the 
 
 a 
 
UNIVERSALS AND INDIVIDUALS 103 
 
 other order. Only the simpler types of symmetry and asym- 
 metry have been illustrated, that is, those which arise through 
 dyadic and triadic relations; but the same principles for dis- 
 tinctions of order hold in facts of any degree of complexity. 
 
 XVII 
 
 The distinction between the terms and elements of unity in 
 groups raises the question as to whether a symbolic group may 
 contain more than one symbol of unity and a fact more than one 
 unifying element. Is every unifying element the center of a 
 single group? 
 
 In cases where simplicity of statement is desired, each group 
 is viewed as if it were constituted by a single relation, operation, 
 or quality. This group may enter as a term in other groups, or 
 may contain terms which are themselves groups, but each group 
 — whatever its part in the whole may be — will be constituted 
 by one and only one unifying universal. In the arithmetical 
 expression (2+ 3) X ((4+ 5) — 6), for example, there are 
 several different groups, each with a single element of unity. 
 The groups are piled upon one another, and none contains more 
 than a single operation. But it is not necessary that only a single 
 element of unity should appear in a group. 
 
 A number of qualities, relations, or operations may act to- 
 gether as unifying universals in the same group. Language 
 affords many examples of expressions of this nature. If I say, 
 “he is poor but proud,” I attribute to the subject, not a single 
 quality, but a complex of qualities — “poor but proud.” In the 
 fact, “Boston is near to and north of New York,” the terms are 
 joined, not by a single relation, but by two relations. 
 
 The elements of unity in these facts are complex. They are 
 themselves groups of universals united by universals; they are 
 elements of unity which themselves contain secondary elements 
 of unity. “Poor but proud” has the réle of a single quality and 
 
104 SYMBOLISM AND TRUTH 
 
 “near to and north of” the réle of a single relation. The facts in 
 which they enter are of the forms, (Q@Ra) and (VMbc), where 
 ® and VY represent the secondary elements of unity. Adverbs and 
 adverbial expressions always modify elements of unity — quali- 
 ties, relations, connectives — and give rise to complex elements 
 of unity. When the forms of symbolic expressions and facts are 
 described, the complexity of the elements of unity cannot be 
 neglected if the description is to be complete; for this is a gen- 
 uine aspect of their form. However, for purposes of simplifica- 
 tion, a complex element of unity can be treated as a single uni- 
 versal; and if this assumption is made, the form (Q®@Ra) is the 
 same as (Na), and the form (7 VMbc) the same as (Kbc). But it 
 must not be forgotten that this is an artificial simplification of 
 the structure, and that a full description of the form would not 
 overlook the complexity of the element of unity. 
 
 XVIII 
 
 The present chapter, beginning with the distinction between 
 universals and individuals, has examined the function of univer- 
 sals as elements of unity in facts, and has shown how this func- 
 tion is mirrored by symbols which perform a corresponding 
 function in symbolic groups. 
 
 The individual and the universal are present in all concrete 
 wholes of knowledge, for there is no presented object which is 
 not at once a unique “this” and a “this” with some characters 
 and relations. For finite knowledge, these characters and rela- 
 
 1 The multiplicity of a group, it has been said, is determined by the number 
 of its constituents, that is, the number of its terms plus one; for the element of 
 unity (which, if it is complex, is treated as a single entity) is a constituent 
 though not a term in the group. But in classifying relations as monadic, dyadic, 
 triadic, etc., account is taken only of the number of terms they unite, and 
 thus, according to our definition of multiplicity, a dyadic relation would cou- 
 stitute a triadic group, etc. This is merely a matter of terminology; the multi- 
 plicity of a group could be defined by the number of its major terms rather than 
 its major constituents, so that a triadic relation would constitute a triadic 
 group, etc. 
 
UNIVERSALS AND INDIVIDUALS 105 
 
 tions do not determine the individual; and in this respect spatial 
 and temporal relations are no exception, for the concepts of 
 space and time are built on the perception of the numerical 
 identity and diversity of individuals, and individuals are lo- 
 cated in space and time only by reference to other individuals. 
 Though it is possible to assume, with Leibniz, that an infinity of 
 universals would determine an individual, this assumption is of 
 no aid to finite knowledge. The distinction between the “what” 
 and the “this” continues in its original form. The individual, 
 however, is brought into conception through the use of a varia- 
 ble symbol, to which no value is assigned; but this is the only 
 way in which the individual as such can be thought. Knowledge, 
 in referring to the individual through a symbol of indeterminate 
 meaning, presupposes its own indeterminateness. 
 
 The universal, on the other hand, is presented as an identity 
 in diverse individuals — in changing and different instances. 
 A changeless universal persists in the background of every 
 change. Therefore the universal can be represented by symbols 
 cf fixed meaning, and knowledge in universal terms, that is, law, 
 is freed from the variability which infects all knowledge of the 
 individual. 
 
 Universals fill a unique réle in groups. They are elements of 
 unity and themselves members of the group, but not members 
 codrdinate with the others, which are terms. A relation, a 
 quality, or an operation is not related to its terms; it is one with 
 them, and at the same time distinguishable from them. The 
 unity of a group is its “‘ what,” different universals are different 
 kinds of group-unity, and there is no group which is not such a 
 unity; the concept of group-unity is an indefinable but essential 
 part of the concept of a group. 
 
 Individuals play the part only of terms; without universals 
 they do not enter into wholes; no fact is constituted solely by 
 individuals. But the terms of a fact, as well as its element of 
 
106 SYMBOLISM AND TRUTH 
 
 unity may be universal, in which case the fact will be abstract. 
 Abstract facts are aspects of concrete facts, that is, of facts whose 
 terms are individual; they are separated out from the individ- 
 ualized data of perception. This separation begins in the per- 
 ception of a universal in its instance, and is completed in the 
 realm of conception by the use of symbols which ignore the in- 
 dividual and refer only to the universal apart from any or all in- 
 stances. The problem of abstraction — whether universals can 
 be thought apart from individual instances — is the problem of 
 the objectivity of universals; for if universals are objects, they 
 can be referred to through symbols as single and self-identical 
 things. Nominalism, by attacking the reality of universals, does 
 not disprove their objectivity; if universals are “appearances” 
 or mentally constructed elements in knowledge, they are still ob- 
 jects of knowledge, for such appearances (or mental constructs) 
 are objects of knowledge. 
 
 A general “grammar” of symbolism rests on the distinction 
 between terms and elements of unity. Symbols of terms alone 
 (substantives), or symbols of unity alone (adjectives), cannot 
 constitute significant expressions; and this fact is recognized in 
 all symbolic systems — in language, in mathematics, in logic. 
 Possibility for knowledge is conceivability in a symbolic system; 
 and any possible object of knowledge must be composed both of 
 terms, which may be individual or universal, and of unifying 
 universals. Special plans of syntax mark the limits of conceiva- 
 bility, of possibility, for special systems, and what is possible in 
 one system may have no counterpart in another. Thus no ex- 
 pression that follows the rules of syntax in a system is nonsense, 
 though its meaning may be fantastic or contradictory, and a 
 possible concept may or may not refer to an actual object. 
 
 Rules of order are a special class of rules of syntax. The spatial 
 and temporal order of the symbols is significant in most sys- 
 tems; it reflects an order in the fact. But order can be described 
 
 
 
UNIVERSALS AND INDIVIDUALS 107 
 
 and represented through group structure alone, since an order- 
 ing relation (or operation) is one that both unites and distin- 
 guishes its terms, this distinction arising through the member- 
 ship of the terms in different sub-groups within the whole. 
 Order must be represented through group structure if all am- 
 biguity of interpretation is to be eliminated. 
 
 Finally, the elements of unity in groups may themselves be 
 complex; they may be groups composed of universals united by 
 a secondary element of unity. 
 
 The study of grouping, of the manner in which elements de- 
 termine wholes, both in the fact and in the symbols, is necessary 
 to the understanding of any expression. It is here that nuances 
 of meaning are hidden. Sentences made up of many qualifying 
 adverbs, adjectives, phrases, and clauses are susceptible of 
 subtle shades of interpretation, or misinterpretation, according 
 as they are taken in one or another of several possible groupings. 
 The group structure, the form, is presented in the symbols and is 
 immediately apprehended in its entirety, as is a musical phrase 
 or a visual design. No description of the intellectual processes is 
 better than Plato’s — “the contemplation of forms”’; for forms 
 do not arise without universals, and they are themselves uni- 
 versals, present in thought, through which the mind fastens on 
 its objects. 
 
CHAPTER IV 
 
 DESCRIPTION AND ANALYSIS 
 
 I 
 
 Tere are two ways of referring to objects —by single 
 words or symbols and by descriptions. A description is a phrase 
 such as “the bard of Avon,” “‘an enemy of the people,” “some 
 member of Parliament,” “the divine right of kings.”’ The de- 
 scription may be either ambiguously or unambiguously inter- 
 preted, and it may refer either to an individual or a universal. 
 In any case, it signifies an object through some of the predicates 
 (relations or qualities) of the object, and it is a different form of 
 reference from a single symbol, which might mean the same 
 object. 
 
 Mr. Bertrand Russell, who has thoroughly analyzed the na- 
 ture of descriptions, believes that a description has meaning 
 only in use; that it is an incomplete symbol which, apart from 
 some proposition in which it occurs, is meaningless; ! while on 
 the contrary he believes that single words and proper names are 
 complete symbols; they have significance in their own right, 
 either in or out of a context. Mr. Russell’s theory of descrip- 
 tions rests on a conception of meaning wholly different from the 
 one developed here. It can be shown that descriptions have syn- 
 tactical meaning, whether or not there is an object for which 
 
 1 In the Principia Mathematica of Messrs. Whitehead and Russell, how- 
 ever, the term “descriptive phrase” is used to cover only expressions pre- 
 ceded by “‘the’’; it is merely these expressions which are said to be incomplete 
 symbols, 7. e., to have meaning only in use. For the purposes of unifying and 
 simplifying the present discussion, we shall speak of all phrases preceded by 
 the particles “‘the,” “‘a,” “any,” “some,” “‘all,” “‘each,” and “every,” as 
 descriptive phrases. But it must be remembered that what Mr. Russell says 
 of descriptive phrases, in the Principia Mathematica at any rate, applies only 
 to expressions preceded by “the.” 
 
 
 
DESCRIPTION AND ANALYSIS 109 
 
 they stand, and that their significance does not depend on their 
 context. 
 
 In The Principles of Mathematics, Mr. Russell deals with de- 
 scriptions under the head of denoting phrases. ‘‘The notion of 
 denoting,” he says, “like most notions of logic, has been ob- 
 scured hitherto by an undue admixture of psychology. There is 
 a sense in which we denote, when we point or describe, or employ 
 words as symbols for concepts; this, however, is not the sense 
 that I wish to discuss. But the fact that description is possible — 
 that we are able, by the employment of concepts, to designate a 
 thing which is not a concept — is due to a logical relation be- 
 tween some concepts and some terms, in virtue of which such 
 concepts inherently and logically denote such terms. It is this 
 sense of denoting which is here in question. . . . A concept de- 
 notes when, if it occurs in a proposition, the proposition is not 
 about the concept, but about a term connected in a certain pe- 
 culiar way with the concept. If I say ‘I met a man,’ the propo- 
 sition is not about a man: this is a concept which does not walk 
 the streets but lives in the shadowy limbo of the logic-books. 
 What I met was a thing, not a concept, an actual man with a 
 tailor and a bank account or a public-house and a drunken 
 wife.” } 
 
 Mr. Russell does not here explicitly take the position that the 
 denoting or descriptive phrase has no meaning apart from a 
 proposition in which it occurs; this is a later addition to his 
 thought. But the problem he puts is the one that must first be 
 faced in examining the nature of descriptions. 
 
 The object meant by a description is a term and not a con- 
 cept or mediating entity of any sort; it is a term referred to 
 through universals which cluster about it. The concept means 
 
 1 B. Russell, The Principles of Mathematics, 1903, ch. 5. In a later state- 
 ment on denoting, Mr. Russell abandons the idea of a relation by which con- 
 cepts inherently and logically denote terms and states his theory of descrip- 
 tions without this presupposition. See, Mind, N. S., 1905, xiv, 479 ff. 
 
110 SYMBOLISM AND TRUTH 
 
 the term indirectly through predicates or relations of the term, 
 and it does not mean simply these predicates or relations. “‘The 
 friend of Caesar” does not mean a concept, nor does it mean 
 “*friendship for Caesar”; “a man”’ does not mean ‘‘manhood”’ 
 or “manliness”; “‘an enemy of the people” does not mean 
 “‘enmity for the people.’’ Each of these phrases means that to 
 which the predicates attach; the term is signified through uni- 
 
 versals which modify it. 
 
 lI 
 
 Now universals always appear in instances; they either mod- 
 ify individual terms directly, or modify universal terms which 
 are themselves attached to individuals; and the “relation” in 
 virtue of which some concepts inherently and logically denote 
 some terms is that they refer to universals which are in unity 
 with these terms, so that the terms are ‘‘an instance of” these 
 universals. The unity of fact is such that any predicates which 
 attach, let us say, to Shakespeare are genuine aspects of this in- 
 dividual, whether or not they completely exhaust his individual- 
 ity. “Bard of Avon” is therefore capable of denoting the term 
 with which it has this unity; “‘man” is capable of denoting any 
 individual of which ‘“‘manhood” is a predicate; every reference 
 to a universal or complex of universals is capable, inherently and 
 logically, of becoming a reference to terms. 
 
 A descriptive phrase rests on the knowledge of a fact in which 
 the object described appears as a term. An object known to have 
 such and such predicates or relations can be described as “the” 
 object or “an”’ object of these predicates and relations. The 
 unity of terms with their predicates makes this possible. But the 
 description is not tantamount to a statement of the fact in which 
 the term appears: to say that “Shakespeare wrote Romeo and 
 Jultet” is not to describe Shakespeare as “the author of Romeo 
 and Juliet.” The description is based on a knowledge of the fact, 
 
 
 
DESCRIPTION AND ANALYSIS 111 
 
 and includes a reference to the fact, but it is something other 
 than a statement of the fact. “Shakespeare wrote Romeo and 
 Juliet” means that there is a certain relation between certain 
 terms. “The author of Romeo and Juliet” means one of these 
 terms — Shakespeare; though in meaning this person, it also 
 means in some sense that this person wrote Romeo and Jultvet. 
 
 There seems to be a reason, therefore, for distinguishing be- 
 tween denoting or descriptive phrases and propositions — propo- 
 sitions being references to complex wholes of terms, predicates, 
 and relations, and denoting phrases being references to terms 
 alone, though not without some accompanying subordinate 
 reference to complex wholes in which the terms occur. In the 
 traditional terminology of logic, a description denotes a term and 
 connotes a proposition about this term; “the author of Romeo 
 and Juliet” denotes Shakespeare and connotes Shakespeare’s 
 writing of Romeo and Juliet. But this separation of connotation 
 and denotation throws no light on the problem; it merely dis- 
 tinguishes two sorts of meaning which, once they are admitted 
 as distinct, cannot be brought together under any single concept 
 of meaning. 
 
 Mr. Russell undoubtedly has in mind some such distinction, 
 
 > 
 
 though he does not speak of “‘connoting,”’ when he says: “A 
 concept denotes when, if it occurs in a proposition, the propo- 
 sition is not about the concept, but about a term connected in a 
 certain peculiar way with the concept.” Without doubt the 
 proposition, “I met a man,” is not about the concept “a man” 
 or about ““manhood.” It refers to a person, an individual. Nor 
 is the proposition, “I have seen the portrait of the author of 
 Romeo and Juliet,” a reference to some mediating entity, to 
 some concept, or merely to the authorship of this play; it is 
 about Shakespeare. And yet each of these propositions is about 
 more than a bare term. It is about the term as it is qualified in 
 a certain way, that is, as “‘an”’ instance or “the” instance of a 
 
112 SYMBOLISM AND TRUTH 
 
 predicate. “I met a man” means more than “I met 2x”; it 
 means “I met x and z is human.” “T have seen the portrait of 
 the author of Romeo and Juliet’? means more than “I have 
 seen Shakespeare’s portrait”; it means this, and “that Shake- 
 speare wrote Romeo and Jultet.” If the proposition is not about 
 a predicate taken in abstraction from a term, neither is it about 
 a term taken in abstraction from a predicate. It means the 
 predicate as it is particularized in a term. 
 
 A descriptive phrase cannot, therefore, be distinguished from 
 a proposition on the ground that a proposition means a complex 
 whole while a descriptive phrase means only a single term. A 
 descriptive phrase means, as any complex of symbols means, 
 through the meanings of its elements, and it means a complex 
 whole. It sets up a complex intention, which is a function of the 
 simple intentions of its elements; and although it does not state 
 the fact on which the description is based, it refers to this fact. 
 It is misleading to say that a descriptive phrase denotes a term, 
 and that this exhausts its meaning. The phrase means (and 
 where connoting is not distinguished from denoting, it denotes) 
 the predicates through which the term is described no less than 
 the term; the term could not be signified through predicates un- 
 less the predicates were also signified. 
 
 III 
 
 A descriptive phrase differs from the proposition on which it 
 is based through its form. It is no less a reference to a complex 
 object, to universals as they enter into unity with terms, than 
 the proposition; but its form, unlike that of the proposition, is 
 one in which a term — the term described — takes a central 
 position, so that this term receives an emphasis it would not 
 have in a different structure of the same elements. The term is 
 viewed (is placed in a group) as a subject qualified by certain 
 predicates — predicates which may be simple qualities such as 
 
 
 
DESCRIPTION AND ANALYSIS 113 
 
 “humanity” or a complex set of relations to other terms, such 
 as “‘author of the greatest tragedies in English literature.” The 
 group revolves about the term. At the same time, this term is 
 symbolized by a variable, which in language is presupposed 
 rather than explicitly presented in the symbolism. Thus a de- 
 scription is a variable reference to a particular instance of a uni- 
 versal or of a complex of universals and terms. 
 
 A particular instance of a universal is a “this of some sort”’ or 
 a “this in certain relations”’; it is an object of the form (xR), 
 where R is the universal (or the complex predicate) and z is a 
 term. The particles which precede descriptions inform us that 
 the expression is to be construed as meaning an object of this 
 general structure. ‘‘ The friend of Caesar” is to be interpreted as 
 standing for z as qualified by friendship-for-Caesar; “the author 
 of Waverley” to mean y as qualified by authorship-of-Waverley; 
 “aman” to mean z as qualified by humanity.! But the particles 
 also tell us more than this; they tell us that a variable is present 
 in the symbolism, and that an interpretation for this variable is 
 to be chosen in a certain way. 
 
 A descriptive phrase refers then to a fact or complex object, 
 one of the constituents of which (in language) is not explicitly 
 mentioned in the phrase but is understood through the use of 
 the particle, and this constituent is the term — the zg, y, or z — 
 described. The very omission of the term focuses the attention 
 on it. Such a phrase is, in one sense at least, an incomplete sym- 
 
 1 The central position of the term described can be indicated by writing it, 
 with different typographical stress, both outside and inside the descriptive 
 expression. Thus “‘the friend of Caesar,’ which means an x as modified by 
 the whole complex “‘friend of Caesar,” could be written “the x ((x friend) of 
 Caesar).”’ This shows that the entire expression, as well as the single predicate 
 “friend,” modifies the term described. In our general schematism, this de- 
 scription is of the form (x ((xJ4)Sa) ); that is, the predicate M attaches im- 
 mediately to x, but at the same time z is modified by the whole complex predi- 
 cate of which M is merely one element. In short, the entire structure pivots 
 about x. If the complex predicate ((xM)Sa) is represented simply by R, the 
 form becomes (aR). 
 
114 SYMBOLISM AND TRUTH 
 
 bol, but not in Mr. Russell’s sense. It is incomplete not because 
 it is meaningless outside a context, but because there is no sym- 
 bolic element in it which corresponds to the term described. 
 This element must be supplied in interpreting the expression; 
 and it is always a variable. 
 
 The discussion of the form of descriptive phrases leads first to 
 an examination of the nature of a variable, and secondly to a 
 reéxamination of the concept of the analysis of objects; for a 
 descriptive phrase is analytical (and variable) in meaning, and 
 in this respect it is distinguished from a proper name or a single 
 symbol, which is unanalytical in meaning. 
 
 IV 
 
 Nothing more is known of the term described than that it is a 
 term modified by certain predicates. The x or y which the par- 
 ticle preceding the description permits us to supply is a symbol 
 of whose meaning we are ignorant. It may stand for anything at 
 all. 
 
 “In mathematical logic,’ 
 
 > 
 
 says the Principia Mathematica- 
 ‘any symbol whose meaning is not determinate is called a vara, 
 able, and the various determinations of which its meaning is 
 susceptible are called values of the variable.’ It is apparent 
 that a variable cannot be without meaning, for if this were the 
 case it would not be a symbol; there is no such thing as a mean- 
 ingless symbol. And yet, if the meaning of a symbol is unde- 
 termined, does this not amount to being without a meaning? 
 Apparently there is an important shade of difference between 
 that which is meaningless and that which is indeterminate in 
 meaning. 
 
 The difference is this: if I know that a mark or a sound — or 
 any other presented object — is to be interpreted as a symbol, 
 
 1 Whitehead and Russell, Principia Mathematica, i, 4. 
 
 
 
DESCRIPTION AND ANALYSIS 115 
 
 but do not know what interpretation is to be put on it, this mark 
 or sound is a variable. The phenomenon is analogous to the sig- 
 nificance present in the words of a foreign language incompletely 
 understood. A sufficient number of the words are grasped to 
 enable us to know vaguely what the ones that are not grasped 
 mean; the latter are treated as symbols, and yet they do not 
 have a determinate meaning. Our attitude toward 2, as it 
 appears in the expression, “xz is human,” is exactly this: if the 
 whole is to be significant, x must have a meaning. We are logi- 
 cally compelled to think of x as a symbol, just as we are logically 
 compelled to think of the words which are not understood in the 
 foreign phrase as symbols; but though z is a symbol its meaning 
 is undetermined. 
 
 A variable is therefore indeterminate in meaning because it is 
 uninterpreted. It functions as a symbol because we know — not 
 through knowing its meaning, but on other grounds — that it is 
 symbolic; and yet, being symbolic, it means nothing in partic- 
 ular. 
 
 Variable symbols do not arise in knowledge merely through 
 the accident of ignorance; the analogy of the uninterpreted 
 words in the foreign language is not perfect. Variables are in- 
 troduced for a purpose. We replace the constant “Socrates” in 
 **Socrates is human implies Socrates is mortal’’ by a variable 
 A, and thus achieve generality of reference — “A is human im- 
 plies A is mortal.” Variables are instruments of thought em- 
 ployed for a definite end. But it is essential to this end that no 
 specific reference, no special intention, be attached to the vari- 
 able; it must continue uninterpreted; it must be used with an 
 intended ignorance of its meaning. 
 
 The circumstance which permits the introduction of variables 
 is that symbolic groups have a structure and a meaning as a 
 whole. A variable presupposes a context — a context of inter- 
 preted symbols or a general schematism of symbolic grouping; 
 
116 SYMBOLISM AND TRUTH 
 
 and thus it is the truly incomplete symbol. In this context, the 
 variable, by virtue of being a part of a whole which is taken to 
 be symbolic, is itself taken to be symbolic. The meaning of the 
 whole tends to lend significance to the parts, which have no 
 specific meanings, that is, which arouse no intentions directed 
 toward objects; and this derived (variable) significance is a new 
 and peculiar kind of meaning, different from syntactical mean- 
 ing or from the direct reference to objects through simple sym- 
 bols. Out of its context a variable is meaningless; it is not a 
 symbol and not a variable. In its context it has meaning, for if 
 any group of marks or sounds is construed as being significant 
 as a whole, the elements must also be construed as being signifi- 
 cant. This is a structural necessity. 
 
 Take any significant group of symbols — a phrase, a mathe- 
 matical or logical expression — the elements of which have a 
 determinate meaning, and replace these one after another by 
 elements which in themselves mean nothing. The substituted 
 (and intrinsically meaningless) elements will become variables, 
 and the group as a whole will continue to be significant so long 
 as it is construed as a group. If in the sentence, “San Francisco 
 is in California, and California is in the United States, implies 
 San Francisco is in the United States,” I insert the otherwise 
 meaningless marks, 2, y, and 2, for the proper names, the phrase 
 becomes, “‘z is in y and y is in z implies z is in z”; and 2, y, and z 
 are now variables. The phrase does not lose its meaning as a 
 whole, but becomes less determinate; it becomes more general. 
 But since the words “‘in,” “and,” and “implies” still have a 
 fixed meaning, the statement is determinate for these, and inde- 
 terminate only for x, y, and z. When all of the constituents of a 
 symbolic expression are replaced by variables, the limit of inde- 
 terminateness is reached. The only constant element of meaning 
 that remains is the form, but so long as this form is not destroyed 
 the expression continues to be significant as a whole. Its mean- 
 
 
 
DESCRIPTION AND ANALYSIS 117 
 
 ing is highly general, for it is restricted to no special object, but 
 only to objects which exhibit this form. 
 
 Only the most abstract kinds of thought make use of symbolic 
 groups in which all the constituents are variable and the form 
 alone is constant.! But if a general schematism of grouping — a 
 plan of syntax — is given, so that any group which falls within 
 the plan can be treated as a significant whole, this condition 
 will determine a sufficient framework for the use of variables as 
 instruments of meaning. Thus ((Rab)S(Qdefg)) is a significant 
 complex in which all the constituents are variables, provided the 
 parentheses are taken as signs of grouping, the small letters as 
 symbols of terms, and the capitals as symbols of unity. With 
 these assumptions, this expression is of determinate logical 
 form; but without the minimal context of a symbolic structure, 
 the letters would not be variable symbols, but mere letters. 
 
 The form of the expression in which a variable occurs there- 
 fore places certain general limitations on the interpretation of 
 the variable. Unless the structure is to be destroyed and the sig- 
 nificance of the whole to disappear, some of the constituents 
 must be interpreted as terms and others as elements of unity. 
 There must be some indications in the symbolism as to which of 
 the variables are to be thus construed. In “a is human implies 
 x is mortal,” x must be taken as a term, or substantive; in 
 “Socrates is R implies Socrates is S,’’ R and S must be con- 
 strued as elements of unity, or adjectives. Universals in their 
 adjectival function are not possible values of variable terms, and 
 substantives (either individual or universal) are not possible 
 values of variable symbols of unity.? Without this restriction, 
 any interpretation would be formless and meaningless. 
 
 1 See ch. VII for an example of such a system and for a discussion of “func- 
 tional” variability, which is different from the “interpretational”’ variability 
 here treated. 
 
 2 This is the idea which lies behind Messrs. Whitehead and Russell’s 
 theory of types. See Principia Mathematica, vol. i, ch. 2 of the Introduction. 
 
118 SYMBOLISM AND TRUTH 
 
 Aside from this general limitation imposed by the form, the 
 variable can stand for any object, or it can be given a meaning 
 which is a reference to no existent object; it can be defined as 
 equivalent to a symbolic group which stands for nothing. The 
 x in “I saw x yesterday’ may mean “‘the prince of fairies”; the 
 y in “‘y is human implies y is mortal”? may mean “the devil” or 
 “the god Pan.” } 
 
 However the variable is interpreted, it must be interpreted 
 univocally; otherwise the principle of identity would be violated. 
 The same symbol can have one and only one meaning; and if an 
 undetermined z is construed in one way in one context, and in 
 another way in another context, it is not the same symbol. In 
 “x is human implies z is mortal,” the two 2’s, if they are given 
 values, must be given one value. In the Principia Mathematica, 
 this is stated as the special principle of “the identity of the 
 variable’’; but this principle is not different from the law of 
 identity in its most general form as a principle of symbolism. 
 If x is the same symbol as x, whether its meaning be constant or 
 variable, the two must have a single meaning. For this reason — 
 that a symbol can stand only for a single (self-identical) object 
 — an ambiguous expression such as “a man,” in “I met a man,” 
 can mean one and only one individual if it is interpreted, but, 
 being uninterpreted, it does as a matter of fact mean no indi- 
 vidual. This raises the question of the ambiguity of the variable. 
 
 1 The borrowed significance of the variable symbols in knowledge is much 
 like that of the nonsense words in Lewis Carroll’s “‘O frabjous day! Callooh! 
 Callay! He chortled in his joy.” And if one gives way to the inevitable drift of 
 significance which is present in these nonsense verses, he finds himself treating 
 “‘chortled” and “‘frabjous” as variables — as words which must have a mean- 
 ing; he is left free to interpret them as he chooses, provided he remains within 
 the structure of the groups. “‘Frabjous” is evidently an adjective, and “chor- 
 tled”’ a verb; this is fixed by the logical form. But the charm of the verse is 
 
 that nothing more is fixed; within these limits the words might mean anything 
 whatsoever. : 
 
 
 

 
 DESCRIPTION AND ANALYSIS 119 
 
 V 
 
 Psychological ambiguity or equivocation is the use of a word 
 in several senses at once, that is, with a number of different 
 intentions; and it is distinguished from the univocal use of 
 words, which is their use in one sense only, that is, with a single 
 intention. Clearly, logical ambiguity is not equivocation. A vari- 
 able does not actually set up an intention; it actually has no 
 reference until it is interpreted. It is ambiguous in the sense 
 that it is susceptible of many interpretations, it can be taken to 
 stand for many different objects or its value can be defined in 
 many different ways, though none of these values is necessarily 
 its interpretation. An equivocal symbol, on the other hand, is 
 susceptible of no interpretations but the ones that already go 
 with it. Each of its interpretations is a constant reference and 
 some one of them must be taken, in any case, as the meaning. An 
 equivocal symbol is never variable. Consider this Shakespearean 
 pun: “Adam was the first that ever bore arms. The Scripture 
 says, he digged: could he dig without arms?” ! “‘Arms” is not a 
 variable, it is not equivalent to an 2; if it had no determinate 
 meanings, there would be no pun. 
 
 Thus a variable is ambiguous — is open to many interpreta- 
 tions — for the same reason that it is a variable, that is, because 
 it is actually uninterpreted. Its values are “possible interpreta- 
 tions”; they are objects which might be but are not meant, or 
 intentions which might be but are not aroused by it. The psy- 
 chological effect of a variable, e¢.g., in “I saw x yesterday,” is to 
 cause one to run over in his mind a number of meanings which 
 could be attached to # and still allow the sentence to be signifi- 
 cant as a whole; but the mind stops at none of these, for x does 
 not mean some one of them. These meanings are possible inter- 
 pretations of x; x has no actual interpretation. 
 
 1 Hamlet, act V, scene 1. 
 
120 SYMBOLISM AND TRUTH 
 
 The variable may be treated, however, as if it had only one 
 possible value, and in this case it will not be a means of generali- 
 zation, as it is when it has many possible values. It will be a 
 variable with a constant (though undetermined) value, an un- 
 ambiguous variable. And this is the difference between the 
 
 99 66 
 
 meaning of “the” and of “a,” “an,” “any,” and “some.” 
 
 These particles, which precede descriptive phrases, are signs 
 of interpretation. They do not signify constituents of the fact (if 
 the expression stands for a fact), but they mean that a variable 
 is present and that this variable is to be interpreted in a certain 
 way. Each of the particles indicates a different manner of inter- 
 pretation.1 
 
 The particle “the” signifies that there is only one possible 
 value of the variable. The meaning of the description, “the cen- 
 ter of gravity of the solar system,” is x as modified by this com- 
 plex predicate, where it is understood that there is one and only 
 one possible a. But how can a variable have no more than one 
 possible value and remain a variable? Does it not then become 
 a constant? Clearly it does not, for the z is a variable so long as 
 that single value is undetermined. If one says that “‘the center of 
 gravity of the solar system is a constant,” he does not mean that 
 this object is determinately (invariably) referred to; he means 
 that there could be no more than one object which this descrip- 
 tion signifies. (The particle “the” is sometimes used as equiva- 
 lent to “‘a.”’ We say that “Brutus was the (a) friend of Caesar, 
 and Anthony was the (a) friend of Caesar,’ where we do not 
 mean that either was the only friend. This is a loose use of 
 “the”, and it is evident that in the phrase, “the center of 
 gravity of the solar system,” it is not to be construed in the 
 sense of “a.” 
 
 99 66 99 66 
 
 The particles “a,” “an,” “any,” and “some,” on the other 
 
 1 “Every” and “‘each”’ must be treated separately since they involve the 
 idea of “‘all,”’ that is, of reference to a class. 
 
 
 
DESCRIPTION AND ANALYSIS 121 
 
 hand, precede descriptions in which the variable is to be am- 
 biguously construed, that is, as susceptible of many possible 
 meanings; and this is the sole difference between a description 
 such as “‘the bard of Avon” and “a bard of the sixteenth cen- 
 
 39 
 
 tury.” Both expressions are of the general form (xR), though x 
 is not explicitly given in the symbolism; both refer through an 
 undetermined symbol to a term as it is modified by a complex 
 predicate. But the one specifies in advance that the variable has 
 only one possible value, while the other specifies that it has many 
 possible values. The one is an indeterminate but unambiguous 
 reference, the other, an ambiguous (and therefore indetermi- 
 nate) reference to a term. 
 
 A description introduced by the particle “a” or “an” can be 
 construed as if it meant either “any” or “‘some”’; but if the 
 particle “any” or “some”’ is present, a further condition of in- 
 terpretation is added to the general condition of ambiguity 
 which is signified by “a” and ‘“‘an.”’ If I say, “‘a woman has the 
 same right to education as a man,” I mean any woman and any 
 man; but if I say, “I saw a woman and a man on the street 
 yesterday,’ I do not mean any woman and any man; I mean 
 some woman and some man. And either of these unexpressed 
 
 ce 99 
 
 meanings can be read into a description prefaced by “‘a”’ or 
 peatits « 
 
 The particle “any” indicates that a value chosen as the in- 
 terpretation of the variable must be chosen at random from 
 among the possible values; there must be no principle of selec- 
 tion. Thus “any man” means “a man” where there is no rea- 
 son to suppose that one of many possible interpretations is pre- 
 ferred to another. ““Some man,” on the other hand, means ‘‘a 
 man” where the interpretation is not chosen at random, but by 
 some principle of selection not stated. “‘Some” is the antithesis 
 of “any,” though both are ambiguous manners of reference, 
 that is, the phrases in which they occur may have many differ- 
 
122 SYMBOLISM AND TRUTH 
 
 ent values. But “some” differs from “‘any’’ in implying a specific 
 condition according to which the value is to be chosen. “Any” 
 implies that there is no such condition. 
 
 If I say, “Some man is your friend,” I am speaking ambigu- 
 ously. There are many possible values of “some man’’; and yet 
 I do not mean that “any man is your friend,” for it is assumed 
 that the choice is limited in some way. What I mean is: ““Some 
 man is your friend, and not any man, because you care only for 
 good men,” or “‘because your tastes in friends are not catholic,” 
 etc. There is a presupposed but unexpressed condition of choice. 
 And if I say, ‘“‘Not some man, but any man, is your friend,” the 
 implication is exactly the opposite: that there is no condition of 
 selection.! 
 
 Whether a descriptive phrase be ambiguously or unambigu- 
 ously interpreted, whether it be preceded by “the,” “a,” “any,” 
 or “some,” it must, if it is assigned a meaning, be given one and 
 only one meaning; it must be univocally interpreted, otherwise 
 the principle of identity would be violated. And this is the para- 
 dox of the variable: that, being capable of many possible deter- 
 minations (excepting when it is preceded by “the”), being an 
 instrument of generality of reference, it must, nevertheless, be 
 given no more than a single meaning, if it is given a determinate 
 meaning. . 
 
 VI 
 
 A term described need not be an individual. ‘‘The divine 
 
 99 66 
 
 right of kings,” “the royal color,” are variable (and unambigu- 
 
 ous) references to universals; while “‘a talent for music,” “any 
 
 33 66 
 
 love of beauty,” “some hope of immortality,” are variable (and 
 ambiguous) references to universals. 
 Universals no less than individuals are instances of universals; 
 
 1 “Some” carries no reference to existence as a necessary part of its mean- 
 ing; it is not to be distinguished from “any” in this respect. “Some angel’s 
 soul” does not mean that “there exists an angel’s soul.” 
 
 
 
DESCRIPTION AND ANALYSIS 123 
 
 and for this reason, they can be described through their predi- 
 cates and relations. A universal need not be particularized in in- 
 dividuals alone; it can be particularized in other universals, 
 which are in their turn particularized in individuals. The uni- 
 versal described is referred to in abstraction from any or all of its 
 individual instances; it becomes the value of z in the description. 
 This x, being a term however, will mean the universal in its sub- 
 stantive rather than in its predicative or relating form. “The 
 divine right of kings” means (unambiguously) a right of a pe- 
 culiar sort; “any interest of mankind’’ means (ambiguously) 
 an interest of a special sort; but neither means an individual. 
 
 A described universal is thus signified through a variable ex- 
 pression, as is a described individual; but a universal is no more 
 completely determined for thought through description than is 
 an individual. A description of “friendship” to a man who had 
 not had a friend, or of “color” to a man who had not seen 
 color, would contain a residuum of uninterpreted meaning which 
 could not be eliminated by description alone. And yet univer- 
 sals differ from individuals in that they can be known as spread- 
 _ ing out through many perceptual wholes; they can be identified 
 and re-identified as persisting elements in the process of change; 
 they can be distinguished and redistinguished from other uni- 
 versals. But once an individual has passed from perception, it 
 cannot be again identified as the same individual. This is why 
 universals can be determinately referred to through single 
 words, if not through descriptions. Every universal, since it is 
 self-identical, — itself and nothing else, —has its distinctive per- 
 ceptual flavor; description points the way, but does not take 
 the place of the presentation of these universal objects. 
 
 Vil 
 
 There is an apparent line of separation between descriptions 
 and proper names or single symbols, and in Mr. Russell’s theory 
 
124 SYMBOLISM AND TRUTH 
 
 this separation becomes extreme. Mr. Russell believes that 
 proper names (or single symbols) have meaning both in and out 
 of a context, while descriptions have meaning only in a context. 
 
 “By an ‘incomplete symbol,’” says the Principia Mathe- 
 matica, “we mean a symbol which is not supposed to have any 
 meaning in isolation, but is only defined in certain contexts. . . . 
 This distinguishes such symbols from what (in a generalized 
 sense) we may call proper names. ‘Socrates,’ for example, stands 
 for a certain man, and therefore has meaning by itself, without 
 the need of any context. If we supply a context, as in “Socrates 
 is mortal,’ these words express a fact of which Socrates himself 
 is a constituent. But in other cases this simple analysis fails.” } 
 These are the cases in which a phrase such as “the author of 
 Waverley’’ is employed. Such expressions in themselves are 
 meaningless; they have meaning only in use. 
 
 This theory is contrary to ordinary interpretations of lan- 
 guage. “The author of Waverley” is capable of standing on its 
 own feet as a significant symbol; one feels no need of a context 
 to give it a meaning. The phrase is used in speech as if it were 
 equivalent to the proper name “Scott,’’ and like the proper 
 name, it is construed as significant both in itself and in a con- 
 text. Mr. Russell’s view is not supported by common sense or 
 usage; it is proved by a number of ingenious arguments which 
 raise fundamental questions as to the nature of meaning. An 
 examination of these arguments discloses a wholly different way 
 of distinguishing between descriptions and proper names (in a 
 generalized sense).“The former are analyzed references or mean- 
 ings; the latter, unanalyzed references. Neither depend on their 
 contexts for significance. At the same time, we discover that a 
 reference to an individual through a proper name is no more 
 determinate than a reference to an individual through a descrip- 
 
 tion. 
 1 Whitehead and Russell, Principia Mathematica (1910), i, 69. 
 
 
 
DESCRIPTION AND ANALYSIS 125 
 
 One of Mr. Russell’s most plausible arguments for the view 
 that descriptions have meaning only in use is the following: 
 “Take, for example, the following proposition: ‘Scott is the 
 author of Waverley.’ This proposition expresses an identity; thus 
 if ‘the author of Waverley’ could be taken as a proper name, and 
 supposed to stand for some object c, the proposition would be 
 ‘Scott is c.’ But if c is anyone except Scott, the proposition is 
 false; while if ¢ is Scott, the proposition is ‘Scott is Scott,’ which 
 is trivial, and plainly different from ‘Scott is the author of 
 Waverley.’” * The conclusion is that “‘the author of Waverley’ 
 cannot mean the same as ‘Scott,’ or ‘Scott is the author of 
 Waverley’ would mean the same as ‘Scott is Scott,’ which it 
 plainly does not; nor can ‘the author of Waverley’ mean any- 
 thing other than ‘Scott,’ or ‘Scott is the author of Waverley’ 
 would be false. Hence ‘the author of Waverley’ means nothing.” 
 Such expressions have a meaning in use, but not in isolation. 
 In use, e.g., in the proposition, “Scott is the author of Wav- 
 erley, “the phrase becomes significant when the proposition is 
 understood to mean “‘x wrote Waverley’ is always equivalent 
 to “x is Scott.’” | 
 
 There is no doubt that propositions in which descriptive 
 phrases occur can be translated into propositions in which these 
 phrases do not occur. A descriptive phrase can always be elim- 
 inated. But this is a symbolic device, and not a proof that the 
 descriptive phrase in itself has no meaning. Usage holds that 
 “Scott”? means the same as “‘the author of Waverley,” that both 
 are significant in isolation from a context, and that “Scott is the 
 author of Waverley” is not, on this account, either a trivial or 
 false proposition. Common usage employs a descriptive phrase 
 interchangeably with a proper name which it takes to stand for 
 the same object, and common usage can be defended. 
 
 The judgment, “Scott is the author of Waverley,” is analytic 
 
 1 Op. cit., p. 70. 
 
126 SYMBOLISM AND TRUTH 
 
 in form. It is of the form, « = (yR), which expresses an identity 
 of meaning between two symbols, or two concepts. But the sym- 
 bol on one side of the identity (if it refers to an object) refers to 
 the object as a single and unanalyzed thing, while the symbol on 
 the other side refers to it as a group of elements — as a complex 
 whole which can be broken up into parts. By substituting x for 
 (yR), which must be possible if these are identical in meaning, 
 the identity x = x can be derived, and this is trivial: it is the 
 law of identity, which is presupposed in the use of x as a symbol. 
 But this does not necessitate the conclusion that either z means 
 something other than (yR) or (yR) is meaningless. The conclu- 
 sion to which it does lead is this: that « (if it means an object) 
 means the same object as (yf), but means it in a different way; 
 that the same object can be meant in two different ways, that is, 
 it can be referred to analytically or unanalytically; and that the 
 exhibition of an analysis — or of different analyses of the same 
 object — is never trivial. If “Scott is the author of Waverley” is 
 either trivial or false, on the usual interpretation of these sym- 
 bols, the equation 2 + 2 = 4 is also trivial or false, for it is an 
 analytic judgment of the same general form. It asserts that 
 what is meant by the complex 2+ 2 is the same as what is 
 meant by the symbol 4; it permits the substitution of 4 for the 
 complex 2 + 2, and yields the identity 4 = 4.7 
 
 Vit 
 
 The judgment is accused of being trivial because it seems not 
 to be synthetic; it seems to add nothing to its subject through its 
 predicate. But a judgment which is analytic in form can be syn- 
 thetic in effect, when one side of the identity expresses an analy- 
 sis of what is represented on the other side without analysis (or 
 through a different analysis). 
 
 1 This assumes that the equations of arithmetic represent identities, which 
 is, we believe, the correct view. 
 
 
 
DESCRIPTION AND ANALYSIS 127 
 
 Single words or symbols can mean a great deal more than we 
 are explicitly aware that they mean, and this is because we can 
 refer to an object as a whole without referring to the parts or 
 aspects of the object. To describe an object, which is originally 
 signified by a single word, is to add to our knowledge a knowl- 
 edge of the fact that the object is composed of elements. To 
 signify the same object in these two different ways is expressly 
 to state that the object has certain lines of structure, that a cer- 
 tain analysis of it is possible. Now one can be aware of an object 
 without expressly representing to himself its lines of structure, 
 its possible analyses. Therefore, such a judgment of identity, 
 though it takes the analytic form, x = (yR), is synthetic in 
 effect. It asserts more than x = x. Statements of identity that 
 present an analysis of what is meant without analysis by a single 
 symbol are the only means by which indefinite concepts can be 
 made definite, the only way in which meanings can be defined. 
 
 But is a description an analysis? If analysis is breaking up an 
 object into its parts, is not the discovery that an object is an in- 
 stance of a universal, or that a certain description fits it, some- 
 thing other than analysis? 
 
 I can analyze an object into parts, a, b, and c, which are re- 
 lated in a certain way. I can discover that my ink-well is com- 
 posed of a small glass jar with a glass cover, and this seems to be 
 genuine analysis. But if I find that the ink-well is black and that 
 it is on the table, I am discovering relations and qualities which 
 attach to it, and these do not seem to be parts in the same sense. 
 And if I now describe it as “‘a black object on the table,” I do 
 not appear to be analyzing the ink-well. 
 
 This is a superficial distinction. Whether its blackness and its 
 position on the table are “parts”’ of the ink-well depends on the 
 point of view. These may be, on one definition, external to the 
 object and, on another definition, internal to it. If by “the ink- 
 well”? I intend the bare z, the individual term — what Locke 
 
128 SYMBOLISM AND TRUTH 
 
 would have called its “‘substance”” — then the fact that it has a 
 glass container and a small glass cover is as external to it as the 
 fact that it is black and on the table. But I can mean by “the 
 ink-well”’ either the individual, the z alone, to which certain 
 predicates attach, or I can mean the individual taken with more 
 or fewer of its predicates and relations. And this is possible be- 
 cause the individual, though it may not be completely deter- 
 mined by its predicates and relations, is continuous with them. 
 They enter into the individual. Any predicates or relations of an 
 object are “parts” of the object in a logical sense, for they par- 
 tucipate in the object; and when the object is described, it is 
 analyzed as a complex whole in which these qualities and rela- 
 tions are elements. The bare individual, the x, of which the 
 predicates and relations hold, becomes one element along with 
 others. 
 
 Description is then analysis, but it may be analysis which 
 leads to an enlargement of concepts — of the meanings of single 
 words or ideas, or of groups — through the discovery of new 
 characters and relations that can be included in the definition. 
 If I make the judgment, “Scott is the author of Waverley,” in 
 ignorance of the fact that Scott wrote Waverley, what this judg- 
 ment tells me is that I can enlarge my concept of Scott to in- 
 clude the authorship of Waverley. I must so enlarge my concept 
 if the judgment is to be true; for if I do not now mean the same 
 thing by “Scott” as by “the author of Waverley,” Iam certainly 
 in error. 
 
 The meaning of a single symbol can be indefinitely expanded 
 to take in more and more of the predicates and relations of an 
 object, so that judgments of the form, x = (yR), continually 
 widen knowledge by giving new definitions, new analyses, of 
 
 * This explains the surprise of George IV (mentioned by Mr. Russell) when 
 
 he learned through a mere statement of identity that Scott was the author of 
 Waverley. 
 
 
 

 
 DESCRIPTION AND ANALYSIS 129 
 
 concepts which have hitherto been used with a restricted or un- 
 analyzed meaning. 
 
 IX 
 
 The most restricted possible concept of an individual is that 
 of an x—a mere “this” — devoid of all characters and relations, 
 a concept which is framed only by abstraction from the con- 
 crete, qualified, and related data of perception. Scott, though a 
 single word is used to refer to this person, is a complex object. 
 He has many aspects beyond his bare individuality, he is an in- 
 dividual of this sort or that sort, and this has been shown to be 
 true of all individuals. Every individual is a vortex of characters 
 and relations. When one uses a proper name for an individual, 
 he cannot in the beginning mean an z, shorn of all relations and 
 characters, for no such thing comes into experience to be named. 
 “Scott,” at the very least, originally means an («R), a complex 
 of predicates individualized in a term. Thus, from the outset, a 
 proper name is equivalent in meaning to a minimal description 
 of the object to which it is applied. Though the bare individual 
 is an element in the whole, it is the whole which is named, and 
 not the individual alone. To break up this whole and take the 
 meaning of the proper name to be the z to which the characters 
 and relations attach, and only this, is to reduce the significance 
 of the name to that of an z. “Scott,” if it means merely the indi- 
 vidual, a “‘this” which is distinct from all other individuals and 
 absolutely unique, is a variable; and the fact that the name is 
 treated as if it had one, and only one interpretation, does not 
 eliminate this indeterminateness, for it does not tell us what 
 this interpretation is. 
 
 No view of knowledge is more inadequate than an extreme 
 nominalism, which holds that individuals can be picked out, 
 apart from their characters and relations, and referred to 
 through determinate concepts, or given distinctive names. And 
 
130 SYMBOLISM AND TRUTH 
 
 yet the opposite extreme is equally inadequate, vzz., that the 
 individual, or any other object, is nothing but its characters and 
 relations. The attempts to reduce terms (whether individual or 
 universal) to their predicates and relations, and the inverse — 
 to reduce predicates and relations to their terms — are destined 
 to failure because they destroy the logical frame-work of fact. 
 The theory of “internal relations” cannot show that terms can 
 be dispensed with in describing the world, without abolishing 
 all distinctions and all description. If all relations and predi- 
 cates completely absorb their terms, everything becomes one 
 and indistinguishable. But it is possible to interpret the “‘inter- 
 nality of relations” in another way. The wholeness of fact is 
 such that the element of unity — the predicate or relation — 
 enters into the terms as well as into the fact. This unity of the 
 terms with the predicate or relation leaves both distinct for 
 knowledge; it is not inconsistent with the externality or dis- 
 tinctness of terms and relations which is necessary to logical 
 structure. But at the same time, the unity of predicates with 
 their terms makes it possible to include in the definition or de- 
 scription of a term a reference to more or fewer of its predicates 
 and relations. 
 
 Where, it will be asked, does this extension of concepts 
 through the description of objects by new characters and rela- 
 tions end? It would seem that a meaning must eventually be- 
 come coextensive with all the predicates of the object meant, 
 that “Scott” or any other name must finally mean an object 
 taken with an indefinite number of predicates. No characters or 
 relations of the object would then be external to the meaning. 
 This would be the necessary outcome of broadening a concept 
 to its utmost possible limits. The name “Scott” would then 
 signify anything which could be said about the individual, Scott; 
 so that any judgment into which “Scott” entered would be- 
 come analytic and trivial in Mr. Russell’s sense. 
 
 
 
DESCRIPTION AND ANALYSIS 131 
 
 X 
 
 Just as a judgment may be analytic in form and synthetic in 
 effect, so a judgment may be synthetic in form and analytic in 
 effect. Judgments such as “‘z has the relation R to y,” where R 
 is not identity, or “x has the quality Q,” are, in general, taken 
 to be synthetic, to add something to their subjects through their 
 predicates. But if the meaning of'z already includes the relation 
 R to y or the quality Q, the judgment is synthetic in form only. 
 Its effect is analytic. Thus Kant’s example of an analytic judg- 
 ment, vzz., “body is extended,” is synthetic in form but analytic 
 in effect because the attribute of extension is by definition 
 
 included in the meaning of the term “body.” If I mean by 
 
 “Scott,” among other things, “the author of Waverley,” then 
 the seemingly synthetic proposition, “Scott wrote Waverley,” is 
 analytic in effect. 
 
 Whether the predicate of a judgment adds something to what 
 is meant by the subject depends, therefore, on what one means 
 by the subject. This is why “Scott is the author of Waverley”’ or 
 any similar statement of identity can convey more to the mind 
 than “Scott is Scott,’ and why “body is extended” or “Scott 
 wrote Waverley” can convey no more than “body is body” or 
 “the author of Waverley wrote Waverley.” 
 
 It is only because we do not know (analytically) what we can 
 mean by a proper name or single word, or because we use them 
 with a deliberately restricted meaning, that any judgments are 
 synthetic in effect. Ignorance is the great restricter of mean- 
 ings, and ignorance renders certain properties external to ob- 
 jects, which on different definitions of these objects, become 
 internal to them. One usually means by a word something 
 less than an object with all its possible predicates and relations, 
 and so the object can be viewed as entering into new relations 
 and acquiring new predicates. “Napoleon conquered Europe” 
 
132 SYMBOLISM AND TRUTH 
 
 shows Napoleon in a new réle, and is a synthetic judgment 
 (both in form and in effect), if one does not include “‘conqueror 
 of Europe” in the meaning of the name “Napoleon.” But this 
 is an arbitrary or accidental restriction of the meaning. 
 
 What has been said of the analysis of the meaning of proper 
 names is true also of single words which stand for universals. A 
 universal can be described, or it can be represented by a single 
 word. The description means the same thing as the single 
 word, but means this analytically, while the word means it un- 
 analytically. The word is capable of being extended or con- 
 tracted in meaning to take in more or fewer of the predicates 
 and relations of the universal meant. A word which signifies a 
 universal may enter in judgments of synthetic or analytic form, 
 and these judgments will be synthetic or analytic in effect ac- 
 cording to the interpretation put on the word. 
 
 That single symbols (proper names in a generalized sense) 
 can mean the same objects as descriptions, and that the state- 
 ment of such identities of meaning is highly fruitful for knowl- 
 edge, rather than trivial, are, then, the consequences of this 
 view of description as analysis. It follows, also, that proper 
 names (in the more restricted sense of this term), if they mean 
 bare individuals, are of no more use to thought than 2’s and y’s 
 whose values are not known. And even when their meanings are 
 wider than such references to bare individuals, proper names 
 give us no more determinate, or invariable, knowledge of indi- 
 viduals than do descriptions. Whatever can be referred to 
 through invariable symbols is universal. Aristotle himself, to 
 whom individual substances were the sole realities (God only 
 being excepted), believed that universals alone were the objects 
 of screntzfic knowledge. What can be said of individuals must be 
 said in universal terms, and only when reference to individuals 
 is dropped is knowledge completely freed from variability of 
 meaning. Completely determinate knowledge is of universals 
 
 
 
DESCRIPTION AND ANALYSIS 133 
 
 and their connections. Hence perceptual knowledge is never 
 completely determinate, never wholly compressed into the con- 
 cepts of invariable meaning which function in perception; and 
 yet it is the only concrete knowledge, that is, the only knowledge 
 in which the individual merges with the universal. Complete 
 conceptual determination and concreteness do not go together; 
 what is completely determined for conception is never concrete, 
 and what is concrete is never completely determined in con- 
 cepts. 
 
 XI 
 
 Knowledge in universal terms tends to become analytic in 
 form, for here, as elsewhere, concepts enlarge themselves by in- 
 cluding more and more of the predicates and relations of the 
 universal meant. To the layman, water is something wet, color- 
 less, tasteless, and odorless; if he were asked to define it, he 
 would describe it in this way. But if he studies chemistry, he 
 finds that water is made up of hydrogen and oxygen in definite 
 proportions, and his concept must be enlarged by the judgment 
 that “water is H.0,” a judgment of analytic form but synthetic 
 effect. He will discover that water boils at 212° Fahrenheit under 
 atmospheric pressure, and at lower temperatures under lower 
 pressures, etc.; and these facts, together with countless others, 
 must be included in his concept. In the end his concept of water 
 will completely sum up his knowledge of it. The word “water’”’ 
 will mean all that water is known to be and do, and a judgment 
 about water, ¢.g., that water boils at 212° Fahrenheit under at- 
 mospheric pressure, will tell him no more than is included in his 
 concept. It will be an analysis of this concept. 
 
 Thus the chemist, if he discovers a property or law which is 
 “external to” water as he conceives it, will straightway take this 
 property or law into the meaning of the term. But in addition, 
 there will always remain a perceptual “somewhat” to which the 
 
134 SYMBOLISM AND TRUTH 
 
 name “water” belongs, and this “somewhat” will be spread out 
 in numberless individual instances. But the evasive element of 
 individuality will never be a part of the meaning of the universal 
 term. The concept will include much that can be known only by 
 inference from the perceptual properties of water; these inferred 
 properties, ¢.g., molecular and atomic structure, etc., will also 
 be described in universal and invariable terms. 
 
 A science becomes analytic in form for this reason: it tends so 
 to broaden its concepts of a subject-matter, originally given in 
 perception, that an analysis of what is meant by these concepts 
 states the laws of the science. The subject-matter is defined as 
 that which follows the laws; anything which does not obey the 
 laws is not included in the scope of the science. Thus matter, 
 originally in perception something solid and extended, becomes 
 anything that conforms to a certain set of principles — physical 
 principles; and mind becomes anything that conforms to an- 
 other set of principles — psychical principles. 
 
 The drift toward the analytic form is especially evident in the 
 mathematical sciences. Crude perceptions of a spread-out and 
 diversified something called “space” are enlarged by the dis- 
 covery of principles which can be exactly stated in universal 
 terms, and which can be interpreted as referring to these percep- 
 tions. “Space” is finally conceived as that system of objects 
 which obey geometrical axioms and postulates; and, when 
 space is thus defined, to say that space conforms to geometrical 
 laws is to say merely that “space is space.” If different sets of 
 axioms and postulates which can be equally well interpreted by 
 the original experience are discovered, these axioms and postu- 
 lates will define different kinds of space — Euclidean, and the 
 numerous varieties of non-Euclidean space. Thus it becomes a 
 trivial and analytic statement to say, e.g., that the parallel pos- 
 tulate holds for Euclidean space, for Euclidean space is defined 
 through this postulate and others. But to say that this postulate 
 
 
 

 
 
 
 DESCRIPTION AND ANALYSIS 135 
 
 holds for space as such is to raise the question as to whether the 
 Euclidean analysis of space is the true analysis, and so to force 
 a choice between this type of geometry and other types. The 
 judgment, “Space as such is Euclidean space,” though analytic 
 in form, is not a trivial statement of identity. It purports to add 
 something to knowledge by showing that what we originally 
 meant by “space” is truly analyzed by the Euclidean axioms 
 and postulates. This judgment is synthetic in effect and can be 
 proved or disproved by experience. 
 
 A science which assumes the analytic form does not lose its 
 experiential content, and this is no less true of the mathematical 
 sciences than of the physical, biological, or psychological sci- 
 ences. Number and space, though they may be defined through 
 the laws of arithmetic and geometry, are still objects (univer- 
 sals) met with in experience. A “‘science” which had no point of 
 application in presented objects would not be a science, but an 
 uninterpreted or partially interpreted system of symbols (or 
 concepts). The description of the subject-matter given in the 
 laws, the postulates and axioms, must be anchored in experi- 
 ence; the variable terms, the z’s and y’s, described must mean 
 something apart from the descriptions in which they appear. 
 Thus if Euclidean space is simply the x which the postulates of 
 Euclidean geometry describe, one does not know fully what this 
 z is. There may be many different objects, e.g., certain series of 
 numbers, etc., which are possible values of this x. These postu- 
 lates become the laws of space only when they are interpreted 
 by the spread-out and diversified something called “space.” 
 The only reason why one can speak of the postulates of Eu- 
 clidean or non-Euclidean geometry as postulates of geometry is 
 that they are rooted in an original experience of space. 
 
 An uninterpreted or partially interpreted system of concepts 
 is merely the possibility of a science. It becomes an actual sci- 
 ence only when it is taken to be a description (or an analysis) of 
 
136 SYMBOLISM AND TRUTH 
 
 some field of presented objects. The fact therefore that a science 
 tends to become analytic in form does not free it from the neces- 
 sity of binding itself to experience by a synthetic judgment — a 
 judgment which conveys the information that the subject- 
 matter as perceived is the subject-matter as described. 
 
 XII 
 
 A second argument by which Mr. Russell supports his theory 
 that descriptive phrases are without meaning excepting as they 
 occur in a context, brings up the problem of “‘reference to the 
 non-existent,”’ that is, of how symbols can be used significantly 
 when there is no object which they mean. 
 
 “Suppose we say: ‘The round square does not exist.’ It seems 
 plain,” says Mr. Russell, “that this is a true proposition, yet we 
 cannot regard it as denying the existence of a certain object 
 called ‘the round square.’ For if there were such an object, it 
 would exist: we cannot first assume that there is a certain ob- 
 ject, and then proceed to deny that there is such an object. 
 Whenever the grammatical subject of a proposition can be sup- 
 posed to be meaningless without rendering the proposition 
 meaningless, it is plain that the grammatical subject is not a 
 proper name, that is, not a name directly representing some ob- 
 ject. Thus in all such cases the proposition must be capable of 
 being so analyzed that what was the grammatical subject shall 
 have disappeared.” ! And this argument is carried still further: 
 the Principia Mathematica asserts that a function (a predicate) 
 which is universally true may nevertheless not be true of an 
 object described as “‘the so-and-so.” Though it is true of every 
 object that it is an identity, it is not true of “the round square” 
 that it is an identity. This object is therefore nothing. 
 
 But if the round square is nothing, does it follow that “the 
 round square” is without meaning? Are not the two phenomena 
 
 1 Whitehead and Russell, Principia Mathematica, i, 69. 
 
 
 
DESCRIPTION AND ANALYSIS 137 
 
 of significance, to be without meaning and to mean something 
 non-existent, different phenomena? 
 
 There is an air of contradiction in the idea of meaning or re- 
 ferring to the non-existent. But this semblance of contradiction 
 disappears if “reference to the non-existent”’ is more accurately 
 described as the significant use of symbols where there is no object 
 for which they stand. It is possible to employ symbols signifi- 
 cantly (with syntactical significance) when there is no object to 
 which the group as a whole refers, and this is what Mr. Russell 
 denies or overlooks. But even if it were true that a phrase which 
 “means a non-entity”’ is without meaning, it would not follow 
 that because some descriptions mean non-entities, all descrip- 
 tions mean non-entities and are therefore without meaning. If 
 “the round square”’ is a meaningless expression because there 
 are no round squares, this fact does not imply that “the Presi- 
 dent of the United States” is meaningless because it is a de- 
 scriptive phrase of the same form as “the round square.” 
 
 However, the important question is— Can a description, or 
 a symbolic group, be significant and yet not refer to an object? 
 
 The Principia Mathematica, being concerned with logic rather 
 than epistemology, does not analyze the concept of meaning. 
 But certain assumptions as to the nature of meaning seem to be 
 implicit in its earlier, more strictly philosophical sections. So far 
 as we can disentangle these assumptions, the view of meaning 
 seems to be this: that groups of symbols which state proposi- 
 tions, and proper names (in a generalized sense), are the only 
 symbols which have meaning in themselves. Thus descriptive 
 phrases fall between two stools: they are groups of symbols, but 
 they do not state propositions; they play a part like that of 
 proper names, yet they are not proper names. If this is the as- 
 sumption of the argument which rejects descriptive phrases as 
 meaningless outside a context, the conclusion must be granted. 
 It then becomes necessary to translate descriptive phrases into 
 
 i PON 5 EE a 
 
 ———— 
 
138 SYMBOLISM AND TRUTH 
 
 another form, that is, to treat them as significant only when 
 they occur in propositions, and to construe these propositions 
 as statements which make use only of proper names (in the 
 generalized sense). But the possibility that groups of symbols 
 which do not state propositions, and yet are not proper names, 
 might be significant in their own right is not considered. And 
 this is what we have been urging all along: that there is some 
 legitimate sense of the term meaning other than those senses 
 which appear to be assumed in the Principia Mathematica. This 
 type of meaning—syntactical significance—covers both prop- 
 ositions and descriptive phrases; and just as a group of symbols 
 which states a proposition may as a whole refer to no object, 
 so a descriptive phrase may as a whole refer to no object and 
 yet be significant. 
 
 While proper names and single words, that is, simple symbols, 
 unless they are defined through symbolic groups, arouse inten- 
 tions directed toward objects — intentions which depend on the 
 existence of these objects — a symbolic group, on the contrary, 
 arouses an intention which is a function only of subordinate in- 
 tentions and of the structure of the group. The meaning of a 
 symbolic complex does not depend on the existence of an object 
 for which it stands as a whole. In order that a symbolic group 
 may be significant, it is necessary only that its constituents be 
 significant (or be definable in terms of significant complexes) 
 and that it have a form. It is in this sense of meaning that 
 “France loves Germany” has meaning. There is no object, 
 France loving Germany, but the phrase is significant because its 
 constituents are significant and grouped according to a plan of 
 logical structure. 
 
 To say that a description “means a non-existent object” is a 
 convenient but inaccurate way of speaking, for a “non-existent 
 object’’ would not be an object and could not be referred to. 
 
 
 

 
 DESCRIPTION AND ANALYSIS 139 
 
 The clearer manner of statement is that a description can be 
 significant apart from any reference, as a whole, to an object. 
 “The round square” means roundness and squareness attaching 
 to a term which is symbolized by a variable; it means “‘z as 
 modified by roundness and squareness.” “‘The king of France”’ 
 means “‘y as modified by the kingship of France.”’ And whether 
 or not any such unities of terms and predicates exist to be re- 
 ferred to is beside the point. Mr. Russell’s argument must be 
 countered by a broader conception of meaning. 
 
 It is because the existence or non-existence of an object sig- 
 nified does not affect the significance of a symbolic group that 
 “to mean a non-entity” is not to be meaningless. Only simple 
 symbols which refer directly to objects require the existence of 
 an object meant. Such symbols mean “‘categorically,” but syn- 
 tactical or group meaning is “hypothetical,” for it presupposes 
 no object corresponding to the group as a whole. 
 
 To assert that “the round square does not exist”’ is not, then, 
 to assume that there is an object called ‘“‘the round square” in 
 order to deny its existence. Nor does the truth of this assertion 
 lead to the conclusion that the phrase “‘the round square”’ is in 
 itself meaningless. 
 
 1 As for the statement of the Principia Mathematica, i, 87, that the law of 
 identity does not apply to descriptions, 7. e., that one cannot say “the round 
 square is identical with the round square,” this depends on what the as- 
 sertion of identity means. It has been shown above that z = z, as a general 
 principle of symbolism, means that the symbol z is always to be interpreted in 
 the same way, whether or not it stands for an existent object. Thus “the 
 round square = the round square” does not necessarily assert the existence of 
 this object, but it does assert that the significance given to this phrase must be 
 the same in all contexts; that “the round square” can be substituted for “‘the 
 round square”’ in any discourse, without an alteration of the meaning. But if 
 ““the round square is identical with the round square” is interpreted existen- 
 tially, to mean that “‘the round square has identity,” this will not be true un- 
 less the round square exists. However, the symbolic interpretation of the law 
 of identity is separable from the existential interpretation: “x is x”’ need not 
 
 be construed as predicating identity of an object meant by z. See above, 
 ch. II, see. vii. 
 
140 SYMBOLISM AND TRUTH 
 
 XILIT 
 
 The particles “all,” “‘every,” and “each”’ introduce a new 
 idea: that of classes. 
 
 “All men,” “every man,” “each man,” are different ways of 
 referring to the class men. As in the case of the other particles, 
 these particles have no meaning in themselves; they must ap- 
 pear in connection with symbols that refer to universals or com- 
 plex predicates. They do not signify constituents of the fact 
 represented by a phrase in which they occur; they are signs of 
 interpretation. Just as “the” tells us that one and only one in- 
 stance of a universal is meant (though this instance is indeter- 
 minate), and “a” that one among many possible instances is 
 meant, so “all” tells us that the universal is signified in a certain 
 manner of its occurrence — in its occurrence in a class. 
 
 Classification rests on universals. Though a universal is some- 
 thing distinct from any or all of its instances, though it is an 
 aspect which can be singled out and made an object of reference, 
 nevertheless, a universal occurs in instances, it modifies a num- 
 ber of terms; and a class is the universal taken in conjunction 
 with the terms it modifies. It is a plurality of terms modified by 
 the same universal. Any predicate determines a class — the 
 class of the terms to which this predicate attaches. A relation de- 
 termines a number of classes: “A hates B” is, for example, a 
 case of the class of ‘“‘hatreds’”’; but from this relation the class 
 of ‘‘those who hate B” and the class of “those whom A hates” 
 can also be derived. “‘A is between b and c”’ is a case of the class 
 of “‘relations of betweenness,”’ but it also determines a class of 
 “those objects which are between 6 and c” and “those objects 
 between which a occurs.” In every case a class is a plurality of 
 terms modified by a single quality or relation.’ 
 
 But a class is at once a plurality and a unity. It derives its 
 
 1 A class of one member is the only exception; this is not a plurality of mem- 
 bers: but if it is a class, it is a totality of one. 
 
 
 
DESCRIPTION AND ANALYSIS 141 
 
 unity from the presence of a predicate in a number of distinct 
 terms, and its plurality from the distinctness of the terms. The 
 difficulty of conceiving a class as an object, says the Principia 
 Mathematica, is connected with the “ancient dilemma of the 
 One and the Many.” “If there is any such object as a class, it 
 must be in some sense one object. Yet it is only of classes that 
 many can be predicated. Hence, if we admit classes as objects, 
 we must suppose that the same object can be both one and 
 many, which seems impossible.” 1 But the impossibility is less 
 real than apparent. It is no more present in the conception of a 
 class than in the conception of any object which is analyzed into 
 constituents, broken up into parts which form a whole. Every 
 analyzable object is both one and many, a unity of diverse ele- 
 ments; and if one balks at the problem of the One and Many, he 
 must reject all analysis. 
 
 The unity of a class, however, is different from the unity of a 
 fact (or a group), and for this reason a class, though it is none 
 the less an object, is not the same kind of object as a fact. It is 
 an object of a different order. “Caesar loving Brutus,” “‘Bos- 
 ton’s being near to but north of New York,” are expressions 
 that stand for factual groups. In these groups the universal 
 unites the terms so that (taken with the universal) they become 
 a single instance of this universal. The predicate which deter- 
 mines a class unites the members in no such way as this. (But if 
 there are classes there will also be factual groups, and if there 
 are factual groups there will also be classes.) The unity of a 
 class is of the peculiar kind called totality, and this is a new prim- 
 itive idea — the defining idea of classes. 
 
 A class is a universal in the totality of its instances, that is, it 
 is an object like “man” as it appears in this sort of unity with 
 diverse terms. “Man” means a universal apart from its in- 
 stances, that is, in abstraction; but man is not only separable 
 
 1 Whitehead and Russell, op. cit., i, 75. 
 
142 SYMBOLISM AND TRUTH 
 
 from its instances, it is also joined to them, spread throughout 
 them. “Men” as distinguished from “‘man” means the universal 
 as it is particularized in a multitude of different terms. This 
 object is one, and can be referred to through a single symbol, 
 because the universal gives it the unity of totality, though this 
 is a “looser” unity than that of a single fact of diverse terms. 
 No part or selection of the terms to which a universal attaches 
 is a class, a totality, through the presence of that universal 
 alone. Every universal determines one and only one totality. 
 Thus a portion of the class men would be a class only through 
 the presence of some other predicate than man, e.g., the predi- 
 cate, brave man, or strong man. A class therefore is nothing short 
 of a universal in its concrete entirety. The universal, in making 
 the instances one, makes them a totality, but at the same time 
 permits them to be distinguished as instances. 
 
 It follows from this notion that a class is not a sum of objects. 
 The expression, “a and b and ¢, etc.,”’ does not designate a class, 
 for objects which do not belong to the same class can be thus 
 added together. A mere summation of objects will not give us a 
 class predicate which determines them to be a totality. “The 
 table and the chair and the book, etc.,” are not a class through 
 the fact of being conjoined; they become a class only if there is 
 some predicate which gives them the unity of totality. If they 
 are “‘all the objects in this room”’ or “‘all the objects I now see,” 
 they are a class. Nor does the similarity of objects alone make 
 them a class, although objects of the same class are similar. 
 Only if x and y and z, etc., are “all the objects similar to a given 
 object c,” do they form a class, and in such cases this class will 
 be a totality determined by a predicate. 
 
 Classes are cross-sections of the world of fact. Only very lim- 
 ited classes are presented in their wholeness; most classes can 
 be known only conceptually or symbolically, that is, as the (x) 
 totality determined by such and such a predicate. Though “all 
 
 
 

 
 DESCRIPTION AND ANALYSIS 143 
 
 men” means one object, no one has known all men; and thus 
 classes seem not to be objects, but constructions of the mind. 
 Yet the inability of knowledge to grasp most classes as totalities 
 in perception does not disprove the objectivity of classes. The 
 idea of totality once being given, —as it is in the restricted 
 totalities of presentation, — this idea can be extended to totali- 
 ties that lie beyond presentation, and to infinite totalities. 
 
 “Each” and “every” as well as “all’’ precede expressions 
 that refer to classes, but the distinctions between ‘“‘each,”’ 
 “every,” and “all” are difficult to draw. The difference seems 
 to be one of emphasis. “All men are sinful’? appears to empha- 
 size the fact that the class of men is a totality. “Every man is 
 sinful”? means the same, that is, that all men are sinful, but em- 
 phasizes the plurality of the class. “‘Each man is sinful” also 
 emphasizes the plurality of the class, but at the same time seems 
 to include a reference to an enumeration of the members. But 
 whatever the shades of difference in the meanings of “each,” 
 “every,” and “all” may be, these three words indicate manners 
 of reference to classes. 
 
 A reference to a class is clearly a description of the form “the 
 so-and-so” rather than “‘a or some so-and-so.” The totality is 
 meant through an undetermined x which has only one possible 
 value, that is, the totality in question. “All persons”? means 
 “the (x) totality determined by the predicate ‘person’”’; this 
 expression is not susceptible of many interpretations as is “a 
 
 299] 
 
 person. 
 
 XIV 
 
 The discussion of description and analysis has brought out 
 the following points: 
 
 1 It is plain that a class could have one member or an infinity of members 
 and still be a totality. ‘‘ All the numbers which, when added to a number give 
 that number,” designates a totality of one member — the number zero. “ All 
 the objects which can be put into one-to-one correspondence with the natural 
 numbers”’ designates an infinite totality. 
 
 { 
 
 
 
144 SYMBOLISM AND TRUTH 
 
 The line of cleavage between proper names or single symbols 
 and descriptive phrases is determined by structure alone; the 
 distinction is not that proper names (in a generalized sense) 
 have meaning in themselves, while descriptive phrases have 
 meaning only in a context. Description is analysis, for the predi- 
 cates and relations of a term are logical “parts” of it, and what 
 is represented analytically by a descriptive phrase is represented 
 unanalytically by a proper name or a single symbol. This agrees 
 with common usage, which treats proper names as equivalent 
 in meaning to descriptive phrases. Syntactical significance is 
 present in all symbolic groups, and only when this type of mean- 
 ing is neglected (or confined to groups which state propositions) 
 does the contrary view, that descriptions have no meaning in 
 themselves, become plausible. 
 
 Symbolic groups are significant apart from the existence or 
 non-existence of objects meant, for their meaning as a whole is 
 a function of the meanings of their parts and their logical form, 
 and nothing else. This wider notion of meaning covers that of 
 descriptions outside a context. If there is no object correspond- 
 ing to a description, this fact does not deprive the description of 
 its syntactical significance. ““To mean a non-entity,” that is, 
 to be significant when there is no object signified, is not to be 
 meaningless. 
 
 A description signifies a term, together with a predicate or 
 complex of predicates attached to this term; but the term is 
 represented by a variable which, in language, is understood to 
 be present through the sign of interpretation (the particle) pre- 
 ceding the phrase. Descriptions are of the general form (xR): 
 the object has this structure and the symbols themselves take on 
 this structure if the variable, which is understood, is supplied. 
 
 99 «66 
 
 Thus ‘‘a man” means “a human 2, some friend’? means 
 “some friendly y,” “the president” means “the presiding 2.” 
 
 The term described becomes the center of a complex of char- 
 
 99 66 
 
 
 

 
 DESCRIPTION AND ANALYSIS 145 
 
 acters and relations, and the variable through which this term is 
 signified is to be interpreted in the sense indicated by the parti- 
 cle. “The” means that the variable has only one possible value. 
 “A” and “an” mean that it has many possible values; “‘any,” 
 that the value is to be chosen at random from among these many 
 possible values; and “some,” that it is to be chosen according to 
 an unspecified condition of selection. 
 
 Though a description does not state a fact, it always has 
 reference to a fact — to the fact through which the object in 
 question is described. “‘The president of the United States”’ re- 
 fers to the fact that “someone presides over the United States”’; 
 “‘a bard of the sixteenth century,” to the fact that “someone 
 wrote poetry in the sixteenth century”; “a man,” to the fact 
 that ‘someone is human.” And whether the description signifies 
 an existent object, or refers to no object, will depend on the truth 
 _ or falsity of the propositions which assert these facts. ‘This is the 
 basis of Mr. Russell’s reduction of descriptions to the form of 
 | propositions which make assertions about terms. 
 
 _ But it is not necessary to translate the description into an- 
 _ other form to observe that it refers to a fact as well as to a term. 
 The term is, as it were, viewed through the fact; the fact is 
 viewed as centering about the term, so that the term assumes a 
 pivotal rather than a subordinate place in the fact. (‘This is sym- 
 bolized by writing the x both inside and outside the group 
 through which it is described. Thus (a((xR)Sa)) indicates that 
 the z is described through the whole complex ((xR)Sa).) This 
 centralization of the fact about a single term is the only differ- 
 ence between the fact as it appears in the description and as it 
 might appear in some other (non-descriptive) form of expres- 
 sion. If a description is asserted, — and it follows from this view 
 that descriptions can be asserted, —it will be seen that the de- 
 scription may state a fact, the fact on which the description is 
 based. “The president of the United States is,” affirms the same 
 
146 SYMBOLISM AND TRUTH 
 
 fact as “someone presides over the United States”; “the author 
 of Waverley is,” makes the same assertion as *“Someone wrote 
 Waverley,’ where “someone” is taken to have only one possible 
 value. “A man is”’ affirms no more nor less than “someone is 
 human.”’ ! The difference in these assertions is one of form only, 
 and not of content. Therefore descriptive phrases are not dis- 
 tinguished from “‘propositions”’ through the fact that the latter 
 mean complexes of terms and predicates or relations, while the 
 former mean only terms. Both stand for complex wholes (if they 
 stand for any objects); both mean facts. 
 
 Variable significance, which is always present in descriptions, 
 is a distinct kind of meaning, different from syntactical meaning 
 or from direct reference to objects through simple symbols. The 
 variable, meaningless in itself, is construed as a symbol because 
 it enters as a constituent in a significant whole; it is a symbol 
 which arouses no specific intention, but which must be treated 
 as symbolic because of its setting. And if it is given a value this 
 can be, by the principle of identity, one and only one value. The 
 variable is no more open to an equivocal interpretation than any 
 other symbol. A variable may, however, have many possible 
 values, and it will then be ambiguous — a means of attaining 
 generality of reference. 
 
 Both universals and individuals can be described, and both 
 are variably (indeterminately) signified by descriptions. But an 
 individual is still variably signified when it is given a proper 
 name, for the proper name must be defined through a descrip- 
 tion, which contains a variable element; otherwise the name 
 would stand merely for a “this” of presentation and would be 
 even less determinate in meaning than if it were defined through 
 a description. 
 
 The only data of perception which can be represented by 
 
 1 “Ts” as a sign of assertion in these expressions adds or subtracts nothing 
 from the meaning of the phrase. 
 
 
 

 
 DESCRIPTION AND ANALYSIS 147 
 
 invariable symbols are universals, and so the only knowledge 
 which is completely free from variability of meaning is knowl- 
 edge in universal terms, that is, abstract statements, laws, which 
 make no reference to individuals. 
 
 Definitions are analytic in form. They are statements of iden- 
 tity, such as a = (#R); and they can be reduced to the form 
 a = a. But they are not on this account trivial, since their effect 
 is synthetic; they add to the knowledge of the object meant, a 
 knowledge that it can be analyzed as (rR), or that predicates 
 which were originally external to the meaning of a can be in- 
 cluded in this meaning. Concepts of restricted meaning enlarge 
 themselves through such statements of identity by taking in 
 more and more of the predicates of the object meant, and in 
 this way knowledge tends to become analytic in form. It tends 
 to sum up all that can be said of an object in the very concept 
 (the very name) of the object. But the postulates and axioms of 
 a science do not completely determine the subject-matter of the 
 science, even though an analysis of what is meant by “the sub- 
 ject-matter” may be a statement of the laws of the science. 
 Knowledge of analytic form must be anchored to experience by 
 a judgment which is synthetic in effect — which asserts that the 
 objects within a certain field of experience are the objects thus 
 analyzed. Euclidean or non-Euclidean geometry is geometry 
 because its postulates can be interpreted in terms of the experi- 
 ence called “space.” 
 
 Lastly, there is a type of object — a class — which is referred 
 to by descriptions prefaced by “all,” “every,” and “each.” 
 Classes are not groups, not wholes of the form (Rab ...), but 
 a class is nevertheless one through the presence of a universal 
 in terms. Its unity is of the undefined sort known as totality. 
 Classes, with the exception of the limited totalities given in per- 
 ception, are known only conceptually, that is, through symbols, 
 as “‘the (x) totality determined by such-and-such a predicate.” 
 
148 SYMBOLISM AND TRUTH 
 
 Descriptions, then, do not stand apart from other symbolic 
 expressions. All symbolic groups have significance in themselves, 
 and this significance is independent of the existence of an object 
 meant. The possibility of using symbols significantly, either in 
 descriptions or in propositions which are not descriptions, when 
 no “real” object is referred to, lies at the basis of the distinction 
 between truth and falsity. Meaning becomes truth when it is 
 joined to existence; it becomes falsity when it is severed from 
 existence; but without meaning there is neither truth nor 
 falsity. 
 
 
 

 
 CHAPTER V 
 
 TRUTH AND FALSITY 
 
 I 
 
 Trourn and falsity are properties of symbols. A symbol is 
 true if it stands for an object; it is false if it is significant, yet 
 stands for no object; or, in the words of Thomas Hobbes, “True 
 and false are attributes of speech, not of things . . . truth is the 
 right-ordering of names.” ! If the term “speech” is widely 
 enough construed, this definition of the aim of knowledge is a 
 corollary of the theory of meaning that has been presented. The 
 “right-ordering of names” is building symbols into structures 
 that correspond to structures of fact, and this correspondence is 
 truth. 
 
 Belief and disbelief do not alter the truth or falsity of sym- 
 bolic expressions, for the existence of meaning is a sufficient as 
 well as a necessary condition of the existence of truth. No one 
 can be in error unless what he believes has meaning, and he can- 
 not be convicted of error if his meaning is misunderstood; nor 
 can he believe truly unless that which he believes is significant. 
 Yet truth and falsity are independent of belief; any idea that 
 can be entertained is either true or false. Once a meaning is 
 fixed, its truth or falsity is fixed; and meanings are carried only 
 in symbols. This is the idea behind Hobbes’s definition. Yet it 
 must not be forgotten that a symbol is more than a mark, a 
 sound, a gesture, or an image; it is any of these together with 
 the effect it has in a mind, that is, together with the psychical 
 attitude to which it gives birth. Symbols are concepts, and to 
 say that truth is a property of symbols is to say that it is a prop- 
 erty of concepts. 
 
 1 T, Hobbes, Leviathan, Part I, ch. 4. 
 
150 SYMBOLISM AND TRUTH 
 
 Truth, moreover, cannot be defined without some reference to 
 reality or existence; ideas, thoughts, perceptions, are true when 
 they present or represent what 7s. To apprehend a truth is to 
 apprehend the existence of something meant. Thus knowledge 
 from the outset is directed toward reality, and finally toward 
 a metaphysical goal. Epistemological questions project them- 
 selves toward metaphysics through the concept of truth. But 
 one must approach metaphysics humbly. He must begin with a 
 limited concept of the real, which he may alter or abandon in 
 the light of further criticism; for a theory of the relation of 
 knowledge to reality can have no basis except in an analysis of 
 knowledge as a phenomenon, and this analysis leads to a limited 
 notion of reality and of truth. 
 
 The definition here set forth is of this sort. Truth as reference 
 through symbols to existent objects may be a reference to ob- 
 jects that are, metaphysically speaking, only “appearances”; 
 or if these objects are not appearances, they may be objects that 
 are not separable from knowledge, they may be mind-objects 
 only. And there are many other metaphysical contingencies 
 which the definition ignores — to which it is, in Mr. White- 
 head’s phrase, “closed.” 1 It adopts a restricted concept of exist- 
 ence, and this yields a restricted concept of truth, whose im- 
 mediate claim to acceptance is that it is workable in science, 
 mathematics, and every-day thought, whether or not it is finally 
 able to withstand metaphysical scrutiny. 
 
 II 
 
 The examination of this definition — of the notion of exist- 
 ence in terms of which it is stated, together with the tests of 
 truth to which it gives rise — can be better understood if it is 
 prefaced by an inquiry into another view of truth: the view that 
 truth is not a property of symbols, but of entities which are 
 
 1 A. N. Whitehead, The Concept of Nature (1920), ch. 1. 
 
 
 

 
 TRUTH AND FALSITY 151 
 
 neither symbols nor existing objects, yet which have a being in 
 themselves. 
 
 On this theory, it is to “propositions” that truth attaches, 
 and a proposition is not thought of as a symbol or symbolic 
 group coupled with the psychical set or intention it arouses in a 
 mind. A proposition is independent of psychical processes; it is a 
 meaning, but a meaning considered apart from its setting in a 
 mind. It is something distinct from symbols, to which they 
 refer, and yet it is not an object. The proposition thus conceived 
 enters as a tertiwm quid between the symbols, in which it is con- 
 veyed, and the datum or object, of which it is true. It is a wedge 
 which opens the way for a new class of entities — subsistent en- 
 tities — which are to be distinguished from objects. The pe- 
 culiar manner in which these subsistents are apprehended is 
 said to be conception; to conceive is to know something, to refer 
 to something, but not to refer to an object. On this view, the 
 initial reference of conception is to a subsistent proposition, and 
 the proposition in its turn may or may not be directed toward 
 an object. If the proposition is directed toward an object, if the 
 tertium quid meant by the symbols exists as well as subsists, it is 
 true; otherwise it is false. 
 
 This theory purifies truth of all psychical elements. Truth and 
 falsity are not determined in any sense by the act of thought; 
 they belong only to these independent entities, which can be 
 thought of but are not created by thinking. At the same time, 
 truth and falsity are not taken to be properties of objects, so 
 that the difficulties of one type of view, which says that there 
 are “false objects,” are avoided. 
 
 The most convincing arguments for the assumption of these 
 subsistent entities are derived from the consideration of false 
 and negative propositions. Mr. G. E. Moore puts the case for 
 them in the following way: “How can a thing ‘appear’ or be 
 ‘thought of’ unless it is there to appear or be thought of? To say 
 
152 SYMBOLISM AND TRUTH 
 
 that it appears or is thought of, and yet that there is no such 
 thing, is plainly self-contradictory. A thing cannot have a prop- 
 erty unless it is there to have it. .. . When I think of a unicorn, 
 what I am thinking of is certainly not nothing; if it were nothing 
 then, when I think of a griffin, I should also be thinking of 
 nothing, and there would be no difference between thinking of a 
 priffin and thinking of a unicorn. But there certainly is a differ- 
 ence; and what can the difference be except that in the one case 
 what I am thinking of is a unicorn, and in the other a griffin? 
 And if the unicorn is what I am thinking of, then there certainly 
 must be a unicorn, in spite of the fact that unicorns are unreal. 
 In other words, though in one sense of the word there certainly 
 are no unicorns — the sense, namely, in which to assert that 
 there are would be equivalent to asserting that unicorns are 
 real — yet there must be some other sense in which there are 
 such things; since, if there were not, we could not think of 
 them.” } 
 
 The status of propositions, on the view in question, is that of 
 Mr. Moore’s unicorns and griffins; they are entities which are 
 “‘there”’ in some sense, though plainly they are not “there”’ in 
 another. They are objectives, which may be real or unreal; which 
 subsist rather than exist.? 
 
 Subsistence is a kind of being to which existence may be 
 added, but to which existence is not necessary. In the realm of 
 subsistence, the lion and the unicorn lie down together. To think 
 of a lion or of a unicorn is to think of entities that partake 
 equally of this impartial being, this thinner reality, which in- 
 cludes the possible and the imaginary as well as the real. 
 
 1G. E. Moore, “The Conception of Reality,” in Philosophical Studies 
 (1922), p. 215. 
 
 2 The terminology is that of A. Meinong’s gegenstandstheorie. Two among 
 Meinong’s important works on this subject are: Untersuchungen zur Gegen- 
 
 standstheorte und Psychologie (1904, Leipzig) (a collection of studies by several 
 authors including Meinong), and Meinong’s Uber Annahmen (1902, Leipzig). 
 
 - ee 
 

 
 TRUTH AND FALSITY 153 
 
 Ii 
 
 The concept of the “objective” springs from what appears to 
 be a logical necessity in the analysis of meaning. Meaning must 
 have an objective reference, and it is thought therefore that 
 there must be a thing meant wherever there is significance. If 
 meaning is reference to something —a relation in which the 
 mind is only one term — unless this relation is to disappear, 
 it must terminate in a referent. This is the idea behind Mr. 
 Moore’s statement that “to say that (a thing) .. . is thought of, 
 and yet that there is no such thing is plainly self-contradictory.” 
 When the referent is a non-entity, it cannot (if the argument is 
 pursued) cease to be a referent; it must therefore have some 
 status. It is not nothing, for if it were the meaning relation 
 would collapse, being deprived of one of its terms. 
 
 Furthermore, the reference of symbols is not merely to psychi- 
 cal states, to images, to the content of the mind. The very es- 
 sence of the meaning activity is that through it the mind reaches 
 out toward something other than its own states;1 and yet, if 
 this “something” is to be grasped, it must be somehow given. 
 It must have a being which allows it to be referred to when it is, 
 in some sense, not a presented or existent content of the mind. 
 It must be “‘there” in some way and not “there” in another; 
 otherwise meaning loses its objectivity of reference and becomes 
 intra-psychical in the narrowest meaning of the term. 
 
 But the dilemma here is not so sharp as it appears. Objectiv- 
 ity of reference does not require the assumption of subsistent 
 (and sometimes unreal) entities as the second term of the mean- 
 ing relation. The reference of a symbol, either simple or com- 
 plex, can be directed beyond the mind’s content when the entity 
 referred to is in no way presented or “‘there’’; and a complex 
 
 1 That is, toward something other than its own present states. This does 
 
 not preclude the metaphysical hypothesis that all objects referred to are ulti- 
 mately ‘“‘mental”’ in a wide sense of the term. 
 
154 SYMBOLISM AND TRUTH 
 
 expression can have an objective reference when there is no ob- 
 ject or objective to which the expression as a whole refers. 
 
 Consider, first, the meaning of simple symbols which stand 
 directly for objects. The theory of objectives assumes that these 
 symbols, no less than complex expressions, have significance 
 through reference to subsistent entities. It is not sufficient that 
 the meaning relation shall have been grounded in an existent 
 term; it must continue to be grounded in a subsistent one. Now, 
 if to mean something is to intend it, to take an attitude of mind 
 appropriate to it, the continued being in any sense — either as 
 a subsistent or existent entity — of that which is meant is not 
 necessary to the meaning. Indeed, anticipating or intending is 
 just the sort of reference to objects that is compatible with the 
 absence, as well as the presence, of what is referred to. Meaning 
 is not a static relation between the mind and any sort of entity. 
 It is an activity, and this activity has a direction away from the 
 mind’s present content, whether or not there is a given object 
 (or objective) in which it terminates. The direction of a meaning 
 is determined once an object has been the terminus of the activ- 
 ity; the activity continues to intend, to be appropriate to this 
 object thereafter, when the object is absent or non-existent. It is 
 sufficient therefore that the things which simple symbols mean 
 shall have existed; the subsequent use of these symbols does not 
 demand the persistence of their referents, either as subsistent 
 objectives or existent objects. A meaning can be carried by an 
 intention alone, and the reference does not lose its objective 
 direction. 
 
 A second type of meaning is that of complex expressions. If 
 the mechanism of conception is analyzed (as it has been) into 
 the grouping of symbols, the groups as a whole continue to 
 refer, to mean — and to mean something other than a present 
 psychical content — whether or not there exists or subsists an 
 object or objective to which they refer. The meaning of a sym- 
 
 
 

 
 TRUTH AND FALSITY 155 
 
 bolic group has been shown to be a function of other mean- 
 ings, together with a scheme of logical structure. A number of 
 subordinate meanings enter into a unity to form a new meaning, 
 
 ‘ 
 
 which cannot be described as a simple “‘mind-referring-to-ob- 
 ject-or-objective,” as Mr. Moore would describe it; for the 
 situation is made complex by a new factor — a plan of structure 
 by which the symbolic elements are welded into a whole. If _ 
 there is an object referred to, the reference is indirect. The sym- 
 bolic group is a construction which is not taken, in its entirety, 
 to stand for an object as a single word or proper name might be. 
 From the direct references of the elements to things that exist 
 or have existed, the mind fashions a secondary reference — a 
 reference composed of references. Thus I build up the group, 
 “the snow will melt to-morrow’”’; I join the several direct refer- 
 ences of the words, whose meanings are determined by previous 
 use, into a single indirect reference of a certain form; but I can 
 know only to-morrow whether this secondary reference does or 
 does not terminate, as a whole, in an object. 
 
 If there is an object corresponding to the whole expression, 
 this object will be both a unity and a plurality, a whole of parts; 
 e.g., the unified fact, “the melting of the snow on the morrow.” 
 But if there is no such unified object, the parts will still exist 
 (or will have existed) as a plurality; e.g., there will be a to- 
 morrow, and there have been snow and melting. Therefore the 
 meaning of the group will be grounded in a reference to objects. 
 The significance of the expression will be directed toward some- 
 thing other than the present content of the mind, despite the 
 fact that it corresponds in its entirety to nothing. 
 
 It is in this sense that the false statement, “Shakespeare 
 wrote The Critique of Pure Reason, has an objective reference. 
 wrote,” “The Critique of Pure Reason,” stand 
 
 99 <¢ 
 
 “Shakespeare, 
 for objects. These references to existent things, or to things that 
 _ have existed, lend objectivity of reference to the whole. They 
 
156 SYMBOLISM AND TRUTH 
 
 give it a foundation in fact, though it corresponds to no fact. 
 And since the symbolic elements of any significant group must 
 stand directly for objects which exist (or have existed), or must 
 be definable in terms of symbols which stand thus for objects, 
 no symbolic group is without an existing locus of reference of 
 the sort that the primary, direct act of meaning demands. The 
 _ meaning of the group cannot collapse into a total absence of re- 
 lation to the objective world, for the objects meant by the ele- 
 ments of the group are in this world and thus determine the 
 mind to have a direction beyond itself. 
 
 This is not all. The plan of structure is no less objective than 
 the constituents meant by the simple symbols, even if there is 
 no fact which combines these constituents in this structure. The 
 logical form intended is presented, and exists, in the symbolic 
 expression as a universal of which the group is itself an instance. 
 The structure meant is identical with the structure of the con- 
 cept, that is, of the symbols; and it is equally as real, equally as 
 objective, in its conceptual or symbolic instance as it would be 
 in a non-conceptual or non-symbolic instance, for it is the same 
 in both. 
 
 The fixity of complex concepts arises from their logical form. 
 Given a certain form in certain symbols whose individual mean- 
 ings are determined, and the meaning of the concept is deter- 
 mined. If there is an object whose elements are the ones meant 
 by the simple symbols, and whose structure is identical with the 
 structure devised by the mind for this group, this object will be 
 the thing meant. But there need be no such object; the meaning 
 is still fixed and still turned toward the world of objects. The 
 mind, once it invents a concept, is bound by it. The concept 
 seems to become external to thought, to pass over into a realm 
 beyond the mind’s caprice; for the form of the concept, though 
 it is constructed in thought, is a universal which may appear 
 elsewhere. The constructive activity of the mind is exercised in a 
 
 
 

 
 TRUTH AND FALSITY 157 
 
 medium which is not purely of the mind — in the medium of 
 logical form. Instead, therefore, of saying that thought arbi- 
 trarily assigns meanings to complex concepts, as it does to single 
 words or signs, one can say that these concepts assign meanings 
 to thought. The logical structure of the concept reaches out 
 toward objects and, as it were, selects the one (if there is one) to 
 which the concept corresponds. The structure of the concept 
 means the structure of the fact because it is identical with the 
 latter. And so the verification of a complex expression is a search 
 in the direction of the objects meant by the constituents of the 
 expression for an instance of the same logical form which is 
 present in the expression. Thus the mind invents its concept 
 but discovers their truth or falsity. 
 
 IV 
 
 The tertitum quid which, on the theory of subsistence, is as- 
 sumed to intervene between symbols and their objects disap- 
 pears in this analysis of meaning. It is absorbed in the symbols 
 themselves. Meaning is not, as the theory of objectives would 
 have it, what is referred to through symbols; it is the referring 
 itself, that is, the meaning rather than the meant. And this act 
 is always turned in the direction of existing objects, even though 
 _ there may be no single object in which it finds its fulfillment; so 
 that meaning does not become purely a relation of one psychical 
 event to another. It is an act in which psychical events point 
 beyond themselves, and symbols are the perceptible embodi- 
 ments of this act. 
 
 Not only are symbols the instruments of knowledge, they are 
 of its very stuff. Mediate knowledge and a large part of immedi- 
 ate knowledge are words, images, signs, taken with the effects of 
 these in minds. There is no independent thing called “knowl- 
 edge,’ which words, images, psychical attitudes, signs signify. 
 _ The act of knowing itself, in so far as it is not pure awareness, is 
 
158 SYMBOLISM AND TRUTH 
 
 the use of symbols. To assume that there is some such thing as 
 the “proposition” or “objective,” which is the referent of sym- 
 bols but which is itself neither a symbol nor an object, is to 
 postulate a detached element of “meaning” as the terminus of 
 thought. All attempts to catch this elusive and independent 
 “meaning” end in the capture of images, of words, of attitudes 
 or sets of the mind. The view that propositions are what sym- 
 bols signify, that they are meanings apart from symbols and 
 from the mind in which these symbols have significance, cuts 
 off meaning and hypostatizes it, as if it might have being in 
 itself; but this is as impossible as that a picture might exist 
 without the canvas on which it is painted. 
 
 The elimination of these subsistent entities subserves the end 
 of economy of assumption. Truth is to be found in the two-term 
 relation between symbols and objects; the proposition as a third 
 entity is not needed. Symbols either signify existent objects or 
 no objects, for the phrase “existent object” is a tautology, and 
 the phrase “non-existent object” is a contradiction. The cate- 
 gory of objectivity is not wider than the category of existence; 
 there are no non-existent entities of any sort. And yet it is possi- 
 ble to speak or think significantly without assuming an object 
 thought or spoken of. 
 
 It is this notion, that a concept need not have an object, 
 which supports Kant’s refutation of the ontological proof of 
 God and makes ontological arguments in general invalid. No 
 concept implies the existence of an object conceived. But the 
 theory of subsistence restores the ontological argument in a rare- 
 fied form. Though one cannot, on this theory, argue from a con- 
 cept to the existence of an object, he can always argue to the 
 subsistence of an objective. “A thing must be in some sense to be 
 thought of.” This gives every concept a referent with a being — 
 a being which is often non-existence. A strange multiplication 
 of ontological types! One sort of being should suffice. If a thing 
 
 
 

 
 TRUTH AND FALSITY 159 
 
 does not exist it has no being; to speak of it as subsisting is 
 merely to attempt to smuggle it back into reality, from which it 
 has been once dismissed. 
 
 An expression which “means a non-entity”’ stands, then, for 
 no sort of entity; but it is still an expression which has signifi- 
 cance and an objective reference, apart from the existence or 
 subsistence of any corresponding referent. 
 
 V. 
 
 Under what conditions is reality or existence predicated of 
 objects? What are the criteria of objectivity? 
 
 The first criterion of existence, as the term is used in the 
 present definition of truth, is perception. In perception, some- 
 thing is given to the mind, there is a datum; and it is to this 
 datum that existence belongs. And yet an uncriticized percep- 
 tion does not guarantee the reality of its object. Dreams, illu- 
 sions, hallucinations, are no less vivid and convincing than 
 waking or normal presentations; they are no less perceptions in 
 which something is given. But one cannot say that a dream 
 object or an illusory object is really what it appears to be. 
 
 Perception is complex; the datum is only one element in it. 
 - What seems to be given as a datum may be largely the creation 
 of concepts, of signs with their attendant mental attitudes, at 
 work in the perception. For an object perceived is always an 
 ) object meant, referred to, intended by, a concept. Concept and 
 datum blend to form a presented whole, and what is merely in- 
 tended or meant cannot easily be separated from what is given. 
 Perceptions must be criticized, and only some of them can be 
 accepted as presenting objects which are really what they seem 
 to be. 
 
 I am walking in a forest, let us say, and I see at some distance 
 the body of a man across my path, which proves on closer in- 
 spection to be the trunk of a fallen tree. What I first saw had the 
 
160 SYMBOLISM AND TRUTH 
 
 appearance of being given; yet it could not have been wholly 
 given or it would have resisted further examination. The percep- 
 tion was an elaboration of data. Images, and perhaps unspoken 
 words, together with their meanings, fused with the data; the 
 mind automatically organized these elements into a whole, so 
 that the data were presented under a concept — they were per- 
 ceived through a meaning. Not only was this the case with the 
 perception of the recumbent body; there is every reason to sup- 
 pose that the perception of the tree-trunk was also an elabora- 
 tion of data. Here, too, concepts were added to what was given, 
 the data were viewed through a meaning, the presentation being 
 no less complex; and if I believe the fallen tree-trunk to be a 
 real object, it cannot be on grounds of its givenness alone. 
 Perception is a union of sensation and conception. Sense data 
 are the simplest observable elements in perception; with them 
 the analysis of a presented whole comes to an end, though it is 
 difficult (and often impossible) to disengage these sense data 
 from their settings. The sense data are obviously supplemented 
 by something non-sensory. They are signs which, in the lan- 
 guage of Thomas Reid, “suggest” what is perceived. Take an 
 extreme example: I hear a footstep outside my closed door and 
 perceive that someone is about to enter the room. The sensory 
 elements are plainly much less than the whole perception. The 
 sound may not be a footstep, it merely “‘suggests” a footstep; 
 and certainly it may not be the footstep of someone who is about 
 to enter the room. This is clearly a conceptual addition to the 
 sense data. Now what is true in the extreme case is true also in 
 other cases. One perceives, for example, that it is raining; but 
 the sensory constituents of this perception are not the whole 
 fact, that it ts raining. There are sensations of dampness, of 
 grayness, of cold, of faint vertical motions in the field of vision; 
 and these sensations together with what they mean make up 
 the fact. They awake in the mind, as do the words on a printed 
 
TRUTH AND FALSITY 161 
 
 page, certain intentions carried by images and half-uttered 
 words; they cause one to take an attitude which is appropriate 
 not only to dampness, to cold, to grayness, but to a whole of 
 which these are parts; and thus they mean that it is raining. 
 The effect of them is as if they caused one to formulate this 
 proposition.! 
 
 The sense data and the concepts, moreover, come into a pe- 
 culiar unity in perception. They coalesce, and the elements that 
 are sensed infect the conceptual elements, so that a large part of 
 what is conceived seems also to be sensed. An excellent illustra- 
 tion of this is the perception of space; we seem actually to see 
 depth, though there is no doubt that much, if not all, of the per- 
 ception of depth is a conceptual elaboration of sensory elements. 
 The sense data are both signs to which concepts attach and 
 parts of the objects which these concepts signify; and in the 
 perception of a complex object or fact the sensory elements fall 
 into their proper places as constituents of a whole which is both 
 conceived and sensed.” 
 
 The presented whole, nevertheless, has the appearance of 
 simplicity. The fact that it 1s raining seems to be given in its en- 
 
 1 Reid adds that in perception we believe “‘irresistibly”’ in the reality of 
 what is presented, and so perception becomes judgment, being conception 
 joined to belief. But perception need not include belief. One often doubts the 
 evidence of the senses; yet the doubt does not do away with the perception. 
 Further, an illusory perception persists when it is disbelieved; this is indeed 
 the very reason why it is illusory. It is nearer to the fact to say that we tend to 
 believe our perceptions, that the perception tends to become a judgment, 
 rather than that it is a judgment. Belief is a new attitude of mind, and one can 
 withold belief in his perceptions. If perception produces immediate and “‘irre- 
 sistible”’ belief, this is a belief that usually gives way to doubt — a belief that 
 does not persist unless it is substantiated by other evidence than the givenness 
 of the perception in question. See T. Reid, Essays on the Intellectual Powers of 
 Man, Essay II, especially ch. 10. 
 
 2 A thing, a complex object, is therefore much more than a class of sense 
 data, as Mr. Russell describes it. It is a unity of sense data according to a 
 definite plan of structure. The data enter into a conceptual scheme, they be- 
 come parts of a meaning, and are at once signs and constituents of the object 
 meant. For Mr. Russell’s view, see Our Knowledge of the External World 
 (1914), ch. 4. 
 
162 SYMBOLISM AND TRUTH 
 
 tirety; the tree-trunk appears to be presented as a solid, three- 
 dimensional object; and even though the perception is known to 
 be a fusion of data with concepts, an inspection of the presented 
 object by itself does not readily separate what is conceptual 
 from what is not conceptual. It may well be that the object ex- 
 ists as it is perceived; that the very whole intended is given, as 
 well as the sensory elements. The concepts may aid the mind to 
 grasp what is actually a complex datum, rather than cut it off 
 from a clear knowledge of the real object. And yet if the whole 
 content of every perception is taken to be a datum, it is impos- 
 sible to deny existence to the objects given in illusions, hallu- 
 cinations, and dreams. If I dream that I am in Thibet and awake 
 to find myself in my bed, I have been in Thibet and have been 
 miraculously transported to my bed. The conclusion must be 
 that, in some perceptions at least, only a part of the content is a 
 datum; in illusory perceptions, the interpretation of the data, 
 rather than the data themselves, creates the illusion. 
 
 There is a compulsion in perception which is not found in con- 
 ception, and this is why we conclude that a part, if not all, of the 
 content of the perception is given to the mind and exists. No 
 analysis of knowledge can ignore this compulsion of perceptions; 
 this is their claim to be presentations of reality. Concepts can be 
 altered at will so long as their references to perceptual objects 
 are disregarded; they are inventions rather than data. But per- 
 ceptions — even illusory and dream perceptions — are not 
 purely invented. There may, to be sure, be some metaphysical 
 sense in which the data of perception are created by mind; 
 nothing may be completely independent of mind in the most in- 
 clusive meaning of the term. The data of perception may be 
 nothing more than lively and compelling psychical states — 
 nothing more than Hume’s impressions; or they may be, as 
 Berkeley would have us believe, thoughts in the Divine Mind. 
 
TRUTH AND FALSITY 163 
 
 But this dependence on mind in a wider sense would not render 
 them, if they are truly data, any the less independent of thought 
 in a narrower sense, that is, of the mind’s conceptual or sym- 
 bolic activity as it has been described. If conceptual activity 
 created objects, there would be a real object for every thought; 
 ontological proofs could not be invalid; one could not think 
 without thinking of the existent, and even a phenomenal dis- 
 tinction between reality and illusion would disappear. Existing 
 objects in the limited sense now in question are independent of 
 concepts. Yet these objects are cognized in perceptions from 
 which concepts are never absent. 
 
 The most that can be said of the reality of a datum, apart 
 from the concepts through which it is known, is that it exists as 
 *‘something-or-other”’; and this is self-evident and trivial, for it 
 asserts merely that it is a datum. Such an indefinite predication 
 of existence is not yet the cognition of an object, and is not suffi- 
 cient for organized knowledge. To apprehend the reality of an 
 object is to apprehend more than the existence of “something- 
 or-other,”’ more than reality in general, though this wholly un- 
 specified reality is the only reality that givenness alone can con- 
 firm. The “something”’ which is real must be perceived to be of 
 a definite nature or in definite relations to other things; it must 
 be placed in reality, as well as perceived simply to exist. It will 
 then be brought under a concept; it will be apprehended through 
 a meaning. 
 
 No presentation can be dismissed as totally unreal, however 
 illusory its content may be. In a dream, the dream places, peo- 
 ple, events, are given to the mind and they exist. But they do 
 not exist as physical realities; they are dream objects only. The 
 fact that I perceive palaces, gardens, and praying fakirs in my 
 dream of Thibet is no illusion; the illusion is that I perceive 
 these as physical rather than dream realities. The deception 
 
164 SYMBOLISM AND TRUTH 
 
 vanishes when the data are differently conceptualized — when 
 the whole is placed in reality as a dream.’ 
 
 When reality is predicated of what is given in perception, this 
 is always a predication of something other than bare reality; it 
 is a predication of reality of a definitely intended sort. If, on the 
 contrary, the content of a perception is judged to be unreal, this 
 judgment does not mean that it is unreal without qualification. 
 It is unreal only under some concept, ¢.g., as a “physical” or 
 “external” object, etc. Bare existence belongs to every datum, 
 and the question for knowledge is: How can this existence be so 
 conceptualized that it fits in with other existences? 
 
 If perception were the apprehension of data and nothing 
 more, everything would be what it is perceived to be, and given- 
 ness in perception would be an absolute guarantee of the reality 
 of the object given as it is given. But a presentation from which 
 all conceptual elements were subtracted could be only an im- 
 mediate awareness of a reality that could be named or char- 
 acterized in no way. The datum would not be articulately expe- 
 rienced; it would be intuited rather than perceived. Truth, as a 
 property of symbols that mean existent objects, is not a refer- 
 ence to reality as it might be known in pure immediacy, but a 
 reference to perceived objects; and givenness in perception goes 
 only part way toward assuring reality to such objects. 
 
 VI 
 
 Do not sensations guarantee the existence of their objects, if 
 perceptions do not? Are not sense data “hard,” indubitable, and 
 free from conceptual elaboration? 
 
 1 “Tife and dreams are leaves of the same book. The systematic reading of 
 this book is real life, but when the reading hours (that is, the day) are over, we 
 often continue idly to turn over the leaves, and read a page here and there 
 without method or connection; often one we have read before, sometimes one 
 that is new to us, but always in the same book. Such an isolated page is indeed 
 out of connection with the systematic study of the book, but it does not seem 
 so very different when we remember that the whole continuous perusal begins 
 
TRUTH AND FALSITY 165 
 
 Sensationalism and empiricism have been frequently con- 
 fused. It has been taken for granted that what is given in ex- 
 perience is given through the senses alone and that there are no 
 data but sense data. And yet, search as we may for a pure sen- 
 sation, one is never found. “A pure sensation is an abstraction.””? 
 Sensations appear only in the context of perception, as the sim- 
 plest elements of presented wholes. Experience itself is of “a 
 teeming multiplicity of objects and events,” which cannot be 
 reduced to or derived from elements so thin as sense data; and 
 the attempt to do so is well characterized by James as “aban- 
 doning the empirical method of investigation.” ? 
 
 To recognize a sense datum is to observe that the complex 
 objects of perception can be analyzed into simpler constituents, 
 but this observation does not carry the implication that these 
 complex objects are (or are known as) sense data and nothing 
 else.* The table on which I write is brown, hard, and rectangular; 
 it is cold and smooth to the touch; yet these sensations, by 
 themselves, do not give the table I perceive. The perceived ob- 
 ject is more than sensory elements; it is these “thought” or 
 meant together into a whole. A pure sensation, or collection of 
 pure sensations, if there could be any such thing, would be as 
 near the negation of experience as anything imaginable. 
 
 Short of a purely intuitive knowledge, which would be an 
 awareness of no specific object or quality — not even of some- 
 thing as definite as a sensory quality — there are no cognitions 
 which do not make use of concepts. The elements in experience 
 which psychologists call “sensations” only approximate toward 
 pure sensations. The concepts through which the content of a 
 
 and ends just as abruptly, and may therefore be regarded as merely a larger 
 single page.” Schopenhauer, The World as Will and Idea, Bk. I, sec. 5. 
 
 1 W. James, The Principles of Psychology, ii, 1. 
 
 2 Op. cit., vol. i, ch. 9, p. 224. 
 
 3 The view which makes sense data the primary units of cognition speaks 
 of objects, situations, facts, as “constructs” from sense data, but we are urg- 
 ing that sense data are “‘destructs”’ from complex objects, situations, or facts. 
 
166 SYMBOLISM AND TRUTH 
 
 sensation is apprehended may have been thinned down to a 
 minimum; yet it cannot be maintained that concepts are wholly 
 absent so long as sense data are known as specific qualities, so 
 long even as they are definitely attributed to the senses. The 
 very predicate “sensation” conceptualizes them. The cognition 
 of objects, qualities, events, no matter how simple, is never any- 
 thing less than recognition; the mind intends, takes an attitude 
 appropriate to, the things it senses, and thus recognizes them as 
 things meant. A bare sensation, ¢.g., of red, does not spring into 
 my mind without a concept to meet it. My mind is prepared for 
 knowing red, and the sense datum stands forth from the back- 
 ground of purely immediate knowledge because “red” is what 
 I mean as well as what I sense. And if I mean “red,” a sign of 
 some sort is present. There is an image or an incipient vocal ut- 
 terance, etc., which carries what is in effect the proposition, 
 “this is red.” Through the concept, the sense datum becomes a 
 part of my articulated knowledge. Sensation then “differs from 
 perception only in the extreme simplicity of its object or con- 
 tent’’; ! and the outer limit of knowledge is not sensation but the 
 pure awareness, or intuition, which surrounds the whole act of 
 concrete knowing.” 
 
 Since conception is present everywhere in knowledge within 
 this outer limit, the richer experience of objects, events, situa- 
 tions, facts, has no less a claim to be taken as a datum, which 
 exists as experienced, than have sensations. The true empiri- 
 cism is not sensationalism. The true empiricism accepts the con- 
 tent of presentations in their wholeness and makes what it can 
 of them, rather than analyzing out the sensory aspects and de- 
 nying reality to all that remains. Sensationalism does violence to 
 experience and is the shortest road to scepticism, for, if only the 
 impermanent and insubstantial data of the senses exist, reality 
 speedily dissolves into a flight of subjective shadows. 
 
 1 W. James, loc. cit. 2 See below, ch. VIII, sec. xii. 
 
TRUTH AND FALSITY 167 
 
 The fact that experience in the full meaning of the term ap- 
 pears only when concepts, that is, thoughts and their references, 
 enter in cognition, does not make it necessary to hold that these 
 conceptual factors cut us off from reality. Concepts may facili- 
 tate as well as hinder the apprehension of data, for it is only by 
 means of concepts that the passing sensation is arrested and 
 experienced as an aspect of an object. When a landscape is be- 
 fore me, I know through the concepts that I am experiencing 
 trees, mountains, and a river, rather than a mere flow of sensa- 
 tions. The concepts may cause me to come into a closer cogni- 
 tive relation to the real, instead of causing me to misinterpret 
 and misconceive the real. Thought is not a veil separating the 
 mind from what exists. 
 
 Kant shattered Locke’s conception of the mind as a tabula 
 rasa; he made it evident that mind is active not passive in per- 
 ception. Even Locke faltered in his “‘blank-sheet”’ sensational- 
 ism. The mind, which, like a dark room with a single window 
 high in the wall, has at the beginning of Locke’s Essay only one 
 aperture of light, sensation, is discovered in the end to gain most 
 of its “complex ideas” from comparing, relating, and abstract- 
 ing the “ideas” which enter through the senses. The mind is 
 found to be active. Knowledge will not submit to the tabula rasa 
 description. 
 
 At every point in experience, thought — organization in a 
 conceptual scheme — is at work. Concepts, symbols and their 
 intentions, bridge the gaps between this experience and that, 
 between disorganized sensory presentations and integrated per- 
 ceptions; and empirical reality — reality in the sense in which 
 we are now speaking of it —comes into knowledge through 
 what might be called “presentational thinking.” 
 
 The view that thought isolates the mind from reality and 
 leaves a thing-in-itself shivering in the empty noumenal spaces 
 ‘beyond experience, might possibly be true for an ultimate real- 
 
168 SYMBOLISM AND TRUTH 
 
 ity. But Kant himself insists that the objects of experience, if 
 they are “transcendentally ideal,” are “empirically real.” They 
 are given in presentational thought, and this is their empirical 
 reality. Whether or not reality is, in the last resort, inaccessible 
 to thought, there must be some sense of the term “reality” 
 which makes the real accessible to thought; otherwise there 
 would be no objects of perception. Objects are capable of exist- 
 ing, in this meaning of the term, as they are perceived through 
 concepts — as presented wholes of definite characters or in 
 definite relations; and truth is reference to these objects. 
 
 Thought, therefore, may cause knowledge to approach the 
 real, or it may remove it from the real. Truth in perception is 
 possible for the same reason that illusion (or falsity) is possible; 
 because thought is a constituent of perception. And for this rea- 
 son, likewise, no perception in itself attests the existence of its 
 object as it is perceived. 
 
 Vil 
 
 The second criterion of existence, which is a necessary supple- 
 ment to givenness in perception, is consistency — consistency 
 with the whole of our organized knowledge. By means of this 
 criterion, the data of any single perception are fitted in with 
 other data and given a place in reality, as well as judged barely 
 to exist. At the same time, this criterion permits us to infer 
 with more or less certainty, depending on the strictness of the 
 inference, the existence of objects not given in perception.’ 
 (That this criterion of existence — consistency with the whole 
 of knowledge — does not render our definition of truth circular 
 will be presently shown.) 
 
 1 This metaphysical hypothesis, however, is extremely unstable, since the 
 thing-in-itself can be positively characterized in no way. It is an x, of which 
 one can say nothing more than that it does not appear in any experience; it is 
 something other than any possible object of experience. See below, ch. VIII, 
 sec. iii. 
 
 t The whole problem of the validity of induction is involved here. But if 
 any inductions are true, the objects they refer to exist. 
 
TRUTH AND FALSITY 169 
 
 The axiom that there can be no inconsistency in the real is 
 open to several interpretations, each of which turns on a differ- 
 ent notion of reality. 
 
 Consistency and inconsistency are relations between propo- 
 sitions or concepts — that is, between symbols. By definition, 
 p and q are inconsistent if, when one of them is true, the other 
 is never true. No two true propositions are inconsistent. Now, 
 on the assumption that an existent object is not a proposition or 
 a concept, it follows that the real cannot be truly said to be eithor 
 consistent or inconsistent, though the concepts through which it 
 is viewed give it the appearance of consistency or inconsistency, 
 
 The thorough-going rationalist, if he grants that reality is not 
 conceptual or propositional, will still believe that a complete 
 knowledge of the real through propositions would be a consistent 
 knowledge. He will postulate that reality is consistent in the 
 sense that it can be consistently conceptualized, even though it 
 is other than concepts. The anti-rationalist, on the contrary, 
 will assert that no consistent or inconsistent body of proposi- 
 tions is adequate to reality; that the real is wholly beyond con- 
 ceptual knowledge and is known no less truly through incon- 
 sistent propositions than through consistent ones — for, to the 
 anti-rationalist, neither could represent reality. Thus the thesis 
 of any one of the Kantian antinomies tells us as much, or as 
 little, about the Kantian reality as the antithesis; and M. Berg- 
 son joyfully embraces contradictions as a means of leading the 
 mind to intuitions, not because reality is contradictory but be- 
 cause it is beyond the grasp of concepts and propositions. “In 
 attempting to describe what we know in the abstract logical 
 terms which are the only means of intercommunication that 
 human beings possess, Bergson is driven into perpetual self- 
 contradiction, indeed, paradoxical though it may sound, unless 
 he contradicted himself his description could not be true.” ! 
 
 1 K. Stephen, The Misuse of Mind (1922), p. 12. 
 
170 SYMBOLISM AND TRUTH 
 
 Each of these interpretations of the axiom of the consistency 
 of the real — the rationalistic and the anti-rationalistic — refers 
 to an unlimited, an ultimate, reality. But the reality we have 
 been considering is limited, and the very principle of its limita- 
 tion is that it must be capable of being consistently presented 
 and represented. If there are realities which cannot be consist- 
 ently conceptualized, these are real in some more extended 
 sense. One cannot deny Kantianism or Bergsonianism unless it 
 be on metaphysical grounds; nor can he affirm the complete con- 
 sistency, the rationality, of the real. It may be that empirical- 
 rational knowledge floats on the surface of a world whose depths 
 are reached neither in perception nor in thought. Yet it is possi- 
 ble to go some distance with a less extended notion of the real, 
 which makes reality rational but does not preclude a final “ir- 
 rationalism.” 
 
 We mean then by a real object one which can be given in (or 
 inferred from) an experience which is consistent with the whole 
 of knowledge. Such real objects can be known through concepts, 
 as these concepts enter in perception; and if an object given in 
 perception is really what it appears to be, its characters and re- 
 lations will not have been created by the act of conception. A 
 real object is independent of concepts, though it may not be in- 
 dependent of mind on a much wider interpretation of this term. 
 Moreover, these real objects must have a structure; otherwise, 
 they could not be known through concepts, nor could they be 
 consistently assimilated to the whole of knowledge. 
 
 These are all necessary conditions of the reality of an object, 
 in the present limited sense, but it must be observed that they 
 are not sufficient conditions. The whole of knowledge might 
 conceivably be false, and then none of the objects presented in 
 such a consistent experience would be really what they are per- 
 ceived to be. The most we could truly say of them would be that 
 they had a bare existence, that they were not non-entities. And 
 

 
 TRUTH AND FALSITY 171 
 
 so we have not completely defined even this limited reality; we 
 have merely laid down certain conditions which it must fulfil, 
 we have confined it within certain boundaries. It remains still a 
 basic and undefined term, necessary to the analysis of truth. 
 
 VIII 
 
 For Kant the limits of experience were marked by the cate- 
 gories, which were necessary principles of thought, implicit in 
 the act of judgment itself. But Kant’s categories are empty of 
 content. The consistency of empirical-rational knowledge is 
 more than a purely formal consistency, more than fidelity to the 
 laws of logic — even of “transcendental logic.” Everything that 
 can be thought or experienced will, it is true, obey these formal 
 laws, but obedience to the laws of logic alone is no criterion of 
 existence. The touchstones of the reality of what is presented to 
 us are general truths which cannot be derived from the princi- 
 ples of logic. They are categories, but not categories which are 
 implicit in the nature of thought; no a priori deduction of them 
 is possible; they are always subject to revision. 
 
 First among these “empirical categories” can be placed the 
 generalizations of common sense that is, prescientific generali- 
 zations: nothing is ever both crooked and straight, round and 
 square, black and white; nothing is ever before something else 
 and at the same time after this same thing; nothing is ever out- 
 side something and at the same time within it; everything has a 
 cause; water does not flow up-hill — and countless other princi- 
 ples which do not follow from the postulates of logic but which 
 operate in determining the reality of objects. When I awake 
 from a dream of the other ends of the earth, though the experi- 
 ence has been sufficiently vivid to convince me of its physical 
 reality, I conclude that I was dreaming; for I could not have 
 been in two such distant places as the remote regions of the 
 earth and my own bed at so nearly the same time. The dream is 
 
172 SYMBOLISM AND TRUTH 
 
 inconsistent with common-sense physical categories. So long as 
 I conceive these events as physically real I am unable to place 
 them in experience without contradiction. 
 
 All well-established scientific principles operate in the same 
 way as the generalizations of common sense in determining the 
 reality of given objects. It is assumed that if an object is really 
 spatial or numerical in its nature it will not violate the principles 
 of geometry or arithmetic; that no material reality would trans- 
 gress the laws of mechanics, and no chemical reality the laws of 
 chemistry. Every new generalization, every new theory, adds a 
 further category under which reality is predicated of presented 
 objects; so that experience both tests and is tested by scientific 
 and prescientific generalizations. Laws, theories, and the facts 
 on which laws and theories are built mutually correct one an- 
 other. A generalization is verified by the existence of an object 
 which conforms to it in a special instance, or by the empirical 
 reality of something which can be deduced from it. At the same 
 time, presented objects are accepted as real because they are 
 perceived as special instances or consequences of general princi- 
 ples. The criterion of the truth of theories is empirical reality, 
 and the criterion of empirical reality, the truth of theories. 
 
 We may be mistaken in our perceptions themselves, or in the 
 assumptions, the body of theory, by which we estimate the real- 
 ity of what is given in perception, or in both. It is always possi- 
 ble that a new set of categories may completely overturn all 
 previous estimations of reality. Yet the fact that all perceptions 
 and all judgments are subject to error does not make it neces- 
 sary to believe that no perceptions, no judgments, give us real- 
 ity. When a presentation is consistent with the whole body of 
 knowledge, the presumption is overwhelmingly in favor of the 
 presented object being really what it is perceived to be. We can 
 
 1 “Theory” is here taken to mean any principle or body of principles that 
 exceeds the given. 
 
TRUTH AND FALSITY 173 
 
 attain no more certainty than this. There is no self-evident, un- 
 deniable badge of reality — unless it be of bare existence. The 
 categories that operate in fixing the places of presented objects 
 in reality are not a priorz and unalterable principles of reason, 
 blank forms of perception and judgment. They are accepted 
 universal truths which are themselves subject to error. The 
 mediaeval philosopher who, when he was asked to view the spots 
 on the sun through a telescope, replied — “‘I have read Aristotle 
 many times and I assure you that there is nothing of the kind 
 mentioned by him; be certain therefore that the spots which 
 you have seen are in your eyes and not in the sun” — was cor- 
 rect in method though not in fact. His categories were anti- 
 quated, but within these categories his reality was consistent. 
 
 A nice balance of theory and fact is for science the very prin- 
 ciple of its life. And if the “delicate, contentious, and fantasti- 
 cal”’ learning of the Middle Ages bore no fruit but the delight 
 in speculation for its own sake, the worship of fact alone cannot 
 bring forth even this fruit. Knowledge is a growing whole of 
 fact and theory. 
 
 IX 
 
 If truth is the correspondence of concepts or symbolic expres- 
 sions with existent objects, and an existent object is one given in 
 a perception that is consistent with the whole of knowledge, is 
 not the definition of truth completely circular? 
 
 It would be circular if consistency with the whole of knowl- 
 edge were identical with existence, that is, if concepts created 
 their own objects. But this is not the case. The existent is in- 
 dependent of the concepts through which it is known. Truth as a 
 property of symbolic expressions, and existence as a property of 
 objects, are not the same. Though existence can be definitely 
 predicated of objects only if certain general truths are consist- 
 ently applied in experience, the objects to which these truths 
 
174 SYMBOLISM AND TRUTH 
 
 refer stubbornly resist being reduced to thought-creations. 
 They are data given to thought but not invented by it, and 
 truth is reference to reality, not reality itself. 
 
 Consistency with the whole of knowledge is therefore a test of 
 existence and of truth, but it constitutes neither truth nor ex- 
 istence. Clearly, if truth is the correspondence of concepts with 
 existing objects, no true generalization could be inconsistent 
 with a perception of existing objects. True generalizations 
 would necessarily become tests of existence. But the existence of 
 objects would not thereby become a function of the truth of 
 these generalizations; nor would the truth of these generaliza- 
 tions be merely their consistency with perceptions of existing 
 objects. The tests of truth follow from the definition; they are 
 not equivalent to the definition. 
 
 Moreover, the consistency which is a function of the truth of 
 propositions ! could not define truth, for 2és definition presup- 
 poses the idea of truth. And if consistency means, as it other- 
 wise would, “conceivability” apart from truth or falsity, this is 
 equally far from being truth. One can invent an infinity of con- 
 sistent systems of concepts, if consistency is a matter of con- 
 ceivability, of definition, alone. Such systems remain non-con- 
 tradictory so long as the ideas in them are used with the original 
 definitions, and so long as the general principles of the construc- 
 tion of concepts are observed. But there is no compulsion, no 
 reason other than caprice, for defining an idea in one way rather 
 than another. The consistency of such a system gives it no refer- 
 ence to reality; it places it merely as one among an infinity of 
 “possibilities for thought.” If I find perceptual objects that can 
 be consistently conceptualized in the propositions of such a sys- 
 tem, the system has passed one test of truth; and if I further 
 discover that it is consistent with the whole of accepted knowl- 
 
 1 p and q are consistent if there is a case in which both are true, and incon- 
 sistent if, when the one is true, the other is never true. 
 

 
 — nl ——- —~- -~+ 
 
 TRUTH AND FALSITY 175 
 
 edge, it has passed another. Its truth is as nearly established as 
 possible. But the proof of truth and truth itself are different 
 things. The truth of the system is its correspondence to reality. 
 
 D4 
 
 The pursuit of “conceivability”” as a definition of truth leads 
 to the “coherence” theory, in which conceivability finally tran- 
 scends the limits of all ordinary thought. The essence of the cor- 
 respondence theory is that it holds thought and reality apart, 
 and the essence of the coherence theory, that it identifies them 
 — that truth, reality, and conceivability become one. Coher- 
 ence, as the term is used in this theory, is more than the con- 
 sistency of a single science or of all sciences. It is an ideal of 
 knowledge beside which all else is fragmentary and “mutilated,” 
 and to which no finite knowledge attains. 
 
 This is made plain by Mr. H. H. Joachim, who carefully dis- 
 tinguishes coherence from consistency: “The ‘systematic co- 
 herence,’ therefore, in which we are looking for the nature of 
 truth, must not be confused with the ‘consistency’ of formal 
 logic. A piece of thinking might be free from self-contradiction, 
 might be ‘consistent’ and ‘valid’ as the formal logician under- 
 stands those terms, and yet it might fail to exhibit that syste- 
 matic coherence which is truth.” ! For Mr. Joachim, to be “con- 
 ceivable” and “coherent” means to be “a significant whole”; 
 and ultimately there is only one significant whole — the Ideal 
 Experience, which is Reality. Nothing short of knowledge of 
 this Whole, this Absolute, is Truth. There are no separable 
 truths. A single isolated proposition is partly true and partly 
 false; it is incomplete, and no more than a faltering step toward 
 the perfection of knowledge — the one Truth. Mr. Russell, in 
 criticising Mr. Joachim, pointedly asks : Is the theory itself, 
 being not the whole of knowledge, wholly true? 2 
 
 1 H. H. Joachim, The Nature of Truth (1906), p. 76. 
 ? B. Russell, Philosophical Essays (1910), p. 150. 
 
176 SYMBOLISM AND TRUTH 
 
 Mr. Joachim’s examination of truth proves one thing cer- 
 tainly: that truth, as it appears in empirical knowledge, in sci- 
 ence and every-day thought, and in the despised reasoning of 
 the formal logician, is not the truth he is speaking of; that a 
 metaphysical criticism of knowledge passes beyond — and it 
 may be reverses — a descriptive epistemology. 
 
 The objections that Mr. Joachim levels against correspond- 
 ence are instructive; they illuminate the nature of this relation.’ 
 He points out that any correspondence must be a correspond- 
 ence of the structure of wholes as well as of their elements. Each 
 element must play the same part, fulfil the same functions, as 
 the corresponding element in the other whole; and thus the two 
 must be identical in structure. But he concludes that it is im- 
 possible to make out any such correspondence between per- 
 ceived wholes and conceptual or propositional wholes, giving as 
 his reason for this that: “‘On the one side, we have a whole of 
 experience at the level of feeling; and, on the other side, a whole 
 of experience at the level of reflective thought. To say that there 
 is (or may be) identity of structure is to maintain that these ex- 
 periences are different matters subsumed under an identical 
 form ... the idea of an identical structure in different materials 
 is quite inadequate when applied to the wholes in question, wz., 
 felt- and thought-wholes.” ? 
 
 The conclusion which Mr. Joachim rejects is exactly the one 
 that the analysis of logical form has led us to accept. Concepts, 
 symbolic expressions, and presented objects are indeed “differ- 
 ent matters subsumed under an identical form.” A perceived 
 
 1 There is no doubt, as Mr. Joachim shows, that unless reality — or a kind 
 of reality — were present in knowledge, the notion of truth as correspondence 
 to existent objects would be an unworkable hypothesis. Locke, for instance, 
 seems to be beating thin air when he describes truth as the reference of ideas 
 to unknowable objects beyond ideas. Yet even this theory cannot be shown to 
 be false. The most serious accusation that can be brought against it is that it is 
 quixotic; that it is impossible to apply the definition as a test of truth. 
 
 2 Op. cit., pp. 26, 29. 
 

 
 
 
 TRUTH AND FALSITY 177 
 
 whole is not merely “felt”’; perception is not on the level of pure 
 awareness in which nothing articulate is given. Objects are per- 
 ceived as having a certain structure, their elements are given as 
 grouped in a definite order, they are composed of major and 
 minor groups of distinct and recognizable forms. Reality, in the 
 present sense, is rationally presented in that it is analyzable, in 
 that its form is presented with it. And what Mr. Joachim calls 
 the structure of “reflective thought” is embodied in the group- 
 ing of the symbols in which the thought is expressed. The iden- 
 tity of form in propositions (symbolic groups) and perceived 
 objects brings about the correspondence of “reflective thought”’ 
 with fact, which is truth. 
 
 Correspondence it is true implies a distinctness, a separate- 
 ness or externality of the corresponding wholes. Yet in percep- 
 tion there is no separation of the concept, which is a constituent 
 of the presentation, from the datum. Datum and concept cannot 
 be disengaged and compared. Must one say that here the rela- 
 tion is no longer correspondence, that datum and concept be- 
 come one in “presentational thought,” where the margin of dis- 
 tinctness between them is so narrowed that the object is given 
 along with (or through) the proposition which is true of it? This 
 is undoubtedly Mr. Joachim’s view; a perception, he believes, is 
 already at the level of “reflective thought”; there is nothing ex- 
 ternal to the perception to which it can correspond. 
 
 A pure concept, that is, a proposition whose object is not 
 given in perception along with it (or through it), is, on the other 
 hand, clearly distinct from its object and can be said to corre- 
 spond to the object; e.g., ““Napoleon escaped from Elba”’ is 
 purely conceptual, its object does not accompany it, and hence 
 there is no difficulty in describing its truth as correspondence to 
 fact. Scientific theories, generalizations, historical statements, 
 memories, predictions — the larger part of knowledge — are 
 purely conceptual; such propositions are distinct from the ob- 
 
178 SYMBOLISM AND TRUTH 
 
 jects of which they are true and can be said to correspond to 
 these objects. But, as Mr. Joachim points out, this is an unim- 
 portant type of correspondence, and it cannot be truly said to be 
 correspondence — but is rather coherence — unless the truths 
 of perception can be likewise shown to be genuine cases of corre- 
 spondence. 
 
 There is no doubt that in perception the proposition and the 
 object cannot be torn apart, the concept fits the object as the 
 die fits its cast, the two coincide as superimposed figures in ge- 
 ometry might; and the only evidence of a discrepancy is the in- 
 consistency of the perception with other experiences. Yet the 
 relation however close must still be correspondence when the 
 concept is true, for so long as the concept and the object are not 
 identical they are distinct. One would be justified in giving up 
 the notion of correspondence only on the hypothesis that the 
 proposition and the datum are the same. And this is the funda- 
 mental reason beneath the objections of the coherence theory to 
 correspondence as a definition of truth: the coherence theory 
 wishes to eliminate the distinction between thought, or concep- 
 tion, and reality. Certainly if an existent object is identical with 
 a coherently thought object, it is absurd to speak of truth as the 
 correspondence of concepts with existent objects. But existence 
 must be independent of concepts, where conception is anything 
 short of the coherent — and unattainable — thought which is, 
 for Mr. Joachim, Reality; especially, where conception is the 
 significant use of symbols. For if existence were identical with 
 conception, every thought would refer to a real object. We could 
 not escape thinking of the existent; there would be no falsity. 
 Since the existent and the conceptual are distinct, their relation 
 is correspondence, however narrow the margin of separation for 
 knowledge between them; nor does identity of structure make 
 the proposition and its object one. 
 
 The notion that the structure of thought is found in the sym- 
 

 
 
 
 TRUTH AND FALSITY 179 
 
 bols it uses to express itself and that this same structure perme- 
 ates the world of real objects, at least the real objects which can 
 be presented in a consistent experience; the further notion that 
 these real objects are not identical with concepts and yet can be 
 apprehended only by the use of concepts, though they may in 
 this way — even in perception — be apprehended falsely; these 
 ideas give a complete and simple meaning to the definition of 
 truth as the correspondence of concepts to reality. At the same 
 time, the notion of syntactical significance, of meaning which is 
 directed toward the world of objects yet need not terminate in a 
 single object or fact, permits propositions to be false without 
 robbing them of their significance. Truth becomes in a literal 
 sense a property of symbols, for propositions and concepts are 
 symbols or symbolic groups as they function in minds. All this is 
 implicit in Hobbes’s statement that “‘true and false are attri- 
 butes of speech, not of things . . . truth is the right-ordering of 
 names.” 
 XI 
 
 Since meaning alone is all that is necessary to truth and fal- 
 sity, belief and disbelief, assertion and denial —in short judg- 
 ment — fall outside the discussion of truth and falsity proper. 
 Yet from one point of view, judgment is closely connected with 
 truth, for no truth is genuinely known until it is judged or be- 
 lieved. To know truth is to judge, but to be in doubt, to enter- 
 tain ideas without assertion, to perceive without believing, is 
 not to know truth. 
 
 Assertion and denial, belief and disbelief, are secondary atti- 
 tudes toward propositions. They supervene on the primary atti- 
 tude of understanding, which is that of holding the proposition, 
 the symbol or group of symbols, before the mind with a con- 
 sciousness of their reference but without regard to whether or 
 not there is an object to which they refer. To understand is to 
 frame a hypothesis, to put one’s self in a state of inward prepa- 
 
180 SYMBOLISM AND TRUTH 
 
 ration for an object when the mind is still in doubt as to the ex- 
 istence of such an object; and here the attitude of understanding 
 ends, or else passes by a gradual transition into that of belief. 
 
 To believe an idea was, for Hume, to have it vividly present in 
 consciousness; but the vividness of ideas is a cause of belief 
 rather than belief itself. It is certainly true that a lively percep- 
 tion of an object or an especially clear understanding of a propo- 
 sition tends to become a belief. Entertain an idea for a suffi- 
 ciently long time and you will believe it; 1 for belief is of the 
 same mental genus as understanding. Both are preparations for 
 objects, both are intentions of the mind with a direction beyond 
 the mind’s present content. Belief differs only in being a more 
 complete preparation, a more earnest intention. Belief is readi- 
 ness to act as if the proposition which is understood meant an 
 existent object. It is willingness to use the proposition as if it 
 were true. 
 
 As against Hume’s notion that belief is the vividness, insist- 
 ence, or compulsion of ideas, it is only necessary to observe that 
 one may suffer from a vivid illusion without believing that the 
 illusory content is what it appears to be. Though one tends to 
 believe anything he understands (or its negative, which is sug- 
 gested by it), and particularly to believe what is given in percep- 
 tion, still there is a point of transition between entertaining an 
 idea or being presented with a content, and believing in the 
 truth of this idea or the existence of this content. This transition 
 cannot be described as a passage to clear understanding or vivid 
 presentation, for the understanding may be already clear, the 
 presentation already vivid. It is a transition to a new state of 
 mind, to a state of mind which has something in common with 
 the apprehension of meanings or of presented contents, but is 
 nevertheless distinct. 
 
 The existence or non-existence of the things our thoughts 
 
 1 Or believe its negative, which is suggested by it. 
 

 
 TRUTH AND FALSITY 181 
 
 mean, the truth or falsity of concepts, adapts these concepts to 
 uses which would not otherwise be possible. A true proposition 
 can be employed as a premise in an inference in a way in which 
 a proposition merely entertained cannot be employed. The 
 truth and falsity of ideas makes possible a calculable and suc- 
 cessful commerce with the world of fact; so that the value of 
 truth is, in the first place, practical. Yet if truth is good as a 
 means toward other ends, it is also good in itself — as an end 
 toward which a certain intellectual interest is directed. 
 
 But there is an intellectual interest which is wider than the 
 interest in truth: this is the interest in possibilities, in fancies or 
 fictions for their own sake. The apprehension of significance, 
 that is, of possibilities for thought (constructive imagination) is 
 the primary function of the intellect, and if the truth of these 
 possibilities added to them no qualities of use or attraction, 
 thought would end in hypothesis. There would be no judgment; 
 the existence or non-existence of objects meant would be of no 
 moment. To the dreamer, the truth of his dream is irrelevant; to 
 the believer, the truth of his belief is indispensable, for the mo- 
 tive of belief is the interest in truth. Thus beyond judgment lies 
 pure speculation; add the interest in truth, which is the widest 
 — the most impractical — of practical interests, and you add 
 belief. 
 
 XII 
 
 Belief is more than the thought of existence coupled to a con- 
 cept, and this is another reason why it must be regarded as a 
 new attitude of mind, distinct from (though continuous with) 
 conceiving and perceiving, however vivid and clear. To assert 
 and believe that “Shakespeare wrote Hamlet” is not to entertain 
 the thought of “the existence of Shakespeare’s authorship of 
 Hamlet,” for this is itself a concept and not a belief. Belief and 
 assertion take a step that carries the mind beyond conception; 
 
182 SYMBOLISM AND TRUTH 
 
 they leap the gap between conception and existence by trans- 
 forming the hypothetical into the categorical. 
 
 This is strikingly put by Hume in a passage in which he also 
 shows that a single concept (that is, on our view, a single word 
 or symbol) can be true or false and can be affirmed or denied. He 
 comments on the accepted definitions of conception, judgment, 
 and reasoning as follows: “‘ Conception is defined to be the simple 
 survey of one or more ideas: judgment to be the separating or | 
 uniting of different ideas: reason to be the separating or uniting 
 of different ideas by the interposition of others, which show the 
 relation they bear to each other. But these distinctions are faulty 
 in very considerable articles. For, first, it is far from being true, 
 that, in every judgment which we form, we unite two different 
 ideas; since in that proposition, God is, or indeed any other 
 which regards existence, the idea of existence is no distinct idea, 
 which we unite with that of the object, and which is capable of 
 forming a compound idea by the union. Secondly, as we can thus 
 form a proposition which contains only one idea, so we can exert 
 our reason without employing more than two ideas... . Whether 
 we consider a single object or several; whether we dwell on these 
 objects, or run from them to others; and in whatever form or 
 order we survey them, the act of the mind exceeds not a simple 
 conception; and the only remarkable difference which occurs on 
 this occasion is when we join belief to conception, and are per- 
 suaded of the truth of what we conceive.” ! 
 
 As for Hume’s first point, judgment is undoubtedly more 
 than a union of the idea of existence with a concept. The onto- 
 logical proof of God fails to produce belief because it is apparent 
 that the addition of the idea of existence to that of God does not 
 make the latter any the less a concept. But Hume, who is con- 
 firmed by Kant on this point, is not wholly correct in saying that 
 ‘*the idea of existence is no distinct idea, which we unite with 
 
 1D. Hume, A Treatise of Human Nature, vol. i, part iii, sec. 7, note. 
 

 
 TRUTH AND FALSITY 183 
 
 that of an object.” It is possible to conceive of the existence, or 
 for that matter of the non-existence, of something meant; e.g., 
 “the non-existence of the round-square”’ is an intelligible ex- 
 pression. Existence can be a predicate, even if it is the most gen- 
 eral possible predicate. The important fact is that, although ez- 
 astence is a predicate which can be added to concepts, belief goes 
 further than the addition of predicates to concepts. It com- 
 pletely removes the concept from the area of the hypothetical. 
 
 The second point made by Hume in this passage is of special 
 interest in connection with the present definition of truth. Hume 
 declares that a single idea or concept can be judged and can be 
 true or false, though truth is usually thought to belong only to 
 propositions and it is not customary to give the name “propo- 
 sition”’ to anything less than what is expressed in a complete 
 sentence. “God,” “evil,” “the king of England,” and similar 
 fragmentary expressions are not commonly said to exhibit truth 
 or falsity. But the difference between a word or a phrase and a 
 full sentence is not that the one is capable of being true or false, 
 while the other is not; the difference is that the one (usually) 
 embodies an assertion or a denial, while the other embodies 
 something merely understood, assumed, held before the mind 
 without assertion or denial. “‘God is,’”’ “‘evil is,” are assertions 
 of what is meant by “God” and by “evil.”’ The single words 
 (unasserted) are therefore as much entitled to be taken as propo- 
 sitions (unasserted) as are any completed sentences.! 
 
 1 Whether we are to name single words and incomplete phrases “propo- 
 sitions,”’ is a verbal question. The term “proposition,” if one so wishes, can be 
 reserved for complex expressions which have the completeness of full sen- 
 tences. But this will not alter the fact that the less complex expressions are 
 either true or false. Propositions — even if they are held always to be complex, 
 a union of subject, predicate, and copula — are unities which are affirmed and 
 denied as wholes, and which are true and false as wholes. The subject-predi- 
 cate logic, which asserts that the predicate is affirmed or denied of the subject, 
 that it is true or false of the subject, breaks un the unity of the proposition and 
 
 is at a loss to restore it. Yet this unity must be restored if there is to be truth. 
 A proposition composed of a subject, predicate, and copula is true only if both 
 
184 SYMBOLISM AND TRUTH 
 
 For some symbols, then, — for those which refer directly to 
 objects and are not merely defined through symbolic groups, — 
 truth and significance are the same thing. Knowledge, being 
 built on elementary simple symbols which refer thus to objects, 
 takes its rise from true concepts or “true symbols,” and falsity, 
 which appears later, rests on truth. Only when a kind of signifi- 
 cance which is other than a direct reference to objects is devised 
 does falsity become possible. But any symbol, either simple or 
 complex, is either true or false, and a full sentence differs from a 
 fragmentary phrase or a single word only in that the former is 
 asserted or judged, while the latter is (usually) simply considered 
 or understood. 
 
 XIII 
 
 Just as the primary attitude of understanding is carried by 
 symbols, so also is the secondary attitude of belief. Beliefs do 
 not hang in mid-air cut off from expression. One believes when 
 he expresses this attitude by some sign to himself or to others, 
 and since belief is readiness to act, a natural and common sign 
 of belief is action. I know that I believe most of my perceptions 
 because I act as if what appears in them were really what it 
 seems to be; moreover, I am often unaware of what I believe un- 
 til I assert it, which shows that belief is inseparably bound to its 
 expressions. 
 
 the subject and predicate mean something existent, and — what is more im- 
 portant still — only if there is an existent whole in which the predicate is 
 united by the relation of predication to the subject. The fact that the propo- 
 sition can be broken up into a subject, predicate, and copula is not therefore 
 the reason for its being true or false. This necessary unity of meaning in a 
 proposition suggests that the term “‘proposition” can be used for any whole 
 which has a unified meaning, and this would not exclude single words or in- 
 complete phrases. We might speak of a single word as an “‘unanalyzed propo- 
 sition” in contrast to all symbolic groups, which would be “‘analyzed propo- 
 sitions.”” Among analyzed propositions we should need to distinguish descrip- 
 tive phrases as a special class. On this more extended interpretation of the 
 term, a proposition would be any unified meaning; and since on our view 
 meanings are carried only by symbols, it would be any symbol or group of 
 symbols taken in its function as an instrument of significance. 
 

 
 TRUTH AND FALSITY 185 
 
 Assertion is so closely related to belief that it is impossible 
 sharply to distinguish them. If there is any difference it is this: 
 that assertion is the inward or outward expression of belief by a 
 sign, while belief itself is the attitude expressed. A full sentence 
 always contains a sign of belief: ““money is the root of all evil” 
 stands for two things, for the fact and the belief in the propo- 
 sition; while “money’s being the root of all evil” signifies the 
 same fact without the belief. (The passage from consideration to 
 belief is often marked in thought by the insertion of the verb 
 “is,” or its equivalent, in the train of inward speech which 
 passes and repasses in the mind.) If one openly asserts some- 
 thing he does not believe, the presence of the sign of assertion is 
 nevertheless calculated to produce belief in others. 
 
 The copula or any symbolic element equivalent to the copula 
 has a triple réle in judgment. Its primary function is to call at- 
 tention to the truth of the proposition in which it appears, to 
 signify that this proposition is believed or ought to be believed. 
 Secondly, it indicates the unity of the whole, though it is not 
 necessary that the copula be present in order that the propo- 
 sition be taken as a whole; the syntactical signs give the sym- 
 bolic group its unity of meaning. Thirdly, the copula adds the 
 predicate existence to the concept. But of these three functions, 
 the first — as a sign of assertion — is the essential one.! 
 
 XIV 
 
 Belief and disbelief appear, on first thought, to be direct 
 opposites which are related to one another as desire is to aver- 
 sion, approach to withdrawal, or acceptance to rejection. Yet 
 disbelief cannot be the witholding of belief, for this is under- 
 standing or consideration without belief or disbelief, without 
 affirmation or denial. Nor can it be the dismissal of the propo- 
 
 1 There is still a fourth meaning of the copula: its use to signify identity, 
 e.g., “Scott zs the author of Waverley.” 
 
186 SYMBOLISM AND TRUTH 
 
 sition disbelieved as meaningless, for an idea must be enter- 
 tained if it is disbelieved. Disbelief if more than the suspension 
 of judgment, the refusal to commit oneself. It is as affirmative 
 as belief. 
 
 “The true opposites of belief, psychologically considered, 
 are,” in the opinion of William James, “‘doubt and inquiry, not 
 disbelief”; 1 and this suggests that disbelief is really a species of 
 belief. Disbelief is a belief in the falsity of a proposition, that is, 
 that there is no existing object corresponding to it; and thus dis- 
 belief is a belief in the truth of the proposition “‘p is false.”’ By 
 the principle of the excluded middle, either p or not-p is true, so 
 that “‘p is false” is equivalent to “not-p is true,” and “‘p is true” 
 is equivalent to “not-p is false.’’ Hence to disbelieve a propo- 
 sition, to believe that “‘p is false,”’ is in effect to believe its nega- 
 tive. (And the converse is also true; to believe a proposition is in 
 effect to disbelieve its negative.) Disbelief, instead of being the 
 negation of a belief, is the belief of a negation. 
 
 But if belief is an attitude of preparation, completer prepara- 
 tion than understanding, for an object intended by a proposi- 
 tion, how can one believe a negative? Are there negative ob- 
 jects? Can one act as if something negative were in existence? 
 For this is what belief in a negative would require. If I assert 
 that “I have not been in China” and expect this proposition to 
 be believed, the assertion must refer to some objective content 
 to which the belief can be fastened. Negatives must have a point 
 of attachment to existing objects. This being the case, denials 
 will take a place beside assertions as positive judgments which 
 are equally useful in inference and equally necessary in bringing 
 about successful adjustments to the world of fact. Full-blown 
 disbelief differs from belief only in the nature of the content 
 toward which it is directed; it is not a different attitude of mind. 
 
 Every proposition tends to suggest its negative. To under- 
 
 1 W. James, Psychology, vol. ii, ch. 21, p. 284. 
 

 
 
 
 TRUTH AND FALSITY 187 
 
 stand the meaning of a proposition is also to understand the 
 meaning of its negative, and hence the intention which carries 
 the significance may as readily pass over into disbelief as belief. 
 To entertain the idea of p is also to entertain the idea of not-p: 
 it is to be in readiness for two mutually exclusive contingencies. 
 The added psychical pressure of belief may be in the direction of 
 one or the other, but in either case this new attitude of mind 
 will be continuous with, not opposed to, the attitude in which 
 the idea is merely understood or considered as a possibility. 
 When it is said that any idea which is understood tends natu- 
 rally to be believed, this means that either its positive or nega- 
 tive tends to be believed; in other words, that the tendency to 
 belief is always present in understanding but forks toward the 
 two alternatives, one of which is disbelief. 
 
 There is, on the other hand, a frame of mind in which one ex- 
 periences an intellectual aversion toward accepting either the 
 truth or falsity of ideas, in which he says “no” without affirm- 
 ing or denying the proposition thus met; an attitude of simple 
 incredulity, appropriate to strange phenomena or extraordinary 
 concepts. It is this attitude which is directly opposed to belief. 
 I may, like Aladdin before the hidden jewels, rub my eyes in the 
 very presence of an unfamiliar sight, and be unwilling to act 
 either as if it were real or unreal. This attitude, which is familiar 
 to all men, completely replaces belief (and disbelief) in the mind 
 of the sceptic, who knows no truth and is not even sure that he 
 knows no truth. 
 
 Incredulity supervenes on and is provoked by the survey of 
 possibilities for thought, but like its opposite, belief, it is a de- 
 parture from the attitude of merely considering possibilities. 
 The sceptic does more than understand or entertain the ideas of 
 which he is sceptical; he sets his mind against them, he inhibits 
 the natural tendency to affirm or deny the propositions he holds 
 before his understanding. Incredulity is a definite shrinking 
 
188 SYMBOLISM AND TRUTH 
 
 from belief or disbelief, and not simply the survey of possibili- 
 ties for thought; and this is why it is the genuine opposite of 
 belief. Thus in a mood of pure speculation or fancy, scepticism 
 has no more place than belief or disbelief. It is quite as inappro- 
 priate to be incredulous of a myth or a romantic tale as to in- 
 quire whether it is true or false; to be sceptical as to whether the 
 Ancient Mariner shot the albatross is no less irrelevant than to 
 believe or disbelieve it. Yet to the thoroughly incredulous per- 
 son, the true sceptic, a world of fancy — whether it be of roman- 
 tic, scientific, or metaphysical fancy —is still open. Thought can 
 range where it will among possibilities, for if possibilities for 
 thought were not left to the sceptic, there would be nothing to 
 be incredulous of. 
 
 Scepticism is a sophisticated philosophy because only by dint 
 of much thinking, much turning over of possibilities, do ideas so 
 completely nullify one another that none seems worthy of ac- 
 ceptance. The unsophisticated man on the contrary is credu- 
 lous, for concepts, ideas merely entertained, project themselves 
 toward action and belief. Incredulity, when it is not erected into 
 a philosophy, is unstable; it can play no positive part in knowl- 
 edge. It can prevent us from falling into error and nothing more» 
 but it can be of no use in shaping a course of action, in arriving 
 at conclusions either in theory or practice, as positive denial 
 can be. The “no” of the sceptic is the “no” of indecision. To 
 be incredulous is to attain no end, but positively to deny a 
 proposition is to believe something which may be of use. 
 
 XV 
 
 Belief and disbelief, denial and assertion, are the only avenues 
 of approach to truth. Though truth is not manufactured by 
 1 Aristotle denies even the consideration of possibilities to the sceptic, for 
 
 he believes that one must accept the truth of the principle of contradiction if 
 he thinks in any sense of the term. See Aristotle, Metaphysics, bk. iii, ch. 4. 
 

 
 TRUTH AND FALSITY 189 
 
 judgments, it does not stand out for knowledge in isolation from 
 the judgments through which it is known. The cognition of 
 truth, like that of beauty or good, is colored by an interest, 
 which is the motive of judgment — the interest in truth. And 
 just as it is possible to lose sight of the objects toward which the 
 moral and aesthetic interests are directed, and to confuse beauty 
 and good with the feelings they arouse, so it is possible to mis- 
 take truth for the feeling of certainty that accompanies satis- 
 factory belief. Truth is then reduced to a psychological state; it 
 becomes a matter of intellectual taste, as beauty and good, on 
 the parallel theory, are matters of aesthetic and moral taste. 
 
 The contradiction in this psychological relativism appears in 
 the answer to the question which Plato put to the Sophists: If 
 belief is the measure of truth, and I believe that this is not so, do 
 I not believe truly? ! There is no reply but an affirmative one on 
 the Sophists’ own hypothesis, and only if the relativist is willing 
 to give up the law of contradiction, does his view sustain itself. 
 
 Scepticism, like relativism, often arises from the fact that 
 truth can be known only through belief; but this philosophy, 
 extending as it does no further than incredulity — incredulity 
 reiterated and reinforced by incredulity — is born of too great 
 rather than too little love of truth. The sceptic disdains to find 
 truth in the feeling of certainty. He withholds judgment to the 
 very last and does not deny truth, for he is aware that a single 
 judgment — even the judgment that there is no truth, or that 
 he doubts that there is truth — is like a stone cast in still water: 
 the circles widen outward, embracing a more and more extended 
 region, so that if one affirmation or denial is ventured on there is 
 no stopping short of a theory of truth and reality. He therefore 
 finds all things, perceived and unperceived, to be unacceptable 
 to the intellect, indifferent to knowledge. 
 
 Hume’s scepticism goes only part way. He is incredulous of all 
 
 1 Plato, Theaetetus, Jowett’s translation, marginal p. 161. 
 
190 SYMBOLISM AND TRUTH 
 
 metaphysical theories, but not of the psychological processes by 
 which ideas are joined together and brought into relation to the 
 “‘impressions’’ of the senses. Yet he is acutely conscious that 
 knowledge is belief — and, it may be, nothing but belief. If we 
 could attain truth, he argues, we could not be certain that we 
 had, for we should still be believing. The mind, like a moth at- 
 tracted by a light, trusts its impressions because it cannot help 
 doing so; but that these impressions are true of a reality given in 
 them or beyond them remains forever no more worthy of belief 
 than disbelief. Hume sees knowledge only from the psychologi- 
 cal angle, and leaves it hopelessly tossed between this “‘irresist- 
 ible” idea or impression and that, but with no anchor for any be- 
 lief. And Hume, too, touches the profounder scepticism that 
 doubts even itself; there are revulsions from philosophy, sudden 
 returns to common sense, when the most ordinary beliefs seem 
 to him no better or worse than the finest-spun philosophy. 
 
 Scepticism of this sort can be escaped but not refuted. One 
 can easily imagine Hume undermining the whole structure of 
 Kant’s “refutation” by merely pointing to the fact that it is 
 built on belief. Scepticism, in its subtler forms, is an over-cau- 
 tious, not a self-contradictory, philosophy. It refuses to take 
 the leap of belief — to undergo the risk of error that is never 
 absent from knowledge. 
 
 The one final criterion of truth is our capacity to believe prop- 
 ositions; though a belief may be arrived at by circuitous routes, 
 the ultimate evidence of truth is the compulsion of a belief. If 
 one asks for what reasons he holds a conviction, it is either on 
 the strength of some other conviction, or on the inherent 
 strength of the conviction itself. Try as he may, he cannot 
 break the circle of his beliefs. To test truth we must assume 
 truth; we must believe that there is some valid principle by 
 which truth can be tested, and that there is a truth to test. 
 
 It is not difficult for the sceptic to show the risk of defining or 
 

 
 
 
 Ht 
 
 TRUTH AND FALSITY 191 
 
 attempting to test truth. Consider the test that has been pro- 
 posed, consistency with the whole of knowledge. How complete 
 must this knowledge be? Clearly, no experience is ever complete; 
 there are always additions and corrections; in the light of fur- 
 ther experience what now appears to be consistent may prove to 
 be inconsistent. Yet if the test of truth is consistency with’an in- 
 complete experience, this is too narrow; no allowance is made for 
 the reversals to which any growing body of knowledge is sub- 
 ject. But what could be meant by a “‘complete experience’’? Is 
 this something more than a personal knowledge—is it all know]- 
 edge, past, future, possible, including that of other minds, as it 
 might be brought together in a single mind? If so, much as one 
 might like to appeal to this complete experience, he cannot do 
 so; for he can see through no other eyes than his own, and know 
 through no other mind than his own; and he can know only in 
 the present. The test he actually can apply is that of consistency 
 in his experience at the present moment — the present including 
 memories of the past; and this is only a small measure, a feeble 
 approximation, to complete consistency. Furthermore, it may 
 be that reality is not self-consistent, that consistency is read into 
 it by the mind, that reality slips between the eager fingers of the 
 intellect, leaving only a shell of empty appearances. 
 
 But the very imperfections of this test show how the circles of 
 belief strive to push outward beyond the phenomenal to that 
 which can in no sense be called an “‘appearance.”’ The concept of 
 truth links itself inevitably to that of reality. A truth grounded 
 in anything less than a complete, a metaphysically conceived, 
 reality will still be open to question in the mind that conceives 
 this truth. A theory of knowledge without a metaphysics is at 
 best only a partial repudiation of scepticism. If one embarks on 
 an examination of truth, the security of his position will ulti- 
 mately depend, not only on a faithful description of knowledge 
 as a phenomenon, but on the scope of the concept of reality to 
 
192 SYMBOLISM AND TRUTH 
 
 which he finally comes. He will need to complete the picture by 
 a metaphysics of knowledge. 
 
 XVI 
 
 What has been said of truth, existence, and judgment can be 
 summarized as follows: 
 
 The correspondence of propositions or concepts with existing 
 objects is truth, but a proposition (or concept) is not a subsist- 
 ing tertium quid interposed between symbols and objects; it is 
 the symbols themselves, taken with the intention or psychical 
 set they arouse in a mind. This does not deprive the proposition 
 (or symbolic expression) of an objective reference, a direction 
 toward the world of objects, even though there exists or subsists 
 no referent for it as a whole. For its meaning is a function of 
 simpler meanings united in a scheme of logical structure; and 
 these simpler meanings, being direct references to objects that 
 exist or have existed (or being definable in terms of such direct 
 references), give the complex meaning a direction beyond the 
 mind’s present content. Moreover, the structure of the expres- 
 sion codperates in determining the whole to have an objective 
 reference, since the object meant (if there is an object meant by 
 the whole) must be identical in this respect with the expression; 
 and if the whole stands for no object, the structure, being a uni- 
 versal which could occur in a factual as well as a symbolic in- 
 stance, will still refer beyond itself. The assumption of subsist- 
 ent entities as the termini of meanings is therefore unnecessary ; 
 especially since meaning is not a static relation between the 
 mind and some second term, but an activity — an activity of 
 preparation or anticipation, which presupposes the presence in 
 no sense of the object anticipated or prepared for. It is necessary 
 only that some objects — those which are directly referred to by 
 the constituents of the symbolic group — shall have been pre- 
 sented, in order that complex expressions should have a mean- 
 

 
 
 
 TRUTH AND FALSITY 193 
 
 ing; these expressions in their entirety do not need to refer to 
 any entity, subsistent or existent. Thus a false proposition is 
 one which is significant, yet stands as a whole for no existing 
 object or subsisting objective. The category of objectivity is no 
 wider than that of existence. 
 
 The term “existence” or “reality” is used in a limited sense, 
 though it is not defined; and the criterion of existence, which is 
 also the criterion of truth, is the presentation of an object in an 
 experience consistent with the whole of knowledge. Inferences 
 based on such perceptions (if these inferences are valid) permit 
 us to reach objects not given in perception. Every perception 
 has a datum, but the datum is always perceived under a con- 
 cept. Concept and datum coalesce to form a whole of presenta- 
 tion, so that what is given and exists independent of the percep- 
 tion cannot be disentangled from what might be added through 
 concepts, by the mind’s invention. Sense data are the simplest 
 elements of presented wholes, but even these data are not purely 
 immediate; the mind in recognizing them brings them under 
 concepts. Therefore sensationalism, which grants existence only 
 to the data of the senses and fails to observe that a sense datum 
 is never known in complete isolation from presented wholes, is 
 not the true empiricism; the complex perceptions of objects, 
 situations, and facts have an equal claim to be taken as presen- 
 tations of reality. Indeed, the concepts in perception may bring 
 us into a closer cognitive relation to the real, rather than sepa- 
 rate us from the real, for the mind is more than a blank sheet on 
 which objects write impressions. 
 
 No presentation in itself guarantees to its datum anything 
 other than bare existence, reality of an indefinite sort; but it 
 does guarantee this thin reality even to the data of dreams, illu- 
 sions, and hallucinations. When the data are apprehended as 
 objects of this or that sort, or in this or that relation (as they 
 must be apprehended if they are to enter into organized knowl- 
 
194 SYMBOLISM AND TRUTH 
 
 edge), a further criterion of existence than givenness is needed. 
 The data must be placed in reality under a concept which makes 
 the presentation consistent with the whole of knowledge. 
 
 This consistency with the whole of knowledge is a criterion of 
 existence for this reason, that the existence which gives truth, in 
 the present meaning of the term, to symbolic expressions is re- 
 stricted to objects which can be consistently conceptualized, 
 which can be fitted into rational knowledge without contradic- 
 tion. This does not assumé that reality is finally self-consistent, 
 or that it can be completely known through consistent concepts. 
 Nor does it assume the contrary, that neither consistent nor in- 
 consistent concepts are adequate to the real. That the existent 
 is capable of being consistently presented and represented is the 
 limiting condition of the notion of reality on which this defini- 
 tion of truth rests, but it need not be a condition of a more ex- 
 tended reality. 
 
 Consistency is determined not by the laws of logic alone, or 
 by formal “categories,” but by general truths, empirical cate- 
 gories, which are subject to revision and reversal. All well-estab- 
 lished scientific principles and a host of prescientific generaliza- 
 tions operate as tests of the reality of perceived objects. The 
 criterion of the existence of objects is the truth of theories, and 
 the criterion of the truth of theories is the existence of objects. 
 Theory and perception mutually support and correct one an- 
 other. This fact does not make the definition of truth circular. 
 Truth is correspondence to reality, and so it follows that per- 
 ceptions of existing objects will be consistent with general 
 truths, but it does not follow that existence is a function of 
 these truths, nor that truth and consistency are the same. Con- 
 sistency is a test of truth but is not equivalent to truth. 
 
 The “coherence theory” rejects correspondence as a defini- 
 tion of truth because this relation implies the distinctness of the 
 corresponding wholes and hence the separateness of knowledge 
 

 
 
 
 TRUTH AND FALSITY 195 
 
 and reality. The “‘systematic coherence” which is, on this view, 
 at once Truth and Reality transcends the consistency of formal 
 logic and ordinary thought. Thus there can be no separable 
 truths, for such truths would not be the whole Truth. Though 
 reality as thus conceived may be identical with thought as thus 
 conceived, the limited reality of perceptual objects cannot be 
 identified with the thought which is embodied in propositions or 
 symbolic expressions, for if this were so there would be no fal- 
 sity; every concept would refer toa real object. Since concepts 
 and objects, in this less extended sense, are not identical but 
 are distinct, the relation of concepts to objects, even when 
 they come together in perception so that the meaning of the 
 concept cannot be distinguished from the object, must be cor- 
 respondence. This correspondence is a correlation such that the 
 elements of the corresponding wholes fulfil the same structural 
 functions in each; the relation of correspondence rests on an 
 identity of logical form in real objects and in propositions or 
 concepts. 
 
 Truths are known only through belief or judgment, which is a 
 secondary attitude toward propositions. This attitude is like 
 understanding in that it is a preparation for an object intended, 
 but it differs from understanding in being a completer prepara- 
 tion — a willingness to act as if the object intended were in ex- 
 istence. Belief is more than the thought of the existence of the 
 object meant, and more than vividness of presentation or clear- 
 ness of understanding. Belief, like meaning, is carried in sym- 
 bols, it is inseparable from its expressions; and if there is any 
 difference between belief and assertion, it is that the latter is an 
 outward or inward signification of belief, while the belief itself 
 is the attitude of mind signified. A full sentence differs from a 
 single word or phrase in that it contains a sign of belief; the es- 
 sential office of the copula is to serve as such a sign. But a word 
 or phrase is no less capable of being true or false, and of being 
 
196 SYMBOLISM AND TRUTH 
 
 asserted or denied, than a full sentence; a single word is a propo- 
 sition. 
 
 Disbelief reduces to belief, to a belief in the negative of the 
 proposition disbelieved, while the true opposite of belief is in- 
 credulity, the attitude of the sceptic. Disbelief is therefore posi- 
 tive and takes a place beside belief as a means of reaching con- 
 clusions through inference or through action; incredulity serves 
 only the negative end of preventing error. 
 
 Finally, the indecision of scepticism, which springs from the 
 fact that truth is reached in no other way than through belief, 
 can be escaped only by taking the risk of error which judg- 
 ment necessarily involves; and belief, once it is set in motion, is 
 carried on by its own momentum toward a theory of truth and 
 reality — and in the end to “first philosophy.” For nowhere 
 else are to be found the principles that justify all others. 
 

 
 
 
 CHAPTER VI 
 
 NEGATION AND CONTRADICTION 
 
 I 
 
 T xx notion of a negative truth — or a true negative — has an 
 intrinsic appearance of paradox and even of self-contradiction, 
 especially when truth is defined as the correspondence of propo- 
 sitions, or symbolic expressions, with objects. 
 
 What sort of object can a true negative mean? Does it stand 
 for a “negative object”’? Clearly it must stand for some object. 
 The significance of a negative cannot be, like that of a false prop- 
 osition, a meaning determined by other meanings and yet corre- 
 sponding to no object, for all negatives would then be false. Nor 
 can it be a direct reference to objects given in perception. There 
 are no negative data; perception is always the perception of 
 something that is, never of something that 2s not. A direct refer- 
 ence to objects cannot be anything but positive. The analysis of 
 negation, therefore, falls between the horns of a dilemma: either 
 negatives refer to no objects and are false, or they refer to ob- 
 jects and are not negatives. 
 
 There are many ways of escaping this dilemma, the simplest 
 of which is to embrace one of its alternatives; and this is what 
 Mr. Bertrand Russell does. He finds that negative propositions 
 mean “negative facts,” which are unanalyzed and necessary 
 elements in the world of fact." 
 
 A negative fact, if there is such a thing, is plainly not of the 
 same order as a positive fact. To observe that “the sun is not 
 shining” is very different from observing the contrary. In the 
 
 1 See B. Russell, “The Philosophy of Logical Atomism,” in The Monist, 
 vol. xxviii (1918), and vol. xxix (1919). 
 
198 SYMBOLISM AND TRUTH 
 
 latter case, a complex object, the shining of the sun, is immedi- 
 ately given; in the former, what is immediately given is some- 
 thing other than what is referred to. To “perceive” that the sun 
 is not shining is to notice clouds in the sky and, perhaps, rain; 
 or it may be, to observe that night has fallen — and these data 
 are not negative facts. If negative facts are “given,” they are 
 not given through perception, as are positive ones; they are in- 
 ferred or constructed from perceptions; their reality, like that of 
 classes, extends far beyond any immediate presentation; they 
 are facts of a highly complex type, and the propriety of using 
 the term “fact” for them is questionable, as it is for classes, 
 which cannot properly be called “facts.” ? 
 
 The assumption of negative facts as the referents of true nega- 
 tive propositions does not analyze negation. It cuts the knot but 
 leaves the threads of the difficulty tangled. Negative significance 
 remains an anomaly unassimilated to the rest of knowledge, un- 
 less it can be shown to have a positive basis in some other sort of 
 meaning. | 
 
 A particularly interesting attack on the problem is that of Mr. 
 Raphael Demos, who, though he does not carry the analysis to 
 its completion, suggests that a negative proposition is like a de- 
 scriptive phrase; it is an ambiguous reference to what is meant 
 by a number of positive propositions, the meaning of some one of 
 which is the meaning of the negation.? Thus the sign of nega- 
 tion, “not” or its equivalent, plays a part similar to that of the 
 signs “‘a,” “any,” “some,” and “the.” It is a sign of interpre- 
 tation. It does not signify a constituent of the fact to which the 
 expression as a whole might refer, but indicates that the propo- 
 sition is to be interpreted in a special way, that is, negatively ; 
 
 1 See above, ch. IV, sec. xiii. 
 
 2 See R. Demos, “A Discussion of a Certain Type of Negative Proposi- 
 tion,” Mind, N.S., vol. xxvi (1917), p. 188. Despite obvious disagreements, the 
 
 central idea of the theory of negation here presented, that of the ambiguity of 
 the negative, is taken from Dr. Demos’ article. 
 

 
 NEGATION AND CONTRADICTION 199 
 
 which is to interpret it as a variable with an ambiguous refer- 
 ence to certain positive propositions. 
 
 II 
 
 The ambiguity of negative propositions is their most striking 
 characteristic. They are variables, and they continue as nega- 
 tions only so long as their significance is not fully determined. 
 
 If I assert that “the sun is not shining,”’ I do not assert that 
 “it is raining,” or that “it is night,” or “that the sky is clouded.” 
 None of these propositions expresses the meaning of the nega- 
 tion. Nor do I assert all of these propositions. The meaning is 
 like that of the statement, “I met a man.” If a value for the 
 variable a man is chosen, so that the statement becomes, “‘I met 
 Mr. X,”’ this is not what I assert; it is more specific than my 
 actual assertion. And though I must have met Mr. X or Mr. Y 
 or Mr. Z, etc., if the statement is true, still it remains undeter- 
 mined which one of these men I did meet, and this indetermi- 
 nateness is an essential element in the meaning. Similarly, what 
 I mean by “‘the sun is not shining” might be either that “‘it is 
 raining,” or that “‘it is night,” or that “the sun is in eclipse,” 
 etc., but it is actually none of these. The negation is essentially 
 unspecific in reference and to make it specific is to rob it of its 
 negativity. 
 
 The observation that negatives are ambiguous is the first step 
 toward freeing us from the error that a negative is merely what 
 zs meant. The manner of significance is no less constitutive of the 
 meaning of a negation than are the things it might signify; and 
 since propositions alone are ambiguous, negation belongs to the 
 realm of propositions or concepts, and not to things. Things do 
 not have negatives, for things are not ambiguous; and without 
 ambiguity there is no negation. 
 
 Toward what objects or facts is this ambiguous reference of 
 the negative directed? 
 
200 SYMBOLISM AND TRUTH 
 
 Every negation has its ground; it rests on a perception or af- 
 firmation of fact. But the ground of a negation is not coexten- 
 sive with the meaning, since the ground is a single fact or com- 
 plex of facts, while the meaning covers a multitude of facts, 
 some undetermined one of which is the value of the negative. 
 I may affirm that “Chaucer’s Canterbury Tales are not good 
 reading” on the ground that they are immoral, but this fact will 
 not be the only possible interpretation of the statement. This 
 negation might mean that the language of these tales is difficult, 
 or that they are dull. If I advise you that “carbolic acid should 
 not be drunk,”’ the ground of my advice may be that it is poison- 
 ous; yet this is not what I assert, and you may construe my 
 statement to mean that “suicide is criminal”’ or that “life is 
 worth living.” To identify the ground of a negation with the 
 meaning is to abolish the negation, for it is to choose one among 
 the possible values; hence the negation is no longer a variable 
 and no longer a negation. If a negative proposition were equiva- 
 lent in meaning to the single positive proposition that is its 
 ground, there would be no reason for employing negatives; they 
 would disappear. Though negatives are often used where posi- 
 tive propositions would serve as well, their function in knowl- 
 edge is the same as that of other ambiguous expressions; 
 namely, to avoid a definite reference or to refer to that which is 
 not determinately known. Negation is notoriously the language 
 of diplomacy and guile. 
 
 In addition to the actual ground of any negation, there are 
 many possible grounds. These possible grounds are all the prop- 
 ositions with which the proposition negated is incompatible; 1 
 and Mr. Demos limits the possible values of a negative to its 
 possible grounds. On his view, then, a negative proposition 
 means (ambiguously) the same as some one of the propositions 
 
 1 Incompatibility is the relation of inconsistency between propositions, dis- 
 cussed in chapter v. p and gq are incompatible if, when the one is true, the 
 other is never true. This does not preclude both being false. 
 

 
 NEGATION AND CONTRADICTION 201 
 
 whose truth excludes the truth of the proposition negated. To 
 say that “‘life is not short, nasty, mean, and brutish” is to refer 
 to the fact that “it is long or happy,” or that “‘it is romantic,” 
 or that “‘it is capable of perfection,” etc., none of these possi- 
 bilities, however, being chosen as the value of the negative. 
 Mr. Demos’s analysis does not go far enough. The relation of 
 incompatibility or logical opposition, in terms of which it is 
 stated, is complex; it rests on truth and falsity and is an extrin- 
 sic rather than an intrinsic relation between concepts. It cannot 
 be apprehended through direct inspection of propositions or con- 
 cepts; one must know more than the meaning of a proposition to 
 know that it is incompatible with another; he must know that 
 it is never true when the other is true. Nor can incompatibility 
 be apprehended as a relation between the data of perception. 
 Logical opposition is not perceived, for what is meant by the 
 logical opposites cannot be in the same universe; and if percep- 
 tions seem to be inconsistent with one another, the inconsistency 
 is in the concepts through which the data are presented, and not 
 in the data themselves. The proposition “‘a is black”’ is incom- 
 patible with the proposition “‘a is white,” “‘ Juliet loved Romeo”’ 
 is incompatible with “Juliet hated Romeo’’; but white is not 
 logically opposed to black, and love is not logically opposed to 
 hate, since all of these qualities or relations exist in the same 
 universe. Propositions alone can be logically opposed, and their 
 logical opposition is a function of their truth and falsity. 
 From the point of view of formal logic, there could be no ob- 
 jection to defining “‘incompatibility ” in terms of truth and fal- 
 sity and to deriving negation from this propositional relation. 
 Nor could there be any objection to assuming incompatibility 
 itself, without definition, as the foundation of a theory of nega- 
 tion and truth. It is also possible to construct a logical system in 
 which negation and incompatibility are both defined in terms 
 of another function of propositions. Mr. H. M. Sheffer’s rejec- 
 
202 SYMBOLISM AND TRUTH 
 
 tion is a primitive idea which makes these latter definitions 
 possible." 
 
 But what is primitive in a set of postulates for logic may be 
 complex as an element in knowledge. The data of epistemology 
 and the primitive ideas of logical systems are not simple in the 
 same sense. For formal logic, the simplest primitive ideas for 
 any system are those which are the smallest in number and 
 which yield by deduction all the propositions belonging to the 
 system; thus a number of different concepts might be chosen as 
 primitive for different sets of postulates which apply, neverthe- 
 less, to the same subject-matter. The facts to which these prim- 
 itive ideas refer might have the appearance of extreme complex- 
 ity, but this would not make the ideas any the less primitive and 
 simple, so far as the logical part they play in the system is con- 
 cerned. This is not the sense in which the basic ideas of a theory 
 of knowledge are simple; these ideas are not arbitrarily chosen 
 because of their economy and fruitfullness in deduction. Their 
 simplicity must correspond to a certain simplicity in the subject- 
 matter; what they mean must present the appearance of sim- 
 plicity, it must appeal to the mind as being capable of no fur- 
 ther analysis. It is this sort of simplicity which is lacking both in 
 the concept of negative facts and in that of incompatibility as 
 the basis of negation. 
 
 It is possible to dissociate negation from truth and falsity, and 
 thus to gain in completeness of analysis. The incompatibility or 
 logical opposition of a negative and its positive is not the most 
 fundamental idea involved in negation; this notion of incompat- 
 ibility arises from a combination of the idea of truth with that of 
 negation in a highly general sense. In order to understand a posi- 
 tive proposition or symbolic expression, it is not necessary to 
 consider whether it is true or false. (The only symbols whose 
 
 1 H. M. Sheffer, A Set of Independent Postulates for Boolean Algebras, 
 Transc. Amer. Math. Soc., vol. xiv, no. 4, pp. 481-488. 
 
NEGATION AND CONTRADICTION 203 
 
 significance involves their truth are the elementary simple sym- 
 bols from which complex expressions are constructed.) It is suf- 
 ficient to know the form of the proposition and the meanings of 
 its elements. The understanding of a negative, similarly, ought 
 not to require a knowledge of its truth or falsity, or — what 
 amounts to the same thing — of its incompatibility with an- 
 other proposition. A negative must be such that it can be enter- 
 tained as a possibility for thought without any consideration 
 whatsoever of any object that it might mean, or that any other 
 proposition might mean. Some relation which can be directly 
 apprehended in apprehending the significance of propositions 
 must be sought to mark the limits of the possible values of nega- 
 tive expressions. This will yield the more general negation which 
 does not depend on truth and falsity. 
 
 Il 
 
 This relation is that of distinctness of meaning; and it is the 
 symbolic counterpart of the diversity or otherness of objects. A 
 negative proposition means “something distinct from that 
 which is meant by the positive’’; and this, coupled with the am- 
 biguity of the reference, is the whole of negation when the ques- 
 tion of the truth or falsity of the negative does not enter — that 
 is, when the negative is purely a possibility for thought. 
 
 This definition of the possible values of a negative proposition 
 seems to remove all limitations and to lead to startling conclu- 
 sions. Among the possible values of “‘the sun is not shining”’ are 
 thus included, not only propositions that might be the ground of 
 this negation, such as “it is night”’ and “‘the sky is overcast,”’ 
 but also propositions that could by no stretch of the imagination 
 be its ground — propositions such as “Chicago is in Illinois,” 
 
 > 
 
 ‘‘man is a rational creature, ” etc. In short, any proposition 
 which is distinct in meaning from “‘the sun is shining”’ is a pos- 
 
 sible interpretation of “‘the sun is not shining.” 
 
204 SYMBOLISM AND TRUTH 
 
 The appearance of paradox is partly removed if it is remem- 
 bered that the negative proposition does not actually mean one 
 of its possible values. It is a negative only while it is ambiguous; 
 and, though some propositions are relevant to it as grounds from 
 which its truth or falsity might be inferred, it no more signifies a 
 particular one of these than it does a particular one of the count- 
 less propositions irrelevant to it as grounds. The statement SiLite 
 sun is not shining” does not actually mean “Chicago is in Tlli- 
 nois,” nor does it mean ‘“‘the sky is overcast.’ It means “‘some- 
 thing other than that the sun is shining.” If a pessimist were 
 asked whether life is good, he might reply, “anything but”; and 
 this inelegant, yet emphatic denial correctly indicates the range 
 of possible values of a negative. 
 
 It must be observed that the limit of the possible values of a 
 negative is marked, not by the diversity of objects signified, 
 but by diversity of significance, irrespective of objects. On this 
 widest interpretation of the principle of negation, false propo- 
 sitions (which correspond to no objects) may be values of the 
 negatives of false propositions. “New York is not in Brazil” 
 need not signify merely what is meant by some true proposition; 
 it might mean (though being ambiguous it does not actually 
 mean) that “New York is in Turkey.” And if I say that “Cin- 
 derella did not love her stepmother,” which is false because 
 there was no Cinderella, still I might mean that “Cinderella 
 hated her stepmother,” which is also false. The question 
 whether or not the truth of a negative precludes the truth of its 
 positive is irrelevant to this purely conceptual negation. 
 
 Any use of symbols presupposes distinctness as well as iden- 
 tity of meaning. Thought is not a repeated series of tautologies, 
 and no symbolic system could be constructed from symbols 
 whose meanings were all equivalent. Just as every symbol, if it 
 is to retain its identity (to be the same symbol) in its recurrent 
 instances, must be interpreted in one and only one way, so a 
 
 
 

 
 NEGATION AND CONTRADICTION 205 
 
 symbol, if it is to have anything other than a reference so vague 
 that it could not be called a meaning, must be distinct in sig- 
 nificance from some other symbol; and where distinctness of 
 meaning is present, negation is also present. The dictum that 
 “determination is negation” is no less true for thought than for 
 reality. Without negation, that is, without distinctness of mean- 
 ing, there is no meaning; and without diversity there are no ob- 
 jects. Everything that zs 1 is diverse from something else, and 
 every significant idea is distinct in meaning from some other 
 idea. Just as the same symbol or concept, when it is applied to 
 the world of objects, will (by the very definition of the same 
 symbol) mean one and only one object, so a symbol that is dis- 
 tinct from it will (by the very definition of a distinct symbol) 
 mean a different object or no object. And the negative, since 
 it has the same significance as any symbol distinct from the 
 positive, will therefore always be distinct in meaning from the 
 positive. 
 
 IV 
 
 This general condition of the use of symbols — that a nega- 
 tive is always distinct in meaning from its positive — which fol- 
 lows from the purely conceptual definition of the meaning of a 
 negative, is the principle of contradiction in its most abstract 
 form. It is like the principle of identity in that it is a general rule 
 of symbolism, and therefore a general principle of thought. 
 
 Now the law of contradiction is often confused with the law of 
 the excluded middle, which states that “either p or not-p is 
 true”’; but this latter principle has no connection with the prin- 
 ciple of contradiction, when truth and falsity are not considered 
 in the definition of negation. As a general rule of symbolism the 
 law of contradiction asserts that to every symbol corresponds 
 another, its negative, whose meaning is distinct from the first. 
 
 1 In the sense of ch. V. 
 
206 SYMBOLISM AND TRUTH 
 
 It can be written, “‘a ¥ not-a,” the sign (#) being taken to 
 mean “distinct from.’ Both the laws of identity and contradic- 
 tion, on their purely symbolic interpretations, state general in- 
 tentions in the use of symbols. The law of identity, “a = a,” 
 tells us that any symbol “a” is equivalent, for symbolic pur- 
 poses, to itself; that it can replace itself in any context without 
 altering the meaning, since every symbol can have one and only 
 one meaning. The law of contradiction, on the other hand, tells 
 us that there is at least one symbol that is distinct, for symbolic 
 purposes, from any given symbol “a,” and this is “not-a”’; if it 
 replaces ‘“‘a’’ in any context, the meaning will be completely 
 altered. 
 
 As statements of general intentions in the use of symbols, the 
 laws of identity and contradiction are a prior? in the sense that 
 they are rules laid down by the mind for its own guidance. They 
 are self-affirming; if they are denied, they are assumed, for no 
 proposition or concept can be framed without them. In knowing 
 what it is to think, we know these laws, and we can escape them 
 only by escaping from the use of propositions or concepts — that 
 is, from the use of symbols. 
 
 There is another interpretation of these principles, an extsten- 
 tial interpretation, which construes them as general truths about 
 objects, as well as general principles of symbolism. If ‘‘a” stands 
 for an object — for any object — “a = a” asserts that “any 
 object is identical with itself,” or simply that “any object has an 
 identity”; while “a # not-a” asserts that “any object is dis- 
 tinct from anything other than itself,” or simply that “any ob- 
 ject stands in the relation of diversity to-something.”’ Both of 
 these statements are tautologies, but they could not be true un- 
 less there were identity and diversity in the world of fact. They 
 express the minimal conditions of the being of objects — that is, 
 of the objects which are presented or represented in empirical- 
 rational knowledge. 
 
 
 
NEGATION AND CONTRADICTION 207 
 
 The very assertion of these general truths, however, assumes 
 the laws of identity and contradiction as principles of symbo- 
 lism. Only if “a” is the same symbol as ‘“‘a” does “a = a” 
 affirm that “‘any object is identical with itself”; and unless “a” 
 and ‘‘not-a” are always distinct in meaning, “a ¥ not-a”’ 
 might mean “‘a # a.” The predication of diversity in objects 
 presupposes diversity in the meanings of symbols, apart from 
 objects meant, but the statement that “‘a # not-a” in the sym- 
 bolic sense does not imply that a or not-a stands for an object. 
 Though it is false to say that “griffins are not not-griffins,” if 
 this means that griffins exist as distinct things, this is not false 
 as a statement of how the concepts “griffin” and “not-griffin” 
 are to be used. 
 
 If the law of contradiction were not valid both on its symbolic 
 and existential interpretation — if there were no distinct sym- 
 bols and no diverse objects — thought would find itself in a 
 strange situation. It would be impossible to think of anything 
 without at the same time thinking of everything. In order that a 
 symbol may mean a specific object, not only must the object be 
 self-identical and the symbol be the same symbol in its different 
 instances, but there must be something that is not meant by 
 this symbol and that can be signified only through a different 
 
 symbol — something for the apprehension of which a new and 
 
 distinct concept is the only appropriate instrument. Without 
 
 negation thought would be even less definite than the Parme- 
 
 nidean tautology, “Being is”; and without diversity in objects, 
 the whole structure of the world of fact, as we know it, would 
 disappear. 
 
 The limiting condition of the reality that gives truth, as we 
 have defined it, to symbolic expressions or propositions is that it 
 must be capable of being consistently presented and represented; 
 and, so, for this reality, the principles of identity and contradic- 
 tion on their existential as well as their symbolic interpretations 
 
208 ’ SYMBOLISM AND TRUTH 
 
 must be true a priori. Anything that could be consistently pre- 
 sented or represented would necessarily be self-identical and 
 diverse from other things. The principles of identity and contra- 
 diction are the “formal” categories of this limited being; the 
 test of consistency, which makes use of the “empirical catego- 
 ries”? of science and common sense, can be applied to existent 
 objects only if these more general principles hold of them. 
 These principles are implicit in the condition that marks the 
 limits of this reality. 
 
 How much further the validity of the laws of identity and 
 contradiction, as truths about reality, can be extended is a 
 matter for speculation; and here again the theory of knowledge 
 finds its completion in metaphysics. If reality were constituted 
 by thought, these most general conditions of thought would 
 certainly be the most general conditions of being. But for a the- 
 ory any less extended than this, it is a wide leap from the most 
 general rules of thought to the most general principles of being. 
 It is possible that reality cannot be trimmed to the neat dimen- 
 sions of thought; there may be nooks and corners of the real 
 hidden from this knowledge which demands the identity and di- 
 versity of its objects. It is even possible that these very require- 
 ments of thought form a barrier between the mind and reality, 
 confining knowledge to a realm of Kantian phenomena. But 
 neither this metaphysical alternative, nor the other — that they 
 are true a priori of reality in the most inclusive sense of the 
 term — can be established on the premises so far laid down. 
 
 V 
 
 What of the third “law of thought,” the principle of the ex- 
 cluded middle? 
 
 To construe the meaning of a negative proposition as “any- 
 thing other than the meaning of the positive” appears to be a 
 direct violation of this law, for this permits a false proposition to 
 
NEGATION AND CONTRADICTION 209 
 
 be a value of the negative of a false proposition and therefore 
 allows the possibility that when p is false not-p might also be 
 false. “Paris is not the principal city of England” might mean 
 “Paris is the capital of the United States,” and this is clearly 
 not allowable if the principle of the excluded middle is true. 
 Moreover, “‘Paris is not the principal city of England”’ could 
 mean (though on account of its ambiguity it does not actually 
 mean) that “birds have wings” or that “to-day is Friday,” and 
 the truth or falsity of these propositions seems to be totally un- 
 connected with the truth or falsity of ‘‘ Paris is the principal city 
 of England.” 
 
 The law of the excluded middle, that “either p or not-p (but 
 not both) is true,” connects negation with truth and falsity by 
 adding a further condition than diversity of meaning to deter- 
 mine the possible values of a negative. We thus return to the 
 more complex and special type of negation, which Mr. Demos 
 defined in terms of incompatibility. This law is not a necessity of 
 thought in the same sense as are the principles of identity and 
 contradiction in their most general forms. The latter are needed 
 if concepts or symbolic expressions are employed in any way 
 whatsoever; the former enters only when truth and falsity (as 
 well as the identity and distinctness of concepts) are considered. 
 It is necessary for inference — for the derivation of the truth or 
 falsity of propositions from the truth or falsity of others; but it 
 is not necessary for the very existence of meaning, as are the 
 first two laws of thought. 
 
 In order that the principle of contradiction may yield the law 
 of the excluded middle, the negative must be interpreted in a 
 special way, which takes account not only of the distinctness of 
 concepts, but of their truth. 
 
 Now true propositions are distinct through the objects they 
 mean, as well as distinct in significance apart from these objects; 
 but false propositions are not distinguished from one another 
 
210 SYMBOLISM AND TRUTH 
 
 through objects meant, since they mean no objects. Moreover, 
 any true proposition is distinct from any false proposition 
 through an object meant, for the one means an object, while the 
 other does not. This notion of “being distinct through an object 
 meant”? supplies the necessary principle for determining the 
 possible values of a negative, when the law of the excluded mid- 
 dle is added to the laws of identity and contradiction. If not-p 
 means (ambiguously) the same as any proposition that is dis- 
 tinct from p through the distinctness of an object meant, it will 
 follow that when p is true not-p is false, and vice versa, that when 
 p is false not-p is true. 
 
 To include the idea of an object meant, that is, of truth, in the 
 definition of negation is to remove negation from the realm of 
 the purely conceptual. It is no longer sufficient merely to know 
 the meaning of a proposition — merely to consider it as a possi- 
 bility for thought — in order to know the meaning of its nega- 
 tive. One must also know whether it is true or false. But if this 
 kind of negation is less simple than the other, it is more effective; 
 negatives now become instruments of inference. All false prop- 
 ositions fall together as indistinguishable through an object 
 meant, though they still remain distinct as concepts; and hence 
 the negative of a false proposition can mean only true proposi- 
 tions. It will be true for any value that can be chosen for it, so 
 that the truth of not-p can always be inferred from the falsity 
 of p. “New York is not in Brazil” will not include among its 
 possible interpretations, “New York is in Turkey” or “New 
 York is in Australia,’ since these propositions are not distinct 
 through an object meant from “‘New York is in Brazil.” Any 
 possible value of “New York is not in Brazil’’ will be a true 
 proposition. Among these possible values there will be one that 
 is the most probable ground of this negation, viz., “New York 
 is in the United States”; but it is not necessary to suppose that 
 this value is the sole possible meaning of the negation in order to 
 
 tml i a 
 
 
 
 sir 
 — 
 
NEGATION AND CONTRADICTION 211 
 
 establish its truth. Any true proposition will be a possible value 
 of this negative. 
 
 On the other hand, if p is true — and if there is a single false 
 proposition among all the propositions which can be formulated 
 — then not-p will be false. For among the possible values of 
 not-p will be included, not only all the true propositions that are 
 distinct from p through an object meant, but also some false 
 proposition; and since the negative is ambiguous, it might mean 
 this false proposition. It cannot be true if there is a single possi- 
 bility of falsity.1 Thus, since it is true that “carbolic acid is 
 poisonous,” and since some false proposition can be stated — let 
 us say the proposition that “carbolic acid is good to drink”? — 
 the negative, “carbolic acid is not poisonous,”’ might mean that 
 *“‘carbolic acid is good to drink.” This latter proposition, being 
 false, is a possible value of the negative of the original true prop- 
 osition, for any true proposition is distinguished from any false 
 proposition by an object meant. And though the negative, “car- 
 bolic acid is not poisonous,” might also mean countless other 
 propositions, both true and false, it cannot be true so long as 
 there is any possible interpretation for which it is false. Thus 
 where the possible values of a negative are the meanings of those 
 propositions which are distinct from the positive through an ob- 
 ject meant, the falsity of a negative can always be inferred from 
 the truth of its positive. 
 
 It is clear that this more restricted type of negation — this 
 inferential negation — eliminates possibilities which the wider 
 and simpler form of negation permits. When the negative is con- 
 strued in this narrower way, “fairies do not live on bread and 
 meat”’ could not possibly mean “fairies live on dew and honey.” 
 Its positive being false (since there are no fairies), this propo- 
 
 1 The assumption that some false proposition can be formulated amounts 
 to the assumption that there is falsity; and certainly a negative could not be 
 false unless there were falsity. There must be some false proposition that it 
 could mean. 
 
212 SYMBOLISM AND TRUTH 
 
 sition must mean the same as some true proposition; it must be 
 true. By the very definition of the meaning of the negative, we 
 are no longer permitted to consider it as a mere possibility that 
 ‘fairies do not live on bread and meat”’; we are forced to infer 
 its truth from the falsity of the proposition of which it is the 
 negative. The principle of the excluded middle thus drags us 
 down to earth from the world of pure speculation. 
 
 VI 
 
 The conditions of the truth and falsity of negatives have al- 
 ready been mentioned in passing. A negative is false if there is a 
 single false proposition among its possible values, and it is true 
 only if all of its possible values are true propositions. This fol- 
 lows from the ambiguity of the negative. Let us examine this 
 idea more closely. 
 
 Now the meaning of a proposition determines whether it is 
 true or false, and if this meaning is not fully specified — that is, 
 if the proposition might mean a number of different things, but 
 actually does mean none of these — the truth of the proposition 
 will depend on what it might mean, not on what it actually does 
 mean; for it actually does mean no specified object. Thus an am- 
 biguous proposition (or one which contains ambiguous constitu- 
 ents) is not true in the same sense as an unambiguous proposi- 
 tion. Its truth, like its meaning, is fixed by possible references to 
 objects, rather than by an actual reference. It is “ambiguously 
 true.”’ To be true in this sense is to be susceptible of many differ- 
 ent interpretations, but not to be susceptible of a false interpreta- 
 tion. Just as ambiguous meaning is an unspecified possibility of 
 meaning, so ambiguous truth is an unspecified possibility of 
 truth, rather than truth for a definite object or class of objects. 
 And if among the possible determinations of such an ambiguous 
 expression there is one for which it would be false — if there is 
 a single possibility of falsity — the proposition fails of truth as 
 
 
 
NEGATION AND CONTRADICTION 213 
 
 an ambiguous proposition, even if it might be true for some of 
 its possible values. Though an ambiguous proposition, if it is 
 asserted, need not be asserted for all of the things it might mean, 
 its truth requires that it be capable of being true for all of these. 
 
 Consider the statement, “‘I saw a friend on the street yester- 
 day.” This is a particular proposition but, since it contains an 
 ambiguous constituent, it does not assert that I saw a particular 
 friend — Brown or Jones; nor does it assert that I saw ali my 
 friends. I might have seen any one of them, and if among them 
 I count, as did the poet Blake, a certain group of friendly spirits, 
 or if some whom I call friends are not friends, the proposition 
 might be false; and the mere possibility of falsity invalidates it 
 as an ambiguous assertion. If the assertion is true — which 
 means that all possibility of interpreting it as false is eliminated 
 — any person that could be meant by the variable “a friend” 
 must be a real person, and must be really a friend. 
 
 A negative is “ambiguously true.” If it is asserted, it is not 
 asserted for one of its possible values or for all of them; it is am- 
 biguously asserted. And if it is true, it must be true for more 
 than one or several possibilities; there must be no possibility for 
 which it could be false. A true negative embraces the entire uni- 
 verse of true propositions, but not one false proposition; while a 
 false negative embraces a universe of true and false propositions 
 —one true proposition, only, being excepted: the positive of this 
 negative. If these conditions of the truth and falsity of negatives 
 are born in mind, the remaining implications of the principle of 
 the excluded middle are easily seen to be true; v2z., that when 
 not-p is false, p is true; and when not-p is true, p: is false. 
 
 Suppose that not-p is false. Then some proposition that could 
 be a value of it, some proposition other than p, must be false. 
 
 1 This principle, “either p or not-p is true (but not both),” implies that 
 (1) if p is false, not-p is true, (2) if p is true, not-p is false — both of which have 
 been demonstrated in the previous section — (3) if not-p is false, p is true, and 
 (4) if not-p is true, p is false. 
 
214 SYMBOLISM AND TRUTH 
 
 But if p is also false, p would not be distinguished ‘‘through an 
 object meant”’ from this value of not-p; that is, not-p would not 
 be the negative of p. And therefore p must be true. Thus, since 
 it is false that “men do not desire pleasure,” it cannot also be 
 false that ‘‘men do desire pleasure.” For, if this were the case, 
 one of the possible values of the negative, “men do not desire 
 pleasure”’ — let us say the false proposition “‘men desire pain” 
 — would fail to be distinct from the positive, ““men desire pleas- 
 ure,” through an object meant; so that “men do not desire 
 pleasure”? would not be the negative of “‘men desire pleasure.” 
 The very definition of the possible values of this negative de- 
 mands that its positive be true when it is false. 
 
 On the other hand, when nof-p is true, p must be false. For, 
 not-p being true can mean only true propositions; and, since it is 
 always possible to state some false proposition (since there is al- 
 ways falsity), unless p were false when not-p is true, not-p would 
 include this false proposition among its possible values, for this 
 false proposition would be distinct from p through an object 
 meant, if p were true. Therefore p must be false. It is true, for 
 example, that “fortune is no respecter of persons”; but some 
 false proposition, g, can be stated; and if it were also true that 
 “fortune is a respecter of persons,” this latter proposition would 
 be distinct from the false proposition, g, through an object 
 meant, and q would be a possible value of its negative. The nega- 
 tive might then be false. Thus it must be false that “fortune is 
 a respecter of persons”’ if it is true that “fortune is no respecter 
 of persons.” 
 
 Where the negative means ambiguously the same as any prop- 
 osition distinct from the positive through an object meant, the 
 law of the excluded middle is therefore valid in all of its implica- 
 tions. From the truth (or falsity) of p, the falsity (or truth) of 
 not-p can always be inferred; and from the truth (or falsity) of 
 not-p, the falsity (or truth) of p can always be inferred. 
 
 
 

 
 NEGATION AND CONTRADICTION 215 
 
 VII 
 
 The examination of judgment led us to the conclusion that to 
 disbelieve or deny a proposition is to believe or assert its nega- 
 tive — belief, like understanding, being an attitude of prepara- 
 tion for or anticipation of something meant. But if the meaning 
 of a true negative might be that of any one of an entire universe 
 of true propositions, what possible attitude of preparation or an- 
 ticipation could be appropriate to it? To prepare for so many 
 truths would be to prepare for — and to believe — no specific 
 truth; so that the analysis of negation seems to have given nega- 
 tives a basis in fact at the cost of rendering their significance so 
 vague that they cannot be believed. 
 
 And yet there is a kind of belief which is appropriate to nega- 
 tive propositions in their total ambiguity — a belief that is di- 
 rected toward no specific object or class of objects. Such a belief 
 is an anticipation of anything at all other than what is denied; it 
 is a general readiness to accept something or other — anything 
 excepting the proposition disbelieved — as true. This is the 
 frame of mind in which the atheist denies God; he is prepared to 
 believe anything but that there is a God. And it is the attitude 
 one takes toward propositions which are plainly self-contradic- 
 tory or false. If you tell me that “triangles have four sides” or 
 that “oxen fly in the air,” I shall probably reply that I can ac- 
 cept anything but this. This kind of disbelief, however, though 
 it has a positive content of a formal and indefinite sort, amounts 
 to little more than turning the mind away from the proposition 
 disbelieved. It is a bare (and often groundless) disbelief which 
 hardly escapes scepticism and which, like the sceptical attitude, 
 can never take the place of a positive judgment in knowledge. 
 
 Negatives are rarely thus asserted or believed in the full ex- 
 tent of their possible meanings. Ordinarily, values which are 
 relevant as grounds to the falsity of the proposition disbelieved 
 
216 : SYMBOLISM AND TRUTH 
 
 are selected from among the possible values, and on these belief 
 centers. 
 
 Now the ground of a negative — and of the assertion of the 
 falsity of a proposition — is some proposition which is incom- 
 patible with the proposition negated or with the proposition 
 that is believed to be false. It is a proposition which is never 
 true when the other is true. And this incompatibility is deter- 
 mined by the “empirical categories” of science and common 
 sense. Scientific theories and laws, and prescientific generaliza- 
 tions, are the tests not only of the existence of objects and the 
 truth of propositions, but also of the “non-existence of objects” 
 and the falsity of propositions. A proposition is false — it stands 
 for no object and is conveniently, if inaccurately, said to mean 
 a “non-existent object’ —when it is inconsistent with the whole 
 of knowledge. The mere failure to discover something in exist- 
 ence that the proposition might mean, though it may be ground 
 for denial, is no proof of the falsity of the proposition, and can 
 lead only to the bare disbelief which is directed toward no spe- 
 cific truth. 
 
 The grounds of negative judgments thus fall into two classes: 
 the failure of verification(which is really privation of ground), 
 and the discovery of true propositions from which the falsity of 
 the proposition denied can be inferred by the aid of the general- 
 izations of science and common sense. In the first case, when I 
 believe a proposition to be false, I can merely deny it by affirm- 
 ing its negative in its full ambiguity. In the second case, my be- 
 lief will be capable of some limitation; I can select as its special 
 objects the truths from which the falsity of the proposition in 
 question follows. I am not therefore always confined to the 
 formal knowledge that ‘“‘anything other than what is denied is 
 true,” in affirming the falsity of propositions, though this is all 
 that the definition of the meaning of the negative can tell me. I 
 can infer, through the laws which I have found to hold in experi- 
 
 
 

 
 NEGATION AND CONTRADICTION 21%, 
 
 ence, that certain propositions are true when the other is false, 
 and I can direct my belief toward these propositions. These are 
 the “‘most probable”’ values of the negative. If I assert that “no 
 man defies the laws of society with impunity,” I most probably 
 believe that “‘crime is always punished” or that “criminals are 
 detected” or that “‘the social outcast is miserable,” any one of 
 which could be the ground of this negative judgment. But since 
 there are, in any case, many possible grounds of falsity,— many 
 propositions which are incompatible with the one negated,— to 
 believe a negative, even when a whole universe of truths is not 
 considered, is to prepare for more than a single contingency. 
 And yet it is to prepare for a contingency, to be ready to act as 
 if some definite propositions were true; and thus disbelief be- 
 comes as fully positive as it is capable of becoming. 
 
 The fact that this more fully positive type of disbelief is di- 
 rected toward specific ones among the possible values of the 
 negative does not restrict the meaning of the negative to these 
 values, that is, to its possible grounds. The negative does not 
 cease to be an “infinite negative” (as the older logicians called 
 it), which might mean the same as any one of an indefinite 
 number of propositions; nor are the formal requisites of its 
 truth — that it cannot be false for any possible interpretation 
 — altered. 
 
 Thus negative judgments are never wholly equivalent in effect 
 to positive ones, for there is always a margin of possibility which 
 is not covered by belief, even when the “most probable” values 
 of the negative are selected as the objects of belief. The “‘infin- 
 ity” of the negative allows for the totally unforeseen and unfore- 
 seeable — for contingencies which none of the principles of sci- 
 ence and common sense embrace. When one believes a negative, 
 therefore, he can find in his belief a residuum of that general 
 readiness for anything other than what is denied — a margin of 
 “preparation for the wholly unexpected’? — which arises from 
 
218 SYMBOLISM AND TRUTH 
 
 the ambiguity of the negative. Negative judgments, no matter 
 what their grounds, remain evasive to the end; they commit one 
 to much less than positive judgments. They do not completely 
 attain to the solidity and certainty of positive judgments. 
 
 Vill 
 
 It must not be forgotten that ideas can be entertained apart 
 from belief and disbelief, as possibilities for thought; that nega- 
 tion can be dissociated from truth and falsity; and that there is 
 a realm of the purely conceptual, where identities and distinc- 
 tions of meaning alone are relevant. 
 
 The fact that the laws of identity and contradiction (when 
 truth is not a part of the definition of the negative) are general 
 rules of symbolism and therefore of thought, irrespective of ob- 
 jects which are or might be meant, makes it possible to distin- 
 guish conceptual validity from truth, and formal consistency from 
 existential consistency. A system is conceptually valid, whether 
 or not it is true, if it does not violate these two principles of the 
 use of concepts. This means that symbols which are originally 
 taken as distinct — to be values of the negatives of one another 
 — must continue to be treated as distinct, and that symbols 
 originally taken as identical must continue to be treated as iden- 
 tical. These conditions are sufficient to give the system formal 
 consistency. Whether it is existentially consistent and true — 
 that is, whether it contains no incompatible propositions — is 
 another matter, but this will in no sense affect its formal con- 
 sistency. The consistency of the system is a consistency of defi- 
 nition only. 
 
 This sort of formal consistency and conceptual validity be- 
 longs to uninterpreted deductive systems and to the whole 
 world of romance and fiction. The canons of the constructive 
 imagination are the laws of identity and contradiction, where 
 these laws are rules of symbolism and nothing more. 
 
 
 

 
 NEGATION AND CONTRADICTION 219 
 
 IX 
 
 The present analysis of negation, beginning with Mr. Demos’s 
 notion that a negative proposition means ambiguously the same 
 as some positive proposition which is incompatible with the 
 proposition negated, has separated the idea of negation from 
 that of truth, thus distinguishing purely conceptual from infer- 
 ential negation. The law of the excluded middle requires that 
 the negative be construed in the latter sense, and the law of con- 
 tradiction in its most general form, that it be construed in the 
 former. 
 
 The assumption of “‘negative facts”’ as the referents of true 
 negative propositions does not analyze negation; nor does the 
 theory that the negative means ambiguously some proposition 
 incompatible with the positive carry the analysis to its comple- 
 tion, for the notion of incompatibility is complex; and though 
 incompatibility might be taken as simple for purposes of deduc- 
 tive exposition, it is not simple as an element in knowledge. 
 Incompatibility is a function of the truth and falsity of prop- 
 ositions. Negatives are unquestionably ambiguous, but if the 
 possible values of a negative are restricted to its possible 
 grounds, that is, to those propositions whose truth excludes the 
 truth of the positive, the meaning of a negative cannot be dis- 
 sociated from its truth or falsity. 
 
 A negative proposition, where the negative is interpreted in 
 the simplest way, means (ambiguously) the same as any propo- 
 sition distinct in meaning from the positive, and this distinct- 
 ness of meaning need not be connected with diversity in objects 
 meant, that is, with truth. Distinctness of meaning, apart from 
 objects referred to, is a necessary presupposition of the use of 
 symbols; and the principle of contradiction, “a # noft-a,” as a 
 general rule of symbolism and hence as an a priori condition of 
 thought, asserts that a negative is always distinct in significance 
 
220 SYMBOLISM AND TRUTH 
 
 from its positive. This principle is codrdinate with the law of 
 identity, “a = a,” which asserts that any symbol is equivalent 
 (or identical) in meaning with itself. Both of these principles can 
 be interpreted in another way, that is, as general conditions of 
 the being of objects, and these existential interpretations assume 
 the principles as rules of symbolism. If a means an object — any 
 object — the law of identity states that “any object is identical 
 with itself,’ and the law of contradiction that “any object is 
 distinct from anything other than itself.’ These statements are 
 true only if existing objects have the formal characters of iden- 
 tity and diversity. For the limited reality which can be con- 
 sistently presented and represented — for the existing objects 
 of empirical-rational knowledge — these laws must hold; but 
 whether they hold for all reality can be determined by nothing 
 less than a complete metaphysical theory. 
 
 The third law of thought, the principle of the excluded middle, 
 joins the idea of truth to that of negation. This principle is not 
 necessary to the very existence of meaning, as are the others, 
 but it is necessary to inference. If the negative means the same 
 as any proposition distinct from the positive through an object 
 meant, it will always be true that “either p or nof-p is true (but 
 not both).” 
 
 To believe a negative in its full ambiguity is to be ready to 
 accept “anything other than the positive,”’ which is disbelieved. 
 This form of bare denial does not limit itself to the possible 
 grounds of the falsity of the proposition disbelieved. More com- 
 monly, denial and disbelief are directed toward values specially 
 selected from among the possible values of the negative; that is, 
 toward the values which might be grounds of the falsity of the 
 proposition denied. These grounds are determined by the gener- 
 alizations of science and common sense, which are the tests of 
 the “non-existence of objects” and the falsity of propositions, 
 as well as of the existence of objects and the truth of proposi- 
 
 
 
 : 
 
NEGATION AND CONTRADICTION 221 
 
 tions. But no negative judgment is wholly equivalent in effect 
 to a positive one, since its ambiguity is never eliminated, and it 
 might mean something other than it is believed to mean. 
 
 The material consistency of the knowledge whose truth and 
 falsity is tested by its compatibility or incompatibility with 
 other portions of knowledge (accepted as true) can be contrasted 
 with the formal consistency of conceptual systems which con- 
 form to the principles of identity and contradiction, as general 
 rules of symbolism, but are not affirmed to be either true or 
 false. Conceptual validity and truth are distinct. It is possible to 
 construct valid deductive systems which are completely unin- 
 terpreted, in which the identity and distinctness of concepts (or 
 symbols) and of logical forms alone are considered. Logical form 
 can be isolated and studied in itself. This is the work of the 
 purely formal deduction which, in Mr. Russell’s phrase, “‘does 
 not know what it is talking about, or whether what it says is 
 true.” 
 
CHAPTER VII 
 
 FORMAL DEDUCTION 
 
 I 
 
 Format logic might be defined as “‘the science of pure form,” 
 for it is interested in forms, and their connections, apart from 
 any “‘matter” in which they might be exemplified. Since sym- 
 bols in themselves embody logical forms, formal deductive sys- 
 tems can be presented in uninterpreted symbols, they can be 
 stated as if they referred to no objects; and logical form, thus 
 dissociated from a “‘matter,”’ becomes a subject of study in itself. 
 
 There are numerous sets of postulates for geometry, — both 
 Euclidean and non-Euclidean, — for arithmetic and algebra, for 
 serial order, and for logic itself, which attain — or nearly attain 
 — this ideal of abstract statement, and it is these systems which 
 best illustrate pure deduction. An examination of them makes it 
 plain that formal deduction is concerned with nothing but forms 
 and their relations. In order that the deductive connections in 
 _ these systems may stand forth clearly, they are separated from 
 the subject-matter and stated in terms of postulates, axioms, 
 and theorems which might equally well apply to other subject- 
 matters. Though these postulates, axioms, and theorems can be 
 interpreted in many different ways, their form remains the same 
 whatever objects they refer to — even if they refer to no ob- 
 jects. Their form is independent of all interpretations. 
 
 Such systems are hypothetical in the sense that they are 
 purely conceptual and not asserted. They conform to the prin- 
 ciples of the construction of concepts, that is, of the use of sym- 
 bols, and are therefore possibilities for thought; but the question 
 of their truth or falsity does not enter. If complete interpretations 
 
 
 
FORMAL DEDUCTION 223 
 
 for them can be found, they will be ‘‘materially”’ consistent and 
 true for these interpretations; the hypothetical connections be- 
 tween the postulates, axioms, and theorems will become infer- 
 ences; the theorems can be truly asserted as consequences of the 
 postulates and axioms. But if they have no interpretations, or 
 only incomplete interpretations, these systems will still be possi- 
 bilities for thought — conceptually “valid” and “formally” 
 consistent; and, from the point of view of formal logic, this is all 
 that they need be. 
 
 It is not possible to empty a set of postulates of all meaning, 
 for it would then cease to be a set of postulates. An uninter- 
 preted deductive system is not a collection of meaningless marks. 
 It has its plan of syntax, its groups, its terms and symbols of 
 unity; its meaning is syntactical; within a general framework 
 of significance, the uninterpreted symbols become variables, 
 which, though they do not actually refer to objects, could refer 
 only to objects whose formal characteristics are those given in 
 the symbolic groups of the system. The general scheme of sym- 
 bolic structure determines the possible values of these variables. 
 
 Some symbolic context is always necessary to a variable. Out- 
 side a context, a variable is not a symbol (and not a variable); 
 and though the context of the variable may include symbols of 
 fixed significance, this context need be only a formal plan of 
 grouping. If every element, excepting the form, of a symbolic 
 expression is a variable, the expression will not lose its meaning. 
 If only one factor in the meaning is determinate, viz., the form, 
 this will be sufficient to give the expression significance as a 
 whole — a significance that has reached the maximum of in- 
 determinateness. It is then the use of variables in a general con- 
 text of logical structure which makes the study of form in itself 
 possible. 
 
 The meaning of a formal deductive system is syntactical, and 
 so the postulates of the system are a plan of syntax, which de- 
 
224 SYMBOLISM AND TRUTH 
 
 termines what groups have significance in the system and how 
 these groups can be derived from one another. The deductive 
 connections appear as rules of substitution, by which one sym- 
 bol (or group) can replace other symbols (or groups) and yield 
 expressions which still have meaning. To state this plan of syn- 
 tax, it is necessary to assume nothing but the general principles 
 of symbolism and certain possibilities of substitution; these as- 
 sumptions are sufficient to make the system a connected whole 
 which embodies a number of different logical forms related (hy- 
 pothetically) to one another as premises to conclusions. The 
 structure alone is constant; all other elements in the meaning 
 are variable. When the system is asserted for a definite (and 
 complete) interpretation, these hypothetical connections be- 
 come the premises and conclusions of inferences, and the propo- 
 sitions that were assumed in their maximum generality, without 
 interpretation, prove to be a deductive exposition of truths 
 which hold for certain sets of objects. But when there is no 
 interpretation, the system retains its syntactical meaning; 
 through the conditions of significance imposed on it, it contin- 
 ues to be a presentation of logical forms connected in certain 
 ways; and this is all it originally purports to be. 
 
 It is not strictly true that, in putting forward a formal deduc- 
 tive system, “we do not know what we are talking about,” 
 though there is no doubt, since all the elements of the system 
 with the exception of the form are variable, that we need not 
 know or care “whether what we say is true.” We are talking 
 about logical forms, which are given in the very symbols through 
 which we talk about them. We are mapping possible systems of 
 concepts, as Columbus mapped the continent of which he dis- 
 covered only the shore; but in this case it is not even necessary 
 to know that there is a continent to be mapped; we need know 
 only the principles of map-making to explore the world of possi- 
 bilities. 
 
 
 
FORMAL DEDUCTION 225 
 
 II 
 
 The general principles of symbolism, that is, the most general 
 conditions of the construction of concepts, have already been 
 stated. They are (1) the principle of group significance, that the 
 meaning of any group is a function of the meanings of its ele- 
 ments and their grouping; (2) the general rule of “‘symbolic 
 grammar,” that every significant group must contain both a 
 symbol of unity and terms (or a term), and this rule demands 
 that the symbols of unity be distinguished from the terms; (3) 
 the principle of identity, that every symbol has one and only one 
 meaning; and (4) the principle of contradiction, that thereis at 
 least one symbol which is always distinct in meaning from any 
 given symbol, that is, its negative, which means (ambiguously) 
 the same as any symbol other than the positive; and this prin- 
 ciple demands that there be distinctness as well as identity of 
 meaning. 
 
 Every symbolic system must be such that it could be inter- 
 preted, even though it refers specifically to no objects; other- 
 wise, it would not be a possibility for thought. The general prin- 
 ciples of symbolism themselves are the conditions under which 
 systems could be interpreted. From these principles, in the 
 above order, it follows that any purely conceptual system must, 
 first, be composed of groups which are taken to be significant as 
 wholes. If the system contained no such groups, its symbolic 
 elements would not be variables, but mere meaningless marks.! 
 Thus there must be certain signs of syntax to indicate the struc- 
 ture of the groups — their divisions into major and minor 
 wholes, and the group relations between these wholes. 
 
 Secondly, the symbols of unity must be distinguished from the 
 terms; and when the system is interpreted, the former will stand 
 
 1 Or else symbols with a determinate reference to objects, in which case the 
 system would not be uninterpreted. 
 
226 SYMBOLISM AND TRUTH 
 
 for relations, operations, or qualities in their rdéle as elements of 
 unity in facts, while the latter will stand for individuals or for 
 universals in their substantive réle. There are no objects which 
 are not terms related or qualified or operated on in some way; 
 hence, without this distinction between symbols of unity and 
 terms, the system could not be interpreted and would not be a 
 possibility for thought. 
 
 Thirdly, every symbol must be identical in meaning with it- 
 self, that is, the equation, a = a, must hold throughout the sys- 
 tem; and this principle (the principle of identity) gives a rule of 
 substitution which is valid in all systems, v2z., the rule that any 
 symbol can be substituted for itself without altering the mean- 
 ing of the group in which it is substituted. The concept of iden- 
 tity makes it possible, moreover, to define symbols which are 
 distinct in character as identical in meaning. Indeed, many of 
 the symbolic elements of a conceptual system may enter the 
 system only through being identical in meaning with the origi- 
 nal groups of other elements, that is, many of the variables may 
 gain their variable significance through definition alone. Such 
 equivalent symbols can replace one another in any of the groups; 
 this also is a rule of substitution which is valid in all systems. 
 
 Fourthly, symbols originally taken as distinct in meaning 
 must be construed as distinct throughout. None of the transfor- 
 mations of the system can result in the use of distinct symbols 
 as the same or equivalent. For this would violate the principle of 
 contradiction, which asserts that any possible value of a nega- 
 tive, that is, any symbol distinct from a given symbol, is always 
 distinct from this symbol. And yet this principle permits the sub- 
 stitution of distinct, as well as identical, symbols for one another, 
 when the special rules of the system so provide. Though such 
 substitutions of distinct symbols for one another will always 
 result in alterations of meaning, this fact does not render such 
 substitutions impossible, for distinct symbols do not become 
 
 
 
FORMAL DEDUCTION Q227 
 
 identical in meaning by being substituted for one another. Iden- 
 tity of meaning is more than a possibility of mutual substitu- 
 tion.’ In fact, the more important transformations in any sys- 
 tem are the ones which come about when the symbols in groups 
 are replaced by other (distinct) symbols. Special rules of substi- 
 tution, which hold only for the special systems in question, pro- 
 vide for transformations of this type. 
 
 A formal set of postulates will begin by assuming that certain 
 symbolic groups, whose terms and symbols of unity have been 
 distinguished, are significant, that is, that these groups have syn- 
 tactical meaning apart from any objects they might represent. 
 A set of postulates will also assume some special rules of substi- 
 tution, in addition to the general rule that the same symbol or 
 symbols of identical meaning can replace one another. It may 
 further assume certain special identities of meaning, that is, 
 special equivalences or definitions, which (when the system is 
 interpreted) will represent identities in objects. With these as- 
 sumptions, the set of postulates is a complete plan of syntax for 
 a symbolic system. Any group or equation which can be derived 
 from the original groups or equations by the rules of substitu- 
 tion will be significant in the system, and combinations of sym- 
 bols which cannot thus be derived will be nonsensical; they will 
 have no meaning in this context. The plan marks the boundaries 
 of an area of concepts; it separates what is conceivable or sig- 
 nificant in terms of its own symbols from what is inconceivable 
 or nonsensical in these terms; but it does not separate what is 
 true from what is false. All of its propositions are “‘thinkable”’; 
 whether they are true or false is another and an irrelevant ques- 
 tion. Deduction in a system of this type is the manipulation of 
 the symbols according to the rules. 
 
 1 Symbols which are identical in meaning must, if they stand for objects, 
 stand for the same object; while symbols which can be substituted for one an- 
 other may stand for diverse objects, and must stand for diverse objects if they 
 are distinct in meaning. 
 
228 SYMBOLISM AND TRUTH 
 
 The process of formal deduction, divorced from a subject- 
 matter and occupied only with logical forms and their connec- 
 tions, is the derivation by substitution of significant symbolic 
 groups of different elements and forms from other symbolic 
 groups; and a formal deductive system is a set of uninterpreted 
 symbolic complexes of many distinct forms and elements built 
 up, by this process of substitution, from a few simple symbols 
 and symbolic complexes. Where possibilities alone are consid- 
 ered, deduction is an engrossing game played with symbols. The 
 rules of the game are the general conditions of the use of sym- 
 bols, together with the possibilities of manipulation opened up 
 by these rules and by any other special rules which may be de- 
 vised for special systems. 
 
 III 
 
 The study of a set of postulates — for geometry, algebra, 
 logic, or any other field of knowledge — reveals the importance 
 of the part which substitution plays in formal deduction. 
 Logicians speak of substitution as an essential modus operandi 
 or real operation in uninterpreted systems.! It is in fact the sole 
 means of connecting the theorems with the postulates and 
 axioms when these postulates and axioms are purely hypotheti- 
 cal, that is, when their truth or falsity as premises and conclu- 
 sions is not even considered. 
 
 Sets of postulates rarely state their rules of substitution ex- 
 plicitly, though they always make use of such rules. One of the 
 simplest methods of providing for the manipulation through 
 substitution of the symbols of a deductive system is that em- 
 ployed by Mr. E. V. Huntington.? As the “base” of a set of 
 postulates, he assumes a class, K, of elements, a, b, c, etc., and 
 
 1 See C. I. Lewis, A Survey of Symbolic Logic (1918), pp. 353 ff.; also A. N. 
 Whitehead, A Treatise on Universal Algebra (1898), Bk. I, ch. 1, “On the 
 Nature of a Calculus.” 
 
 ? See E. V. Huntington, Sets of Independent Postulates for the Algebra of 
 Logic, Transc. Amer. Math. Soe. (1904), v, 288-309. 
 
 
 
FORMAL DEDUCTION 229 
 
 relations or operations, R, S, etc. Since the postulates hold for 
 any element of K, the terms, a, b, c, etc., can be mutually substi- 
 tuted for one another without rendering the postulates invalid. 
 Thus, if (aRb) is postulated in the system, (aRc) and (bRc) will 
 also be in the system, Further, if the group (aRb), is itself an 
 element of the class, K, it can be substituted for a, b, or c (since 
 it might be any element of K), giving the complex ((aRb) Rb), 
 etc. And if the substitutions were carried forward — (aRb) re- 
 placing a or 6 in this latter group, and so on — an infinity of 
 complexes of different forms would be provided for by this sin- 
 gle possibility of substitution. The result of assuming the class, 
 K, as a “‘base”’ is then the same as if it were explicitly stated, in 
 the beginning, that any of the simple symbols of the system can 
 be mutually substituted for one another, and any of the original 
 groups can be substituted for any of the simple symbols. 
 
 In the Principia Mathematica, Messrs. Whitehead and Rus- 
 sell make use of substitutions in most of their proofs, especially 
 in those of the earlier propositions from which the later ones 
 follow by implication; and they speak of this process as “notic- 
 ing that (these propositions) are instances of general rules,” ! 
 that is, of the primitive propositions given in the first section of 
 their work. These substitutions are possible, in the symbolic 
 system of the Principia Mathematica, because these primitive 
 propositions are principles of logic asserted for any proposition, 
 rather than purely uninterpreted groups of symbols. In Mr. 
 Huntington’s language, the class, K, of the Principia Mathe- 
 matica is the class of all propositions; any proposition can be 
 substituted for any other in the original complexes of the sys- 
 tem. For example, p v p->- p, states that ‘“‘any proposition or 
 the same proposition implies itself.’’ And from this postulate, 
 together with the definition of implication, p > g-=-~pvq, 
 which asserts that “‘an implication between two propositions 
 
 1 Whitehead and Russell, Principia Mathematica, i, 102. 
 
230 SYMBOLISM AND TRUTH 
 
 means that either the first is false or the second true,” the princi- 
 ple of reductio ad absurdum, p > ~p:+ >+~>p (“any proposition 
 that implies its negative implies its own falsity”), can be de- 
 rived by substitution as follows: The proposition, ~p, (not-p), 
 is substituted for p in the primitive proposition, pv p:>:?p, 
 giving ~pv op->+ op. Now, if wp is substituted for q in 
 the definition of implication, the resultisp 3 ~p-=: pvp; 
 and if p > ~p (being equivalent to ~pv ~p) is substituted 
 for the latter in ~pv w~p:>5-~p, we have p > ~p->. op, 
 the principle of reductio ad absurdum, which was to be proved. 
 This proof illustrates how the Principia Mathematica derives the 
 ‘“‘immediate consequences of the primitive propositions.” “‘The 
 recognition that a certain proposition is an instance of some gen- 
 eral proposition previously proved or assumed,” say Messrs. 
 Whitehead and Russell, “‘is essential to the process of deduction 
 from general rules”’; ! and this is, in effect, the recognition that 
 certain substitutions are permitted in the system. 
 
 It must be observed that these deductive substitutions are al- 
 ways carried through completely. If one symbol replaces an- 
 other in a group, it replaces the latter wherever it occurs. Thus, 
 when ~7 is substituted for p in pv p->->=, every instance of 
 the symbol p becomes an instance of ~p, giving ~pV ~p+a- 
 op. That the substitutions must be complete is a general prin- 
 ciple of deductive substitutions, the reason for which is not im- 
 mediately evident. 
 
 It will be remembered that the distribution of tautologous 
 (or recurrent) elements is a formal feature of symbolic groups. 
 Now, if the rule of completeness of substitution were not followed, 
 groups that include tautologous members could be transformed 
 into groups in which no tautologous members were present. A 
 reflexive group, such as (Raa), could yield a non-reflexive group, 
 such as (Rab). There is no objection to this if the system in ques- 
 
 1 Loe. cit. 
 
 
 
FORMAL DEDUCTION 231 
 
 tion contains a non-reflexive group (which is otherwise the same 
 in form) for every reflexive group.’ But if the system contains no 
 non-reflexive groups (or only non-reflexive groups which do not 
 correspond in other formal features with its reflexive groups), 
 the rule of completeness of substitution will be needed; other- 
 wise, complexes which have no significance in the system will be 
 introduced. In the first type of system (one which contains a 
 non-reflexive group corresponding to every reflexive group), it 
 is always possible on the other hand to derive the reflexive from 
 the non-reflexive groups by substituting instances of the same 
 symbol for distinct symbols: (Rabe), for example, gives (Raaa) 
 if a is substituted for both b and ¢, so that the rule of complete- 
 ness of substitution can be imposed on these systems without 
 decreasing their deductive possibilities. The rule is therefore 
 assumed as a general principle, applicable alike to those systems 
 for which it is necessary and to those for which it is redundant. 
 The reason is, in short, that non-reflexive complexes are more 
 general in form than reflexive ones. The rule of completeness of 
 substitution prevents us from deriving the more general forms 
 (the non-reflexive) from the less general (the reflexive), but per- 
 mits us to derive the less general from the more general by sub- 
 stituting instances of the same symbol for distinct symbols. 
 Though this latter type of substitution — of instances of the 
 same symbol for distinct symbols — is permitted by the rule of 
 completeness of substitution, it is not required by this rule, and 
 it cannot be assumed that in all systems instances of the same 
 symbol can replace distinct symbols. If this were erected into 
 a general principle, there would be no systems which did not 
 include reflexive groups, and there are many such — notably, 
 systems of serial order. Indeed, for some systems, it can be laid 
 down as a special rule that distinct symbols must always be re- 
 
 2 The term “reflexive group” is here taken in a general sense to mean any 
 group containing tautologous members, however distributed. 
 
232 SYMBOLISM AND TRUTH 
 
 placed by distinct symbols. In these systems it would be impos- 
 sible to derive a complex such as (Raaa) from one such as (Rabe). 
 This special rule prevents the introduction of tautologous ele- 
 ments where tautologous elements were not originally present; 
 it is applicable to systems whose complexes are irreflexive 
 throughout. But if this narrower condition of substitution is not 
 introduced, it is taken for granted that instances of the same 
 symbol (that is, tautologous symbols) can replace distinct 
 symbols; that reflexive groups can be derived from all the non- 
 reflexive groups in the system. 
 
 In most deductive systems, then, the rules of manipulation 
 permit any of the original terms mutually to replace one an- 
 other, and any of the basic or derived groups to replace any of 
 these terms — the rule of completeness of substitution being al- 
 ways observed, and the rule that distinct symbols must be sub- 
 stituted for distinct symbols being sometimes added. 
 
 Still other possibilities of manipulation than these highly gen- 
 eral ones are usually provided for in a set of postulates. It may 
 be specified that some of the groups are identical in meaning 
 with others or with some of the original terms, and hence that 
 these symbols of identical meaning can be mutually substituted 
 for one another. In Mr. Huntington’s first set of postulates for 
 the algebra of logic, among other equations, the following ap- 
 pears: a® (b@c) = (a@®b) @ (a@c). When the system is 
 interpreted, this equation means “a or b and ¢ is identical with 
 a or b and aor ec.” ? It represents different structures in an iden- 
 tical object, that is, on the class interpretation of the algebra, 
 the expressions on each side of the sign of equality stand for the 
 same class. But when the system is uninterpreted, the equation 
 merely states an intention to use these groups as identical in 
 
 1 There are some systems, however, in which the basic or derived groups 
 cannot be substituted for the original terms, and an example of such a system 
 is given below. See below, sec. vii, note. 
 
 ? See E. V. Huntington, op. cit. 
 
 
 
FORMAL DEDUCTION 233 
 
 meaning, whether or not they refer to objects. Since such as- 
 sumed identities of meaning equate different logical forms, they 
 are “equations of structure.” 
 
 In lieu of or in addition to these equations of structure, a sys- 
 tem may include connections of meaning which appear as impli- 
 cations. It may be specifically provided that some of the groups 
 imply others. For instance, in Mr. Huntington’s postulates for 
 serial order, it is stated that (afb) (bRc) “implies” (aRc), and 
 this asserts (where R stands for the relation “‘precedes”’) that “if 
 a precedes b and b precedes c, a precedes c.”’ ! Now, in an unin- 
 terpreted system, these cannot be implications of the usual sort, 
 for ordinarily implications are functions of the truth values of 
 the propositions they unite; p implies g means that “either p is 
 false or q is true,” that is, that when p is true, q is also true. Truth 
 values are not considered in an uninterpreted system, and so 
 these implications cannot be truth-implications. They become 
 truth-implications when the system is interpreted. Otherwise, 
 they are connections of meaning apart from truth and falsity, 
 and as such are nothing but possibilities of substitution. If p im- 
 plies q in an uninterpreted system, this implication means sim- 
 ply that q can replace p as a conclusion in any deduction. Any 
 series of transformations that leads to =: leads also to q. 
 
 These “implicational substitutions” belong to a special class, 
 and must not be confused with the others. If q is an “implica- 
 tional substitute” for p, this provision does not allow q to take 
 the place of p in any complex in which p appears; but it does 
 allow q to be substituted for p when p appears at the end of a 
 chain of deductions. And this is readily verified by any concrete 
 example of implication: “x is human” implies “x is mortal,” 
 and if “‘x is human” is deduced from the fact that “x walks 
 erect and speaks,” “‘x is mortal”’ can also be deduced from this 
 fact. But “x is mortal” cannot replace “‘x is human” wherever 
 
 1 E. V. Huntington, The Continuum (1917), p. 10. 
 
234 SYMBOLISM AND TRUTH 
 
 the latter occurs; for instance, ‘zx is human” implies that “zx 
 thinks’; and yet “x is mortal” does not imply that “x thinks.” 
 An implicational substitute for any expression cannot replace 
 this expression as a premise, or as a constituent in any expres- 
 sion whatsoever, but it can replace it as a conclusion. 
 
 There is one other important type of manipulation which 
 must be noticed. The process of substitution is transitive, that 
 is, if a can be substituted for b and 6 can be substituted for ¢, a 
 can be substituted for c. If each of a series of propositions can 
 replace one another in order, all of the intermediate steps can be 
 dropped; the first of the series can be replaced by the last. This 
 transitivity of substitutions enables us to bring together the 
 premise and conclusion of a long line of deductions, the interven- 
 ing links being omitted. And this principle applies where the 
 substitutions proceed via identities of meaning, or where a con- 
 clusion is replaced by something that it implies. Such condensa- 
 tions of chains of deduction are employed in all systems; and the 
 general rule that permits them will hereafter be used without 
 specific statement, and will be referred to in proofs as “conden- 
 sation.” 
 
 The single modus operandi of pure deduction is the “real oper- 
 ation” of substitution. By this operation alone the theorems of 
 a deductive system are developed from the basic groups, equa- 
 tions, and implications; and by this operation, also, the pre- 
 mises and conclusions of the system are brought together or 
 “condensed.”’ The postulates and theorems affirm no truths and 
 no relations between truths. All that is considered is what groups 
 have meaning in the system, and how these groups can replace 
 one another. 
 
 The manner of formulating a plan of syntax, that is, a set of 
 postulates, for a deductive system, so that the basic groups can 
 be transformed by substitutions into theorems, will be better 
 understood through a more complete illustration, in which there 
 
 
 
FORMAL DEDUCTION 235 
 
 are many different possibilities of symbolic manipulation. The 
 substitutions will always follow (1) the rule of completeness and 
 (2) the rule that the same symbol, or symbols of identical mean- 
 ing, can replace one another; but the special condition, that dis- 
 tinct symbols must be substituted for distinct symbols, will not 
 be imposed. When this system is before us, we can ask what con- 
 nections among facts the deductive manipulations of the sym- 
 bols might represent. 
 
 IV 
 
 The system chosen as an illustration is a Boolean Algebra, an 
 algebra of logic; and it will be interpreted as referring to classes 
 and class relationships, though it can be interpreted in several 
 other ways, e.g., in terms of regions in space together with cer- 
 tain relations between these regions.! But no interpretation is 
 necessary to it. Through symbolic complexes of variable ele- 
 ments, which have syntactical meaning apart from objects they 
 might mean, it presents an area of possible logical forms and 
 shows how, from a few of these forms, all the others can be de- 
 rived. Logical forms and their connections are its sole concern. 
 It is complete in itself as a collection of symbolic groups, equa- 
 tions, and rules of manipulation; and if it had no interpretation 
 it would still be an experiment in possibilities for thought. That 
 it happens to be a class algebra is an interesting and useful acci- 
 dent, but not essential to it. 
 
 (1) The basic groups of this system are (Rab), (Sab), and 
 (Na). R, S, and N are undefined symbols of unity, and a and b 
 are undefined terms. The parentheses are signs of syntax or 
 grouping, to be construed in the way in which such signs are 
 always construed. (Since these groups have a logical structure, 
 they are significant, and the symbols R, S, N, a, and b are vari- 
 
 1 See E. V. Huntington, op. cit. 
 
236 SYMBOLISM AND TRUTH 
 
 ables.) A third undefined term, c, will also be assumed. R, S, N, 
 a, b, and c are symbolically distinct.’ 
 
 (2) The substitutions permitted are: (a) any of the undefined 
 terms can be mutually substituted for one another, and (b) any 
 of the basic symbolic groups, or any groups derived from them, 
 can be substituted for any of the undefined terms. This latter 
 rule permits substitutions in one direction only, that is, the un- 
 defined terms cannot be substituted for any of the groups, un- 
 less they are equivalent to them. (The rule of completeness of 
 substitution, and the principle that the same or equivalent sym- 
 bols can replace one another, are taken for granted.) 
 
 (3) The following identities of meaning are assumed: 
 
 A. Ra(Sb(Nb)) = a. C. Ra(Sbc) = S(Rab)(Rac). 
 B. Sa(Rb(Nb)) = a. D. Sa(Rbe) = R(Sab)(Sac). 
 Since the original undefined terms of the system appear on 
 both sides of these identities, these identities are not definitions. 
 When the system is interpreted, these equivalences will repre- 
 sent differences of structure in an identical object. ? They are 
 *“‘equations of structure.” 
 (4) Two symbols which are not among the undefined terms 
 are introduced by definitions: 
 E. z = Sa(Na). F. u = Ra(Na). 
 
 These are definitions because z and wu are not included in the 
 original terms but enter the system only through being identical 
 in meaning with certain ones of its significant groups. Such 
 definitions are not necessary to the exposition; they are merely 
 symbolic conveniences which condense complex expressions. 
 But it would be uneconomical to take as undefined, and hence to 
 
 1 The spatial order of the symbols in the groups is irrelevant; it plays no 
 part in their logical form, which is determined by grouping alone; and there- 
 fore it is not necessary to mention the fact that (Rab), (aRb), and (abR) are 
 the same symbol. 
 
 2 See above, ch. II, sec. vi. 
 
 
 
 . 
 1 
 ; 
 ’ 
 ‘ 
 { 
 
FORMAL DEDUCTION 237 
 
 place among the original (primitive) symbols of the system, a 
 symbol whose meaning could be defined through some of the 
 groups. “Occam’s razor”’ must always be applied; entities must 
 not be assumed unless they are necessary. (It is to be noted that 
 the rules of substitution given in (2) hold for the original terms, 
 and not for z and wu. There are special rules for these terms, which 
 can be deduced from the other rules.) 
 
 The general and special conditions of substitution permit 
 three classes of transformations in this system: (1) The elements 
 of a group can be altered without altering its form. If, for ex- 
 ample, a replaces b, and ¢ replaces a, in Ra(Sb(Nb)) = a, this 
 substitution will give the equation, Re(Sa(Na)) = c, which is of 
 the same form as the first, but of different elements. Such trans- 
 formations are unimportant. (2) Tautologies can be introduced 
 where tautologies did not originally appear, for there is no pro- 
 viso that distinct symbols must be replaced by distinct symbols. 
 Thus from Ra(Sb(Nb)) = a, we can derive Ra(Sa(Na)) = a; 
 from (Rab) or (Sab) we can derive (Raa) or (Saa), etc. The sys- 
 tem therefore contains reflexive forms corresponding to all its 
 non-reflexive forms. (3) Complexes of a higher type can be de- 
 rived from complexes of a lower type, and this process can be 
 carried, theoretically, to infinity. (Rab), for example, yields 
 (Ra(Rab)), and this complex yields (Ra(Ra(Rab))), etc., when 
 (Rab) is substituted for b; so that the system contains an infinity 
 of possible forms. 
 
 It is apparent that all of the complexes which appear in the 
 equations, A, B, C, and D, and in the definitions, E and F, are 
 significant in the system; they can all be derived from the basic 
 groups by these rules of substitution. 
 
 The “equations of structure”’ and the definitions, moreover, 
 make possible a fourth class of transformations, those obtained 
 by substituting equivalent symbols or groups in groups. With- 
 out the “equations of structure,” each of the groups in the sys- 
 
238 SYMBOLISM AND TRUTH 
 
 tem might, when the whole is interpreted, stand for a distinct 
 object. The equations impose limitations on these possible dis- 
 tinctions of meaning, as do also all the other equations which 
 can be deduced from them by proper substitutions; and at the 
 same time these equations increase the number of manipula- 
 tions which can be performed in the system. 
 
 (5) Some of the most important theorems, and their deriva- 
 tions, are the following: 
 
 1. Raz = a. 2. Sau = a. 
 
 The proof of these two theorems requires the definitions, E 
 and F.. These definitions are, like the other equivalences in the 
 system, subject to all the permitted transformations by substi- 
 tution. Therefore, z = Sa(Na) yields z = Sb(Nb) by the sub- 
 stitution of 6 for a; and u = Ra(Na) yields u = Rb(Nb), by a 
 similar substitution. And, since equivalent symbols can be sub- 
 stituted for one another, we can derive Raz = a from the equa- 
 tion Ra(Sb(Nb)) = a by replacing Sb(Nb) by z. Similarly, we 
 can derive Sau = a by replacing Rb(Nb) by u in the equation 
 Sa(Rb(Nb)) = a. This is the deduction of theorems 1 and 2. 
 
 The rules for the substitution of these two special symbols, z 
 and u, follow from their definitions. Since they are equivalent, 
 respectively, to Sa(Na) and Ra(Na), they can be substituted for 
 any symbol for which these groups can be substituted. There- 
 fore, they can replace any of the terms, a, b, c, ete., of the sys- 
 tem; but these terms cannot replace them, for these terms can- 
 not replace the groups through which z and wu are defined. In 
 other words, so far as concerns the manipulation of the symbols 
 in this system, z and u are values of any of the variable terms, 
 but they are not themselves variables; they are constants.! 
 
 1 This introduces a new kind of variability, “functional variability,” which 
 is something other than indeterminateness of significance; z and wu are func- 
 tional constants, rather than functional variables; but their meaning is still 
 undetermined. This is explained below, sec. vi. 
 
 
 
FORMAL DEDUCTION 239 
 
 Other theorems are the following: 
 
 8. Raa =a 
 Proof: 
 a = Sau (by theorem 2). 
 Raa = Su(Raa) (Raa replaces a in 2.) 
 Su(Raa) = S(Ra(Na)) (Raa) (By def. F, Ra(Na) replaces u). 
 
 S(Ra(Na))(Raa) = Ra(Sa(Na)) (where a replaces b, and Na re- 
 places c, in C). 
 
 Ra(Sa(Na)) = Raz (By def. E, z replaces Sa(Na)). 
 Raz =a (by theorem 1). 
 
 Therefore: a = Raa (“‘condensation”’). 
 
 4. Saa =a. 
 
 This can be deduced in exactly the same manner as 3, by 
 using theorem 1 for 2 and u for z. Theorems 3 and 4 are the 
 analogues of one another for the symbols of unity R and S 
 
 respectively. 
 5. a = N(Na) 
 Proof: 
 1’. 2 = S(Na)(N(Na)) (by def. E, where Na replaces a). 
 2’, u = R(Na)(N(Na)) (by def. F, where Na replaces a). 
 a = Raz (by theorem 1). 
 Raz = Ra(S(Na)(N(Na))) (By 1’, S(Na)(N(Na)), replaces z). 
 
 Ra(S(Na)(N(Na))) = S(Ra(Na))(Ra(N(Na))) 
 (by C, where Na replaces 6 and N(Na) replaces c). 
 S(Ra(Na))(Ra(N(Na) = Su(Ra(N(Na))). 
 (By def. F, u replaces Ra(Na)). 
 Su(Ra(N(Na))) = Ra(N(Na)) (by theorem 2, where Ra(N(Na)) 
 
 replaces a). 
 
 Therefore: 3’. Ra(N(Na)) =a (“condensation”’). 
 N(Na) = R(N(Na))z (by theorem 1, where N(Na) re- 
 places a). 
 
 R(N(Na))z = R(N(Na))(Sa(Na)). (By def. E, Sa(Na) replaces z). 
 R(N(Na))(Sa(Na)) = S(R(N(Na))a)(R(N(Na))(Na)) 
 (by C, where N(Na) replaces a, a replaces b, and Na replaces c). 
 S(R(N(Na))a)(R(N(Na))(Na)) = S(R(N(Na))a)u 
 (By 2’, u replaces the group R(N(Na))(Na)). 
 S(R(N(Na))a)u = R(N(Na))a (by theorem 2, where R(N(Na))a 
 replaces a). 
 Therefore: 4’. N(Na) = R(N(Na))a_ (“condensation”). 
 Therefore: N(Na) =a (by “‘condensation” of 3’ and 4’). 
 
240 SYMBOLISM AND TRUTH 
 
 When the system is interpreted as a Boolean Algebra, this 
 theorem is the principle of double negation. (It is to be noted in 
 the proof that the group Ra(N(Na)) in 3’ is the same as the 
 group R(N(Na))a in 4’, since the spatial order of the symbols is 
 irrelevant.) 
 
 6. 2=Nu 
 
 Proof: 
 
 z = Sa(Na) (by def. E). 
 
 z= Su(Nu) (u replaces a in def. E). 
 
 Su(Nu) = Nu (by theorem 2, where Nu replaces a). 
 Therefore: z = Nu (“‘condensation”’). 
 7. ui= Nz 
 
 Proof: 
 
 u = Ra(Na) (by def. F). 
 
 u = Rz(Nz) (z replaces a in def. F). 
 
 Rz(Nz) = Nz (by theorem 1, where Nz replaces a). 
 Therefore: u = Nz (“‘condensation’’). 
 
 Some of the other theorems which can be derived in the sys- 
 tem, but of which the proofs are not given, are the following: 
 
 8. Rau = u 12. Rab = N(S(Na)(Nb)) 
 9. Saz =z 13. Sab = N(R(Na)(Nb)) 
 10. Ra(Sab) =a 14. R(Rab)b = Ra(Rab) 
 11. Sa(Rab) = a 15. S(Sab)b = Sa(Sab) 
 
 The introduction by definition of the group (b(Za)) simplifies 
 the system; on the class interpretation of the algebra this group 
 means that the class a is included in, or “subsumed under,” the 
 class 6.! This new complex can be defined in several different 
 
 ways: 
 (b(Ta)) =(Rab = b) (G) 
 (b(Ia)) = (Sab = a) (H) 
 (b(Ia)) = (Rb(Na) = u) (I) 
 (b(Ia)) = (Sa(Nb) = z) (J) 
 
 1 The grouping of (6(Ia)) indicates that it has a “‘sense”’ or order; the al- 
 ternative order is (a(Ib)). No specific symbol of unity is inserted to join the 
 sub-group (Ja) or (Ib), as the case may be, to the term a or b; the outer paren- 
 theses show that they form a group, and this is all that is necessary; their 
 group unity is of the most general sort — simply “‘togetherness”’ or “unity.” 
 
 
 
FORMAL DEDUCTION 241 
 
 Some of the postulates and theorems stated above can be 
 translated into the terms of this new group, and this translation 
 will give, among others, the following theorems: 
 
 16. (a(Iz)) 
 Proof: 
 (Rbz = b) is in the system (b replaces a in theorem 1). 
 (Rab = b) = (b(Ia)) (by def. G). 
 (Rzb = b) = (b(Iz)) (z replaces a in def. G). 
 
 Therefore: (b(Iz)) is in the system, since it is equivalent by definition to a 
 group in the system. 
 
 17. (u(Ia)) 
 
 Proof: 
 
 (Rau = u) is in the system (by theorem 8). 
 
 (Rab = b) = (b(Ia)) (by def. G). 
 
 (Rau = u) = (u(Ia)) (u replaces 6 in def. G). 
 Therefore: (u(Za)) is in the system. 
 18. (u(Iz)) 
 
 Proof: 
 
 (Ruz = u) is in the system. (u replaces a in theorem 1). 
 
 (Ruz = u) = (u(Iz)) (u replaces b, and z replaces a, in 
 
 def. G). 
 Therefore: (u(Iz)) is in the system. 
 
 19. (a(I(Sab))) 
 20. ((Rab)(Ia)) 
 
 The proof of theorems 19 and 20 is similar to that of 16, 17, 
 and 18, where theorems 10 and 11 and definitions G and H are 
 
 employed. 
 21. (a(Ia)) 
 Proof: 
 (Raa = a) is in the system (by theorem 8). 
 (Raa = a) = (a(Ia)) (a replaces b in def, G). 
 
 Therefore: (a(Ia)) is in the system. 
 
 There are many more theorems in terms of the group (b(Ja)) 
 which are not stated. 
 
 This group is unlike the groups in terms of R, S, and N in that 
 there are no rules which permit the substitution of (b(Ia)), or 
 
242 SYMBOLISM AND TRUTH 
 
 its derivatives, for the original terms, a, b, and c, of the system. 
 The group is defined as identical in meaning with the equiva- 
 lence (Rab = b), or with the other equivalences given as H, I, 
 and J. It can, therefore, be substituted for these equivalences; 
 and when the latter, or their derivatives, are members of the 
 system, some J-groups will also be, by definition, members of 
 the system. But (Rab = 6), or the other equivalences, H, I, and 
 J, cannot be substituted for a, b, and c; and hence the J-groups 
 cannot be substituted for these terms.! 
 
 V 
 
 In practice, all deductive systems are devised with one eye on 
 the facts, that is, on an interpretation. They are stated as if they 
 referred to no objects, but they prove in the end to be connected 
 expositions of truths which hold in some realm of experience, 
 that is, to be systems of geometry, algebra, logic, etc. And if the 
 plan of a system were constructed without this arriére pensée, it 
 is not likely that an interpretation — or anything more than a 
 trivial one — could be found for it. To explore all possibilities 
 for thought, cut off from moorings in the world of the actual, 
 would be an interesting but an endless experiment, for the num- 
 ber of possible conceptual systems is infinite; and so those sys- 
 tems which embody the structure of actual sets of objects are 
 selected. Pure speculation then gives way to assertion, what 
 seem to be arbitrary manipulations of symbols become infer- 
 ences, and the significance of the whole is bound down to the 
 real. A conceptual system which corresponded to no subject- 
 matter would be an exercise in logical construction, and nothing 
 more. Yet such exercises show that from the point of view of 
 
 1 The original rule of manipulation, that any of the basic groups or their 
 derivatives can replace any of the basic terms, does not provide that the 
 “equations of structure”’ or the definitions, taken as wholes, can replace these 
 terms; for these identities of meaning are not derived from the basic groups 
 (though their constituents are), but are postulated on their own account. 
 
 
 
FORMAL DEDUCTION 243 
 
 formal logic all that need. be considered, even in an interpreted 
 system, are logical forms and their connections. 
 
 The system which has been developed here is adapted to sev- 
 eral different subject-matters. The symbols a, b, and c can stand 
 for propositions, and the groups (Rab), (Sab), and (Na) for cer- 
 tain “truth-functions”’ of propositions; v2z., (Rab) will mean the 
 proposition, “either a or b (not excluding both) is true”; (Sab) 
 will mean the proposition, “‘a and 6 are both true’; and (Na) 
 will mean the negative of a. Another interpretation can be given 
 in terms of regions of a plane surface, together with certain rela- 
 tions between these regions; viz., (Rab) represents the region 
 that includes both regions a and 6; (Sab) represents the region 
 where a and b intersect; and (Na) represents all of the plane 
 that lies outside the region a.1 We shall interpret the system as a 
 logic of classes. 
 
 A class has previously been described as a totality of distinct 
 objects which have some predicate in common. Every predicate 
 determines such a totality, e.g., the predicate “‘man”’ deter- 
 mines the class ““men.”’ Classes may be related to one another in 
 many ways, and these class relationships can be employed in 
 reasoning. Classes may overlap, they may include or exclude onc 
 another, their members may be added together to form a new 
 class. There is also a null class, one that has no members, the 
 class of “nothing”; and this class is determined by any predi- 
 cates of which there are no instances, e.g., “‘the present King of 
 France”’ determines the null class. Further, there is a universal 
 class of which everything, excepting this class itself, is a mem- 
 ber.? Every postulate and theorem of the system can be inter- 
 
 1 See E. V. Huntington, Sets of Independent Postulates for the Algebra of 
 Logic, cited above. 
 
 2 This exception is necessary to avoid the difficulties involved in the notion 
 of “the class of all classes.” See Whitehead and Russell, Principia Mathe- 
 matica, ch. 2. Though the universal class is not a member of itself, still it is 
 coextensive with itself; 7.e., the relation of class inclusion or subsumption, 
 represented by the J-groups of the system, holds for it; so that (w(Zu)) is true. 
 
244. SYMBOLISM AND TRUTH 
 
 preted as a true statement about classes, and every manipula- 
 tion as a true inference, leading from premises to conclusions 
 that concern classes, 
 
 The original terms of the system, a, b, and ¢ stand for any 
 classes; but since these terms are symbolically distinct, they can 
 not, in any expression, be interpreted as signifying the same 
 class. (Rab) means the class that includes all the members of a 
 and 6, and only these members; this is called the “logical sum” 
 of a and b. (Sab) means the class whose members belong both to 
 a and 0; it is the “logical product” of a and b. (Na) means the 
 class of all objects excluded by the class a. The symbol z stands 
 for the null class, and wu for the universal class, for “nothing” 
 and “everything,” respectively. The expression (b(Ia)) means 
 that the class a is included in the class b. 
 
 The rules of substitution tell us: 
 
 (1) That any of the original terms can be mutually substi- 
 tuted for one another, and that any of the basic groups, or 
 groups derived from them, can be substituted for any of the 
 original terms. Now if, on the class interpretation, (Rab), (Sab), 
 (Na) and their derivatives represent anything, they will stand 
 for classes. The logical sums, products, and negatives of classes, 
 together with their derivatives, are themselves classes. Hence 
 they can replace the variables a, b, and c in any expression and 
 the expression will still be true, for a, b, and ¢ are any classes. 
 Moreover, every sum and product might be the sum or product 
 of a class and itself; so that every expression containing distinct 
 symbols can be altered, by substitutions, into one containing 
 tautologous symbols without rendering the expression untrue. 
 (For the reason that groups formed by R, S, and N stand for the 
 same general sort of entities, that is, classes, as those meant by 
 their terms, these symbols of unity represent operations, rather 
 than relations.) } 
 
 1 See below, sec. vii. 
 
 
 
 
 
FORMAL DEDUCTION 245 
 
 (2) The group (b(Za)), which means that the class a is in- 
 cluded in the class 6, cannot, on the other hand, be substituted 
 for a, b, and ¢, since it does not stand for a class. If a is included 
 in b, the classes a and b are related, but this relation constitutes 
 a new sort of fact, which is not itself a class. 
 
 (3) The classes z and u can replace any of the original terms, 
 a, b, and c, but these terms cannot replace z and u; for the null 
 and universal classes are special elements, they are unique. 
 What is true of any class is true of them, since they are classes, 
 but the converse does not hold. 
 
 (4) Equivalent groups or symbols can replace one another, 
 for they represent the same class. Thus the null class is defined 
 by and can be substituted for Sa(Na); it is the logical product 
 of any class and its negative, that is, it is the class that includes 
 all the members both belonging to and excluded by any class 
 a— and these are no members. 
 
 Obviously, these rules of manipulation make it possible, 
 through the substitution of interpreted symbols or groups in 
 other interpreted groups, to derive true propositions about 
 classes from other true propositions about classes; they yield 
 true inferences. 
 
 The interpretations of the postulates are not so simple as 
 those of some of the theorems. Theorem 1, Raz = a, is the fa- 
 miliar proposition that “‘the logical sum of any class and the 
 null class is identical with the first class,” that is, ‘the class in- 
 cluding all members of a and of the null class is the same as a.”’ 
 Theorem 2, Sau = a, states that “the class of members common 
 to a and the class of everything is the same as a.” Definition E, 
 z = Sa(Na), is the principle of contradiction for classes, and 
 asserts that “‘a class and its negative have nothing in common.” 
 Definition F, u = Ra(Na), is, on the other hand, the law of the 
 excluded middle for classes; it affirms that “the class including 
 all members of a and all members excluded by a is the class of 
 
246 SYMBOLISM AND TRUTH 
 
 everything,” or simply “that a class and its negative exhaust the 
 universe.’ Theorems 3 and 4, Raa =a and Saa = a, are two 
 forms of the principle of identity for classes. The first states that 
 “the class including all the members of a and of a is the class a”’; 
 and the second, that “‘the class of members common to a and a 
 is the class a.’’ Theorem 5, a = N(Na), that is, ‘‘the class that 
 excludes all that is excluded by any class a is the class a,” is the 
 principle of double negation; “‘not-not-a is identical with a.” 
 Theorems 6 and7,z = Nuandu = Nz, show that the universal 
 and null classes exclude, or are the negatives of, one another, 
 that is, “nothing” excludes “everything” and “everything” 
 excludes “nothing.” ! Theorem 8, Rau = u, states that ‘the uni- 
 versal class added to any class a gives the universal class”; and 
 this theorem differentiates the wu (and the “‘addition’’) of the 
 class algebra from the number 1 (and the “‘addition”’) of ordi- 
 nary algebra; 1 added to any number does not give 1. Theo- 
 rem 9, Saz = z, however, shows an analogy between the null 
 class and the zero of numerical algebra: “the logical product of 
 any class a and the null class is the null class.”” Theorems 10 and 
 11 are two forms of the principle of “absorption”: Ra(Sab) = a 
 asserts that “any class a absorbs by addition a logical product 
 of itself”’; and Sa(Rab) = a, that “‘any class a absorbs the sum 
 of itself and another class in a logical product of itself and this 
 sum.”’ Theorems 12 and 13 are forms of the principle of “‘trans- 
 position”: Rab = N(S(Na)(Nb)) allows a sum of classes to be 
 transposed into the negative of the product of the negatives 
 of these classes; while Sab = N(R(Na)(Nb)) allows a logical 
 product of classes to be transposed into the negative of the sum 
 of the negatives of these classes. Theorems 14 and 15 are the “‘as- 
 sociative”’ law for class sums and products, respectively. Postu- 
 lates C and D are the “distributive” law; Ra(Sbc) = S(Rab) 
 
 1 By theorem 18, “nothing”’ is also subsumed under or included by “every- 
 thing.” The null class has the peculiar property of implying its own negative. 
 
 
 

 
 FORMAL DEDUCTION 247 
 
 (Rac) states that “the sum of aclass and a product of classes 
 is the same as a product of two sums” (loosely put); while 
 Sa(Rbe) = R(Sab) (Sac) states that “the product of a class and 
 a sum of classes is the same as a sum of products” (loosely put). 
 The symbols express this proposition more clearly than a brief 
 form of words can, as is also the case with postulates A and B: 
 Ra(Sb(Nb)) = a asserts that “if the logical product of a class 
 and its negative is added to another class, the whole will be 
 identical with this latter class”; and Sa(Rb(Nb)) = a asserts 
 that “if the logical sum of any class and its negative forms a 
 product with another class, the whole will be identical with this 
 latter class.” 
 
 The “commutative” law, Rab = Rba and Sab = Sba, does 
 not appear in this system. It is unnecessary to state that “the 
 logical sum or product of a and b is the same as the logical sum 
 or product of 6 and a” for the reason that the spatial order of 
 the symbols in the groups is not relevant to their significance. 
 Rab is the same symbol as Rba, and Sab is the same symbol as 
 Sba; the operations of class addition and class multiplication are 
 symmetrical, and these symbolic groups — which are without 
 order — represent them as such. 
 
 The group (b(Ia)), however, has an order; “the class a is sub- 
 sumed under the class b” means something different from “the 
 class 6 is subsumed under the class a.’’ The order (6(Ta)) stands 
 for the first of these facts, and the order (a(Ib)), for the second; 
 and these differences of order are represented by the distribu- 
 tion of the terms a and 6 in the two constituent groups of the ex- 
 pression (a(Jb)), not by the spatial arrangement of the symbols. 
 
 The theorems in terms of J-groups, interpreted as class inclu- 
 sions or subsumptions, state the following propositions: Theo- 
 rem 16, (a(Jz)), affirms that “the null class is included in any 
 class,” that is, any class covers as great a logical area as a class of 
 no members, and, if it is not itself a class of no members, covers 
 
248 SYMBOLISM AND TRUTH 
 
 a wider area. Theorem 17, (u(Ia)), expresses the fact that “any 
 class is included in the class of everything,” which is plainly true. 
 Theorem 18, (w(Zz)), is, like theorem 16, paradoxical; it asserts 
 that “the null class is included in the class of everything,” that 
 is, that the universal class covers everything which is covered by 
 the null class—and much more. Theorem 19, (a(I(Sab))), states 
 that “any class includes the members common to itself and an- 
 other class’’; and theorem 20, ((Rab) (Ia)), that “any class is 
 included in the class formed by itself and another added to- 
 gether.” Theorem 21, (a(Ja)), tells us that “‘any class includes 
 and is included by itself.”” The definitions of class inclusion, G 
 and H, are clearly true: (b(Ja)) = (Rab = b) says that “if a 
 class 6 is identical with the class composed of all the members of 
 a and 6, this is equivalent to the statement that } includes a’’; 
 and definition H, (b([a)) = (Sab = a), says that “if a class a is 
 identical with the class whose members are common to a and b, 
 this is equivalent to the statement that a is included in 6.” 
 
 All of the original postulates, definitions, rules of substitution, 
 and many of the theorems of this deductive system are thus 
 seen by inspection to be true for classes. But in order to verify 
 the system as a whole for this interpretation, it is necessary to 
 verify only the postulates, definitions, and rules of substitution, 
 for if these original propositions hold for classes, all the propo- 
 sitions derived from them will hold for classes. The reason for 
 this will be apparent from a further consideration of the mean- 
 ing of rules of substitution in general, and of the inferences to 
 which they lead when they are interpreted. 
 
 VI 
 
 Symbolic groups built up from other symbolic groups or from 
 simple terms are functions of these groups or terms. (We have 
 observed before that the idea of a group is the same as that of a 
 function.) Every symbol in an uninterpreted deductive system 
 
 
 
FORMAL DEDUCTION 249 
 
 has a functional range, which is simply all the groups into which 
 it can enter as a constituent. A rule of substitution lays down 
 conditions determining the functional ranges of symbols; it tells 
 us either that the functional ranges of two symbols coincide or 
 that the one is wider than the other, that is to say, it prescribes 
 what their functional ranges shall be. If it were possible to 
 spread out on a single page all the groups of a symbolic system, 
 there would be no need for rules of substitution; we could see at 
 a glance what was the functional range of every symbol. But 
 in all except trivial systems the number of possible groups is 
 very great, usually infinite, and so rules of substitution are 
 necessary. 
 
 If a symbol z can be substituted for a symbol y in an uninter- 
 preted system, the functional range of z is wider than that of Y 
 that is, for every group in the system containing y as a member 
 there is a group (similar in every other respect, both in its con- 
 stituents and in its form) containing x as a member, but not the 
 reverse. And if x and y can be mutually substituted for one an- 
 other, their functional ranges coincide, that is, there are no 
 groups in the system containing x which are not paralleled by 
 groups (similar in every respect except for the presence of 2) 
 containing y, and vice versa. 
 
 This conception of the functional range of a symbol intro- 
 duces a new kind of variability, functional variability, which is 
 wholly different from the interpretational variability — inde- 
 terminateness of reference — hitherto considered. A functional 
 variable is a variable with respect to the groups in which it can 
 play a part; and objects, no less than symbols, exhibit this type 
 of variability. Just as a symbol composed of other symbols is a 
 symbolic function, so an object composed of other objects, that 
 is, a factual complex, is an objective function. We describe ob- 
 jects through their predicates and relations; any object may 
 have many different predicates and relations, it may enter into 
 
250 SYMBOLISM AND TRUTH 
 
 many different complexes; and its functional range is all the 
 complexes in which it can be a member. With respect to these 
 groups the object is a variable; it may appear now in one group 
 and now in another, and other objects may take its place in 
 groups. Thus a deductive system, when it is interpreted, will 
 describe a certain set of objects through certain selected func- 
 tions of these objects. ¢ 
 
 Strangely enough, the variables of wider functional range are 
 the values of the variables of narrower range; the former are the 
 more specific in meaning, while the ones of narrower range are 
 the less specific. Thus, in the system now under consideration, 
 the terms z and wu enter in functions in which the terms a, b, and 
 c cannot play a similar part; z and wu are functional variables of 
 wider range than a, b, and c, and hence are special values of the 
 latter. (Theorem 6,2 = (Nu), for example, cannot be translated 
 into z = (Na) ora = (Nu).) But the reason for this is evident. 
 The more we know about an object, the more determinate it be- 
 comes for thought, and the more functions in which a symbol 
 enters, the more completely is its réle in the system fixed. 
 
 A rule of substitution, then, lays down the conditions of func- 
 tional variability for the interpretational variables of a symbolic 
 system. In doing so it prescribes the form of the system and at 
 the same time, through prescribing the form, imposes limitations 
 on the interpretation. When the symbols are given (interpreta- 
 tional) values, these values must be such that the facts into 
 which they enter are of the same structure as the symbolic 
 groups into which the uninterpreted symbols enter; and even so, 
 a wide range of possible (interpretational) values is permitted to 
 any of the symbols of the system. But the interpretation must 
 always fulfill the conditions imposed by the rules of substitu- 
 tion, and this requires that the objects meant by any symbol or 
 group must have a functional range in the world of fact which 
 corresponds to the functional range of this symbol or group in 
 
 
 

 
 FORMAL DEDUCTION 251 
 
 the uninterpreted system. This being the case, the manipula- 
 tions of the symbols will always yield true propositions. 
 
 Thus, if the terms a, b, and c, in the Boolean Algebra stand for 
 classes and the symbols of unity R, S, and N signify the opera- 
 tions of class addition, multiplication, and negation, it will be 
 possible to substitute a, b, and c for one another for the reason 
 that any class forms a sum or product with any other class, and 
 also has a negative. The groups (Rab), (Sab), (Na), and their 
 derivatives can be substituted for these terms, for these groups 
 also signify classes (complex classes) and so can have sums, 
 products, and negatives of their own. Every complex class en- 
 ters into the same sort of class operations as every simple class. 
 But the simple terms a, 6, and ¢ cannot replace the symbols 
 for these complex classes for the reason that there are certain 
 functions of complex classes which are not functions of simple 
 classes. 
 
 In the interpreted system, the rules of substitution cover a 
 multitude of existential or “‘material”’ implications which hold 
 for the objects meant. The rule which permits the substitution 
 of (Rab), (Sab), (Na), for the terms a, b, and c informs us that 
 “if there are classes, there are sums, products, and negatives of 
 these classes’’; the provision that a, 6, and ¢ can be mutually 
 substituted for one another tells us that “‘if there are functions 
 of one class, there are similar functions of other classes.’ But 
 these existential implications must not be confused with spe- 
 cially postulated, and uninterpreted, implications of the sort 
 mentioned before, which permit the substitution of certain sym- 
 bols for others as conclusions in chains of deduction. When the 
 system is interpreted, these specially postulated connections of 
 meaning will be “formal” rather than existential implications. 
 Thus, though (Na) yields by substitution (and hence existen- 
 tially implies) the complex (N(Na)), this could not mean that 
 (Na) “formally” implies (N(Na)), for this would assert that 
 
252 SYMBOLISM AND TRUTH 
 
 “any negative implies its own negative.” The substitution really 
 means that “the negative of a negative is an instance of a nega- 
 tive,” or “if there is a negative of a class, there is also a negative 
 of this negative.” } 
 
 A symbol whose range of functional variability includes but 
 does not coincide with that of another is a constant with respect 
 to this variable of narrower functional range. The symbols z and 
 u in the Boolean Algebra are constants with respect to the terms 
 a, 6, and ¢, since z and u can be substituted for these terms, but 
 not the reverse. Yet z and u are not completely determined in 
 significance by this fact; there are still as many possible inter- 
 pretations for them as there are for the system. A symbol whose 
 meaning is variable in interpretation may function as a con- 
 stant, when its part in an uninterpreted system alone is consid- 
 ered. Such a symbol is a “functional constant,” and is known in 
 mathematics as a parameter. Moreover, all the groups of our 
 system are, with respect to the terms a, b, and c, functional con- 
 stants; any one of these groups stands for some particular sort 
 of combination of classes. Indeed, if the system is taken merely 
 as an uninterpreted set of symbols, the only elements in it that 
 function as variables are the terms a, b, and c. Every other ele- 
 ment or expression is a value of these variables. Therefore, a, b, 
 and c, which have the narrowest range of functionality in the 
 system, are the “functional variables’’; and each of the substi- 
 tutions of a group or other element (unless it be of the elements 
 
 1 The notion that a rule of substitution is to be interpreted as stating a 
 relation between the functional ranges of two variables makes it clear why 
 symbols of indistinct meaning, 7.e., the symbols on either side of the sign of 
 identity, can be mutually substituted for one another. When the system is 
 interpreted, these symbols must always be given an identical value, they must 
 stand for the same object; and obviously every object has the same functional 
 range as itself. Further, it is clear that a coincidence of functional ranges, and 
 
 hence a possibility of mutual substitution, is not the same as identity of 
 meaning. 
 
 
 

 
 FORMAL DEDUCTION 253 
 
 a, b, or c) for a, b, and ce, puts a functional constant in place of 
 one of these functional variables. 
 
 VII 
 
 The symbols of unity R, S, and N stand for operations. That 
 they must stand for operations, and not relations, is determined 
 by the deductive use made of the groups in which they appear. 
 The distinguishing feature of an operational group is that it can 
 be substituted in ctself for one of its terms; and in the Boolean 
 Algebra this is provided for by the rule that (Rab), (Sab), and 
 (Na) can take the place of a in any group, and hence in these 
 very groups. In other words, an operational group is a value of 
 the functional variables that enter into it. 
 
 The “‘plus,” ‘‘minus,”’ and “‘times”’ of numerical algebra, for 
 instance, are operations because the complexes they form are 
 numbers. If a and b represent numbers, (a — b) will be a num- 
 ber; it may be the number a, where b is zero, or the number 
 (—b), where a is zero. But it will always be some number, and 
 thus it can take the place of a or b in any algebraic expression 
 and still give a number; it can be substituted in the very combi- 
 nation (a — b), giving ((a — b) — b), which is a number. 
 
 A relational group, on the other hand, is not a value of the 
 variable terms that appear in it. If a and b are points, and (Rab) 
 means “‘a follows b,”’ this fact is not also a point, and it cannot 
 take the place of a or b in any complex of points. For this reason, 
 the I of the Boolean Algebra is a relation rather than an opera- 
 tion. The I-groupscannot be substituted for the terms that enter 
 
 1 It is possible to consider these ‘‘constants” as functional variables of dif- 
 ferent orders. What is a functional constant with respect to one symbol might 
 be a functional variable with respect to another. The order of variability of the 
 symbols is shown by the rules of substitution. Thus, in the Boolean Algebra 
 (Rab) is a functional constant with respect to a and a functional variable with 
 respect to (R(Rab)b), which is a special case of it. But for purposes of simplifi- 
 
 cation, all the groups can be lumped together as constants with respect to the 
 terms a, b, and c. 
 
254 SYMBOLISM AND TRUTH 
 
 into them, for if a class a is included in a class b, this does not 
 
 form a class, as does the logical sum or product or negative of a 
 and b. 
 
 Operations give rise to systems of an infinite number of possi- 
 ble forms; an operational group can replace again and again a 
 term which appears in this group itself, yielding each time a 
 group of higher type. For every complex that contains a, in the 
 Boolean Algebra, there is one of higher type that contains (Rab), 
 (Sab), or (Na); so that a “proper part” of the collection of 
 groups in which a is a member can be put into one-to-one corre- 
 spondence with the whole of this collection. And this proves 
 that these groups are infinite in number. 
 
 1 For a definition of an infinite collection, see E. V. Huntington, The Con- 
 tinuum, pp. 7 ff. 
 
 ? A set of postulates for serial order of the simplest sort illustrates the dif- 
 ference between operations and relations, and also shows how a system wholly 
 different from the Boolean Algebra is constructed: 
 
 (1) Assume that a, 6, and ¢ are distinct symbols for terms; and that the 
 system is built on the basic group (a(0b)) v (b(Oa)). (The symbols (v) and (.), 
 which stand respectively for the logical ideas “or” and “and,” are used in the 
 statement of the plan of this system; and if the system is to be completely un- 
 interpreted, these symbols might be replaced by symbols that do not suggest 
 these logical ideas, e.g., by L and N.) It will be observed that the grouping of 
 the complex (a(0b)) shows that it has an order, irrespective of the spatial ar- 
 rangement of the symbols; and that (b(Qa)) is the alternative order of this 
 asymmetrical form. 
 
 (2) The symbols a, b, and ¢ can be mutually substituted for one another; 
 but distinct symbols must always be replaced by distinct symbols. 
 
 (3) The special “formal” implication, (a(0b)). (b(Oc)) ““implies”’ (a(Oc)), 
 holds in the system. 
 
 It is apparent that (a(Oa)) or any combination in which this group might 
 appear is not in the system; for the provision that distinct symbols must al- 
 ways be substituted for distinct symbols will not permit us to derive (a(Oa)) 
 from (a(0b)) or from any of the other O-groups. These O-groups are therefore 
 wreflexwe. Further, the group (a(0b)) is, by its grouping, distinct from (b(0a)); 
 and this is a distinction of sense, 7.e., of the distribution of the terms in the 
 constituent groups. The O-groups are therefore asymmetrical for distinct 
 terms. (Obviously, if there were an O-group of indistinct terms, e.g., (a(Oa)), 
 this would be symmetrical; but there is no such group.) The implication 
 (a(Ob)) . (b(Oc)) “implies” (a(Oc)), shows that the O-groups are transitive; 
 but transitive only when a, b, and ¢ are distinct, for (a(Qa)). (a(Oa)) “‘implies” 
 (a(Oa)), and (a(0b)) . (b(Oa)) “implies” (a(Oa)) cannot be derived from this 
 implication without violating the rules of substitution. The fact that the O- 
 groups cannot be substituted for the terms a, b, and ¢ shows that they are 
 
 
 
FORMAL DEDUCTION 255 
 
 Vill 
 
 The apparently arbitrary manipulations of the symbols of an 
 uninterpreted system are “deductions” for this reason: that, 
 when the system is interpreted, that is, when the postulates are 
 asserted for a set of objects, these manipulations become infer- 
 ences. The theorems are then asserted on the strength of their 
 connection with the postulates; the truth of the postulates 
 strictly proves the truth of the theorems. 
 
 Inference is allied to assertion and belief. There is no such 
 thing as a hypothetical inference, just as there is no such thing 
 as a hypothetical belief. If a proposition is believed, it is re- 
 moved from the realm of the hypothetical; it is no longer an idea 
 merely entertained, but is accepted as true or, it may be, “‘ac- 
 
 relational, rather than operational, groups; and since (a(Ob)) v (b(Oa)) is sig- 
 nificant in the system, the terms a and 6 (or a and ce, and b and ¢, if these are 
 properly substituted in this expression) are connected in one sense or the other 
 by the relation O. This is the postulate of “connexity.” 
 
 Now, a relation which is connected, irreflexive, transitive for distinct terms, 
 and asymmetrical for distinct terms, is a “serial relation.” (See E. V. Hunting- 
 ton, op. cit., pp. 11 ff.) If a, b, and ¢ stand for points on a line, and (a(0b)) 
 means that “the point a precedes the point b, in the order left to right,” the 
 postulates can be interpreted as follows: 
 
 (1) Asserts that “any point precedes any other point, or this latter precedes 
 it.” The condition that the points must be distinct is added by the second 
 half of the rule of substitution under (2). 
 
 (2) The first half of this rule of substitution asserts that “if there is a point, 
 there are also two other points”; and the second half asserts that “if any 
 point precedes a point, these two are distinct,” since only symbols that refer 
 to distinct points can appear in the complex “a precedes b.”’ 
 
 (3) Asserts that “if any point precedes a second, and this second precedes a 
 third, the first point precedes the third.” 
 
 That the proposition (a(0b)) . (b(Oa)), t.e., “a point a precedes point b and 
 this latter point also precedes a,” does not hold in the system is proved by the 
 fact that in order to derive this group from the similar group in the implica- 
 tion, (a(0b)). (b(Oc)) “implies” (a(Oc)), we must assume a contradiction; we 
 must suppose that a is a distinct symbol from a. With this supposition, a can 
 be substituted, according to the latter half of rule (2), for c in this implication, 
 giving (a(O0b)) . (b(Oa)) “implies” (a(Oa)). But if a ¥ a, this is a violation of 
 the principle of contradiction, which is always assumed as a general rule of 
 symbolism. 
 
256 SYMBOLISM AND TRUTH 
 
 cepted as false,’’ which means that its negative is accepted as 
 true. And similarly, a proposition that is inferred from another 
 is accepted as true (or false), not because it is verified in itself, 
 but because it is believed to be connected in a certain way with a 
 proposition previously accepted as true (or false). Inference is 
 the passage from a belief, by way of a belief, to a belief, and is 
 expressed by the assertion of a premise and of a connection be- 
 tween this premise and a conclusion, followed by the assertion of 
 the conclusion. The connections on which inferences rest are im- 
 plications. (There arc, however, certain types of inference — 
 probable or inductive inferences — which do not rest on the 
 strict implications considered here.) 
 
 It is characteristic of true propositions that they can stand 
 alone as objects of belief. Though most propositions have their 
 “reasons,” that is, their premises, by which they are implied, 
 any truth can be severed from its premises and believed on its 
 own account. Its truth does not consist merely in the “reasons” 
 that can be given for it. If it is true, it is equally true apart from 
 the propositions which imply it, equally true with or without 
 “reasons.”’ If it were necessary to remember all the logical con- 
 nections of a proposition believed, belief and assertion would be 
 difficult undertakings; but fortunately the premises of a belief 
 can be forgotten without destroying the truth of the proposition 
 believed (if it is true). Therefore inference, since it leads from 
 one proposition believed to be true to another believed to be 
 true, is well described as “the dropping of a true premise . . . the 
 dissolution of an implication.” ! 
 
 But a premise which is not believed cannot be dropped, and 
 for this reason the asscrtion of a chain of implications is not an 
 inference. “‘p implies q” means that whenever p is true, q is true; 
 but it does not assert the truth or falsity of p or of q; it merely 
 excludes the possibility that “‘p is true and q false.” So far as its 
 
 1 Whitehead and Russell, Principia Mathematica, p. 9. 
 
 
 
FORMAL DEDUCTION 257 
 
 constituent propositions are concerned, a true implication is still 
 hypothetical; though a connection between p and q is asserted, 
 p and q themselves are still entertained and not believed. And if 
 the supposition that the premise of this implication is true is 
 added, this supposition will not result in an inference to the 
 truth of q; it will yield nothing but the supposition that q is true 
 “if p is true and p implies g.” One might go on forever asserting 
 implications and supposing that their premises are true without 
 performing an inference. The chain of implications is broken 
 only when the premises, as well as the implications themselves, 
 are asserted. Every one of the series of propositions which are 
 believed to be connected by these implications can then be be- 
 lieved, by themselves, to be true. 
 
 Inference is, in short, a form of judgment and, like all judg- 
 ment, it takes the leap of belief; it introduces a new attitude of 
 mind toward propositions. But it differs from simple judgment 
 in that it must take two leaps of belief; it must accept the truth 
 of an implication (or series of implications) and of the premise of 
 this implication (or series of implications). Thus, from survey- 
 ing propositions and asserting that they are connected in certain 
 ways, it passes to the affirmation of these propositions apart 
 from their connections. 
 
 That a belief in the truth of a proposition implied by a true 
 premise is justified follows from the nature of implication. Any- 
 thing implied by a true premise is true; for the truth of the im- 
 plication, “‘p implies g,”’ does not admit the possibility of p be- 
 ing true and q false. To believe p, and to believe that Pp implies 
 certain propositions, is inconsistent with believing that these 
 latter propositions are false. And though one is not compelled to 
 believe the consequences of p when he believes p (for he always 
 has the alternative of being sceptical), he cannot consistently 
 believe that these consequences are false. Here as always the 
 goal of his belief is consistency. 
 
258 SYMBOLISM AND TRUTH 
 
 The two principles which underlie inference, then, are: (1) 
 that any true proposition is true apart from its connections with 
 other propositions, and can be asserted on its own account; and 
 (2) that a true implication and a true premise always yield a 
 true conclusion. These principles permit us to move in thought 
 from one assertion or belief to another; to wipe the slate clean 
 and start afresh with each new conclusion. 
 
 When a formal deductive system is taken to refer to certain 
 objects, it is asserted, and if its postulates and rules of substitu- 
 tion are true for these objects, the conditions necessary for in- 
 ference are satisfied. But it is more important still to observe an- 
 other fact which follows from the complete interpretation of a 
 deductive system. The conditions of truth and of significance in 
 the system become the same. Every proposition which has a mean- 
 ing is true, the system contains no significant propositions which 
 are false. 
 
 The symbolic manipulations, which are the inferences of the 
 asserted system, arise in the unasserted (purely hypothetical) 
 system from rules of syntax which prescribe how the symbols 
 are to be taken together as significant groups — rules analogous 
 to rules of grammar. General principles of symbolism, a “uni- 
 versal grammar,” necessary in all systems or “languages,” are 
 laid down, and within this framework special conditions of sig- 
 nificance are provided for, so that each deductive system be- 
 comes a special “language.” Its postulates state nothing more 
 than what expressions are to be considered significant, what 
 symbols are identical in meaning, and what symbols can be sub- 
 stituted for one another without rendering the expressions in 
 which they appear meaningless. The system differs from more 
 concrete languages in that its “words” and “phrases” refer to 
 no objects but are variables, grouped about certain fixed ele- 
 ments, v2z., certain logical forms. These logical forms are the 
 sole subject-matter of the uninterpreted language; they are em- 
 
 
 
 
 
FORMAL DEDUCTION 259 
 
 bodied in the “words” and “phrases,” the symbols and groups 
 of symbols, but they are not asserted to exist elsewhere. The 
 language asserts no truths but simply surveys logical forms. On 
 the other hand, when the system is completely interpreted, the 
 language that previously asserted no truths becomes a language 
 that asserts nothing but truths; there is no expression in it which 
 is both significant and false. 
 
 The so-called “false propositions” of a completely inter- 
 preted deductive system are “pseudo-propositions,”’ that is, 
 meaningless collections of the symbols, and not significant 
 groups permitted by the syntactical rules. Such “ pseudo-propo- 
 sitions” can be introduced only by violating the conditions of 
 significance. In the postulates for serial order,! for example, the 
 group (a(Oa)) does not enter; it is nonsense so far as the syntac- 
 tical plan of this “language” is concerned. Interpreted as the 
 system is interpreted, this pseudo-proposition asserts that “any 
 point, a, precedes itself,” but though this idea can be expressed 
 in words, it cannot be significantly stated in the symbols of the 
 system. T’hus it is superfluous (in fact absurd) to say that 
 (a(Oa)) is false, for only a significant expression can be false. 
 
 Completely interpreted deductive systems are therefore com- 
 pletely inferential. Every transformation which conforms to the 
 “grammar” of the system is an inference; every “grammatical” 
 expression is true. 
 
 IX 
 
 Ordinary language, on the contrary (as well as the system of 
 mental images), is incompletely inferential. The conditions of sig- 
 nificance and truth for its expressions are not the same. Clearly 
 if one follows merely its grammatical rules, he will not be led 
 from true premises to true conclusions. Only some of the manip- 
 ulations of its words and phrases will be inferences. But the pro- 
 cess of thought, as it is carried on in language and in images, 
 
 1 See above, sec. vii, note. 
 
260 SYMBOLISM AND TRUTH 
 
 presents an interesting analogy to the transformations of formal 
 deductive systems, for thought in these former media is also the 
 manipulation of symbols. 
 
 Thought has two aspects: it is both dynamic and static; 
 and inference belongs to its dynamic side. Inference is a 
 movement of thought coupled with belief, but strict inference 
 arises in a wider setting of thought-movement — a setting 
 which Hobbes calls “mental discourse” or the “train of imagi- 
 nations.” 
 
 “Mental discourse,” beginning with presented objects, mir- 
 rors a world of fact in a world of representations; it builds simple 
 symbols which refer to objects into complexes, which may or 
 may not correspond to objects. The drama of “‘ideas”” makes use 
 of symbols as its puppets; the symbols combine and recombine, 
 the puppets move on the stage, and one grouping succeeds an- 
 other to the end of the piece. Words and images are the primary 
 instruments of this “mental discourse.”” They combine, dissolve, 
 and recombine, pass and repass in new and changing unities, 
 and here and there they precipitate a reference to fact. Such 
 discourse is the free play of the imagination, musing or dream- 
 ing, rather than deductive reasoning, but it is akin to deduc- 
 tive reasoning in that it is a process of substitution within a 
 plan of syntax. Images (both simple and complex), words, and 
 phrases, take the places of one another in groups; the group that 
 was now of one form assumes a different form; but throughout 
 all these mutations, the plan of syntax on which the system of 
 images or of words is based is never violated. The “mental dis- 
 course”’ confines itself within the limits of intelligibility which 
 this plan imposes. Yet this discourse is not inference, as it would 
 be in a completely interpreted deductive system, for the plan of 
 syntax within which it is carried forward cannot be so inter- 
 preted that every significant proposition to which it gives rise is 
 true. There is no difficulty in abandoning fact for fancy within 
 
 
 
FORMAL DEDUCTION 261 
 
 the systems of language and images; but ina completely inferen- 
 tial system nothing that is conceivable is false. 
 
 We cease to dream and begin to infer when our purpose in the 
 manipulation of symbols is to arrive at truth. A completely in- 
 ferential (and interpreted) deductive system is so constructed 
 . that this purpose can be accomplished merely by following its 
 tules of significance, for these rules sum up a multitude of impli- 
 cations which hold for the subject-matter. But the syntactical 
 plans of language and the imagination do not run parallel to 
 logical connections of the subject-matter. In these media, only 
 a limited number of expressions will imply or be implied by 
 others, and so can be inferred from others. These expressions 
 will form a solid island of true inferences in a sea of fancies. Yet 
 there is a marked analogy between free imagination, “mental 
 discourse,” and formal deductive inference. The constructive 
 imagination is a genus of which the process of formal deduction 
 is a species; imagination is necessary to reason. 
 
 Xx 
 
 The principal points that have been brought forward in this 
 examination of formal deduction are the following: 
 
 For formal logic, all that is essential in any subject-matter is 
 its logical structure, and this structure can be isolated and stud- 
 ied in itself through uninterpreted symbols whose forms and 
 their connections alone are considered. Such uninterpreted sys- 
 tems of symbols are not without meaning, however. In the con- 
 text of logical structure, all the elements of these systems, with 
 the exception of their logical forms, are variables, that is, sym- 
 bols of undetermined meaning; and the groups as wholes have 
 significance, though they refer to no objects, for any symbolic 
 group with a structure is significant. The forms to be studied are 
 presented in the very symbols through which they are studied. 
 
 The postulates of these systems are plans of syntax which de- 
 
262 SYMBOLISM AND TRUTH 
 
 termine what groupings of the symbols are permissible, that is, 
 what the possibilities for thought in the system are; and the 
 whole becomes a special “language” with a “grammar”’ of its 
 own marking the boundary between sense and nonsense for the 
 system. All special plans of syntax assume the general principles 
 of symbolism: (1) the principle of group significance; (2) the dis- 
 tinction between symbols of unity and terms; (3) the law of 
 identity and (4) the law of contradiction. From these principles, 
 it follows that the system must be composed of groups of terms 
 joined by symbols of unity; the same symbols must always be 
 used with the same significance, though symbols of different 
 characters and forms can be taken as identical in meaning; and 
 symbols that are originally distinct in meaning must always be 
 distinct. 
 
 All the significant complexes of the system are derived from 
 certain basic complexes by substitutions, and this process of 
 transformation by substitution 7s formal deduction; it is the 
 manipulation of symbols within a plan of syntax. Two general 
 rules of substitution are always followed: (1) the same symbol 
 can be substituted for the same symbol, and symbols of identical 
 meaning can be substituted for one another, in any complex; (2) 
 all substitutions must be carried through completely. In addi- 
 tion to these general rules, every system has its special rules of 
 manipulation, and among these may appear certain “equations 
 of structure,”’ definitions, and specially postulated implications. 
 The latter permit the substitution of one group for another only 
 when this other group appears as a conclusion of a series of de- 
 ductions. Deduction in these systems is nothing but the manipu- 
 lation of the symbols according to these rules, as is illustrated by 
 the Boolean Algebra, which, though it can be completely inter- 
 preted in terms of classes and class relations and operations, can 
 be stated as a system of uninterpreted groups and rules of sub- 
 stitution. 
 
 
 
FORMAL DEDUCTION 263 
 
 A rule of substitution, in general, is based on a relation be- 
 tween the functional ranges of the variables. If symbols coincide 
 in their ranges of functional variability, they can be mutually 
 substituted for one another; and if the range of one includes 
 that of another, the former can be substituted for the latter, for 
 it will be a functional value of the latter. With respect to vari- 
 ables of a less inclusive range, those of wider range are “func- 
 tional constants’’; while the variables of narrowest functional 
 range in any system — those for which all other expressions of 
 the system can be substituted, but which can not be substituted 
 for these expressions — are the most general “functional vari- 
 ables” of the system. Both functional constants and functional 
 variables are undetermined in meaning; both are ““interpreta- 
 tional”’ variables. 
 
 If a group is a possible value of the variable terms which enter 
 in this group itself, this group is operational rather than rela- 
 tional. Operational are distinguished from relational complexes 
 by the use which can be made of them in formal deduction, by 
 the fact that they can be substituted in themselves for their own 
 terms. Thus they give rise to an infinity of distinct possible 
 forms. 
 
 When a deductive system is interpreted, the arbitrary manip- 
 ulations of the symbols become inferences, for the postulates 
 and rules of substitution then embody implications, and if the 
 postulates are true, the theorems are also true. To perform an 
 inference is to pass from a premise that is believed, by way of an 
 implication that is believed, to a conclusion that is believed on 
 the strength of these other beliefs. Inference cannot be sepa- 
 rated from belief and assertion; it cannot be purely hypothetical 
 and the principles on which it rests are: (1) that any true propo- 
 sition is true, and can be asserted, apart from its premises; and 
 (2) that what is implied by a true proposition is true. Inference 
 is “the dropping of a true premise.” 
 
264 SYMBOLISM AND TRUTH 
 
 In a completely interpreted deductive system, whatever is 
 significant is true; any of the permitted transformations of 
 meaning lead from true premises to true conclusions, so that 
 these systems are completely inferential. They are to be con- 
 trasted with zncompletely inferential systems, such as language 
 and the imagination, in which there is a discrepancy between 
 significance or conceivability and truth. Though these latter 
 systems resemble the former in that thought is carried forward 
 in them by the manipulation of symbols within a plan of syn- 
 tax, they differ from the former in that the pursuit of their rules 
 of significance, alone, gives rise to fancy and free imagination 
 rather than to inference. 
 
 These formal deductive systems, in which everything but the 
 logical structure of the matter referred to (if there is a matter 
 referred to) is pruned away, show much more clearly than other 
 symbolic systems how symbols copy the forms of facts and why 
 the logical structure, which is present in the symbols as it is in 
 the objects, is the essential bond of meaning between the mind 
 and its objects. The mirror of thought, which reflects in the be- 
 ginning a world of concrete facts, may send back a reflection of 
 forms alone and these forms may belong to no world of fact, 
 they may be merely possibilities for thought embodied in sym- 
 bols. But the structure of these possible concepts will determine 
 what they can stand for; if they represent objects, these objects 
 must correspond to them in logical form. Whether formal de- 
 ductive systems are interpreted or uninterpreted, thought 
 reaches in them its maximum of clarity.! 
 
 1 The views of formal deduction and truth here set forth are closely similar 
 to those of Leibniz as interpreted by L. Couturat in La Logique de Leibniz 
 (Paris, 1901). ‘“‘In an unpublished fragment relating to the universal lan- 
 guage,” says Couturat (pp. 88, 89), “‘Leibniz imposes another condition on 
 signs: it must be possible to deduce from their form alone, and from their 
 composition, all the properties of the concepts which they represent. . . . Their 
 combinations must depict for the imagination the logical connections of the 
 corresponding concepts, so that the composition of the signs agrees with the 
 
 
 

 
 FORMAL DEDUCTION 265 
 
 composition of the ideas, following an exact analogy. . . . Moreover, not only 
 does the symbolism translate the thought under an intuitive form, but it 
 serves also to guide, to relieve, and even to supplant or replace thought. Just 
 as the combinations of the ideas are represented by combinations of the corre- 
 sponding signs, so the operations of the mind — that is to say, the reasoning 
 which is carried on with these ideas — is expressed in concrete and sensible 
 operations performed on the symbols. The abstract laws of logic are thus 
 translated into intuitive laws which govern the manipulations of signs.” 
 
 To the nominalism of Hobbes “Leibniz replies peremptorily,” continues 
 Couturat (pp. 104, 105), “that, if signs are arbitrary, the relations between 
 signs, which express or constitute propositions, are in no sense arbitrary; and 
 that they (signs) are true or false according as they correspond or not with the 
 relations of the things signified. Thus truth consists in the connection of signs 
 so that they agree with a real and necessary connection of ideas or objects, 
 which does not depend on us; or, in other words, it consists in that similarity 
 of the relations of signs and the relations of things which constitutes an 
 analogy in the proper mathematical sense of the term, that is to say, a propor- 
 tion or equality of relationships. . . . The choice of signs and the definitions of 
 words can, then, be arbitrary, but the linkage of the words and signs does not 
 become so; and it is in this linkage alone that truth and falsity reside. We can 
 even change the system of signs at will without changing a truth or making it 
 dependent on our wishes; for, whatever symbols are chosen, there will be an 
 arrangement of these symbols — and only one arrangement — which will be 
 true, that is, which will correspond to the real order of things or facts. There is 
 then an analogy, not only between signs and objects, but between different 
 systems of signs in so far as they express the same reality. 
 
 “This necessary rather than arbitrary order which exists in things is, 
 though unknown, the objective basis of all truth. Once a certain system of 
 arbitrary signs or a certain set of conventional definitions has been adopted, it 
 no longer depends on us what combinations are true and what false; and this 
 proves that truth, although it resides solely in our minds, rests on a principle 
 outside us and expresses symbolically a reality of some sort.” 
 
CHAPTER VIII 
 THE METAPHYSICS OF KNOWLEDGE 
 
 I 
 
 A tHEory of knowledge must come at last to metaphysics, for 
 the aim of knowledge is to grasp reality, and without some no- 
 tion of what reality in the broadest sense of the term is, we can- 
 not say whether knowledge succeeds or fails. The limited reality 
 of which we have spoken up to this point — which can be 
 given in or inferred from an experience consistent with the 
 whole of knowledge — is not enough. It is always possible that 
 what can be thus given or inferred is merely an appearance, and 
 that reality is something deeper, inscrutable to perception and 
 perhaps even to reason. And so we must set out without any arti- 
 ficial restriction of our concept of reality to answer, or rather to 
 sketch the barest outlines of answers, to these fundamental 
 questions: Can reality be known? If so, what is reality and how 
 is it known? 
 
 The first question is prompted by the sceptical impulse of 
 knowledge to self-criticism; it arises from a mood of doubt which 
 is unfamiliar to very few men. Walt Whitman speaks of this 
 mood as “‘the terrible doubt of appearances, 
 
 Of the uncertainty after all that we may be deluded; 
 May-be the things I perceive — the animals, plants, men, hills, shin- 
 ing and flowing waters, 
 The skies of day and night — colors, densities, forms — 
 May-be these are (as doubtless they are) only apparitions, and 
 the real something has yet to be known.! 
 
 1 Walt Whitman, “Of the Terrible Doubt of Appearances,” first published 
 in Leaves of Grass, 1860. 
 
 
 
THE METAPHYSICS OF KNOWLEDGE 267 
 
 Most of us easily shed this “terrible doubt of appearances.” 
 Practical life obscures it, common sense engulfs it, and only 
 poets, mystics, and metaphysicians are left to worry over it. 
 But those whom it haunts find that there is no compromising 
 with it; either all knowledge gives way before it or else thought 
 is driven back and back till it touches first principles — and lays 
 the foundations of a system of metaphysics. 
 
 The peculiar thing about this question is that it cannot be sig- 
 nificantly answered in the negative. Either we are condemned to 
 perpetual asking without an answer or else we know reality. The 
 sceptical impulse of knowledge to self-criticism defeats itself, at- 
 tains no end, unless there is knowledge, not merely knowledge 
 of appearances but of reality. A criticism of knowledge makes 
 use of the very thing it criticizes, and unless the argument is to 
 become circular or lead back indefinitely from premise to prem- 
 ise, the knowledge on which the criticism is based must itself 
 be exempt from criticism.! If knowledge fails (in some sense) to 
 grasp reality, in knowing this fact it attains an ultimate truth 
 and does not fail completely; and if it succeeds, the knowledge of 
 why it succeeds cannot stand in need of justification, and so on 
 through a series of justifications that has no end. 
 
 This suggests either that no final criticism of knowledge is 
 possible, that suspension of judgment is the way of sanity (and 
 this means equally that knowledge cannot be vindicated or dis- 
 
 1 This idea is clearly put by Aristotle; see W. D. Ross, Aristotle (1924), 
 p. 45. “There are, says Aristotle, two errors (with respect to the ultimate 
 validity of knowledge) which rest on a common basis. There is that of suppos- 
 ing that knowledge implies either an infinite regress from premise to premise 
 in order that nothing may be accepted as unproved, or else the acceptance of 
 unproved and therefore unknown premises, and that knowledge is therefore 
 impossible. And there is the error of supposing that knowledge is possible but 
 proceeds in a circle — truth being thus reduced to the mutual implications of 
 propositions none of which are independently known to be true. The common 
 basis of the two errors is the assumption that proof is the only way of know- 
 
 ledge, and against them both he affirms his principle that there are first prem- 
 ises which neither need nor admit of proof.” 
 
268 SYMBOLISM AND TRUTH 
 
 credited); or that there are first principles, final insights into the 
 nature of the real, on which all knowledge rests. The former al- 
 ternative is scepticism; the latter, the necessary starting-point 
 of any metaphysics. 
 
 And yet there have been attempts to compromise with doubt 
 by answering this initial question — can reality be known? — in 
 the negative, attempts to maintain that knowledge is of appear- 
 ances only and that reality is hidden and unknowable. Herbert 
 Spencer makes his bow in the opening chapters of his First Prin- 
 cuples to the eternal mysteries of the universe, leaving this empty 
 but venerated realm of the Unknowable to religion and meta- 
 physics, and choosing for science the full and certain area of the 
 Knowable. A strange, unstable dichotomy! There is to be no 
 poaching of metaphysics and religion on science, and none of 
 science on religion and metaphysics. Each goes its own way, 
 metaphysics to the Unknowable, which is the real, and science 
 to the Knowable, which is the unreal or half-real. Metaphysics 
 becomes an unfulfilled aspiration toward the ultimate, and sci- 
 ence a description of phenomena which, so far as we can tell, are 
 less than shadows flitting before the senses. 
 
 The agnostic compromise with doubt attains no better suc- 
 cess than this. Clearly it is no compromise. Agnosticism is not a 
 half-way house on the road between scepticism and meta- 
 physics. There is no half-way house. If one accepts any truth, he 
 accepts a standard by which he discriminates the true from the 
 false, and beneath this standard is found his metaphysics. From 
 the beginning of thought a concept of reality is present, making 
 itself clearer as thought goes forward but never abandoned — 
 unless thought thins out into scepticism. 
 
 Men are for the most part neither self-conscious metaphysi- 
 cians nor self-conscious sceptics; the temper of most minds 
 strangely blends these two tendencies. But if either of these in- 
 compatible strains is brought to light, it must exclude the other. 
 
 
 
THE METAPHYSICS OF KNOWLEDGE 269 
 
 The scepticism which is fully aware of itself witholds all belief, 
 ventures on no single affirmation, — not so much as the affirma- 
 tion that belief is fruitless and unjustified, —and is thus reduced 
 to silence, or at best to a vagrant roaming among possibilities, 
 none of which is affirmed to be actual. But if one asks himself 
 how it is that he can assert any truth, even the most meagre, he 
 begins to uncover a metaphysics, for truth is never anything 
 less than knowledge of the real. To become alive to any truth he 
 must bring to the surface of thought the concept of reality he 
 now discovers to be buried there. 
 
 The description of knowledge which has occupied us so far 
 takes its departure from the point of view of the plain man and 
 hence is neither self-consciously sceptical nor self-consciously 
 metaphysical. It appeals to experience in a wide meaning of the 
 term, witholds judgment on ultimate questions, but at the same 
 time is aware of its assumptions and does not assert that they 
 are more than assumptions. The upshot of the positive theory 
 of knowledge is this: the truth of ordinary experience is the cor- 
 respondence of concepts through their structure with real ob- 
 jects, and this reality can be given in or inferred from an experi- 
 ence consistent with the whole of knowledge. Whether reality 
 as such has a structure, whether the objects that appear in ex- 
 perience are finally real, whether the mind in knowing is sepa- 
 rated from or joined to an ultimate reality — all these ques- 
 tions remain untouched. And yet, if they are swept aside, the 
 door is left open for scepticism. In the face of these questions 
 the limited truth and reality of the positive theory of knowledge 
 must expand into a final truth and a full reality or contract 
 into a flux of impressions and ideas — leaving only doubt. The 
 positive theory of knowledge, including as it does the two 
 incompatible strains, is unstable; it is a metaphysics tinc- 
 tured with scepticism, a scepticism tinged with metaphysics. 
 The task of speculative philosophy is to bring to complete self- 
 
270 SYMBOLISM AND TRUTH 
 
 consciousness the one or the other of these warring attitudes 
 of mind. 
 
 It is this aim which distinguishes speculative philosophy from 
 the special sciences. Science tolerates the frame of mind that 
 joins scepticism to the assertion of truths. The scientist does not 
 doubt that he is approaching a completer knowledge of reality, 
 though he could not say why this is so without becoming a meta- 
 physician; and yet he refuses all commerce with ultimates and 
 thinks of his premises as working assumptions which he is not 
 averse to discarding for better ones. Hesitating to affirm that he 
 has reached a final truth, the scientist still believes that his 
 growing knowledge is an indefinite approximation to such a 
 truth. Here the metaphysician makes his point. If one’s stand- 
 ards of truth are not themselves finally true, if one does not in 
 some way already grasp reality when he sets forth on the jour- 
 ney of thought, he cannot even conceive of attaining truth. 
 
 The method of science is the method of assumption, hypothe- 
 sis, postulation, and this way of thought falls between scepti- 
 cism and metaphysics; it holds the two in an unsteady balance 
 within itself. A full-grown metaphysics cannot rely on postu- 
 lates or assumptions, for if these assumptions are false the whole 
 of knowledge collapses, and assuming them to be true does not 
 make them true. A full-grown scepticism, on the contrary, is 
 equally receptive to all assumptions, not excluding contradic- 
 tory ones. 
 
 II 
 
 A tradition of critical philosophy which purports to be neither 
 sceptical nor metaphysical, nor yet to be poised as are the spe- 
 cial sciences between these extremes, appears in the thought of 
 the eighteenth and late seventeenth centuries. Kant is the 
 father and Locke the forerunner of this more carefully reasoned 
 agnosticism. By an examination of the nature of knowledge; 
 this critical philosophy hopes to determine whether or not meta- 
 
 
 
THE METAPHYSICS OF KNOWLEDGE 271 
 
 physics is possible, and it concludes that metaphysics is impossi- 
 ble — that knowledge, being limited not only in extent but in its 
 very essence, cannot penetrate through appearances to reality. 
 
 The distinction between appearance and reality is as old as 
 thought; indeed philosophy was bred in the suspicion that the 
 real world is not what it appears to be, and the first philoso- 
 phers set out with the confidence of adventure to discover the 
 ultimate beneath the surfaces of things. But a second suspicion 
 followed speedily on the first: that knowledge is without power 
 to reach this ultimate. And so thought turned inward, its confi- 
 dence shaken, to a criticism of its own capacities and aims. 
 
 Whether knowledge is able impartially, and without begging 
 the question by assuming its own validity, to criticize itself, is a 
 query that does not occur to the agnostic. Pretending with Kant 
 that this self-examination of thought will show whether a final 
 truth can be reached, the agnostic forgets that his own theory is 
 built on a metaphysical first principle, and that he himself 
 claims one final insight — namely, that knowledge is confined to 
 appearances. ‘Though all other truths are in his opinion limited 
 and phenomenal, this truth — that we cannot know the ulti- 
 mate — is absolute. 
 
 Stated thus in outline, critical agnosticism appears self-con- 
 tradictory. It is as if we were saying that by sight man can dis- 
 cover that he cannot see. Yet both Locke’s Essay Concerning 
 Human Understanding and Kant’s Critique of Pure Reason, hav- 
 ing begun with the conviction that knowledge by internal criti- 
 cism can reveal its own frailties, arrive at this conclusion. Kant 
 and Locke have fostered a tradition which gives epistemology a 
 peculiar authority in the field of philosophy, but their episte- 
 mology is in reality a metaphysics. The philosophy that Kant 
 terms critique is speculation of a most insidious sort, disguising 
 itself as it does under another name. Though its aim is to dis- 
 cover “whether such a thing as metaphysics be at all possible,” 
 
272 SYMBOLISM AND TRUTH 
 
 it is itself impossible without the metaphysics whose wings it 
 hopes to clip. The epistemological tradition of Locke and Kant 
 is an unsuccessful attempt to straddle the issue between scepti- 
 cism and metaphysics. 
 
 Before the Kantian critical philosophy was born, a reply to 1t 
 was framed by one of the metaphysicians whose dogmatism 
 Kant condemned. In Spinoza’s Tractatus de Intellectus Emenda- 
 tione, Kantianism is forestalled by the following argument: “In 
 order to find the best method of investigating what is true, we 
 must not stand in need of another method to investigate this 
 method of investigating, nor in need of a third one to investigate 
 the second, and so on to infinity. For by such a method we can 
 never arrive at a knowledge of what is true, nor at any knowl- 
 edge whatever. For it is the same thing as with artificial instru- 
 ments, of which we might argue in the same manner. For inorder 
 to work iron a hammer is needed, and in order to have a ham- 
 mer it must be made, for which another hammer and other in- 
 struments are needed, and so on to infinity; and in this manner 
 any one might vainly endeavor to prove that men have no 
 power of working iron. But in the same way as men in the be- 
 ginning were able with great labor and imperfection to make the 
 most simple things from instruments already supplied by nature 
 
 . so also the understanding by its native strength (vis sua 
 nativa) makes for itself its intellectual instruments wherewith it 
 acquires new strength for other intellectual works, and so gradu- 
 ally proceeds until it attains the summit of wisdom.” ! This na- 
 tive strength of the intellect is its power of insight into reality, 
 which is present in thought from the first. 
 
 The severance of appearance from reality, on which most 
 criticisms of knowledge are based, may be more or less com- 
 plete. It may be sharp and irreparable as in Kant, or it may be 
 partial and reconcilable as in the Absolute Idealists, who be- 
 
 1 B. de Spinoza, T'ractatus de Intellectus Emendatione, sec. 6. 
 
 
 
 : 
 . 
 | 
 
THE METAPHYSICS OF KNOWLEDGE 273 
 
 lieve that “there is no truth but the whole truth,” and yet that 
 no appearance is denied its small grain of reality and truth. The 
 breach between appearance and reality once opened must be 
 healed, and the reason is not far to seek. What appears must 
 have some sort of reality or it could not appear; it would be 
 simply nothing. The important question then is, not how are 
 appearance and reality separated, but how are they united? — 
 how, in Spinoza’s language, does reality manifest itself in attri- 
 butes and modes? To hold that there is a world of absolute ap- 
 pearance cut off from a world of absolute reality, as Plato’s 
 realm of opinion is from his realm of ideas! and Kant’s nou- 
 menal realm from the phenomenal, is to fall into a difficult di- 
 lemma. Either the world of absolute appearance or the world of 
 absolute reality should be dropped; the two refuse to stand side 
 by side unrelated. Just as Aristotle attempted to bring the Pla- 
 tonic ideas into the concrete matter of experience, so the Post- 
 Kantians attempted to raise the Kantian phenomena toward 
 the level of the noumena by making the phenomena finite parts 
 of an infinite and absolute whole. 
 
 iil 
 
 Before we consider ways of healing the breach between ap- 
 pearance and reality, let us examine the breach itself in its most 
 extreme form, as it occurs in Locke and Kant. It arises here 
 from a theory of mind-isolation which places appearances in the 
 knowing subject and leaves reality out in the cold beyond the 
 grasp of the knower. 
 
 Locke’s metaphysics of mind-isolation rests on two premises: 
 that “all our knowledge is conversant only with ideas,” and 
 that ideas are of qualities only, never of substances, which are 
 the substrata of qualities. Locke’s view presupposes the passiv- 
 
 1 There is a question as to whether Plato intends completely to sever his 
 two worlds. 
 
274 SYMBOLISM AND TRUTH 
 
 ity rather than the activity of mind; a static screen of ideas im- 
 poses itself from outside between the knower and reality, never 
 to be swept aside. 
 
 This is the crudest and simplest statement of the mind-isola- 
 tion theory —the theory of epistemological dualism. Since 
 Berkeley, it has had little currency in this form. The crux of 
 Locke’s argument is the second premise, the distinction be- 
 tween substance and its qualities; but just why substance, 
 which Locke sometimes says is known in a confused way and 
 other times not known at all, should be retained — why qual- 
 ities (appearances) do not make up a self-sufficient and com- 
 plete reality — does not become evident. Locke’s substance is 
 nothing more than an arbitrary limit set to knowledge for no 
 other reason than to satisfy the common-sense prejudice that 
 things must have a substratum in which their qualities inhere, 
 and the slender thread that holds together substance and its 
 qualities snaps under the tension of Berkeley’s criticism; qual- 
 ities alone are left, the unknowable xz, substance, being can- 
 celled out. 
 
 Locke’s first premise, that “knowledge is conversant only 
 with ideas,” supports the theory of mind-isolation if one thinks 
 of ideas as essentially disparate from real objects and (in Locke’s 
 language) real qualities. One can for example suppose that real 
 objects cause ideas different from themselves. How one can 
 know this is another question, for apparently he must go be- 
 yond ideas to do so. Therefore, if knowledge is conversant only 
 with ideas, it is by hypothesis not conversant with objects which 
 cause, bound, or limit ideas; and so the statement that knowl- 
 edge is restricted to ideas has no foundation, unless it affirms 
 merely that “we know what we know.” This is again the typical 
 difficulty of agnosticism: if the mind is isolated, it would need to 
 escape its isolation to know this fact. 
 
 Though Kant’s formulation of the theory is more profound 
 
THE METAPHYSICS OF KNOWLEDGE Q75 
 
 than Locke’s, it comes in the end to the same thing — agnosti- 
 cism and mind-isolation. Kant does not argue from the distinc- 
 tion of substance and its qualities, and he supports the notion 
 that knowledge is conversant only with ideal objects by nega- 
 tive if not by positive proofs. Kant insists as against Locke that 
 the mind is active in cognition; this is perhaps his most impor- 
 tant observation on knowledge as a whole. Yet from this prem- 
 ise he draws the amazing conclusion that in the very act of 
 knowing the mind shuts out from itself the reality (the thing- 
 in-itself), and thus becomes ignorant of what it is striving finally 
 to reach. As soon as the work of knowledge begins, the mind like 
 a snail in its shell withdraws within itself. The concepts (cate- 
 gories and forms of perception) which determine the mind’s 
 essential directions of activity, far from causing it to expand 
 outward to a fuller apprehension of the real, which it has some- 
 how touched in “‘the original receptivity of the senses,” turn it 
 away toward ideal objects which correspond in no intelligible 
 way with the ultimate reality. Knowledge is not a passive recep- 
 tion of impressions (Kant argues), but an active assimilation of 
 them under concepts,—the mind is not a blank sheet, but a 
 working organic whole with a structure, — and so knowledge is 
 confined to appearances, which are the products of the under- 
 standing at work with concepts on the materials of the senses. 
 Thus the objects of knowledge form a neat and orderly closed 
 system through which the wind of reality does not blow. The 
 safe and sheltered island mapped out by thought is untroubled 
 by the waves of the ding-an-sich which beat along its shore. 
 Why must this strange introversion go with the notion that 
 the mind is active in knowledge? Granted that thought works 
 with concepts and categories, that the mind is not like a vat of 
 dough, merely receptive to external impressions, but that it does 
 something in cognizing an object. Still, it does not follow that 
 this activity is a contraction of the mind within itself. The con- 
 
276 SYMBOLISM AND TRUTH 
 
 cepts along the grooves of which cognition is directed may lead 
 the mind outward to a more complete knowledge of the real, 
 rather than twist it inward upon itself. The more reasonable 
 corollary to the observation that the mind is active in cognition 
 is the exact opposite of mind-isolation. The activity of thought 
 through concepts, intentions, (that is, symbols with their atten- 
 dant mental attitudes), should bring the mind into more perfect 
 and stable relations with the reality it touches in “the original 
 receptivity of the senses.”’ We cannot conclude that the organ- 
 ized knowledge of perception and experience is not knowledge of 
 realities simply because thought plays a part in the organization. 
 If reality itself is a complex whole, with “a time-less subtlety 
 of complexity,” ! surely it is not strange that reality should be 
 clearly apprehended only by an organized and active mentality. 
 What is needed in place of the Kantian theory of isolation is the 
 notion that mind by its activity joins itself to real things in 
 knowledge, that is, an epistemological monism which takes ac- 
 count of thought-activity in cognition. Mind grows into a cog- 
 nitive unity with the reality it originally knows only in fleeting 
 and momentary glimpses; the mind in knowing is actively con- 
 tinuous with real objects. We shall presently say more of this 
 continuity. 
 
 Kant’s tidy world of experience, created by the mind at work 
 with concepts and categories, could be peopled only by objects 
 for which these concepts and categories are universally and nec- 
 essarily true; and so necessity is brought into connections of 
 “matters of fact” (as against Hume) at the cost of severing the 
 whole world of fact from a vast and incomprehensible realm be- 
 yond fact. One feels cheated, tricked, by this vindication of a 
 priori knowledge. It is a peace without victory. And what of this 
 theory of mind-creation itself? Is it, too, nothing but a mind- 
 creation? If not, Kant is thrown back on the insight into real- 
 
 1 A. N. Whitehead, The Principles of Natural Knowledge (1919), p. 15. 
 
THE METAPHYSICS OF KNOWLEDGE Q77 
 
 ity of which Aristotle and Spinoza speak. Kantianism is slain by 
 its own hand unless its own first principle — that knowledge 
 cannot go beyond appearances — is apprehended as not itself 
 an appearance, apprehended by a kind of reason not subject to 
 the limiting categories of ordinary thought. But to admit such a 
 rational insight or “intuition” would have been a return to dog- 
 matism of the sort Kant hoped forever, by a dogmatism peculiar 
 to himself, to demolish. 
 
 Kant’s “dialectical” arguments attempt to show the futility 
 of offering rational answers to metaphysical questions. But the 
 cure is more reason, closer analysis, clearer concepts, and not, 
 as Kant would have us believe, the surrender of rational meta- 
 physics. A growing knowledge is bound to meet contradictions 
 and thus to alter its concepts, and here lies the correction for the 
 Kantian antinomies as well as for the more numerous contradic- 
 tions which Mr. F. H. Bradley — following the scent of the dia- 
 lectical argument even further than Kant — finds, in his Ap- 
 pearance and Reality, to be inherent in discursive thought. This 
 much truth can be distilled from both the Kantian and the 
 Bradleyan dialectic: it is fatal to employ the concepts of the 
 special sciences for unscientific, that is to say, for metaphysical 
 purposes. Metaphysical categories (if there are any such) must 
 be the widest possible categories. Mr. Bradley finds that thought 
 in the effort to complete itself does not attain to wider concepts, 
 but “commits suicide” by transcending its own forms, thus 
 making way for the dim apprehension of an Absolute of which 
 discursive knowledge gives only an imperfect and restless fore- 
 sight. In this way Mr. Bradley escapes agnosticism to fall into 
 something very close to mysticism. Kant’s conclusion from his 
 antinomies is, on the other hand, the most glaring and insoluble 
 antinomy of all. An inherently defective reason becomes able to 
 know its own defects; a mind isolated from reality and confined 
 to a world of phenomena becomes negatively but not positively 
 
278 SYMBOLISM AND TRUTH 
 
 aware of its isolation. Even so the mind craves a positive knowl- 
 edge of this reality and its relation to the world of experience. 
 The noumena do not cause phenomena, for causation is a con- 
 nection between objects of experience only. Indeed, theconclusion 
 ought to be that the noumena are not related to the phenom- 
 ena, for relations hold only between phenomena. The thing-in- 
 itself, the ultimate reality thus severed from its appearances, is 
 an entity which plays the same part in knowledge as zero in 
 arithmetic; the addition or subtraction of it does not alter the 
 value of the other elements. The outcome of the Kantian“ dia- 
 lectic” is that knowledge of that which limits knowledge is 
 negative only; which amounts to saying that knowledge is 
 limited in a way that is not known by something that is not 
 known. And it is a short step to the conclusion that knowledge is 
 not limited, and hence to a rejection of the whole theory of 
 mind-isolation. 
 
 One other conclusion stands out in the “dialectic.” Reason is 
 always attempting to complete the synthesis of experience, to 
 effect a “complete unity of knowledge . . . by which that know]l- 
 edge becomes not only a mere aggregate, but a system con- 
 nected according to necessary laws.’ Kant sees reason as dy- 
 namic and directed toward a goal, which it approaches but does 
 not reach. Not content with a slow process of growth and cor- 
 rection, it takes disastrous short-cuts, falling thus into self- 
 contradiction. But this incompleteness of knowledge is not a 
 sufficient ground for the agnostic separation of appearance from 
 reality. It is one thing to assert that knowledge at any particu- 
 lar time does not give us the whole of reality. This is a mild con- 
 fession of ignorance and finitude, a gentle and tolerable agnosti- 
 cism, which is the part of intellectual humility in the face of 
 changing concepts, shattered theories, and discredited beliefs. 
 It is quite another thing to assert that knowledge never grasps 
 more than an appearance. A knowledge that is not complete in 
 
THE METAPHYSICS OF KNOWLEDGE 279 
 
 detail must nevertheless reach through to reality; otherwise, it is 
 
 not knowledge. 
 IV 
 
 Four major points emerge from this discussion of agnosti- 
 cism. (1) Any final criticism of the validity of knowledge must 
 rest on metaphysical premises. The epistemological tradition 
 which pretends to determine the limits and extent of human 
 knowledge — especially, whether metaphysical knowledge is 
 possible — appeals itself to metaphysical premises which are 
 true without limitation. Appearance and reality cannot be held 
 _ apart. (2) Though the mind is active in cognition, this fact need 
 not lead to the conclusion that the mind shuts itself out from 
 reality, building a world wholly its own. To the theory of mind- 
 isolation must be opposed that of the continuity of the mind 
 with real objects in the act of knowledge. The activity of the 
 mind in the channels of concepts brings it into more complete 
 touch with the reality of which sensation gives only passing 
 glimpses. Through the use of concepts knowledge expands out- 
 ward to reality, rather than inward to its own ideal world. (3) 
 At every moment knowledge is incomplete, the whole of reality 
 is not known in detail; the truths of to-day may be reversed by 
 those of to-morrow. Yet the very notion that knowledge is in- 
 complete demands that some knowledge be ultimate. Thus (4) 
 a rational insight or intuition is needed to take account of meta- 
 physical truth, for the truths that vindicate (or enable us to 
 repudiate) all others cannot themselves be vindicated or repudi- 
 ated, nor can they be merely postulated. They must be appre- 
 hended as final. 
 
 These conclusions must be expanded and correlated with the 
 description of knowledge previously given. 
 
280 SYMBOLISM AND TRUTH 
 
 V 
 
 The essence of the first point is this: if there is any knowledge, 
 there is knowledge of reality. An appearance is never a bare ap- 
 pearance, for if it is true that it is an appearance, then it has 
 some status in reality. It is really an appearance. The opposi- 
 tion between appearance and reality becomes less and less sig- 
 nificant the more one contemplates it. The question is, not 
 whether what appears is a reality, but what sort of reality it is. 
 What is its place in the scheme of reality? An appearance de- 
 ceives when it is misplaced in reality or judged to be all there is, 
 yet even a deceptive appearance is something; it cannot be dis- 
 missed as not being. To hold that appearances have no reality is 
 to deny that they are appearances, and hence to wipe them, and 
 all the problems connected with them, clean off the slate. If the 
 distinction between appearance and reality is to have a mean- 
 ing it must fall within experience, and not between what is 
 known and what is unknown or unknowable. It must fall within 
 an apprehended reality. The very terms “appearance” and 
 “reality” mislead one. We ought not to say that the reality we 
 know differentiates itself into appearances, but into parts, 
 aspects, elements, modes, which never lose their essential real- 
 ity. What we call “appearances” are fragments of reality, and 
 reality is in the fragments no less than in the complex structures, 
 that is, objects, situations, facts, into which these fragments 
 fit to form a world. 
 
 The task of metaphysics is to describe what is most general 
 (and hence least noticeable) in this apprehended reality, how- 
 ever fragmentary the part apprehended may be. Metaphysics 
 cannot look for the real beyond or behind experience, nor in an 
 ideally complete experience. It must, like any other effort to 
 think clearly, dig into the basic units of knowledge which are 
 presentations or wholes of experience. Metaphysics is the most 
 searching possible analysis of these wholes. 
 
THE METAPHYSICS OF KNOWLEDGE 281 
 
 This analysis should reveal what part the mind plays in ap- 
 prehending these wholes. Does the mind in some far-reaching 
 sense create their reality? Or do they in some mysterious way 
 enter the mind from outside and mold it to their own forms? 
 
 VI 
 
 There has always been a tendency to break up the act of 
 knowledge into sensation and thought, sensation being passive 
 and thought active, and this has led to curious results, some 
 of which have already been observed. In the main, those who 
 have stressed sensation and the passive réle of mind have in- 
 sisted that reality is external and indifferent to mind, and that 
 reality becomes known through impressing itself on the mind; 
 while those who have stressed thought have made the opposite 
 claim — that reality is mental, rational, a thought-creation, and 
 that it is known through the mind’s activity. There is something 
 to be said for both of these views for the reason that the act of 
 knowing is not sensation with thought added, or thought with 
 sensation entering accidentally in it. To know is to be at once 
 active and passive, to receive an impression and reflect upon it. 
 The act is a single whole in which thought and sensation are 
 blended; what is impressed on the mind is assimilated to, and 
 not distinguished from, what is meant, imagined, thought. Con- 
 crete knowing is the active assimilation of reality through sen- 
 sational-thought. We have spoken of this before as presentational- 
 thinking. It is impossible to say where the receptivity of the 
 mind leaves off and its activity begins. Certainly it is highly 
 artificial to draw this line at sensation, for there is no such thing 
 as a pure sensation in abstraction from the cognitive act as a 
 whole. As an element within this whole, sensation or sensing no 
 less than thought is active. Moreover thought, as an element 
 within the cognitive whole, has its passive side; it comes 
 sharply against the thing it means given in experience, and 
 
282 SYMBOLISM AND TRUTH 
 
 this encounter checks and at the same time fulfills its inten- 
 tions. 
 
 What has been previously said of thought must be recalled: 
 that thought is essentially reference through symbols, an out- 
 ward reach of the mind toward objects. There is a distinction 
 between pure thought, which is reference and nothing more, and 
 perceptual thought — which is reference when what is referred 
 to is also immediately presented. The latter is what we are now 
 speaking of as “concrete knowing.” This is the basic form of 
 knowledge. Pure thought, purely mediate knowledge, is knowing 
 in which the element of presentation (that is, passivity) is re- 
 fined away, so that the thing meant is no longer given but merely 
 intended. I do not know the other side of the moon concretely, 
 but I do know concretely the facade of the house opposite upon 
 which my window looks. Since pure thought is a distillation, an 
 abstraction, from concrete thought, it is to the latter that we 
 must look for the fullest relation of the mind to real objects in 
 knowledge.! 
 
 The view that objects impress themselves on the mind 
 through the senses is insufficient for many reasons. Sensations 
 are nothing in themselves; they are always parts of larger 
 wholes. It is not correct to say that we “sense” relations, facts, 
 complex structures; yet we experience these things. Cognition is 
 always recognition; memory plays a part in it, and what is given 
 has a reference before and beyond itself. There is an adjustment 
 to experienced objects; they are classed, catalogued, fitted into a 
 scheme of things in the very act of perception. The fact that 
 objects are experienced as “black,” ‘‘white,” “round,” or even 
 as “objects” or “‘sense data,” shows that a concept is actively 
 
 1 This distinction between pure and concrete thought corresponds to 
 Aristotle’s distinction between potential and actual knowledge. In actual 
 knowledge we grasp the real; potential knowledge needs something, a fulfill- 
 ment or realization, to become actual knowledge. See W. D. Ross, Aristotle 
 (1924), p. 171; also Aristotle, Metaphysics, Bk. XIII (M), ch. 10. 
 
THE METAPHYSICS OF KNOWLEDGE 283 
 
 at work in the apprehension of them. Unless objects can be con- 
 sistently assimilated to the knowledge already present to us, 
 they puzzle us; we feel that they are not clearly apprehended, 
 that we have not yet succeeded in perceiving them. Thus not 
 only is a single concept present in the apprehension of objects, 
 but a whole body of theory — certainly the whole body of com- 
 mon sense — presses forward to enter into the act of knowing, 
 and the perception remains unstable until it is reconciled with 
 this body of knowledge. All these and many other arguments 
 point to the inadequacy of the notion that knowledge is a pas- 
 sive reception of impressions. Concrete knowing feeds on the 
 whole of knowledge; what has been experienced, and the use the 
 mind makes of it, determines what is and will be experienced. 
 The direction of one’s thoughts, meanings, intentions, codperate 
 in what he sees and hears, no less than does the external situa- 
 tion in which he happens to find himself. If the mind were a 
 tabula rasa, there is no reason why first impressions should not 
 be as clear, as complete and final, as last impressions. 
 
 Yet there is a stubbornness, a resistance, an alien character, 
 in the objects of concrete experience which prevents us from 
 taking the opposite point of view, namely that they are thought- 
 creations, things merely meant and in no sense given. We do not 
 invent the things we see about us; they force themselves in upon 
 us, and though the mind goes forth through its intentions to 
 meet reality, still thought comes in the end to something un- 
 yielding. If experience deceives us, we do not get rid of the ex- 
 perience by apprehending it under proper categories and thus 
 doing away with the deception. The data remain, however we 
 conceptualize them. It is impossible to convince one’s self that 
 the world is merely a coherent set of meanings. Whatever the 
 activity of thought does in contributing to concrete knowing, 
 there always remains a matter not its own creation. However 
 thought may elaborate this matter, the matter persists, to con- 
 
284 SYMBOLISM AND TRUTH 
 
 fine and complete concrete thought.! Of the infinity of worlds 
 possible to purely abstract thought, one is realized, and it is this 
 one which experience reveals to us. For abstract thought alone 
 any other world might equally well have been. 
 
 The idealist, who looks on reality as a rational system of 
 meanings or concepts, still finds it necessary to account for the 
 stubborn givenness of this world; he cannot ignore the specific 
 materials of knowledge; he must make it clear why this rather 
 than that possibility is realized. And quite properly, not wishing 
 to fall into the Kantian predicament, which places reality be- 
 yond the reach of hought and yet maintains that in some 
 strange way this reality limits and molds experience, even 
 though this experience is always of ideal (mental) objects only 
 —not wishing to fall into this difficulty, the idealist distin- 
 guishes between subjective and objective thought, between 
 relative and absolute knowledge. Finite experience is a frag- 
 ment of the absolute experience, finite thought a part of the ab- 
 solute thought. Through entering (partially) into this absolute 
 thought, we know reality, and so the world about us is more 
 than the creation of our own minds. 
 
 This idea is most simply put by Berkeley, who interpreted 
 the whole of nature as a direct communication from God. In the 
 hills, the trees, the stones, the events of history, we read the 
 thoughts of the Deity; all are signs of what is passing in His 
 mind, The stability of nature, the persistence and externality of 
 perceptual objects, arise from the stability, persistence, and ex- 
 ternality of God’s thought. Illusion and error are man’s dream; 
 truth is the apprehension of what God compels us to know. 
 Berkeley’s idealism has a fresh, naive beauty not found in his 
 more sophisticated brethren, the Post-Kantians; but in essence 
 it is absolutism. 
 
 Absolute Idealism, then, does not do away with the alien qual- 
 
 1 Matter in the Aristotelian sense. 
 
THE METAPHYSICS OF KNOWLEDGE 285 
 
 ity of the objects of experience, and at the same time it takes 
 complete account of the work of thought in apprehending these 
 objects. It does not ask us to believe that reality stamps itself 
 on the mind from outside, that we are mere receptacles of im- 
 pressions and ideas. Knowing becomes an entering into reality, 
 a sympathetic understanding of a thought-world which is alien 
 to and more inclusive than our own world of thought. The ac- 
 tivity of the human mind is compelled and illuminated by the 
 activity of the Absolute Mind in which it has its being. 
 
 f 
 
 VII 
 
 This is a heady doctrine, and one pauses to ask himself what 
 it comes to. What is the Absolute Mind? Need one call it a 
 “mind” ? What significance remains in speaking of reality as 
 essentially “thought”? 
 
 The chief argument for idealism, aside from the necessity of 
 accounting for the mind’s activity in knowledge, is one that has 
 been mentioned above; the mind must be continuous with the 
 reality it knows. Thus it is easy to leap to the conclusion that 
 reality is mental, to Berkeley’s esse est percipi. Yet objects re- 
 fuse to be reduced to my mental states or my meanings; they 
 persist, I believe, when my back is turned (and certainly Berke- 
 ley also believed this). The laws of nature, of mathematics and 
 logic, are not my thoughts; I discover and do not invent them. 
 And though Berkeley would have admitted that he “ate, drank, 
 and was clothed with ideas,”’ these were God’s ideas and not 
 his own. Reality must be sufficiently close to the mental to be 
 known through the activity of my mind, but it must not be so 
 completely mental as to be reduced to this activity. The ideal- 
 ist’s argument comes to this: he is forced to distinguish “men- 
 tal,” from “mental ,”, and what remains? Merely lip-service 
 to a word. What he is saying, apart from this word “mental,” 
 is that his mind is so related to reality that it can know reality 
 
286 SYMBOLISM AND TRUTH 
 
 through its activity. Obviously, no mind can be completely 
 foreign to the reality it knows; the mind and its objects must be 
 in the same universe; they must not be so wholly sundered that 
 no relation, no sort of community or continuity, can exist be- 
 tween them. But it profits me nothing to insist that this reality 
 is mental, a thing of thought. I mean that it is “mental ,” and 
 not “‘mental,” and these are very different. 
 
 “Reality”’ is the most inclusive of all possible terms; if any 
 distinctions of meaning exist, these must arise within reality. 
 There can be no significance in defining reality in one way rather 
 than another, for whatever special term be taken as its defini- 
 tion, this term will have arisen as a distinct “‘somewhat”’ within 
 reality, and it will lose its special meaning if it is made equiva- 
 lent to reality. To speak of reality as mental is to spread mental- 
 ity so thin that, to all intents, it becomes “‘not-mental.’’ We are 
 driven to qualifications — “‘objectively”’ and “‘subjectively”’ 
 mental — to bring back the significance that has departed from 
 the term. 
 
 One might as well recognize at once that reality is reducible 
 to none of its aspects or modes, and be content with the term 
 “‘reality”’ in its simplicity as undefined. For the logic of the 
 situation will finally force him virtually, if not explicitly, into 
 this position. The realist declares that “reality is independent of 
 the knowing subject and not essentially mental, though it can 
 be known”’; the idealist — what appears to be the same thing — 
 that “‘reality is mental (but not subjectively so) and dependent 
 on mind (but not on the subjective mind).’”’ Both agree on the 
 fundamental point that the mind in knowing is continuous with 
 real objects; both repudiate the Kantian dualism of idea and 
 real object, of phenomenon and thing-in-itself. In this respect 
 the American realists go further than many idealists; they assert 
 not merely that the mind is continuous with the real objects it 
 
THE METAPHYSICS OF KNOWLEDGE 287 
 
 knows, but that it is identical with them — or at least partly 
 so. 
 
 The truly significant tendency in modern metaphysics, 
 whether it be idealistic or realistic, is toward breaking through 
 the old fixed categories of the mental and the physical. We are 
 returning to the point of view of the ancients, having suffered 
 for three centuries from the blindness of the Cartesian dualism. 
 If a chasm is opened, as it was by Descartes, between the physi- 
 cal and the mental, there is no way of closing it. We have strug- 
 gled vainly throughout most of modern philosophy to solve a 
 problem which, as it is stated, is insoluble: that of the relation 
 of “thinking substance” to “extended substance.”’ In psy- 
 chology it has appeared as the mind-body problem: How can a 
 physical thing be related to, act upon, control or be controlled 
 by, a non-physical thing? And there is no answer in terms of the 
 Cartesian concepts. The theory of psycho-physical parallelism 
 merely restates the problem in a more vivid way. Psychologists 
 have learned that they must go back to earlier notions and 
 merge “body” and “mind” in larger concepts such as “‘struc- 
 ture” and “‘function.” Mind and body are aspects of, abstrac- 
 tions from, a known reality which is wider and richer than either. 
 In the theory of knowledge, the dualism of the mental and the 
 physical has led to that extraordinary difficulty — how can one 
 know the physical world? — a question which, rightly, did not 
 enter Aristotle’s head. Descartes solved it by a tour de force, 
 but it would not have needed to be solved unless he had assumed 
 that physical objects are so completely disparate from minds, 
 so wholly resident in another universe, that nothing short of a 
 miracle could bring them together. Physical objects are not so 
 
 1 See E. B. Holt, The Concept of Consciousness (1914), chs. 8, 9. Mr. Nor- 
 man Kemp Smith’s recent Prolegomena to an Idealist Theory of Knowledge 
 (1924), points out that the idealism, realism, and naturalism of current philos- 
 ophy are indistinguishable on many fundamental issues. 
 
288 SYMBOLISM AND TRUTH 
 
 foreign to minds that they cannot be known, nor are they so 
 akin to minds that they cannot be when they are not known. 
 
 This is what both idealists and realists recognize, that the 
 knowing relation is an entrance of the mind into external ob- 
 jects, or an entrance of external objects into the mind — which- 
 ever way one chooses to put it. 
 
 Idealism as it appears in Berkeley is a polemic against ma- 
 terialism rather than against realism.! In his day materialism 
 was showing its head everywhere, and the good Bishop of 
 Cloyne wished to refute a doctrine against which all that has 
 been said above concerning idealism can be equally well main- 
 tained. To speak of reality as “‘matter’’ is to divest the term 
 “material”? (or physical”) of its specific meaning; for within 
 this so-called ‘‘material” reality mind arises, at least as an epi- 
 phenomenon—a shadowof a shadow of matter. And this subtler 
 thinking matter is no less a reality than the cruder unthink- 
 ing matter. We have “matter ,” and “matter,.” Thus “real- 
 ity,” following the inevitable logic of the meaning of this term, 
 widens out and transcends its physical as well as its mental 
 
 aspect. 
 VIL 
 
 The capital crime of metaphysics is the attempt to reduce re- 
 ality to one of its aspects or modes, a crime which is equalled 
 only by its converse — the attempt to sever reality from all of 
 its aspects or modes. Reality is fuller than any single set of rela- 
 tions, laws, principles, which can be discovered within it. It is all 
 these, and more. But though it is not possible to define reality 
 — to state exhaustively in conceptual terms exactly what it is to 
 be real — there are perfectly general truths which hold without 
 qualification for reality. Any one who believes that a rational 
 
 1 We mean “realism” in the modern rather than the mediaeval sense. 
 
 Berkeley’s repudiation of abstract ideas can certainly be construed as a 
 polemic against the realism of the schools. 
 
THE METAPHYSICS OF KNOWLEDGE 289 
 
 metaphysics, or for that matter rational knowledge, is possible 
 must believe that there are such general truths. The terms in 
 which these truths are stated must be sufficiently wide to include 
 both the mental and the physical; they must spring from the 
 observation that reality is neither physical nor mental exclu- 
 sively, but that it can be both. The physical and the mental 
 must be capable of fusion. Further, it must be recognized that 
 the dichotomy of the physical and the mental does not exhaust 
 reality, but that there are other orders of being — perhaps, as 
 Spinoza thought, an infinity of such orders.! 
 
 No metaphysics can successfully maintain that reality is 
 ~ essentially disparate from mind. Non-mental objects must be 
 capable of coming into the knowing relation, and hence there 
 must be unities which include both the mental and the non- 
 mental. Nor can a metaphysics maintain that reality is essen- 
 tially internal to mind in any significant sense of the term 
 “mind.” “Idealism” and “spiritualism” suggest the latter 
 point of view, while ‘“‘realism,” by a modern perversion of its 
 meaning — by stressing the externality of terms and relations, 
 of mind and its objects, and forgetting that all relations also en- 
 ter into and modify their terms — suggests the former. There 
 should be a name for the metaphysics which consciously repudi- 
 ates both of these points of view and sets out from the notion 
 that reality is an unbroken whole whose parts mutually if not 
 completely determine one another, the mental and the non- 
 mental being phases within this whole. Our answer to the 
 question — how is the mind related to real objects in the act’of 
 knowledge? — rests then on this premise, that reality is neither 
 essentially disparate from or internal to mind. Concrete knowl- 
 
 1 Mr. A. N. Whitehead’s recent lectures at Harvard have, for the present 
 writer, thrown a wholly fresh light on metaphysical problems; especially on 
 this question of how, in detail, a set of general concepts can be framed which 
 
 embrace the physical, the organic, the mental, and at the same time leave 
 room for other orders of being. 
 
290 SYMBOLISM AND TRUTH 
 
 edge is first of all knowledge of the real, and only secondarily 
 knowledge of the mental or the physical. Within this appre- 
 hended reality, two orders can be distinguished, the mental and 
 the physical, but the one is no more essentially real than the 
 other; each is a mode of reality, bearing on itself the stamp of 
 being. 
 
 Furthermore, the act of knowing has both its passive and ac- 
 tive side; here as in physics the law of action and reaction ap- 
 plies. The mind receives an impression and correlates it with 
 other impressions, fits it under concepts, actively assimilates it 
 to the whole body of knowledge. Objects are perceived through 
 thought and thought through perception, for as Kant’s phrase 
 runs, ‘percepts without concepts are blind, and concepts with- 
 out percepts are empty.” Yet the activity of thought, rather 
 than estranging us from external reality, brings us into contact 
 with a reality other than thought. 
 
 1X 
 
 Let us examine more fully what is meant by the “mental” 
 with a view to showing how the mental can be continuous with 
 the non-mental in cognition, and why thought-activity is needed 
 to put us in touch with objects. 
 
 Forget as completely as may be the distinction between the 
 physical and the mental; put yourself in the most naive possible 
 frame of mind and gaze on the things about you. What you see 
 before you is a field of objects, probably a changing field; you 
 close your eyes and see other, fainter objects, or perhaps only a 
 dark area illuminated by dim streaks of light; you open your 
 eyes, and perceive objects closely if not indistinguishably like 
 those you first saw; and all the while within your body you ex- 
 perience faint or vivid sensations of movement, perhaps of pain 
 or of a vague well-being. There is no reason for singling out any 
 part of this whole experience as mental. Some parts of it are 
 
THE METAPHYSICS OF KNOWLEDGE 291 
 
 more closely associated with the body than others; the pain is 
 localized in the body, while the wall of the room is not; but ex- 
 ternality or internality to the organism gives us no criterion of 
 the mental. 
 
 The distinction is certainly not an early datum of experience; 
 it comes to the surface only after reflection, only after certain 
 sequences and orders of events have been observed. Then it is 
 discovered that some of the things experienced hang together 
 by a different sort of coherence from others. Within the single 
 field of real objects, which is the original cognitum, we find two 
 worlds which differ in structure but easily become a single 
 world, and there can be no question as to how knowledge passes 
 from the one to the other. From the beginning knowledge is 
 synoptic, it covers both. 
 
 The lineage of this view, which was strikingly put by William 
 James in his essay, Does Consciousness Exist,’ can be traced at 
 least to Spinoza: “‘thinking substance and extended substance 
 are one and the same thing, which is now comprehended through 
 this and now through that attribute.” *? James need only have 
 added to the two types of structure found in the world of “pure 
 experience,” an infinity of types of structure (corresponding to 
 the infinite attributes) to have become a thorough-going Spino- 
 zist. Mr. Bertrand Russell, who has elaborated James’s view, 
 as distinguished from 
 
 ’ 
 
 gives the name ‘‘mnemic causation,’ 
 “physical causation,” to the type of law which is characteristic 
 of the mental realm.® 
 
 Memory is certainly one of the chief principles of order in the 
 mental world, but the term “‘mnemic causation” is too sug- 
 gestive of Hume. Its effect is to turn the attention away from 
 the very essense of mind, activity toward an end — the unity of 
 
 1 W. James, Essays in Radical Empiricism, 1912. 
 
 2 B. de Spinoza, Ethics, Bk. II, Prop. VII, note. 
 3 B. Russell, The Analysis of Mind (1921), sect. 4. 
 
292 SYMBOLISM AND TRUTH 
 
 memory and purpose, of backward and forward looking inten- 
 tions, which is a personality or self. If the soul-substance view of 
 mind is dead, so also is that of Hume — that the mind is a stage 
 where ideas pass and repass without a spectator to take account 
 of them. The stuff of “pure experience” does not combine and 
 recombine of its own weight, according to the principles of asso- 
 ciation or of mnemic causation, to form a mind. The laws of 
 mind are laws of purposive activity; memory is itself an activ- 
 ity; will, striving, conation, are at the core of mind; and these 
 strands of activity are always caught together in a unity which 
 is the self of the moment. This self changes, but not without per- 
 sistence of its structure. At any moment a definite past, which 
 can be called up and known again (though not exactly as be- 
 fore), converges toward the present, and a future — purposed, 
 desired, intended, striven for — expands from the present. This 
 is a mind. 
 
 Moreover, the activity of the mind can become reflexive, it 
 can be turned upon itself or its own products; and this “‘reflec- 
 tion” occurs in two very different ways. (1) In desiring, we know 
 that we are desiring; in knowing, we know that we are knowing. 
 Josiah Royce speaks of this as the “self-representative”” power 
 of knowledge,! that is, knowledge can reflect on its own proc- 
 esses. (2) The activity of the mind tends also to crystallize into 
 a content which is still wholly within the mind. To think of or 
 intend something is to set in motion the whole apparatus of 
 cognition; the thought refuses to continue merely as a pure 
 intention but strives to become concrete, that is, to fulfill itself; 
 and thus an image or “reflexive content” appears. The image 
 is a deposit of the activity. To know the image is therefore 
 not merely to know that we are knowing; it is to be aware of 
 something the mind creates. Images are the products of minds 
 rather than minds themselves; they arise in the process of 
 
 1 J. Royce, The World and the Individual (1901), Vol. II, pp. 509 ff. 
 
THE METAPHYSICS OF KNOWLEDGE 293 
 
 mental activity, but they are not the activity, nor are they of 
 the same stuff as non-mental objects. Though the activity of 
 the mind creates reflexive contents, there is no foundation for 
 the belief that all experience is of reflexive contents only; and 
 if this is the meaning of Locke’s statement that “knowledge 
 is conversant only with ideas,” an essential fact’of knowledge is 
 overlooked, that one knows ideas and the mind that creates 
 them only by distinguishing them in a reality which extends 
 beyond both. 
 
 Given, then, that the mind from the outset knows something 
 other than itself, and it still remains to be shown how the mind 
 is continuous with this non-mental reality in cognition. 
 
 This continuity is not identity. The mind is other than the ex- 
 ternal reality it knows; there is always more of the reality to be 
 known, and always the knowing, which is of the mind but not 
 the same as the non-mental object. (The knowing tends also to 
 create a reflexive content which fuses with the non-mental 
 object, but, difficult as these images are to distinguish from 
 the object, they are not identical with this object.) The epis- 
 temological monism which identifies mind with its non-men- 
 tal objects makes the object of knowledge a sponge that ab- 
 sorbs everything — error and illusion, as well as meaning and 
 truth. 
 
 Mind is cognitively continuous with non-mental objects in 
 the same general sense as other things in this world are continu- 
 ous with one another. And we are not speaking here of the math- 
 ematical theory of continuity, but of something found in experi- 
 ence, which M. Bergson describes as “interpenetration” and 
 Mr. Whitehead as the general ‘“‘togetherness’’ of objects and 
 events. This continuity is not, we believe, a relation. It is rather 
 the unity or wholeness within which both terms and relations 
 arise. Distinct things singled out as self-identical always merge 
 in the wholes within which they are distinguished, and this union 
 
294 SYMBOLISM AND TRUTH 
 
 of the parts in the whole is not due to confusion in the perception 
 that distinguishes them, but to the nature of reality. Though 
 reality at all points takes on distinct structures or forms, these 
 structures are always elements in wider structures, and every 
 whole is continuous with other wholes. 
 
 Let us recall what was said previously in connection with 
 relations| A is related to B not because the relation R which 
 unites A and B is related to its terms, for if this were so an in- 
 finity of relations would be needed to bring about a unity of the 
 terms. The terms and relation are joined once for all. They form 
 a whole in which the aspects A, B, and R can be distinguished; 
 this is what we mean by saying the relation R holds between A 
 and B. There is no point where the relation ceases to be a rela- 
 tion and becomes a term, or where the terms cease to be terms 
 and become a relation. Motion is an apparent case of such con- 
 tinuity. There is no point at which the moving object ceases to 
 be in one place and passes into another; in fact, the passage is 
 just a continuous process which cannot be completely described 
 in terms of places or points, any more than a relation between 
 terms can be described in terms of elements and a relation. We 
 must have the ultimate concept of the unity of the elements. We 
 must think of the elements as abstracted from this unity, in- 
 stead of thinking of the unity as added to the elements. We must 
 think of the points and instants, in terms of which we describe 
 the motion, as abstracted from the passage, rather than of the 
 passage as superimposed on the points and instants. 
 
 The mind and its objects fuse as one segment of a motion 
 fuses with another, as a relation merges with its terms, as any 
 part of a whole or any whole, with another. The mind projects 
 itself into the non-mental and the non-mental into the mind. 
 There is an unbroken flow of process, and throughout a stretch 
 of this process—at the segment of “greatest luminosity ’’—the 
 
 1 See above, ch. III, sec. vii. 
 
 —— sO 
 
THE METAPHYSICS OF KNOWLEDGE 295 
 
 cognition of the object comes into being. Minds are together 
 with external objects in the same general way as objects, events, 
 situations, are together with one another. 
 
 This continuity of mind and its objects needs, however, to be 
 further specified. Continuity (or unity) is a general background 
 against which any elements of reality — whether they be minds, 
 physical objects, or what not — stand out; and in each distin- 
 guishable whole of experience this continuity is of a specific sort. 
 Thus the whole (ARB) might be a whole of “spatial before- 
 ness”, that is, it might be the fact “A is before B in space.” 
 Motion is obviously a spatio-temporal unity of a specific kind. 
 _ What sort of unity or continuity is this cognition of a non- 
 mental object? Certainly it is not a spatial continuity. Though 
 the object known may be spatial, the cognition is not in space 
 but of space. These two types of whole —the spatial and the 
 non-spatial — come together in the wider whole of cognition. 
 On the other hand, the continuity of mind and its non-mental 
 objects is both zn and of time; the mind as well as the world it 
 cognizes is a changing, temporal unity. In the specious present 
 of knowledge we grasp, in an act which is itself temporal, the im- 
 mediate past and future of the thing known, so that each whole 
 of cognition — being itself in time — is nevertheless a survey of 
 time. And yet the object of knowledge has its non-temporal 
 aspect. It is a “‘what,”’ a universal as well as an individual, and 
 its “what” cuts across time as well as across space and belongs 
 intrinsically to no single time or space. This is indeed the great- 
 est paradox of knowledge, that being in time it takes hold of 
 both the temporal and the non-temporal. The key to this para- 
 dox is memory. In so far as we attain to any knowledge of uni- 
 versals, of timeless objects, we do so through memory; and 
 since concrete knowing is always the seizure of something both 
 universal and individual, of something unique and passing which 
 is nevertheless blended with something that has been and may 
 
296 SYMBOLISM AND TRUTH 
 
 be again — for this reason, concrete knowing is a continuity of 
 a remembered past with a new, yet familiar present. 
 
 The passage of thought is plainly not motion, though it is 
 activity; and one speaks only metaphorically of the mind as 
 “going forth to meet its object.” Knowing is a fulfillment, a 
 realization, in which the mind attains an end which has been 
 obscurely before it; and whether or not teleological categories 
 are of use in describing nature, they are indispensable in describ- 
 ing mind. 
 
 Finally, the act of knowledge is inclusive of itself. In knowing 
 objects we know the process by which we know, the mind re- 
 veals itself through its commerce with its non-mental environ- 
 ment. And beyond all this, knowing has its peculiar tang which 
 is no more subject to description than the sound of a tonic triad 
 or achord of the seventh. Analysis discerns in knowing, as in the 
 chord of the seventh, a number of phases, but it still remains 
 simply what it is — a unique union of mind and object. 
 
 xX 
 
 It must not be supposed that the external objects which pro- 
 ject themselves into knowledge are those that act on the senses. 
 We perceive colors, shapes, smells, sounds, motions, houses, 
 trees; we observe relations between these objects and laws that 
 hold for them; but we do not perceive light-waves or sound- 
 waves, molecules, electrons or electronic structures, nor do we 
 perceive the bodily processes which light-waves or sound-waves, 
 molecules or electrons, arouse in us. One can construct a theory 
 of how these infra-experiential entities act on the sense-organs, 
 but it is not possible to perceive these entities through their ac- 
 tion on these organs. 
 
 An immense amount of error has been propagated by the 
 view that the only real physical objects — or, for that matter, 
 the only real objects — are these infra-experiential entities in 
 
THE METAPHYSICS OF KNOWLEDGE 297 
 
 terms of which physical theory is constructed. The problem of 
 our knowledge of physical reality is totally misconceived if one 
 attempts to solve it by explaining how these entities, which are 
 undoubtedly connected in some way with our sensory reactions 
 and with all our intellectual processes, can be known through 
 this connection. Whatever the relation of these entities to men- 
 tal processes may be, it is certainly not the cognitive relation. 
 This must be sought elsewhere. 
 
 The physical objects of concrete knowledge must be distin- 
 guished from the physical objects of scientific theory; these two 
 types of physical object together make up the complete physi- 
 cal object. There is no doubt that perception penetrates only a 
 short way into the complete physical object; what is perceived 
 must be pieced out by a theory as to the nature of this whole 
 object. But this lack of concrete knowledge of the whole physi- 
 cal object does not make the objects of perception purely men- 
 tal. They retain their otherness, they still belong to an order dif- 
 ferent from that of mind. The presented physical object is a 
 mediating link between the mind and the physical object of sci- 
 entific theory. It is sufficiently like the mind’s reflexive content 
 (images, dream-perceptions, etc.), to be deceptive when taken 
 out of its setting. (There is no intrinsic difference for perception 
 between an isolated physical sound, for example, and an isolated 
 sound-image.) Yet the presented physical object, in its setting, 
 bears the marks of a structure different from that of the mind or 
 the mind’s reflexive contents; and it is on this observed differ- 
 ence of structure that a theoretical world of physical objects, 
 extending completely beyond concrete knowledge, is built. In 
 the act of cognition, we are aware at once of the distinctness and 
 the unity of our minds with the presented physical object; but 
 we are never concretely aware of how this perceptual object, or 
 the mind, is related to the scientific physical objects. A color is 
 doubtless vastly unlike a light-wave, yet the color is a physical 
 
298 SYMBOLISM AND TRUTH 
 
 phenomenon, a non-mental reality. It comes into being in a cer- 
 tain situation, theoretically represented as a light-wave striking 
 an eye. It is a part of the whole physical situation of which the 
 light-wave is a part; it is that part of the situation which can be 
 in knowledge and at the same time in the external world. 
 
 The problem of how the objects of physical theory are related 
 through the presented physical objects to the mind, of how 
 these three can be together, is a phase of the problem of mind 
 and body. But the problem of the cognition of the physical 
 world, or for that matter of any order of being beyond our own 
 minds, is wholly another question. If there is to be any physical 
 theory and any problem of mind and body, both the physical 
 and the mental must be known. The mind could not leap mirac- 
 ulously to the notion of an infra-experiential world of atoms and 
 electrons and then ask, ‘“‘What is the relation of this world to 
 the mind?” Whatever the solution to the mind-body problem 
 may be, the mental and the physical are continuous in a specific 
 way in cognition. They must also be continuous in some other 
 specific way through the action of molecules, electrons, light- 
 waves, on the nervous system. 
 
 Since the presented physical object arises in a situation in 
 which both a mind and other physical objects, not presented, 
 codperate, one can ask — what aspects of the presented object 
 are relative to this situation? — and what aspects extend be- 
 yond it? 
 
 These questions can be generalized for any situation. Every 
 situation is altered in general complexion if some of its elements 
 are removed. Something more than these elements goes out of 
 existence; the original “‘what”’ of the whole is extinguished and 
 the remaining whole is a new “what,” perhaps of a very differ- 
 ent complexion. Thus there is something in every situation 
 which is relative simply to that situation. Take away the spires 
 of the cathedral at Chartres and the proportions of the building 
 
THE METAPHYSICS OF KNOWLEDGE 299 
 
 are destroyed; new, probably ugly, proportions come into being. 
 It is not simply that the spires are missing; the personality of 
 the cathedral has vanished, to be replaced by another. And yet 
 the two personalities have something in common; the mutilated 
 whole can be pieced out to give the original; there are hints as to 
 what the old personality might have been. So also in every whole 
 there are suggestions of other wholes of which it might be a part. 
 The presented physical object, issuing as it does from the 
 unity of a mind and other physical objects not presented, must 
 be a distinct “what” relative to this situation. But to call atten- 
 tion to the fact that its general complexion is determined by the 
 psycho-physical situation is not to deprive the presented physi- 
 cal object of its reality; nor does it make the object any more 
 essentially relative to mind than to the physical world beyond. 
 Just as a real object other than the single notes comes into exist- 
 ence when a chord in C-major is sounded, so a real (perceptual) 
 physical object comes into existence in the proper situation.1 
 What is the nature of the physical object when it is not per- 
 ceived? All one can answer is that it cannot be exactly the same 
 as when it is perceived. The situation has altered. One element, 
 the element that makes the object perceptual, is absent; but just 
 what aspects of the object pass out of existence with the absence 
 of perception we certainly cannot say. Locke describes the un- 
 
 1 The question of the relevance of the perceptual object to a psycho-physical 
 situation is not the same as that of the “privacy” of this object for an indi- 
 vidual perceiver. Every real situation is individual, and this individuality is 
 determined by that of its elements; hence, there must be an individuality in 
 the perceptual object which is bound up with (though not reducible to) the in- 
 dividuality of the perceiving mind. But every situation has, also, its universal 
 aspects, so that the “privacy” of the perceptual object is not incompatible 
 with its “‘publicity.” Indeed, as has been shown in the discussion of the indi- 
 vidual (above, ch. III), only the public aspects of the object are clearly and 
 determinately known. The perceptions that men share are those of general 
 natures and relations, 7.e., of red, motion, etc., rather than of natures and re- 
 lations as individualized in particular situations, The question of the “priv- 
 acy”’ of the perceptual object is one phase of the more general metaphysical 
 question — how can a real object be at once individual and universal, abso- 
 lutely unique yet like other real objects? See below, secs. xii and xiii. 
 
300 SYMBOLISM AND TRUTH 
 
 perceived physical object as colorless, tasteless, odorless, sound- 
 less, but insists that it retains its geometrical and mechanical 
 properties. Yet even Locke admits that the colors, smells, tastes, 
 odors, are still in the physical object as ““powers”’, that is, there 
 is something in the unperceived physical situation which be- 
 comes a color, taste, smell, or odor when perception is added. 
 Perhaps an unperceived color differs much more widely from a 
 perceived color than an unperceived motion differs from a per- 
 ceived motion, but this supposition would not warrant us (fol- 
 lowing the distinction between primary and secondary qualities) 
 in placing some of the modes of being of the perceptual object 
 only in the mind and others both in the mind and in the physical 
 field beyond the mind. Certainly the whole object as unper- 
 ceived is continuous with the object as perceived; the latter is a 
 real whole merging with another (unperceived) real whole and 
 giving indications as to its nature. 
 
 Thus, if there is a ‘‘somewhat”’ in the perceptual object which 
 is peculiar to it, there are also a vast number of properties and 
 relations which are not peculiar to it, but which stretch out into 
 the unperceived reality. For all reality is shot through and 
 through with the general. Though each real whole is unique, it 
 is still an instance of many universals which link it to other 
 wholes. Physical theory seizes on certain relations and proper- 
 ties found in the perceptual physical object,— for example, mo- 
 tion, acceleration, mass, spatial relations, etc., — and by refin- 
 ing and extending these properties and relations, so that they 
 can be used as instruments of exact description, pieces out the 
 picture of the whole physical reality. 
 
 1 Along with the tendency of the mind to codperate with the elements of 
 the physical situation in giving birth to the perceptual physical object goes an 
 opposite tendency — the tendency not to codperate. Certain elements of the 
 physical situation are excluded from the perceptual physical object. Thus, not 
 only is there the problem of how the unperceived color or motion is perceived, 
 but there is also the problem of why the light-waves, electrons, molecules, 
 etc., are not perceived. 
 
THE METAPHYSICS OF KNOWLEDGE 301 
 
 XI 
 
 What has been said of the relation of the mind to its non- 
 mental objects makes it even more difficult to believe that these 
 objects are known passively by impressing themselves on the 
 mind. Both the mind and a perceptual (external) object are to- 
 gether in the earliest wholes of cognition. The object is in the 
 mind, the mind is in the object, and there is no reason to think 
 that the impulse to a more complete cognition comes — as the 
 blank-sheet view of mind would have it — from the object 
 rather than from the mind. It is most unlikely that the mere 
 repetition of a situation in which a mind and a perceptual ob- 
 ject are together leads to a clearer knowledge of the object. 
 Some other factor must also be at work. The object must catch 
 the attention; it must attract as well as impress the mind, and 
 this means that it must complete the mind’s intention. 
 
 Cognition is always the fulfillment of an intention, and so 
 there must be native impulses to cognition from which the first 
 knowledge of objects springs. The mind no less than the body 
 must have its initial structure, which grows and is modified by 
 successive acts of knowledge. And the structure of the mind, 
 like that of the body, must be adapted to its environment. This 
 is — if one wishes so to speak of it — a theory of innate ideas; 
 but just as most criticisms of the “instinct psychology” object 
 to the specificity of the instincts assumed rather than to the 
 fact that there are instincts, so one can repudiate innate ideas 
 so special as those of God, of right and wrong, of mathematical 
 truth, without repudiating all innate cognitive tendencies. 
 
 An original impulse toward analysis, toward selection or sift- 
 ing, is found in knowledge. To cognize anything clearly is to 
 isolate it from its surroundings. This tendency toward analysis 
 is accompanied by another, the tendency to hold together with 
 its surroundings what has been sifted out. Not only is a single 
 
302 SYMBOLISM AND TRUTH 
 
 element more clearly known through selection, but the whole 
 of which it is a part is also more clearly known. And these most 
 general impulses are associated with more special ones, such as 
 jumping at a noise, turning the eyes toward a light, grasping, 
 etc. Indeed, every special instinct is cognitive in that it leads us 
 to analyze and to take account of the unity of our environment. 
 Objects do not of their own accord separate themselves out from 
 experience; they might impress themselves forever on the mind 
 without giving rise to the dissociation of their parts which is 
 analysis. Yet reality is so put together that it permits this dis- 
 memberment and also resists it, thus satisfying both the impulse 
 to analysis and to unification. The mind finds real chinks and 
 crannies in the object, real lines of stratification along which it 
 breaks up for thought, so that we do not create out of whole 
 cloth a mere appearance of analysis. We adjust ourselves 
 through analysis to something real in the world beyond. (The 
 reason why knowledge is for Kant an act of introversion is that 
 the cognitive impulses are totally out of adjustment to reality; 
 there is no trace of agreement between the way in which the 
 mind tends to think and the way in which objects are beyond 
 the mind. It would be strange if, with bodies so nicely adapted 
 to the physical world, our mental impulses were completely 
 askew to reality. The theory of evolution ought to apply to 
 minds no less than to organisms.) 
 
 Analysis is a cumulative process; what has been analyzed can 
 be further analyzed, one analysis makes possible another. We 
 select from what has been selected, we learn that things are to- 
 gether which have not been previously observed to be together, 
 the channels of cognition become more and more complex, more 
 and more numerous, enabling us in the end to take account of 
 subtleties, distinctions, unities, which were before obscured. 
 
 Finally, we become aware of the widest intentions of thought, 
 which make analysis possible. These are the intention to direct 
 
THE METAPHYSICS OF KNOWLEDGE 303 
 
 every intention toward one and only one object (the principle of 
 identity as a rule of symbolism); the intention to direct distinct 
 intentions toward distinct objects (the principle of contradic- 
 tion as a rule of symbolism);! and the intention to apprehend 
 facts, situations, objects, as unified groups of distinct elements. 
 We discover that reality yields to these intentions, that every 
 object is what it is, self-identical and distinct from other ob- 
 jects, yet joined with them in continuous wholes. The mind thus 
 learns to be conscious of its categories, its structure, through the 
 operation of these categories, the functioning of this structure, 
 in concrete knowing. At the same time its contacts with special 
 aspects of its environment multiply and refine its more special 
 concepts. 
 
 But the activity of the mind in the grooves of concepts would 
 not bring us into touch with reality unless reality were perme- 
 ated by the general. This fact is what adapts the environment to 
 our cognitive impulses. Every concrete object is at once uni- 
 versal and individual, absolutely unique and yet like other ob- 
 jects. It is the universal — which is itself an object — which ful- 
 fills our intentions in knowledge. For, as has been pointed out 
 in another place,’ analysis is first of all the dissection of an 
 object into a “what” and a “‘this,”’ a universal and an individual 
 aspect. If there were nothing in the real which persisted, if 
 every object came once and never again, our concepts could 
 take hold of nothing. Reality would slip by unanalyzed, taken 
 account of only in that pure awareness which lies below the level 
 of clear cognition. No situation is wholly new; hence, it can be 
 assimilated to knowledge held in the memory, the mind can 
 come to rest in the apprehension of something which completes 
 its intentions. In any moment of time (and knowledge is both 
 an and of time) the mind, through the fulfillment of intentions 
 
 1 See above, ch. VI, sec. iv. 
 2 See above, ch. III, sec. i. 
 
304 SYMBOLISM AND TRUTH 
 
 which bridge many times, attains a knowledge of a reality 
 stretching far beyond the moment. With the conceptual tools 
 forged by the aid of cruder tools, the mind digs into the object 
 before it to discover principles which radiate into other objects 
 — and into all reality. Thus the immediate impression is the 
 occasion of true knowledge; yet knowledge in expanding beyond 
 the moment does not turn upon itself to a world of appearances. 
 It grows always in the direction of the real. 
 
 In all this something which remains to be considered has 
 been anticipated. It has been assumed that reality has a struc- 
 ture. The essence of structure is logical form. Does reality 
 exhibit logical form? Is reality made up of self-identical and 
 distinct objects which coalesce into wholes (groups) with 
 elements of unity and terms? Are universals, that is, elements 
 of unity, real? Do the principles of identity and contradiction, 
 which are the formal conditions of the being of self-identical 
 and distinct objects, apply to reality? 
 
 If these questions must be answered in the negative, not only 
 does the activity of thought end in a blind-alley, but, from the 
 metaphysical point of view, the truth which we have described 
 as the correspondence of concepts through their structure with 
 real objects becomes error. If reality is structureless, it cannot 
 be adequately known through a thought bound to logical forms. 
 
 XII 
 
 Here is a turning-point in any metaphysics of knowledge. 
 How are we to stand off from thought and hold it up beside its 
 objects to discover whether the two are commensurate? If they 
 are commensurate, if there can be a real identity of structure in 
 concepts and the things they refer to, we cannot demonstrate 
 through concepts that such an identity is possible, for this cor- 
 respondence of concepts with objects is itself the condition of 
 rational truth and demonstration. Nor can we know this struc- 
 
THE METAPHYSICS OF KNOWLEDGE 305 
 
 tured reality in a cognitive act which takes no account of struc- 
 ture. And if thought and its objects are incommensurate, we can 
 not prove them to be so by going back to the negative arguments 
 of agnosticism. We cannot, through the logical forms of thought, 
 show that reality is without logical form; some positive knowl- 
 edge, not through thought, of this formless reality would be 
 needed. 
 
 Beside agnosticism, which on purely negative grounds denies 
 reason access to reality, stands positive irrationalism — a meta- 
 physics which condemns reason on the strength of an intuition 
 that goes deeper than thought to a mystic union with the real. 
 ‘Agnosticism does not successfully negate rational metaphysics. 
 Does this positive irrationalism meet with better success? To 
 answer this question, we must consider in what sense the act 
 of cognition as a whole escapes from the concepts which at 
 once confine and guide it. 
 
 Every act of concrete knowing overflows the conceptual. To 
 perceive an object is to capture in experience what one intends, 
 but it is also to capture more than one intends. This is one rea- 
 son why the real is alien to thought. Concepts can be multiplied 
 indefinitely, yet the real object to which they lead is not ex- 
 hausted and is always ready to yield further analyses, to submit 
 to new descriptions. I conceive the object as a unique “some- 
 what” in certain relations to other unique “somewhats’’; but 
 when I grasp the object concretely I know that these concepts 
 direct me only to some of its aspects. The object zs as I conceive 
 it, but is also other than I conceive it; and in knowing that what 
 can be picked out clearly and stated as true of the object is only 
 an aspect, I must apprehend the object as transcending and in- 
 cluding all its aspects. 
 
 What has been said before of the universal and the individual 
 sharpens this point. For conceptual knowledge, the individual 
 
306 SYMBOLISM AND TRUTH 
 
 is always attempting to become universal by dissolving into a 
 complex infinity of characters and relations, but it succeeds only 
 in being an indeterminate x; while the universal is always seek- 
 ing to become individual by qualifying and requalifying itself in 
 an infinity of ways. If I wish to conceptualize the individuality 
 of a pebble picked up on the beach, I am driven to hundreds of 
 characterizations, of measurements, of minute observations; 
 yet the pebble is still the x of which these relations and qualities 
 can be predicated, and I cannot even be certain (with Leibniz) 
 that an infinity of such predicates would distinguish this pebble. 
 I cannot, in thought alone, bridge the gap between the x, which 
 means indeterminately an individual, and the other concepts, 
 which stand for its predicates and relations. It is in vain that I 
 fill in with more predicates. In concrete knowledge the gap is 
 closed, though not by concepts. I know the pebble, hold it in my 
 hand, as a unique object in which all the predicates I have ob- 
 served are reconciled. It is not merely that concrete knowledge 
 adds sensation to thought; I do not sense the unity of the predi- 
 cates in the individual. The act of knowing has pushed out be- 
 yond sensation and thought to an intuition of the object. This 
 intuition has been spoken of before as pure awareness. Pure 
 awareness issues from thought and sensation; we cannot catch 
 it in itself apart from the other phases of cognition, and yet it is 
 not the same as either of these other phases. What intuition 
 gives us is a residue of knowledge, left over when all that is 
 clearly conceived or sensed in the object has been analyzed 
 away. 
 
 Consider the knowledge of a personality. Here intuition is 
 especially prominent. Calculation, analysis, will carry one only 
 a short way in adjusting himself to persons; something like 
 talent, skill, tact, is needed — not a talent separated from the 
 power of analysis, but a talent which makes use of every shred 
 of clear knowledge, and yet does not rely wholly on clear knowl- 
 
 KS eee ee eee ee ee eee ee 
 
THE METAPHYSICS OF KNOWLEDGE 307 
 
 edge. To know a personality is to enter into that personal- 
 ity, not blindly, but so that analysis plays its part and is left 
 behind. 
 
 Pure awareness is not sensation for the reason that a sensa- 
 tion is atomic; it is a distinct “‘what,” e.g., this redness, this 
 sourness, distinguished within a perceived whole. Moreover, a 
 “pure sensation” would be a sensation of nothing whatsoever, 
 for sensation cannot be thinned down till every vestige of mean- 
 ing, thought, has been wiped away. When this search for a 
 “pure sensation”’ is pursued, the sensum approaches a vanish- 
 ing point. A “‘pure sensation” is the thinnest of abstractions, an 
 _ imaginary limit which cognition never reaches. When knowledge 
 overflows the conceptual, it does not do so in the direction of 
 sensation. Nor does knowledge pass beyond concepts by going 
 to the other extreme, by sifting out all traces of sensation, leav- 
 ing the materials of experience behind and attaining an esoteric 
 vision of a reality that never was and never could be found in 
 perception. Yet to speak of pure awareness, of non-conceptual 
 knowledge, is to suggest the one or the other of these views — 
 sensationalism, or rationalism become esoteric. 
 
 An act of concrete knowing is bathed in an atmosphere of the 
 non-conceptual; it has a part of its being in a medium which is 
 neither pure thought nor pure sensation; and no act of concrete 
 knowing is complete until it finds itself surrounded and upheld 
 by the non-conceptual. This ever-present background of pure 
 awareness tends, like other backgrounds, to be forgotten and to 
 emerge only when a foreground has been clearly distinguished. 
 But it is always there, bringing thought and sensation together 
 and completing knowledge as neither thought nor sensation can. 
 It is impossible to isolate thought from sensation, and equally 
 impossible to isolate pure awareness from sensation and thought. 
 Perceptual thought transforms itself into pure awareness and 
 pure awareness passes smoothly into perceptual thought. There 
 
308 SYMBOLISM AND TRUTH 
 
 is no pure awareness dissociated from these other modes of cog- 
 nition. 
 
 An anti-intellectualistic philosophy such as M. Bergson’s 
 wishes to set pure awareness or intuition on its own feet, to 
 sever rational thought from the non-conceptual medium into 
 which and from which it flows. M. Bergson does violence to the 
 cognitive act; he looks at cognition abstractly in the very effort 
 to fasten on that which is most concrete in it. Instead of seeing 
 it as it is, a fusion of reason, sensation, and intuition, he exalts 
 the irrational component at the expense of the rational. 
 
 “By intuition,” M. Bergson explains, “is meant the kind of 
 intellectual sympathy by which one places oneself within an ob- 
 ject in order to coincide with what is unique in it and conse- 
 quently inexpressible. Analysis, on the contrary, is the opera- 
 tion which reduces the object to elements already known, that 
 is, to elements common both to itself and to other objects. To 
 analyze, therefore, is to express a thing as a function of some- 
 thing other than itself. All analysis is thus a translation, a de- 
 velopment into symbols, a representation taken from successive 
 points of view from which we note as many resemblances as 
 possible between the new object which we are studying and 
 others which we believe we know already. In its eternally un- 
 satisfied desire to embrace the object around which it is com- 
 pelled to turn, analysis multiplies without end the number of its 
 points of view in order to complete its always incomplete repre- 
 snetation, and ceaselessly varies its symbols that it may perfect 
 the always imperfect translation. It goes on, therefore, to infin- 
 ity. But intuition is a simple act.” ! 
 
 M. Bergson’s writings, like his snowball rolling down hill and 
 growing as it rolls, bulk together to force it on the mind that 
 concrete knowing is more than analysis. But that analysis is es- 
 
 1 H. Bergson, An Introduction to Metaphysics, T. E. Hulme’s translation 
 (1912), p. 8. 
 
THE METAPHYSICS OF KNOWLEDGE 309 
 
 sentially falsification, that intuition enters into reality to find a 
 changing, formless, flowing durée which eludes all concepts — 
 these are conclusions which follow only from making a part of 
 concrete knowing equal to the whole. M. Bergson is Heracleitus 
 with the logos left out. If reality is change, this fact, as Heraclei- 
 tus observed, does not itself change, and here is an entering 
 wedge for the permanent. An intuition cut off from concepts 
 could not name the reality it knows. Just as the concrete con- 
 tent of pure sensation or of pure thought would approach a zero, 
 so the concrete content of pure intuition tends to be nothing. 
 M. Bergson insists, for example, that to conceive a motion as an 
 infinite series of brief motions taking place at point-instants ar- 
 ranged in order is to fail to know the passage which is the es- 
 sence of the motion. One must identify himself with this passage 
 by intuition. Yet this pure intuition of the wholeness of the mo- 
 tion is, in itself, no less empty than the representation in terms 
 of point-instants. Though there is something real in the passage 
 which is given only in intuition, there is also something real in it 
 which corresponds to the conceptual series of point-instants.’ 
 To know the motion either simply as passage or simply as a re- 
 lated series of motions at point-instants is, in each case, to have 
 an insecure hold on its reality. 
 
 Irrationalism springs from a desire deeply rooted in human 
 nature — the desire to give oneself up, like a resting swimmer 
 on a bright sea, to the sustaining buoyancy of a limitless and 
 intimate reality. But one knows the buoyancy of the sea only 
 by learning to swim, and one knows reality only by learning to 
 think out his intuitions and to gain new intuitions through his 
 thought. 
 
 M. Bergson’s feeling that the deliverances of intuition prove 
 
 1 See A. N. Whitehead, The Principles of Natural Knowledge (1919), chs. 8, 
 9, 10, 11 on extensive abstraction for a definition of points and instants which 
 correlates these entities with the perceived reality. 
 
310 SYMBOLISM AND TRUTH 
 
 the inadequacy of thought cannot rest on a contradiction be- 
 tween what is known without concepts and what is known in 
 concepts, for contradiction has meaning only where concepts 
 apply. Intuition could not contradict reason. When the cogni- 
 tive act is taken in its wholeness as the convergence of thought, 
 sensation, and intuition upon an object, this feeling of the inad- 
 equacy of thought to reality melts away. Though one is aware 
 that reality is not completely compressed into the molds of 
 reason, he still finds something in the real which fits these 
 molds. Reality exhibits logical form. 
 
 XI 
 
 That reality is logical in form means that the distinction be- 
 tween terms and the universals, that is, the qualities and rela- 
 tions, which modify and unite these terms, is a real distinction. 
 It means that there are basic terms, individuals, about which 
 qualities and relations cluster to form concrete facts. It means 
 that every object, whether individual or universal, is self-identi- 
 cal and distinct from other objects, and finally that these ob- 
 jects unite into wholes, groups, which are themselves real ob- 
 jects. 
 
 For Kant it is just this logical form which is created by 
 thought and which confines thought to a world of phenomena; 
 and for M. Bergson this logical form is the product of a platoniz- 
 ing intellect. But since the mind from the outset of knowledge 
 is in contact with the real, in knowing objects it must be able 
 to know that logical form is in reality and not merely in a mind 
 compelled to think in this fashion. This is the first and most 
 fundamental metaphysical insight. 
 
 Let us return to the vis sua nativa of the intellect of which 
 Spinoza speaks. If there is any knowledge, there is a metaphysi- 
 cal insight which upholds knowledge at every stage and which 
 becomes conscious of its own general intentions and, through 
 
 
 
 >? a oe 
 
THE METAPHYSICS OF KNOWLEDGE 311 
 
 these, of the general structure of reality, when knowledge is faced 
 with the question of its own validity. To know is, from the be- 
 ginning, to have an insight into the real. This power is not at- 
 tained after long meditation. It is not by falling into antinomies 
 and seeking a way out that thought is enabled finally to seize 
 reality; nor is it by dismembering the act of knowledge and at- 
 tempting to know through pure sensation, pure reason, or pure 
 intuition. This power is a crude and original endowment of the 
 mind. It is manifest in the simplest act of concrete knowing, not 
 as one component but as the very life of the act itself. To reflect 
 on knowledge, to ask how we can know and what we can know, 
 is to bring this original metaphysical insight to a consciousness 
 of itself. Instead of being aware of objects as fulfilling specific 
 intentions, as being of this or that sort, we become aware of ob- 
 jects as fulfilling the most general intentions of thought, and 
 thus we discover the logical structure of the reality to which our 
 thought is from the first adapted, and from which it is never cut 
 off. We cannot step outside the act of knowledge to an intuition 
 which renders all knowledge but itself invalid. 
 
 Knowledge from its inception embraces a reality which is 
 logical in form, without being aware of what constitutes logical 
 form. We do not pause to reflect that in knowing we are distin- 
 guishing terms from their qualities and relations, that we are 
 taking some terms as individual, that we are treating objects as 
 self-identical and distinct, though as united into real wholes. 
 But if we do pause to reflect, we know that only because objects 
 conform to these highly general conditions are they real. To 
 know that the widest intentions of thought are fulfilled by ob- 
 jects is to tighten rather than loosen the native grasp of the 
 mind on reality. In perceiving the logical framework of the real- 
 ity within which it operates, the mind knows its own power with 
 a new clarity. 
 
 That concrete knowing even of the most elementary sort is 
 
312 SYMBOLISM AND TRUTH 
 
 insight into the real, and that the act of knowing as a whole is 
 the source of this insight, are the basic propositions of a meta- 
 physics which justifies knowledge. These propositions do not 
 assert that all concrete knowledge is true. An object may not be 
 as it is known, it may be misconceived. But even a miscon- 
 ceived object zs, if it is known concretely; it is there to be reck- 
 oned with, to be fitted into the scheme of reality. The act of 
 knowledge, becoming conscious of itself, reveals the essential pat- 
 tern of this scheme, but it does not reach through more readily 
 to the details than it would without this self-consciousness. By 
 discovering that the general principles of knowledge are rooted 
 in the general structure of the real, we learn that a rational 
 truth is possible, but we do not establish specific truths. Spe- 
 cific truths must be hewn out laboriously from the materials of 
 experience by many cumulating acts of knowing. The details 
 must be fitted into the general pattern, and for this the skill 
 which grows with the expansion of knowledge is needed. 
 
 Thus in one direction knowledge is complete, it can take se- 
 cure hold of the form of the real; while in another direction it is 
 never complete, it is being continually enlarged and fortified by 
 new details. 
 
 Within the essential scheme of the real, there is room for an 
 infinite variety of detail. The form is in the detail; the variety of 
 detail, in the form. The metaphysical insight which makes use 
 of the complete cognitive act shows us how passing and tem- 
 porary objects embody universal principles and yet are them- 
 selves unique products of an ever-renewed process of becoming. 
 Reality is as changeful and growing as M. Bergson finds it to be, 
 but the change is an affirmation rather than a denial of logical 
 form. Against the newness, the individuality, of the thing of the 
 moment, the universal, which is neither new nor individual, 
 stands out. M. Bergson condemns analysis because it must “ex- 
 press a thing as a function of something other than itself” and 
 
THE METAPHYSICS OF KNOWLEDGE 313 
 
 so miss what is unique in the thing. One can condemn pure in- 
 tuition because, in refusing to express a thing as a function of 
 something other than itself, it misses what is not unique in the 
 thing — and so fails to know this very uniqueness as sharply as 
 might be if analysis were joined to intuition. 
 
 To the irrationalist, reality cannot be self-contradictory for 
 this reason, that it resists concepts — and contradiction is a logi- 
 cal relation between concepts; the term has no meaning for him 
 as applied to the real. The reality known through the fuller 
 metaphysical insight of which we are speaking is non-contra- 
 dictory in another sense; the principles of identity and contra- 
 diction can be truly affirmed of it. This reality can be consist- 
 ently presented and represented through concepts. And yet, if 
 we consider these principles themselves, it is plain that they 
 permit an endless mutability of the particular. As statements 
 about the real world they affirm that “any object is identical 
 with itself and distinct from other objects,” but they give us no 
 information as to what objects are self-identical and distinct. 
 They tell us merely that, however tangled the lines of identity 
 and distinctness may be, there must still be such lines. Con- 
 sistency has thus its metaphysical basis as a test of truth which 
 is valid even though no experience includes a reality which is 
 complete, full-grown, in every respect. Judgments can go on 
 correcting themselves by their consistency even though con- 
 sistency does not determine the subject-matter of any truth. 
 
 This infinite perfectibility of knowledge does not lead to the 
 corollary that there is no truth except through an infinite pro- 
 cess of correction. We know the logical form of reality without 
 such a process; logical form is a perfectly general aspect of the 
 real which can be grasped in finite knowledge. Yet it is only an 
 aspect. And if we can know one perfectly general aspect of real- 
 ity in finite knowledge, we can know others— provided there are 
 
 such aspects to be known. 
 
314 SYMBOLISM AND TRUTH 
 
 The laws of nature seem to hang midway between these 
 purely formal principles and particular truths. It is possible, as 
 C. S. Peirce, H. Poincare,’ and others have suggested, that 
 whole systems of natural law are superseded by other systems, 
 as one event in history is superseded by another, or old sets of 
 personal habits by new ones. But if the universe, from time to 
 time, gives up one general mode of behavior to adopt another, it 
 does not contradict itself. The particular events of history can 
 be truly known, so long as we do not insist that they are more 
 than particular events; and so a system of natural laws, which 
 might dissolve and pass, could be truly known if we did not be- 
 lieve it to be eternal — if we could see what went before and 
 came after. But just as every set of personal habits embodies the 
 laws of human psychology, so every one of a successive infinity 
 of cosmic habits would embody the psychology of the universe. 
 And even if the laws of this cosmic psychology were more con- 
 crete than the formal principles of structure we have discussed, 
 they could be known in perfect generality. 
 
 Whatever the whole of reality may be — if there be a whole— 
 we can be certain that we do not know this whole. A complete 
 understanding of any whole rests on a knowledge of its parts, 
 and a complete understanding of the parts on a knowledge of 
 the whole, but it does not follow that there are no truths which 
 are valid for the parts alone. Though the process of the growth, 
 the becoming, of reality may go on infinitely, and though it may 
 be impossible to know all there is (or will be) to be known con- 
 cerning any fragment of the real — unless it be in a mind which 
 spans this infinite process,— still these considerations do not 
 demonstrate the impossibility of attaining truth in a knowledge 
 which is immersed in the process of becoming. 
 
 1 C.S. Peirce, Chance, Love, and Logic (1923), ““The Doctrine of Necessity 
 Examined”; also, H. Poincare, La Valeur de la Science (1905), ch. 11, and 
 Derniéres Pensées (1913), ch. 1. 
 
THE METAPHYSICS OF KNOWLEDGE 315 
 
 XIV 
 
 No criticism of knowledge, then, can destroy knowledge; no 
 
 theory of appearances can prove that reality is unknown or un- 
 knowable. For a knowledge of even the most contradictory of 
 appearances is the beginning of an insight into the real. The 
 theory of knowledge clarifies this insight as one clarifies his 
 speech by learning the grammar of the language to which he is 
 born. But without speech we could not learn the rules of speech, 
 and without true knowledge we could not construct a theory of 
 truth. 
 _ At the poles of knowledge, beyond clear statement and ra- 
 tional proof or disproof, are scepticism and mysticism. The 
 sceptic believes nothing he can state; the mystic can state 
 nothing he believes. Rational knowledge shares with scepticism 
 a readiness to revise itself but refuses to join scepticism in re- 
 vising itself into a state of total incredulity. Something stands 
 firm, if it be no more than the good sense which Descartes found 
 “is of all things among men the most equally distributed.” With 
 the irrationalist and the mystic, rational knowledge shares the 
 conviction that reality cannot be completely packed into neat 
 concepts, but rational knowledge cannot believe that there is no 
 neatness in reality, that because something escapes nice formu- 
 lation, everything does. 
 
 Making use of all the instruments at its command — sensa- 
 tion, thought, intuition — knowledge can reflect on its own pro- 
 cesses and reaffirm, as against scepticism, mysticism, and ag- 
 nosticism, its own ability to take at least partial possession of 
 the real in a rational experience. But in order to know, it is not 
 necessary to inquire how it is possible to know. As the lungs are 
 prepared by nature for breathing, the hands for grasping, the 
 legs for walking, so the mind is prepared for knowing. We may 
 with infinite patience lay bare the anatomy of the mind, but we 
 
316 SYMBOLISM AND TRUTH 
 
 cannot in doing so discover that the mind’s function is to trick — 
 us or to shut us off from the real. The air the mind breathes, the 
 substance it grasps, the ground it walks on, is reality. The theory 
 of knowledge, like the knife of the surgeon, may be able to sepa- 
 rate the delicately woven tissues of thought, but it cannot give 
 or take away the power to know. 
 
 
 
SUPPLEMENTARY READINGS 
 
 Tars list of supplementary readings is not a bibliography; it is in- 
 tended to bring together for the use of the student some of the contem- 
 porary literature — chiefly in English — on the theory of knowledge, 
 and to suggest directions in which the topics treated in the text can 
 be expanded. It will be well for the reader to take up the selections 
 under each heading in the order given here; the readings most closely 
 allied to the text are placed first in each group. References to the 
 classical philosophers are omitted, except in a few instances. 
 
 INTRODUCTION 
 
 On the relation of the theory of knowledge to metaphysics: 
 C. D. Broad, Scientific Thought (1923), Introduction. 
 W. T. Marvin, The New Realism (1912), “The Emancipation of 
 Metaphysics from Epistemology.” 
 S. Alexander, Space, Time, and Deity (1920), Introduction. 
 
 Cuapter I, Meaninea 
 
 On the psychology of meaning: 
 
 E. B. Titchener, The Experimental Psychology of the Thought Process 
 (1909), Lect. 2, “‘Reference to Object as the Criterion of Mind,” 
 Lect. 5, “The Experimental Psychology of the Thought Process.” 
 
 E. Rignano, The Psychology of Reasoning (1923), ch. 4, “What is 
 Reasoning?” 
 
 K. Koffka, The Growth of Mind (1924), ch. 5, sec. 10, “The First Use 
 of Language.” 
 
 J. B. Watson, Psychology from the Standpoint of a Behaviorist (1919) 
 ch. 9, secs. A, B, “Explicit and Implicit Language Habits.” 
 
 G. F. Stout, Analytic Psychology (1896), bk. ii, ch. 10, “Thought 
 and Language.” 
 
 On the philosophy of meaning: 
 
 F. C. S. Schiller, B. Russell, H. H. Joachim, Mind, N. S. vol. 29 
 (1920), pp. 385 ff., “The Meaning of Meaning, a Symposium.” 
 
 R. F. A. Hoernlé, Mind, N. S. vol. 16 (1907), pp. 70 ff., “Image, 
 Idea, and Meaning.” 
 
 C. K. Ogden and I. A. Richards, The Meaning of Meaning (1923), 
 ch. 2, part 2, “Towards a Science of Symbolism,” ch. 9, “The 
 Meaning of Meaning,” ch. 10, “Symbol Situations.” 
 
 On mediate and immediate knowledge: 
 
 W. James, The Principles of Psychology (1890), vol. 1, ch. 8, “The 
 Relations of Minds to Other Things,” ch. 9, “The Stream of 
 Thought.” 
 
 317 
 
318 SUPPLEMENTARY READINGS 
 
 G. F. Stout, Analytic Psychology (1896), bk. i, ch. 2, ““The Analysis 
 of Presentations,” ch. 3, “The Apprehension of Form,” bk. ii, 
 ch. 5, ““Noetic Synthesis.” 
 
 J. Ward, Psychological Principles (1918), ch. 4, secs. 1, 2, “‘The 
 Presentational Continuum,” ch. 6, secs. 1, 2, 6, 7, “‘Perception,” 
 ch. 12, “Thought and Language.” 
 
 Cuapter II, Logica Form 
 
 On the structure of complexes: 
 B. Russell, Monist, vol. 28 (1918), pp. 509 ff., “The Philosophy of 
 Logical Atomism,” lect. 2. 
 L. Wittgenstein, Tractatus Logico-Philosophicus (1922), Introduction 
 (by B. Russell), Preface, and Text through prop. 4.04. 
 
 On identity and diversity: 
 G. E. Moore, Proceedings of the Aristotelian Society, vol. 1 (1900- 
 1901), pp. 103 ff., “Identity.” 
 
 Cuapter III, Universats AND INDIVIDUALS: ORDER 
 
 On universals and individuals: 
 
 J. Laird, A Study in Realism (1920), ch. 6, “‘ Principles.” 
 
 S. Alexander, Space, Time, and Deity (1920), vol. 1, bk. i, ch. 3, 
 “Universal, Particular, Individual,” ch. 4, “‘ Relation.” 
 
 B. Russell, Proceedings of the Aristotelian Society, vol. 12 (1911-1912), 
 pp. 1 ff., “On the Relations of Universals and Particulars.” 
 
 G. F. Stout, Proceedings of the British Academy (1921), “The Nature 
 of Universals and Propositions.” 
 
 W. E. Johnson, Logic (1921), Part I, ch. 11, ‘“‘The Determinable,” 
 ch. 12, ““The Relation of Identity,” ch. 13, “Relations or Transi- 
 tive Adjectives.” 
 
 On space, time, and objects: 
 
 C. D. Broad, Scientific Thought (1923), ch. 1, ‘The Traditional Con- 
 ception of Space and the Principle of Extensive Abstraction,” 
 ch. 2, “Time and Change.” 
 
 A. N. Whitehead, The Concept of Nature (1920), ch. 3, “Time,” ch. 5, 
 “Space and Motion,” ch. 7, “Objects”; also, The Principles of 
 Natural Knowledge (1919), Part II, ch. 6, “Events,” ch. .7, 
 “Objects.” 
 
 On abstraction: 
 G. Berkeley, The Principles of Human Knowledge (1710), Introduc- 
 tion. 
 A. N. Whitehead, The Principles of Natural Knowledge (1919), 
 Part II, chs. 8, 9, ‘Extensive Abstraction.” 
 
 On order: 
 B. Russell, The Principles of Mathematics (1903), ch. 9, “Relations.” 
 S. Alexander, Space, Time, and Deity (1920), vol. i, bk. i, ch. 5, 
 “Order.” 
 
 SS) eS a eel 
 
SUPPLEMENTARY READINGS 319 
 
 CuHapteR IV, Description AND ANALYSIS 
 
 On naming, description, and the variable: 
 
 B. Russell, The Problems of Philosophy, ch. 5, ‘Knowledge by Ac- 
 quaintance and Knowledge by Description,” ch. 9, “The World 
 of Universals”; also, The Principles of Mathematics (1903), 
 ch. 5, “On Denoting,” ch. 8, “The Variable’; and Mind, N. S., 
 vol. 15 (1905), pp. 479 ff., “On Denoting.” 
 
 B. Bosanquet, Logic (1888), vol. 1, Introduction. 
 
 A. N. Whitehead, An Introduction to Mathematics (1911), ch. 2, 
 “Variables,” ch. 5, “The Symbolism of Mathematics.” 
 
 On internal and external relations: 
 F. H. Bradley, Appearance and Reality (1893), ch. 2, “Substantive 
 and Adjective,” ch. 3, “Relation and Quality.” 
 G. E. Moore, Philosophical Studies (1922), ch. 9, ‘‘External and In- 
 ternal Relations.” 
 
 Cuapter V, TrutH anv Fatsity 
 
 On truth and falsity: 
 
 L. A. Reid, Knowledge and Truth (1923), omitting ch. 9 (for a gen- 
 eral survey of contemporary theories of truth). 
 
 S. Alexander, Space, Time, and Deity (1920), vol. 2, bk. iti, ch. 8, 
 “Tllusion and Ideas,” ch. 9, sec. B, “Truth and Error.” 
 
 F. H. Bradley, Essays on Truth and Reality (1914), ch. 5, “On Truth 
 and Copying,” ch. 9, “On Appearance, Error, and Contradic- 
 tion.” 
 
 H. H. Joachim, The Nature of Truth (1906), ch. 1, ““Truth as Corre- 
 spondence,”’ ch. 3, Part I, ‘““The Coherence Notion of Truth.” 
 
 On sensation and perception: 
 
 Plato, Theaetetus, Jowett’s translation. 
 
 J. Laird, A Study in Realism (1920), ch. 2, “The Things We Per- 
 ceive.” 
 
 R. F. A. Hoernlé, Studies in Contemporary Metaphysics (1920), 
 ch. 4, “On ‘Doubting the Reality of the World of Sense’,”’ ch. 5, 
 ***Saving the Appearances’ in the Physical World.” 
 
 W. James, The Principles of Psychology (1890), vol. 2, ch. 21, ‘The 
 Perception of Reality.” 
 
 B. Russell, Our Knowledge of the External World (1914), Lect. 3, 
 ‘The External World.” 
 
 C. D. Broad, Scientific Thought (1923), ch. 7, “‘Matter and its Ap- 
 pearances,”’ ch. 8, ““The Theory of Sensa.” 
 
 On the theory of “objectives”: 
 G. D. Hicks, Mind, N.5S., vol. 31 (1922), pp. 1 ff., “‘The Philosophical 
 Researches of Meinong.”’ 
 B. Russell, Mind, N. §., vol. 13 (1904), pp. 204 ff., 336 ff., 509 ff., 
 *Meinong’s Theory of Complexes and Assumptions.” 
 

 
 320 SUPPLEMENTARY READINGS 
 
 On belief: 
 D. Hume, A Treatise of Human Nature (1738), bk. i, Part ITI, secs. 7, 
 8, 10. 
 F. C.S. Schiller, Problems of Belief (1924), chs. 1, 3, 9, 10, 11, 12. 
 C. S. Peirce, Chance, Love, and Logic (1923), First Paper, “The 
 Fixation of Belief.” 
 
 CuapterR VI, NEGATION AND CONTRADICTION 
 
 Se . 
 
 On negation: 
 R. Demos, Mind, N. S., vol. 24 (1917), pp. 188 ff., “A Discussion of 
 a Certain Type of Negative Proposition.” 
 F. H. Bradley, The Principles of Logic (2d ed. 1922), vol. 1, bk. i, 
 ch. 3, “The Negative Judgment,” and Terminal Essay 6. 
 B. Bosanquet, Logic (1888), vol. 1, ch. 7, secs. 1, 2, 3, 5. 
 W. E. Johnson, Logic (1921), Part I, ch. 5, “Negation.” 
 H. Bergson, Creative Evolution (1911, transl. by A. Mitchell), ch. 4, 
 “The Idea of Nothing.” 
 On contradiction and the “‘laws of thought”: 
 F. C.S. Schiller, Formal Logic (1912), ch. 10, “The Laws of Thought.” 
 C. Sigwart, Logic (2d ed. 1895, transl.), vol. 1, ch. 4, “The Negation.” 
 
 ee a ee ee ee ee 
 
 Cuapter VII, Format DepuctTIion 
 
 On formal deduction in general: 
 
 J. W. Young, Fundamental Concepts of Algebra and Geometry (1911), 
 lects. 1, 4, 5, 19, 21. 
 
 A. N. Whitehead, A Treatise on Universal Algebra (1898), ch. 1, 
 “On the Nature of a Calculus.” 
 
 C. I. Lewis, A Survey of Symbolic Logic (1918), ch. 6, secs. 1, 3. 
 
 L. Couturat, La Logique de Leibniz (Paris, 1901), ch. 4, sec. 4 ff., 
 “La Caractéristique Universelle.”’ 
 
 On the Boolean Algebra: 
 
 E. V. Huntington, Transactions of the American Mathematical So- 
 ciety, vol. 5, no. 3 (1904), pp. 288 ff., “Sets of Independent Pos- 
 tulates for the Algebra of Logic.” 
 
 H. M. Sheffer, Transactions of the American Mathematical Society, 
 vol. 14, no. 4 (1913), pp. 481 ff., “A Set of Five Independent 
 Postulates for Boolean Algebra.” 
 
 > 
 
 sis 
 
 CuHapter VIII, Toe Merapnysics or KNowLEDGE 
 
 On appearance and reality: 
 
 F. H. Bradley, Appearance and Reality (1893), bk. xi, chs. 13, 14, 
 “The General Nature of Reality,” ch. 15, “‘Thought and Real- 
 ity,” ch. 27, “Ultimate Doubts.” 
 
 J. Ward, Naturalism and Agnosticism (1899), vol. i, Introduction, 
 vol. 2, Part IV, lects. 14, 15. 
 
 A. J. Balfour, A Defence of Philosophic Doubt (1879), ch. 1, “On the 
 Idea of a Philosophy,” ch. 6, “Transcendentalism,” ch. 13, 
 “Evolution of Belief.’ 
 
 Sg ee SR ee ee a ee a ee 
 
 
 
 Se 
 
SUPPLEMENTARY READINGS 321 
 
 On the relation of mind and its objects: 
 W. James, Essays in Radical Empiricism (1912), Essay 1, ‘Does 
 Consciousness Exist?” 
 S. Alexander, Space, Time, and Deity (1920), vol. 2, bk. iii, ch. 4, 
 “Mind and Knowing.” 
 R. B. Perry, Present Philosophical Tendencies (1912), Part V, ch. 13, 
 ““A Realistic Theory of Knowledge.” 
 
 On idealism and its critics: 
 
 R. F. A. Hoernlé, Idealism (1924), especially chs. 4, 5, “Idealism as 
 the Theory of the Absolute.” 
 
 J. Royce, The World and the Individual (1900), vol. 1, lects. 3, 4, 5, 
 6, 7, 8, 10 (an examination of realism, mysticism, Kantianism, 
 and absolute idealism). 
 
 T. H. Greene, Prolegomena to Ethics (1883), bk. i, ch. 1, “The Spirit- 
 ual Principle in Knowledge and in Nature,” ch. 2, “The Relation 
 of Man as Intelligence to the Spiritual Principle in Nature.” 
 
 R. B. Perry, Present Philosophical Tendencies (1912), Part III, ch. 6, 
 “The Cardinal Principle of Idealism,” ch. 7, “Objective or 
 Transcendental Idealism.” 
 
 On intuitionism: 
 
 H. Bergson, Creative Evolution (1911, transl. by A. Mitchell), In- 
 troduction, ch. 4, pp. 298 ff., “‘Form and Becoming’’; also An 
 Introduction to Metaphysics (1912, trans. by E. Hulme). 
 
 General reference: 
 C. D. Macintosh, The Problem of Knowledge (1915). 
 

 

 

 
INDEX 
 
 “A,”? 120, 121, 145. 
 
 Absolute, The, 175, 277, 285. 
 
 Absolute Idealism, 272, 273. 
 
 Abstract facts, 82, 106. 
 
 Abstract ideas, 85. 
 
 Abstract thought, 117. 
 
 Abstraction, 83-85, 88, 106. 
 
 Absurdity, 94, 95. 
 
 Acquaintance, 13, 38. 
 
 Action, versus thought, 28. 
 
 Active form, grammatical, 98. 
 
 Adjectives, 89 ff., 117. 
 
 Agnosticism, 268 ff., 278, 279. 
 
 Algebra, Boolean, 335 ff. 
 
 “All,” 140. 
 
 Ambiguity, 56; logical, 119 ff.; psy- 
 chological, 119, 120; of the nega- 
 tive, 198 ff., 219. 
 
 Ambiguous truth and falsity, 212 ff. 
 
 An,” 120, 121. 
 
 Analysis, 31, 47,54, 64, ch. iv (108 ff.), 
 126; original impulse to, 301, 302. 
 
 Analytic form, in scientific knowl- 
 edge, 133 ff. 
 
 Analytic judgments, 126 ff., 131, 147. 
 
 Analytical representation, 31. 
 
 Antinomies, Kantian, 169, 277. 
 
 Antirationalism, 169, 305 ff. 
 
 “Any,” 121, 122, 145. 
 
 Appearance, 150; and reality, 272 ff., 
 280. 
 
 A priori, The, 208, 219. 
 
 Aristotle, 44, 66, 84, 132, 173, 188, 
 267, 282 (note), 287. 
 
 Assertion, of descriptions, 145, 146. 
 
 Assertion, 179 ff., 184, 185; sign of, 
 185. 
 
 Association, 22. 
 
 Asymmetry, 96 ff. 
 
 Aufgabe, 17, 22. 
 
 Awareness, pure, 18, 20, 39, 43, 66, 
 157, 305 ff. 
 
 Bacon, F., 5, 7. 
 
 Behaviorism, theory of meaning, 
 25 ff. 
 
 Belief, 16, 24, 25, 29, 37, 149, 179 ff., 
 195; and inference 255 ff. 
 
 Bergson, H., 18, 89, 169, 289, 312, 
 313; theory of intuition, 308 ff. 
 
 Berkeley, 7, 21, 85, 162, 274, 284, 285, 
 288. 
 
 Boolean Algebra, 235 ff. 
 
 Bradley, F. H., 67, 89, 277. 
 
 Broad, C. D., 8. 
 
 Carroll, Lewis, 94, 118. 
 
 Case, grammatical distinctions of, 98. 
 
 Categories, 194; Kantian, 171; em- 
 pirical, 171; principles of identity 
 and contradiction as formal cate- 
 gories, 208. 
 
 Change, 69 ff., 77, 78, 105. 
 
 Classes, 140 ff.; infinite, 143; of one 
 member, 143; logic of, 243 ff. 
 
 Coherence theory of truth, 175 ff, 
 194. 
 
 Commutative law, 100, 247. 
 
 Comparison, 87. 
 
 Completely inferential systems, 259, 
 264. 
 
 Complexes, 30, 42 ff.; order of poly- 
 adic complexes, 98; meaning of, 
 154, 155. 
 
 Complex elements of unity, 103 ff., 
 107. 
 
 Complex objects, 35. 
 
 Complex symbols, 35 ff. 
 
 Conception, 17, 38. 
 
 Conceptual validity, distinguished 
 from truth, 218, 219. 
 
 Concrete facts, 82, 106. 
 
 Concrete thought, 282, 283. 
 
 Condensation of substitutions, 234. 
 
 Connoting, 111. 
 
 325 
 
326 
 
 Consistency, 168 ff., 194; as truth, 
 174; formal, 218, 223; as a real 
 category, 313. 
 
 Constants, functional, 252. 
 
 Construction of concepts, 156; con- 
 structs, 165. 
 
 Continuity, of mind and objects, 276, 
 293-295. 
 
 Contradiction, principle of, ch. vi 
 (205 ff.), 219, 226; as a formal 
 category, 208. 
 
 Copula, 185. 
 
 Correspondence, 42; of form, 52; of 
 symbols and objects, 60. 
 
 Correspondence theory of truth, 
 173 ff., 176 ff., 192. 
 
 Critical philosophy, 270 ff. 
 
 Data, 34; sense data, 14ff., 19, 
 160 ff.; reality of, 159 ff., 193. 
 
 Deduction, ch. vii (222 ff.), 261 ff. 
 
 Deductive systems, 92; conditions of 
 significance and truth in, 258 ff. 
 
 Definition, 32, 34, 58, 118, 146, 226, 
 236, 231%. 
 
 Demos, R., theory of negation, 198 ff., 
 219. 
 
 Denial, 185 ff.; bare, 215; privation 
 of ground, 216; positive denial, 
 216 ff. 
 
 Denoting, 109 ff. 
 
 Descartes, 70, 287, 315. 
 
 Description, 35, 74, ch. iv (108 ff.); 
 of universals, 122; form of, 112, 
 113, 145; assertion of, 145, 146. 
 
 Determinism, 68, 72. 
 
 ‘Determination is negation,”’ 205. 
 
 Dialectic, Kantian, 277, 278. 
 
 Disbelief, 185 ff., 196, 215. 
 
 Distinctness of meaning, as basis of 
 negation, 203 ff. 
 
 Diversity, numerical, 46, 59, 60; per- 
 ception of, 68; as a real category, 
 313 
 
 Dreams, 162 ff. 
 
 Dualism, epistemological, 274; Car- 
 tesian, 287, 288. 
 
 “*Each,” 143. 
 Empiricism, 165 ff. 
 
 INDEX 
 
 Equations of structure, 233, 236. 
 
 Equivalence, 58. 
 
 Equivocation, 56, 57, 64, 119. 
 
 Error, 16, 149, 163 ff., 172, 173, 191. 
 
 Essence, 66. 
 
 Euclidean space, 134 ff., 147. 
 
 “Every,” 143. 
 
 Excluded middle, 186, 208 ff., 219. 
 
 Existence, criteria of, 159 ff.; as a 
 predicate, 183; limited meaning of, 
 193. 
 
 External relations, 130. 
 
 Fact, 44 ff., 65; unity of, 78 ff.; con- 
 crete, 82; abstract, 82; syntax of, 
 91; negative, 197 ff., 219. 
 
 Falsity, 148, ch. v (149 ff.), 193, 197; 
 ambiguous falsity, 212 ff. 
 
 Fancy, 188. 
 
 First philosophy, 195. 
 
 Form, 37; of objects, 43; logical 
 form, ch. ii (41 ff.), 78 ff.; general 
 schematism of, 52; correspondence 
 of, 53; presentation of, 107; of 
 descriptions, 112, 113, 145; objec- 
 tivity of symbolic form, 156; iden- 
 tity of form in fact and symbol, 
 178; science of pure form, 222. 
 
 Function, 45. 
 
 Functional constants, 252. 
 
 Functional range, 249 ff. 
 
 Functional variability, 249 ff., 263. 
 
 Generalization, 116 ff. 
 
 Geometry, 134 ff.; Euclidean, 147, 
 222; non-Euclidean, 134f., 147,222. 
 
 Grammar, 37, 40; of symbolism,. 
 89 ff., 106. 
 
 Ground, of negation, 200, 204, 216 ff.; 
 privation of, 216. 
 
 Groups, symbolic, 35 ff., 40; defini- 
 tion of a group, 45 ff., 64; type of, 
 47, 48, 63; multiplicity of, 48, 63; 
 major members of, 48, 49; reflex- 
 ive, 61, 62; unity of, 78 ff. 
 
 Group meaning, 31 ff. 
 
 Habits, of meaning, 26; of language, 
 27. 
 Heracleitus, 309. 
 
 
 
INDEX 
 
 Hobbes, 22, 149, 179, 260. 
 
 Holt, E. B., 287 (note). 
 
 Hume, 7, 8, 59, 60, 162; theory of 
 belief, 180 ff.; scepticism, 189 ff.; 
 276, 291, 292. 
 
 Huntington, E. V., 228, 232, 233, 243. 
 
 Husserl, E., 8. 
 
 Idealism, 272, 273, 284 ff., 289. 
 
 Ideas, 9 ff., 38; abstract, 85; innate, 
 301. 
 
 Identity, 44, 46; statements of, 54; 
 principle of, 56-58, 64, 139, 206, 
 207, 226; of objects, 56, 59; of 
 indiscernibles, 71, 74; of univer- 
 sals, 76 ff.; of the variable, 118; of 
 meaning, 126 ff.; as a formal cate- 
 gory, 208; as a real category, 313. 
 
 Tllusion, 163, 164. 
 
 Images, 10 ff., 38, 94, 95, 153, 292. 
 
 Imagination, 35, 36, 73; syntax of, 
 93 ff.; constructive, 181; and rea- 
 son, 260, 261. 
 
 Immediate knowledge, 13 ff., 19, 38, 
 305 ff. 
 
 Implications, in formal systems, 233, 
 234, 251, 252. 
 
 Incompatibility, 200, 219. 
 
 Incomplete symbols, 108 ff., 124. 
 
 Incompletely inferential systems, 259, 
 260, 264. 
 
 Incredulity, 187 ff. 
 
 Indiscernibles, identity of, '71, 74. 
 
 Individuality, reality of, 306. 
 
 Individuals, ch. iii (66 ff.); determi- 
 nation of, by universals, 67 ff.; 
 principle of individuation, 70; 
 representation of, 71, 72; bare in- 
 dividuals, 129. 
 
 Induction, 168. 
 
 Anference, 223; general nature of, 
 255 ff., 263. 
 
 Inferential negation, 211. 
 
 Infinite classes, 143. 
 
 Infinite negative, 217. 
 
 Innate ideas, 301. 
 
 Insight, metaphysical, 272, 277, 279, 
 
 . 810 fi. 
 
 Intention, 29, 38, 39. 
 
 Internal relations, 130. 
 
 327 
 
 Interpretation, signs of, 120ff.; of 
 formal systems, 224 ff., 242 ff. 
 
 Intuition, 18 ff., 20, 43, 165, 279, 301, 
 305 fi. 
 
 Irrationalism, 305 ff. 
 
 V8 7185. 
 
 James, W., 15, 16, 22, 24, 165, 186; 
 theory of consciousness, 291. 
 
 Joachim, H. H., 175 ff. 
 
 Judgment, 179 ff.; synthetic, 126 ff.; 
 analytic, 126 ff.; inference as a 
 form of, 257. 
 
 Kant, 7, 81, 88, 131, 158, 167, 168, 
 169, 171, 182, 190, 208; agnosti- 
 cism, 270 ff., 290, 302, 310. 
 
 Knowing relation, 295, 296. 
 
 Kiilpe, O., 17 (note). 
 
 Language, 51, 81, 90; habits of, 27; 
 origin of, 33; syntax of, 93 ff., 102; 
 inference in, 259, 260. 
 
 Laws, 89, 147; of thought, 205 ff. 
 
 Leibniz, 71, 72, 74, 105; theory of 
 truth and deduction, 264, 265 
 (note), 306. 
 
 Locke, 7, 9, 10, 22, 30, 85, 127, 167, 
 176; agnosticism, 270ff., 293, 
 299, 300. 
 
 Logic, 5; formal logic, 201, 202, 222; 
 algebra of, 235 ff.; of classes, 
 248 ff. 
 
 Logical ambiguity, 119 ff. 
 
 Logical form, ch. ii (41 ff.); general 
 schematism of, 52; reality of, 
 304 ff. 
 
 Logical opposition, 201. 
 
 Major members, of symbolic groups, 
 48, 49. 
 
 Materialism, 288. 
 
 Matter, 66, 84. 
 
 Meaning, ch. i (9ff.), 21 ff.; psy- 
 chology of, 23 ff., 28, 29;  be- 
 havioristic theory of, 25 ff.; habits 
 of, 26; syntactical, 31, 35 ff., 39, 
 40; the non-existent, 35, 36; of 
 complexes, 154, 155; hypostatiza- 
 tion of, 158; in perception, 166... 
 
328 INDEX 
 
 Mediate knowledge, 13 ff., 38. 
 
 Meinong, A., 8, 152. 
 
 Memory, 291, 292, 295. 
 
 Metaphysical insight, 272, 277, 279, 
 310 ff. 
 
 Metaphysics, 5 ff., 150, 170, 191, 208; 
 of knowledge, ch. viii (266 ff.). 
 
 Mind-body, problem of, 287, 298. 
 
 Mind-isolation, in Locke and Kant, 
 Q73 ff. 
 
 Monism, epistemological, 276, 293. 
 
 Moore, G. E., 8, 76, 151-153. 
 
 Multiplicity, of groups, 48, 63. 
 
 Mysticism, 315. 
 
 Negation, ch. vi (197 ff.); negative 
 facts, 197 ff., 219; ambiguity of 
 negative, 198 ff., 219; as variable, 
 199; meaning of, 200; ground of, 
 200, 204, 216 ff.; defined through 
 truth, 209 ff.; negation and infer- 
 ence, 210 ff.; truth and falsity of 
 negatives, 212; purely conceptual 
 negation, 219; inferential nega- 
 tion, 219; double negation, 239, 
 240. 
 
 Negatives, 186. 
 
 Nominalism, 67, 86 ff., 106, 129. 
 
 Non-deductive systems, 91. 
 
 Non-Euclidean geometry, 134, 147. 
 
 Non-existent objects, 35, 36, 158; 
 reference to, 136 ff., 144, 159. 
 
 Nonsense, 93 ff., 106. 
 
 Null class, 243. 
 
 Number, 46. 
 
 Objectives, 152 ff. 
 
 Objective reference, 153 ff., 192. 
 
 Objectivity, of symbolic forms, 156; 
 criteria of, 159. 
 
 Objects, complex, 35; formal char- 
 acters of, 43 ff.; identity of, 59; 
 relational object, 97; non-existent, 
 objects, 35, 36, 158; perceptual 
 object, 161, 162, 164, 296 ff. 
 
 Occam’s razor, 237. 
 
 One and Many, The, 141. 
 
 Ontological argument, 158, 159, 182, 
 183. 
 
 Operations, 52, 79, 80; perception of, 
 
 88; criterion of, 244, 253 ff.; dis- 
 tinguished from relations, 263. 
 
 Opposition, logical, 201. 
 
 Order, 62, 95 ff., 106, 107; of poly- 
 adic complexes, 98; postulates for 
 serial order, 254, 255 (note). 
 
 Otherness, 203. 
 
 Parameters, 252. 
 
 Parmenides, 207. 
 
 Particularity, 83. 
 
 Passive form, grammatical, 98. 
 
 Peirce, C. S., 314. 
 
 Perception, 32, 34, 66, 133, 159 ff.; 
 of numerical diversity, 68; of uni- 
 versals, 75 ff.; of operations, 88; 
 of relations, 88. 
 
 Perceptual object, 161, 162, 296 ff.; 
 reality of, 164. 
 
 Physical objects, 296-298. 
 
 Plato, 36, 66, 81, 107, 189, 273. 
 
 Poincaré, H., 314. 
 
 Positive theory of knowledge, 6 ff., 
 86, 269. 
 
 Possibility, for knowledge, 92, 93, 
 106. 
 
 Post-Kantians, 273. 
 
 Postulate-sets, 227 ff. 
 
 Presentation, 13, 32, 33; of logical 
 forms, 107. 
 
 Presentational thought, 167, 168, 
 193. 
 
 Primary and secondary qualities, 
 299, 300. 
 
 Principia Mathematica, 51, 108, 114, 
 117, 118, 124, 136-141, 229, 230, 
 243, 256. : 
 
 Privacy, of objects, 229 (note). 
 
 Proper names, 47, 74, 108, 114, 123 ff., 
 129, 144, 146. 
 
 Proposition, 35, 111, 112, 146, 151; 
 definition of, 183, 184; asa tertium 
 quid, 151 ff.; simple symbols as 
 propositions, 183, 184. 
 
 Psychological ambiguity, 119, 120. 
 
 Psychology, of meaning, 23 ff., 28, 29. 
 
 Punctuation, 51. 
 
 Pure awareness, 18, 20, 39, 43, 66, 
 157, 305 ff. 
 
 Pythagoreans, 46. 
 
 2 a 
 
 ee a ee SO ee ee ee oe 
 
 a 
 
 
 
INDEX 
 
 Qualities, 52,79; distinguished from 
 relations, 80 (note); primary and 
 secondary, 299, 300. 
 
 Rationalism, 169, 315. 
 
 Realism, 67, 286, 288, 289. 
 
 Reality, 150; of perceptual objects, 
 164 ff.; limited concept of, 170, 
 193; definition of, 286, 287. 
 
 Recurrence, of symbols, 55 ff. 
 
 Referent, of relations, 98 ff. 
 
 Reflexive expressions, 61, 62, 230, 
 wale 
 
 Reflexive relations, 80. 
 
 Reid, T., 16, 161. 
 
 Relations, 45, 52, 79, 80, 100 ff.; 
 reflexive, 80; perception of, 88; 
 triadic, dyadic, monadic, 104; ex- 
 ternality of, 130; internality of, 
 130; distinguished from operations, 
 245, 253 ff. 
 
 Relativism, 189. 
 
 Relatum, 98 ff. 
 
 Representation, analytical, 31; scale 
 of, 47. 
 
 Round-square, The, 136 ff. 
 
 Royce, J., 292. 
 
 Russell, B., 8, 51, 100; theory of 
 descriptions, 108 ff., 124 ff., 136, 
 145, 161, 175; theory of negation, 
 197 ff., 221, 291. 
 
 Scepticism, 166, 187 ff., 268-270. 
 
 Schopenhauer, 164, 165 (note). 
 
 Scientific knowledge, 133 ff. 
 
 Scientific method, as hypothetical, 
 270. 
 
 Sensation, 281-283, 307. 
 
 Sensationalism, 164 ff. 
 
 Sense data, 14 ff., 19, 160 ff. 
 
 Serial order, postulates for, 254, 
 255 (note). 
 
 Sheffer, H. M., 201, 202. 
 
 Signs, of syntax, 51, 65, 225; of in- 
 terpretation, 120 ff. 
 
 Simple symbols, 31 ff., 39, 64, 154; 
 form of, 47; as propositions, 183, 
 184. 
 
 Simplicity, 202. 
 
 *““Some,”’ 121, 122, 145. 
 
 329 
 
 Sophists, The, 189. 
 
 Space, 69 ff., 105; Euclidean, 134 ff. 
 
 Speech, 149. 
 
 Spencer, H., 268. 
 
 Spinoza, 273, 277, 289, 291, 310; on 
 agnosticism, 272. 
 
 Spiritualism, 289. 
 
 Structure, symbolic, 41 ff.; of real- 
 ity, 304 ff. 
 
 Subject, of relations, 97. 
 
 Subsistent entities, 151 ff. 
 
 Substance, 44, 128; and quality, in 
 Locke, 274. 
 
 Substantives, 89 ff., 117. 
 
 Substitution, 27; deductive, 224, 
 226, 227, 228 ff.; completeness of, 
 230, 231; interpretation of rules 
 of, 250 ff. 
 
 Subsumption, of classes, 240 ff., 247. 
 
 Sufficient reason, 72, 74. 
 
 Symbol, general nature of, 21. 
 
 Symbolic groups, 35 ff., 40. 
 
 Symbolism, general principles of, 225. 
 
 Symmetry, 99 ff. 
 
 Syntactical meaning, 31, 35 ff., 37, 
 39, 40. 
 
 Syntax, 40, 41, 106; rules of, 41; 
 plans of, 91; of fact, 91; of the 
 imagination, 93 ff.; of language, 
 93 ff., 102; signs of, 51, 65, 225; 
 in formal systems, 224 ff. 
 
 Synthetic judgments, 126 ff., 147. 
 
 Tabula rasa, 34, 38, 167, 283. 
 
 Tautologous symbols, 48, 55 ff., 62, 
 63. 
 
 Terms, 82 ff., 105. 
 
 Tests of truth, 174ff., 190, 191, 
 194. 
 
 “The,” 120, 145. 
 
 Theory, 172, 173. 
 
 Thing-in-itself, 167, 168, 275, 278. 
 
 Thought, 29, 30, 281-283; and 
 action, 28; abstract, 117; presen- 
 tational, 167, 168, 193; laws of, 
 205 ff.; as symbolic manipulation, 
 260, 261. 
 
 Time, 69 ff., 105. 
 
 Totality, as defining concept of 
 classes, 141 ff. 
 
330 
 
 Truth, 91, 92, 148, ch. v (149 ff.); as 
 
 » conceivability, 174 ff.; as con- 
 
 sistency, 174; as correspondence, 
 173, 176 ff., 192; coherence theory 
 of, 175 ff.; tests of, 174 ff., 190, 
 191; value of, 181; ambiguous 
 truth, 212 ff. 
 
 Type, of symbolic groups, 47, 48, 63. 
 
 Understanding, 25, 29. 
 
 Unity, of groups, 78 ff.; of facts, 
 78 ff., 88; elements of, 52, 53, 65, 
 104; complex elements of, 103 ff.; 
 symbols of, 89ff.; of mind and 
 objects, 294 ff. 
 
 Universals, ch. iii (66 ff.); percep- 
 tion of, 75 ff.; identity of, 76 ff.; 
 
 INDEX 
 
 reality of, 85 ff.; descriptions of, 
 122; as object of thought-activity, 
 303. 
 
 Universal class, 243. 
 
 Validity, conceptual, 223. 
 
 Variables, 73, 114 ff., 146, 223; iden- 
 tity of, 118; negative as a variable, 
 119 ff.; functional variables dis- 
 tinguished from interpretational, 
 249 ff.; functional, 263. 
 
 Watson, J. B., 27. 
 
 Whitehead, A.N., 8, 20, 52, 150, 
 289 (note), 293. 
 
 Whitman, Walt, 226. 
 
 Willis, G., 33. 
 

 
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