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This institution reserves the right to refuse to accept a copy order if, in its judgement, fulfillment of the order would involve violation of the copyright law. AUTHOR: STINSON, JOHN H. TITLE: ORGANON OF SCIENCE PLACE: EUREKA, CALIF DA TE : 1879 COLUMBIA UNIVERSITY LIBRARIES PRESERVATION DEPARTMENT t BIBLIOGRA PHIC MTCRnFORM TARHFT Master Negative # Restrictions on Use: Original Material as Filmed - Existing Bibliographic Record 108 Z3 V.2 Stinson, John Harrison. 1330- isoo . Orgaiioii of science. Three books in one volume, by Jolin Ilarnson Stinson ... Eureka, Cal., W. Ayres, printer, 18/9. - *^ ' 115, 35, 43 p. diagrs. I7i'"^.in 25f, en. Voli:no of panphlct'j. I. Philosophy— Miscellanea. 11-24661 Library of Congress Copyright 1871 : 6466 (• I BD701.S8 ^t TECHNICAL MICROFORM DATA FILM SIZE: li>^^^_ REDUCTION RATIO- /^X IMAGE PLACEMENT: lA /1ia7 IB IIB kauu. ^Ct.. 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K Philosopliy and theinlt-IIectual sciences like statues/' sa3^ri Bacon, (I are ndorncd and ceUbraled, bnt are nol made to advance; nay, they are frequently vi«;:(>n)us in the hand* of their author, and thencefor nmark of Bacon's is iitferaliv true of Locic; which ward tlegenerate." This BUj^iiest t«) tiie reader that diss of studies at the present ( related than any rMher to the suhjfvt matter of thi^ hook. And in altmipt word Mill piobnbly ime more nearly to explain somethinj^ new and unknr>wn to the read int; er, we are frerjueully- ohliged to make ourselves undjTstood hy rcferjuce to somelhinc already' known, [n our introdrction of tjie reader to the explanations and substances of the science which we have endeavored to exhibit in the subsequent oaj^es, therefore, we W( uld ask and expect that he has some knowledsrcof il»e stand- ard works upon logic, among which that of Arehbislu p Whateir is as able a specimen ut in making iiderenees from trull IS know'n to trutl.9 unko.wn, the mind does not proceeil upon the principles "set forth in the Aristotelian method., and therefore these methods arc ol no value to science. In the language of Bacon "They force assent not things. AUhough the dialects of Aristotle have been before the world tor many cen- turies yet no one, however well acquainted with the system, has advanced to one n;w truth in science by the method therein laid down. And , logic is not a peculiar method of reasoning, but tub method upon which all true re.son.n.' proceeds, as contended by Whaley and others, then the grea advance wliich has been made in the sciences must have been mn»le without reasoning at all, or else the method of reasoning is not shell as it has becu stalctl and explained by those authors. But although the popular systems of logic are of no value in assisting to lav the foundations, or to rear the superstructure of the physical, abstract or mental sciences, yet for the purposes of adorning and giving force to speech •they are not without value. Archbishop Whately regards rhet-ric as the off- shoot from logic ; in our estimation all that is valuable in the popular systems of logic belongs more properly to rhetoric than to any other science It is °rue that whenever we reason i.e. we make inferences from truths known to truths unknown certain processes take place in the mind, and that these processes are alike in the minds of all men who re,«on correctly. It is also true that the popular systems of logic explain with tolerable c.rrectness the manner of word.n- our premis.- and conclu..ioDs in what is called ratiocination. And to go even thus far is an acquisition of no small value. But it is somewhat stranc^e that writers on logic, of the most brilliant talents, who so requently warn°us against the liability of being imposed upon by w .rds, should ye never have penetrated beneath the words to the things that hav. bronght aLut these words with their manner of usage. Words are used in every science- but no science constructed upon word.can touch the limits of things ment'al or physical nature. The processes of the mind in reasoning eave ,o sensible trace behind them; words do not stand as sensible signs of l.ese ;;.cesscs. The mind by its pr„cesses forms words but the P''--- '^;- selvcs are at the bottom, and they lie deeper than the words. • A pr»p..s.- U< . " says Whately, " is defined logically a sentence in.Ucat.ve .. e afflrming o deny ng; (this exclu.les commands and questions) sentenck being the genus and ND.CAT.VE the difference, this definition expresses the whole tZce- and it relates entirely to the words of a proposition." Any one can e^"vs ethat the above definition is grounded entirely upon gram.natical dtilctions, and as s.at..d by Whately, "It relates ent(My to the words of a '"'"'"' T,', make a scientific analysis and explain the processes of the mind in rensonin" require a difteren. treatment and mode of investigation rom that X"o pursued by writers upon Ugic. -And we may in truth say that in the pagea of this book, we have pursued a method, in the greater part, unattemp- ted heretofore. And certainly tlie exigencies ot the world demand a better^ philosophy of reasoning than writers heretofore have given. If we look about us in our own country, or travel abroad and observe the various opin- ions concerning the most common aflairs and effects, and notice the zeal with which men pursue the most absurd theories, we will conclude with the great English philosopher, that "the specious meditations, speculations and theories of mankind, are but a kind of insanity, only there is no one to stand by and observe it." It is true thai m.idmen may agree pretty well on many points and the grave digger in the play thought that Hamlet's madness would not be noticed in England among a people as mad as himself. And notwithstand- ing the advancement which kas been made in the arts, and many of the sciences during the present century, men yet are driven about in their opin- ions as though there was no certain truth to be obtained, or else they pursue some absurdity as though error and truth both were in effect the same thing. And from these sources of trouble, which set men to travel the wrong road to happiness and true progress, there is no escape for mankind except in the further development of the sciences. But in the words of Bacon, "The pres- ent systems of logic are useless for the discovery of the sciences," and "they rather assist in confirming and rendering inveterate the errors founded on vulgar notions than in searching after truth." "The unassisted hand," however, "and the understanding left to itself posesses but little power. Effects are produced by the means of instruments and helps, which the understanding requires no less than the hand." And. in looking after helps for the understanding, we would naturally inquire by what means any one, who had madedisco^^eries in science, had been assisted in his efforts. If any one should see a mathematician calculate the distance to a certain object, or tell the highl of a tree without measuring it. and he find the result to be as the mathematician had stated, he would very naturally inquire how such knowledge could be obtained; by what means could such conclusions be reached. And every one knows that the science of mathe- matics is a most i>owerful instrument for solving those problems ©f nature wliich come within its province. But tlie science of mathematics itself has been discovered and its truths have been brought to light by certain processes of the ind And those processes of the mind, which have brought to light some truths in any given case, will, if exercised again in like manner, bring to light other truths of a like nature. The mind cerlamly possesses the power to gain knowle(lge by some method, and were this method certainly known and cl«arly explained, it could be used to advance «ir knowledge in science, unless all the subjects to which it is applicable are exhausted. But the greater number of the sciences are confessedly yet in their infancy, and the progress, which is made in them^ecms to proceed in most instances 8 rather bv nhance Ihan bv any direction wbirh plnN-.^plior^ have ur/en. Tbe scbool-boy al the pifsent day stiulies his loi^ic; but tl-e man who goos forlh in the ficarch ot truth, throws it away expecting no hrlp from it. Thos« men who have advanced science the most, have paid but liltle r«gaj-d to those phib)Hlphers who have treated of tiie science of reasoning; whde those viho have bH)ked and relieil r.pon help and din ction fn>m such philoaophns, have produced nulhini; of importance. Nn person, who has n»anU' discoveries iQ^^cuDce will, up«m reviewinu: his experience, acknowlHge either Ihat his mtndbaa'beenUdlou»e habilually the mode of reasonin- alwjiyi to be adopted or that this mode was »uig.slwd to him in ^ivtn enses by his previous studie««of the theorHriral systems of reasoning used in the scho(ds. Most per^oD^ indeed, who have advanced science, have been so inleul upon their concbiMon?; Ihat, they have not coisidered the processes of Iheir mmd. ustd in n^ainimr those conclusions to be w(»rthy of ctmsideralion. ~ Ibit if ihc true processes of rea.^onini; were underttoou.t of any truth which can be -aincd by reasooing, \That method we mua pur- Mio in order to gain thai truth : a..d if the s^llo-ism as explained by ihe urilers upon ioirir- be (he mtlhod <.f all true reasoning, then we must lind a msior and min.M- premises which w ill lead us to the trnih in quMition. Uut a-ccudin- to all the author^ up.)n logic, when we lay down our major pi emise Avevirtuallv assert the conclusion; and hence we must virtually gam the knowled-eot the etter underslank is mU only in it.self n vnydilbcult one, |> t Jhal U.ep.'|tnlic'e.^ "^- l^acon's attempt to m.rodu c the inductivrsysturnVf philosoj.hv has chartd away In some measure llie preju- dices of m inv in favor of thL- Ari^torcde iii m •l!i.> 1 ^. Uat 15 icu;i did not per- fect the mducfivf .vsftiif, and al:h..n-h he hi. Ufi lerc and there very rA' y^uhhk Mntson the olhei* processes of the mind, yfet l\fe'4^^ t *s^'stfe^a^|e th#lti^ itid of thetroe princlpleJs of rtt!ocltta;ti^ii he iip^fekri^'^'lriffe }iid' no bWter eonceptlon* thftn Ariistottle knel hl^.follOT^^fi, ^dr the tttist ' fa^t, * tfeerefote^ i-eadtrs who have tomiied any opiiilbtt tpon stTjli iji^tt^^a; wijt, besides^the difficulties of the subject, hitte to o^ftWne prejudice's in their ' study of this book. A careful study we believe, however, will conquer thoss prejudices. Before proceeding to the details of a treatise it is usual with writers to give some definition of the science which they claim to teach in their work, and we will probably be expected to do the same. Some writers have defined Logic to be the art of thinking; others call it the science and also the art of reasoning; and still others consider it to be the science of the laws of thought as thought. For ourselves we do not expect that any definition of Algebra, which can t>e framed, will assist the student of that science very much in his studies, tfnd therefore, a definition of that or of this science at the outset we ^ do not consider of importance. But besides this we do not wish by a defini- tion to put a band around the inquirers thoughts in the beginning. If a definition convey wrong impressions, it must fetter the mind in its contempla- tions ; and to lead a reader who has not yet studied the science, bj a defini- tion to understand the whole drift of \he matter would require a full exposi- tion of the definition, i. e. a full treatise upon the de^nition. We may say, however, that the present .treatise is a scientific work, and that the science, whoso principles are herein set forth, difiiers from all other sciences in the respect that it shows the only keys which can be used in unlocking the mynteries of any science. And hence, in general language, this work may be called the philosophy of science. In the title page we have denominated it the Organon of Science — not either from honor or derision of Axistottle's Organon ; but because in it we propose to show the instrument or instruments by which sciences are constructed. Bacon called his w*rk the **Novum Organ um," and since hi^time several works bearing that name have appeared, all of which, so far as we know, follow Aristottle rather than Bacon. The word logic has so many vague meanings in the iLinds of men at the present day that we have used that word but little in this treatise; although our aim and the aim of most writers upon logic are so far the same that they both propose to lay down gome method by which we may be guided and kept from errors. We, however, go much further and assert that our method exhibits the mental foundations of all the fciences and the modes of their construction; and that by the judicious application of our method, whether the thinkers were or shall be conscious of it or not, discoveries in any science always have been made, and always must be made, if made at all. Nor do we believe that we are endeavoring to excite vain hopes when we say that, the thorough understanding of this treatise by the scientific men of the world 10 • c«n not fail to open to th% world a more prosperous era f«r science than it has had hitlycrto. And therefore we have the boldness to call upon scientific men and upon all me A, who wish for the prosperity and adyancement of the human race, to glTe their serious ittention to it, so that ictelli^nce maj work out order and 'happiness^ our civilization. • book: I. CHAPTER I. Highest Generalization anb Fiest Division^. In erery endearor to prosecute science, we start by dividing off and classifying those entities, which are familiar to us, and which are to^he the subjects of our consideration. One class of philosophers, for the purposes which they have in yiew. divide the objects of earth into the animal, vegetable and mineral kingdoms ; and under each of these classes they make numerous subclassifications. The natural philosopher, techpically so called, whose object is to ascertain the effects of material masses upon each other the laws which govern them, and the changes which they undergo without* affecting their internal constitutions, commences by classifying matter into solid' fluids and gasses. The astronomer, the chemist, the philologist and historian' have each of them their subjects, objects and classifications. And the necessity of a proper classification, in order to reduce any subject to a science, will readily be perceived from the following consideration: Suppose a cer- tain ^eld to contain several specimens of each of the classes of animals and t^i^T^ ^f'°'' ^"^ *°^'' '^ for the purpose of acquiring knowledge,. if his mind should not generalize and classify, though he might multiply observa- tions fer half a life time, he must leave the field eventually without havinc gained any scientific knowledge. In order to succeed, therefore, the naturalist commences to classify ; and his field of 9bservation.being.animaie nature, he seeks for the highest generalization, which his mind can make, and which may embrace in one class, all the objects of his regard. Each subject before him, he perceives, has something in common- with every other one to-wit anmiation: and to tlus highest generalization, he gives the name of 'animal* to distinguish his whole field of research from other things. He then seeks X.. MM 13 . ' tor other less extensive generalizations, and soon perceives vertcbrata, articn- lata radiata and molusca. Tlius tlie naturalist proceeds, and by classification alon. he is able to gain a scientific knowledge of the relations existing among animals. In like manner a proper classification of those things about which the laws of mind ari concerned in reasoning, is indispensable to the clear understanding of the process employed in acquiring knowledge by reason ins ■ without a classification as a basis, all before us will be chaos. But how shall the metaphysician and logician classify ? The object, at which he must aim, is to obtain the knowledge of the relations, or rather the knowledge of the results of relation. actuaUy existing between the mind iwelf and all other things, which can b« made by the mind the subjects of its cognitions. Now every subject of the mind's cognitions must bear some relation to the mind itself or no result whatever could be produced. And in order to contradistinguish the objecU between which the relations exist, from which intellectual results are .volvedi the mind itself may be called the ego and all other things the h6n-eck). The *ord son-ego, however, in this cas. is not.a negative term in nwaaing, but a positive name for any and eveirything excepting the ego, .r mind itself. Th. German metachsicians distinguishthe mind iUielf by "Das Ich," and the French by '•!>«''•": ^^JJ' J^m. Hamilton has brought the ego and non-ego into vogrfe in the English Nom- enclature. Most persons will know that eoo is the Latin personal pronmin corresponding to ourV"onal pronoun I of the first person ; ego s more con- venient to be used as a noun than our pronoun I, a single Ictfcr of ^e ^Ipbabet and therefor, it is used. And we consider these contradistmgulshlng term, to be apt and Oseful ; for, betwe«n the ego and the non-ego. we »™ »» """^ »' the relations and results in question. But yet, how shall weclassHy the object, of our cognitions in a manner which will evolveand clearly set before us these reteUons lud their results. We cannot ctearly set before us these relations by a classification of the various objects comprehended in thenon-ego, according to some-peculiarities existing inter se, for this does not in a sufflcienUy appar- ent manner, involve theego: and unless both the eg, and """-^^ '"^"^J*? there can be no relations existing between them, and no results can be PrOdiCed rbeclassifiction necessary, as a basis of reasoning, ">««/ '^of"'^: """!''* the highest generalization; for to plunge -in medias.res,' and class, y cert^a objects, as plantigrade, and others as degitjgrade, only points out the Com- parative anatomy and r.lations of these objects inter se; and to cl»»lfy ^he faculUes of the mind into memory, wni,imagimition, etc., only brings ou he relations existing between these faculties. The mind itself, or ego. is not n- volved in th. classification; and consequently the results, springmfc from he relations of all other things to ttie mind itself, with their.connectloDs on the one hand with the ego. and on the other with the non-ego. can^not be appre- cial«l without finding a generalization, which shall comprehend tlM;m all. "ORq inttBt, tfcerelore, «<«k'llie lij^*st jjencrahiatidn of bolt tLc ego' ahd poij- ego that can 1m made^mnd ti^iafi: this for our atartihg point, descend/drnde :add dasBify, in a manner tery similar to tUat pursued by the naturalist _- Now the highest generalization that ourtnind can make 9f both the ego and non-^go is sxibtbkcb. Exi^t^nce is 'a term that m^y with propriety be applied to-iny and ererything of >rhich we can have any knowledge;, f^aefa and eatery #hade of thought and feeling, the aCtiT* prfnctjole itiitlf or^ (fl|^; asalier, tipace, time Itnd the Deity, ibay each of theih, be called an exist- ■tnce; tl^at whioH dan be.^nd is, is txk iaxistence: ^^ tiits is flie h^hest -generalization wlMch w% can make Of things; it ihcludes tlie ego and ajlpf 'the non-^go, the mind itseif and ererything else, of whicli we can hay^ cogni- tions. Now the results about Which We are concerned for logical purposes, are evolved ft'ofn ftie relations between one existe^icl, our iniihd itself, and all f ther •exiifencea. The first ditision, therefore, ai e^fstence^ In order to keep i^^ re- lations of the fhind to olfhet things in View, mtist beinto the ego and npn^go ; . thaKB are the two clashes of things from whos^ retatiohi our intellectual results are produced: l*he hf^hest generalization itself of all thiuj^s iXtoixX wlilich m» can hare any knowledge, can not, indeed, be ]ifoperly cebsidei^ a class of THiNOs; fur, the term ExisTENCfi dots- not distinguish things inter se, but it merely distinguishes, as it were, things frOm nre siicb, things as notions, thoughts, conceptions, feelidgs, meiiuhs, etc., and although these ar^ ratimately connected wfth the ejg^o * lidd could not exist without it, yet, tj|^y are not the ihlnd itself, 6ut they are of the msTn-ego. 'there is a wiile differ- ence '^tWeen ttie thought^, feeling etc., produced, and the active prin^cipley let itb6 What4rm«y, which is ehgaged, in some manner in their productioj^ Matoyof the t&oii^hts of Shakespeare caii be fodnd inal>ook: the activ^ principle, his mind itself, can not be foUbh on pap^rj his work^ are tbe pr<>7 ducttons of hi« niind, not lili mind itselfl But agaia, ifie believe pujr pwa min^lg' to exist, and that oflhier men have minds. NoW luy mind is to a^ tb^ egb, but all other ipinds in reference to my mind belong to the npn-ego; for every portion must make* his DWh n^ind idode the point from wlxich and \jf^ whieh^ie' mnst%iak« all his beariogs^ in gainihg^kno wledge. But agaip mfe belicre that there Is apace, ti lie, eternity and that there is a God; and'i^i 14 these things are non-ego; my mind ilself only for me and year mind only for you are the ego; all other things belong to tCi non-ego. Now for further clas^fications, we have to deal onljr with theoon ego: for th« ego being a single ejcistence is incapable ot diVisjon and subclassifi- cation ; but the non-ego is capable of division i^ infinitum, and therefore, •wie may n ake numerous subclassifications of it The non-ego, hQwerer, must always be subclassified with reference to the ego and not jnerely with reference to the constituents of the noDr-ego inter se.. The ego and non-ego merge in existence and this must be borne in mind ; jfor, ipb^teyer Relations, if any, may exist between the earlh and thennoon, they n^ver could be any- thing to us unless each of these objects sustain some relation or relations to the ego. my mind for me and your mind for you. That which bears na re- lation to the ego can not be the subject of our cognitions and H must be to us as though it had no existence; it is only by means of the relations of objects to &ur minds that we can gain any knowledge of the relations existing be- tween the objects themselves. In our classifications, therefore, it is impor - tant to keep in view and take .the ego, my mind for me and your mind for you, as the point from whioh to/un to every object of the non-ego. • CHAPTER II. « Tacts and Truths. Having in the previous chapter divided existences into two clasjes in such manher tliat the relations between them will always involve the mind as one of the things related, we come "how to the classification of the non- ego with reference to the ego. Anfl a. very obvious diiisioi of the oon-ego with referenc6 tathe ego weuid be into existences o^ the pas*, of the present and ot the future. Most of. us, no doubt, have had /riends whose phj sical forms have piasscd away ; their forms were existences in the past, bnt in the present they do not exist; apd to-morrow is but a present themght concern- ng the future. But we must observe that, these divisions onlj^ bring out the relations between points of time, in one of whlob points the ego is now situated ; nevertheless, as the ego and non-ego are existences bearing towards each other th^ relations of time, these divisions, according to the po4Bt«»of time occupied by each, do bring to view the relations between the ego occu- pying the present pointy and those existences of the non-ego occupying the same and ^Jifferent points. But all the existences comprehended in the non-ego may be thrown into another claisificationi which shall inyolve the relations existing between the ego and non-efo in other respects than thatt^f time and of that as well. ^ ^ » \ * The first sub-classification, therefore, of ' the existences ot the non -ego, which we will make, will be into pacts and truths. And in-order tbat we may understand this division, it is necessary t« consider the relations of the 15 ego merely as an existence anu)ng. other existences. That which has had a beginning, must have been brought icto existence by some anterior existence or existences. We will not stop to argue this point now, for we da not think it will be doubUd. And if our minds have not always existed, their very beginnings of existence must be dependencies; and dependent existences come and remain as existences by the influence of that up6n which they depend. And when olher existences like itself with respect to dependence, •urround the ego, the ego and these ether existences must be so related to each other that they may act and re act Upon each other, if each be affected hj the other: and each is either affected by the other directly or indirectly or the one only is effected by the other, oi; neither the one dt)r the other is aftecied by the circumstance of their both being existences. Kow between material objecU, it is declared to be a Hiniversal law of nature, that action and re^ctioh are always equal and' in opposite directions. Whether this law be extended to the relations between mind and mind, and between mind and matter, it is not necessary now for us to inquire. But of one thing we must feel assured, that the external nop-ego, when its existence is the immediate subject of our cognitions, acts directly or indirecily on the ego. For a tree either acts upon and affects the mind, or to change the expression, the mind is affected hy it in some manner, or the mind can have no cognitions of the existence of a tree, and it would be to Uie mind as though it were not The mind had a beginning and therefore it is a dependent existence; and an existence, whose coming to be an ezistence is dependent, must ab initio be passive: and its activity and pasivity both, must hare been eittter given to it Bimultaneously, or the former must have been developed from (he later. For the acting power of a dependent existence can not exist of itself ind^ndent of other things, but another or other existences are presupposed to generate it. And if the ego be dependent, iu dependence must be upon the external non-ego, otherwise it would be independent; and dependence implies the reception of action. The dependent mind, therefore, is dependent fgr its existence upon the action of that part of the non-ego, from which its exis- tence came, and for its knowledge upon the action ot that part Of the external nen-ego, of whose existence it gains knowledge. Now at the first with respect to knowled^, other existences act niion the mind without its inherent energy being exerted. That we are bom with- out any knowledge, will not be doubted by anyiwell informed student since the days of Locke. The mind must exist for a ceruin period in its incepiion without consciousness: for to be conscious at all, it mi^t be conscious of something: to be conscious of noUiing is to be without consciousness •* if consciousness can be contained m mere pasivity then a rock can be cmiieiout But activity is necesssary to consciousness: and mental activity musl be de- veiopea from the mind's passivity by the*action of that part of the non-ego ^^ 16 upon which the mind'« depeudtpce in this respect cougisU. For the power lo re^ ceTve an action mu^t Xje contegiporaneou* with the mind'* existence : .but the mind must exist in the world before it can be acted upon by Any power, other than that Which created its being before it was really a mind. When, therefore, the ego first coines into the relations of that part of the non-eg«, from which lU existence was not derived, It must first be acted «pon aid act in resi^nse •before it can be conscious of that part of the non-egoi And when ^e reflect that the external non-ego afects the. mind only through the gensei, and that in the foetal state, all these senses, even that of touch in « great measure at least, are securea against external impressions, we can not doubt that tlii mind at first is^nconscious of an external world. And the only ^ther thing* of which it could be cQnscrous, Are the action or actions of the power which caused it to exist, aod oX yis own existence. Now the action of that existence or of those existences which created the mind, must still cohtinue to be exerted or the ego becomes either an independent existence or a nt)n-cntity. Bat we have shown the mind to be dependent, if it had a beginning; and therefore we may with matured faculties appeal to our consciousness respect- ing the action of that creating power, and all persons will say that they are entirely uncoiiscious of the action of that power which prolongs our existence, it is however, commonly said that we are conscious of our own existence, i e \hat the ego is conscious of iUelf per se; but we rtgard this as an error. For'unless the mind act, it can not be conscious at all : and when it does act, it is conscious of Iti acts, states and feelings; but of itself per se it U not con- scious. Each person can test the truth of. this by his own consciousness And if the mind at first be unconscious of the action of the external world through the senses, and also unconsciousness of the powers which prolong our existence and jinconscyousness too of its own existence per se it must at first be without consciousness. The. mind, indeed, can be conscious of lu own kcts and feelings; but independently of the action of other existences upon it, it can not begin to act Dr to teel. ' Now we find that a material body made up of bones, muscles, cartilage-, membranes, nerves etc., t^!l of which belong to to the non-ego, coniains the mind This body Is related both to other existences without and to the mind within- it is a medium betw^em the mind and existences external to itself. And the first effect produced upon the ego by or through this body §!▼•« th« min^ merely that s^te of activity which we call intensified P*»ivity. The ' mind does not yet notice; but It possesses more than mere passivity: it doei not yet pu^ fbrth Its energy In any definite direction, but it possesses energr- BTit fn a little time alter birth, by being continually acted upon by \he exUr- nal world through the senses, the mind's intensification is i.creascd, aa4 ifa energUstart in definite directions, and then it notices. But it merelynoticeik By the eye, the ear and the other senses, it notices existences : but the whbke, 17 the WHEN, the what, or the why, it does not know. But in a little more time, the mind begins to discriminate and then it begins to know and to have knowledge. Without the power to discriminate, we could know nothing, although Ve might notice some things : and the possibility of discriminating lies in the relations between the non-efio and the ego. Now the only relations, which can exist with referecce to the ego, between the existences among which the ego is placed, and with which ihe ego itself must be contemplated^ are those between the ego and external non-ego directly, those between on© external object and an other of* the non-ego indirectly through the ego, those between one external and one internal object of the non-ego through the ego, and those between one internal object and another of the non-ego. From each of these relations and from them only can we discriminate and, gain knowledge. From the relations existing between the ego and the external non-ego directly, we have the action of the non-ego upon the ego, and the response of the mind itself in a directly opposite direction to the one received; This is the mere noticing of an object by the mind and it constitutes a fact. But if in the noticing of an external object of the non-ego, which is a fact, the mind also notices its own Set, which, we think, is the case, here is another thing noticed, a fact diflerent from the former, and these two facts may be compared. And let the sanic process be repeated with the same external object of the non-ego, and we have a relation between two acts of the mind itself, between two internal objects of the non-ego; and also a relation be- tween each act of the mind and the external object. And hence among these relations, three comparisons may be made, viz., between each act of the mind and the external object, and between the two mental acts inter se: and from either of these comparisons, the mind can gain knowledge. From the com- parison between the action of an external object of the non-ego upon the ego and the act of the mind itself in return, we gain the knowledge, that the act of the mind itself and the action of the external object are separate existences: and from the comparison between two acts of the mind itselt, we can also discriminate and gain the knowledge of separate existences. For two acts of the mind in the same direction can not be simultaneous: and the interval of lime, however small, forms a relation by which the mind can discriminate and separate internal existences. Separate existsnces hereafter we will call hetera. (Greek— heteros, a, on-yothers). We use the neuter plural of the Greek adjective as a noun^ meaning other things — separate existences. And hence the evolution of hetera by the mind is the inception of human knowledge. By the mere noticing of an object^ the mind indeed acts, but can know nothing, because one object per se can not be compared and.discriminated. But if the mind notices its own acts in noticing external influences and compares them with that of the thing noticed, from the rela- 18 • tion existing between the two, the mind can evolve the knowledge of hetera. And we must here remark again, that the mind does not and can not notice itself. Its acts, states and feelings, it can BoMce: but the knowledge of its own existence, as^ potential mind per se, is gained only by comparison. Now things merely noticed by the mind we call facts: the knowledge gained by the comparison of noticed existences, we call truth: and this is our first classification of the existences of the non-ego. Facts then, are existences', each one of which is noticed by a single act of the mind and without comparison : truths are the results of comparisons made by the mind between facts and also between truths themselves. Now facts are all comprehended in the non-ego, and of them we m^y niake two classes : the one class having their where without and the other liaving their w'HEKE within the ego. The first of these classes we will call perceptional and Jhe second selfconscional facts. And although neither of these terras are in common use in our language, we tliink we have tlie ri^ht to adapt terms to our own purposes. From the Latin fractio, we have fraction, from "Which the adjective fractional is constructed : and from perceplio, we have perception, from which in like manner perceptional may be made in har- mony with the principles of our language. And thus, also, we may deal with conscio and prefix sellT Aijd each of theses classes of facts may again be divided into five sub- classes. Perceptional facts are naturally subclassified into the five classes, viz.: visual and auricular facts, facts of touch, of taste and of scent. And hence one external aggregate existence— and by aggregate existence we mean an existence to which we can apt^ly our o/gans of touch, of taste, of smell, of sight and hearing— may contain five perceptional factS or exteinal noticeable «xistences. Such an existence as red, or an existence to which we can apply but one specific organ of sense, we call a simple existence and not an aggregate one. But two aggregate existences, then, will contain ren perceptional facts. And if each fact of the same aggregate existence^ be compared with the others, there will be ten comparisons of facts inter sc of the same aggregate existence. And if we compare each fact in an aggre- gate existence with each fact in another aggregate existence, we will have twenty-five comparisons. And hence two aggregate existences contain ten facts and afford forty-five comparisons, from all of which truths can be gained. CHAPTER III. CONSCIOUS TRUTHS. 4 • In the prccecding chapter we explained what we mean by facts and endeavored to shoir to what existences we apply that term. We showed that those existences which we call facts, in and by Uiemselves separately con- sidered, make no part of our knowledge; but that they are the foundations .-Trr- 19 and pre-exis(en^ substrata upon which all our knowledge stands and from which it springs. All knowledge fies in relations, and the mind evolves it by comparisons. Were a person so brolight into life that he could see the sun, i. e., notice this perceptional fact, but notice nothing else, i. e., have no self consclonal fact, he could not know that the^un exists. We can not say that the sun exists wilhout having the knowledge ©f existence. For, the phrase *'The sun exists," or "The sun is," is equivalent to this, viz.: the sun is an existence. And unless we first have the knowledge of existence, we can not know the sun to be one: not a single fact but facts must come to the mind before knowledge begins. And when the mind first notices a percep- tional fact, there is. also always lodged in it aself-conscional one; these facts, the one perceptional and the othejr self-conscioual alway enter the mind in a binary manner. For, as we have already said, the ego unconscious of itsqlf per se, takes its place among other existences to be acted upon and to act in return. And these perceptional and sclf-conscional facts keep coming in a binary manner repeatedly befor^the mind compares them at all: but when it does once make the comparison, the knowjcdge of separate existence -is evolved. This knowledge we call conscious truth, ^nd hence we say that we are conscious of an existence though the knowledge of an existence be not a fact to us, but a truth evolved from the relation of facts: the fact of an existence per se is noticed but not known by us. The relation of perceptional and self-conscional facts is necessary to the beginning of consciousness. For, as already said, to be conscious implies to be conscious of something, and to be conscious of nothing is to be without consciousness; and the human mind had a beginning of existence and it is a dependent being. And although, indeed, we can not tell by the proofs which nature offers, but that the materia mentis, s(^ to speak, may have always existed, and that at the first it may have been inclosed within a human body and afterwards handed dowji from generation to generation ; yet that there? was a time when our consciousness did not exist, is clear. For, the materia mentis, let it be what it maj^ could not, per se, by its own inherent power separated and independent of all things else in the universe, be conscious of anything except ifself per sc. And although the mind be conscious of its acts, states and feelings, yet that it is not conscious of itself, i. e., not con- scious of the fact of a materia mentis, our own consciousness teaches us< And if the mind be not conscious of the fact of its existence, or to use a phraseology more tangible to some minds, if the mind can not feel itself per Be, i{ must be a dependent being, and its dependence must be a dependence in every respect at least except existence alone. And that the materia mentis in such relations as entitle it to be called a human mind had a beginning can not be denied : and hence its conciousness in thoso relations must have had a l)eginning also. And as the human mind is inclosed wi'hin a body, were 18 tion existiDg between the two, ll.e mind can evolve (he knowledge of hetera itself. Is acts, states and feeling., it can .o-iee: but the knowledge of ,t^ own existence as^ potential mind per se, i, gained only by comparLn Now ihmgs merely noticed by themind we call facts: the knowled^ gamed by the comparison of noticed existence., we call trit «mJ n r • our first Cassincation of the existences of th'e non ' g^ fIcts n. n ar" ex.8,enees, each »ne of which is noticed by a single act of th^m^ 'and wthout comparison: truths are the results of comparisons n!ade bv Te «und between facts and also between truths themselves Now Acts Jo all comprehended in the non-ego. and of thcm we „,«y n,akV two ciLses tl^ one class having n,eirw„EHK without and the other having tl^irwnE«E w.thin the ego. The first of these classes we will call pehc^io J" and Jhe second sei.fconscional pacts. And although neither of t™,ms arf n common use in our language, we think we have the ri^t Hdaot terms to our own purposes. From the Latin fraclio we have fr.l, 1 7 "^ Which the adjective fraction..! is constructed: and^rZ percenUo w .' 7'" perception from which in like manner percep.iolj may'^beX^ i.' T niony with the principles of our lan'-ua-e And tlu,« „! with conscio and prefi.x sell? ""'="''=«• ^nd thus, also, we may deal • classes'^'^teTcemioI^rr ,""'''' "'" '''"" '"•''^' "»"*'" ^<= '"^•'"^^ '"'" "^e sub- c asses Perceptional tacts are naturally subclassifiod into the five classes T.2.: visual and auricular facts, facts of touch, of taste and o? sc^t Z.' hence one external aggregate existence-an 1 by a cciuie existences. Such an existence as red, or an existence to whipi. ZZ rrr onrS T" "' -"'''' ^^ •=''" - ^""P>-U°ncran .en perce;rion°arfa:s An ireaclrXf Tf t"™^' '""' ^•"" ^-'""1 1. compared with .he others, Oiere wi.?tren'L7rL;f Xts^ inrte le exTsTenefJT Tl""""- ^'"' '^ ^' '=°'"P-'"« "<='' foct in an aSre- .ets L a.ordT;;r cot-pis^ ^z^2.::i:z:^t^::i JOH AFTER III. CONSCIOUS TRUTHS. and pre-exislen* substrata upon which all our knowledge stands and from which It springs. AH knowledge fies in relations, and tie mind etoLs U by comparisons. Were a person so bro>,ght into life that he could see the sun 1. e., notice this perceptional fact, but notice nothing else 7" have Tn ■ sell consclonal fact, he could not know that the sun exist. We cainoTs^v that the sun exists wi-hout having the knowledge »f existrnce Pnr ^^ phrase '"^o sun exists," or "The sun xs." is equivalen to J v z Mhe sun' IS an existence. And unless we first have the knowledge of eX2lc.ll ! not know ,he sun .o be one: not a single fact but pac™ must "^^ ^o t^e t"onal f! r:, ""''i'"'-" ^'"''- ^"^ "'"=" *« "'""' first no cesTprcet tional fact, there is also always lodged in it a self-consc.onal one these fX he one perceptional and the othe, self-conscioual alway enter ^heminH- binary manner. For, as we have already said, the egolconscforo? i^ return. And these perceptional and self-conscional facts keen rrlil • bmary manner repeatedly befor*the mind compare them at all bnwhn > ■v":L°rVhi?k '"^'r^"™""' "^* •'""^^''^^ of «ex .:';.; evolved. This knowledge we call conscious .ru.h. And hence we savTh»t we are conscious of an existence thouWi the kBowl^rt7» „f T • .^ acts, states and feelings, yet that it is not conscious of itself i e not onn IndTfl '.rr' '"^^"'^ "^"^^^'-^ -- cons iTusness ;;^^^^^^^^ And If the mind be not conscious of the fact of its oxWi^nnr^JV 20 this body impervious to the action of alj external things, tlftmiud must con- tinue unconscious. And although it is often said that consciousness is. the very thing that distinguishes animate life: yet the lack of actual conscious- ness does not establish the lack of potential consciousness or the nonentity of mind. Consciousness is not the mind itself: the materia mentis must first exist befo/e consciousness can. And if, as we have shown, the mind in order to be conscious, must be conscious of something, that something of which it is conscious, must be brought to the mind itself by the external non-ego: otherwise the human mind could rear a structure of knowled^^e from out of itself and independently of all things else in the universe. Con- sciousness, therefore, as it can not exist without a minn to contain it, so like- wise It can Dot txist in the human mind independent of all things except the mind : without the non-ego the ego could not be conscious. Now there is in man a meteria mentis, or an immaterial substance, or it you please and as some suppose an arrangement of physical organs in some manner so that the arrangement aftords the^onditions necessary to become conscious when acted upon: we start no question respecting: either of those or of any theories. What may be the essence of mind, we do not know, but whatever it may be, we find it, in a proper organization, to bo capable of knowledge; and our inquiry here is with reference to this knowledge. And the first knowledge, which the mind gains, is cokscious truth. And if consciousness depend upon the relations of facts, i. e., upon existences which are inter se hetera, it must spring from tftese relations. We may say, that the mind has knowledge of something. This sentence contains the mention of three existences viz. : mind, knowledge and thing." Wo may say that the- mind is conscious ot somethins; and this sentence contains mind, coiicious- ness and thing. And if, as \^ have shown, the mind notices its acts, but not itself, and consciousness be dependent for its existence, then, if the later sen - tence be true, consciousness must have been evolved from the relation of the action ot the mind, and that of the thing. An object of the non-ego aflects the materia mentis, the mind acts; and from the relation of the effect pro- duced upon the materia mentis, and the returned action of the mind, spring consciousness or the knowledge of existence. Consciousness is the result of relatiens and it is envolvcd from facts. When we say that we know that stove is not an act of our minds, because we are conscious of this, we state what is not true. We become conscious of the existence of 'an act of. mind aud of a stove, and the judgment then discriminates between the twg by comparison. Conciousness is merely the knowledge of existence; and the thing or existence of which we are conscious, we call a conscious truth. Now we have shown that there are perceptional and sclf-conscional facts; there will be evolved therefore, from the relations of these two chisses conscious truths grounded in the non-ego and also conscious truths grounded 21 in the ego. And^s numerous as the perceptional and ^elf-conscional facts may be, so numerous will be the conscious truths. For every relation be- tween perceptional and self-conscional facts evolves twocoifSciONAL truths. The relation between the perceptional fact of a tree and the self-conscional fact of the mind's act in noticing that tree evolves two conscious truths the one being external and the other internal. From the relations of self-con- scional facts inter se, however, or from the relation of perceptional facts inter se, conscious truths can not spring. From the relations of perceptional and self-conscional facts, spring conscious truths, and then these conscious truths can be compared promiscuously. Conscious truths, therefore like perceptional and self-consci«nal facts, upon which they immediately depend come to the mind in a binary manner. * Now by each of the five senses, the mind notices perceptional fact^- when these facts by their relation to self-conscional ones, rise into conscious ' ness, they become conscious titiths which are grounded in the non-etro So likewise when self-conscional facts from their relation to perceptional one. rise into consciousness, they become conscious truths, which are grounded iu tlieego. There are. then, two great classes of conscious truths viz- con- scious trutJis grounded in the non-ego, and conscious truths grounded In th'e ego. r>ut that the one class is grounded in the ego aud the other in the non- ego, is not determined by consciousness, i. e., we are not conscious of th-U but this knowledge arises from an act of judgment in comparing two con' scfous miths, i. e., two existences iff which which we have become conscious ^ow It is said by some piiilosophers, that the mind does not occupy space,!, e., that space is not necessary, not one of the conditions -of its existence. But nothing certainly can be more absurd: for that, which does not exist ANYwiiERE, can havero existence. Because we can not tell the precise wheue in which it does exist, does not prove that it hasnotawHERF in which to exist. That, which has an existence NOwnERE,Jias no existence at all: anf every where is a where infbace. The ego exists somewherf and in this WHERE lie the conscious truths grounded in the ego- the non- «go exists somewhere and in this where lie the conscious truths o-rounded in the non-ego: the wheres of tlie ego and of the external nou-e-o^ are heteri of si>ace. Now we must recollect that the conscious truths gro°unded in the ego aud those grounded in the non^go come into existence simultaneously - the only things th.refore, which the mind can discriminate, between con- scious truths grounded in the ego and conscious trulhs grounded in the non- ego, merely as exisrt?nccs, are the wheres occupied by each, i. e., the wheres can be discriminated into hetera. We classify, therefore, all conscious truths into conscious truths grounded in the ego, and conscious truths grounded in the non-ego: and that these two classes of t.uths respectively are thus grounded, the mind determines by heteratino their wherfs. Each of these great classes of conscious truths may be again subcljissifio^. The conscious truths grounded in the external non-ego are classified into conscious truths of touch, of taste, of color, of scent and of sound; and the conscious truths grounded in the ego, into hearing, seeing, feeling, smelling and tasting. All these, both those grounded in the ion-ego, and those grounded in the ego, are inter se hetera. A sound is not the same thing as hearing, nor a scent the same as a souid; any two of the same class or of ditt'erent classes, are hetera. And hence of the conscious truths grounded in the non-ego there arc five classes, and of the conscious truths grounded in the ego, there are five classes; making in all tfrn heteiiical subclasses of conscious trutljs. CHAPTER IV. NOMINAL AND PKOPOFITIONAL TRl'TIIS. In the last chapter we endeavored to show what we mean by conscious truths. We do not mean my conscious truths, tri^tlis which possess con- sciousness, but exisiences of whose entity we become conscious, And we showed that we gain Jhe knowledge of conscious truths by being able to separate the external and internal existences of the non-ego into heter.^. This is the first step in the acquisition of knowledge. And were we not able to do this, all woAld be chaos; But this once done, chaos breaks and order takes a beginning: and then we proceed further and discriminate in- ternal existences inter se, and also external existences inter sc into hetera. But, as yet, we know heterical existenccsrwe have the knowledge of existence merely as existence; and merely as existence, existences arc all alike. A sound, a taste, a color, etc , merely as existences are l^etera but alike: they arc, as existences, heterical similia (Neuter plural of Latin; similis,c— things resembling each other). But sound, taste, scent, color and touch, being existences grounded in the external nc^-ego, may be further discriminated by the diflerent modes or manners by which they are rclatecfto the ego. And hearing, seling, smell- ing, tastinff and feeling being existences grounded in the ego may also be discriminated inter se by the modes or manner by which they are related jo the external non-ego. The manner of receiving visual impressions and see- ing is diflferent from that of receiving aricular impressions and hearing. And this difference of mode or manner, whether there be any other difter- ence or not, distinguishes the five classes of conscious existences grounded the non-ego inter se, aiul also the five classes of conscious existences grounded in the ego inter se. These modes or manners by which\he mind is brought into relations with the external non-ego, belong to our physical organiza- tions, and inter se they are defercntia (Neuter plural of Lntm ditfercns, ens — things differing. By DIFFERENTIA wc do not mean difference, Init thing*; differing, hetera 23 unlike. The diffrtcnce between two feet and one foot is one foot: the differ- euce in area between a parallelogram and triangle of the same base and altitude is one-half the area of the paralellogram : but the difference l>etween red and green can not be pointed out. The difference lies in the causes of these effects upon the mind; but what those causes are, we do not under- stand sufficiently, so that we can contemplate them otherwise than by the effects themselves, which we can only discriminate into things differing— differentia. If we resolve a ray of light into its elements by the prismatic •spectrum, and then from diflerent combinations of elements, each combina- tion having one element at least in it the same as in the others, we find different colors to result, the difference between these' combinations, is the additional element or elements in the one more than in another: but the differtmce between the effects per se of these combinations upon the mind, we can not point out. That these effects per se are differentia, hetera unlike, we know; but that is all we know about them per se. Now had it been possible for man to have become conscious of only one existence, he never would have inveoted a name for that existence. For everything which has a name, has leceived that name to distinguish the re- sult of a heteralion of a diflerentiation or of a comparison of things. Suppose, for instance, that every object of visi6n had possessed but one color: no dis- tinguishing name then for any color to distinguish it from others, could have l>een introduced into language. For flie word "color," would have expressed all the knowledge that man could have hji^l in that regard. And although this existence (color) would have arisen into. ^nsciousness: yet the only necessity in a name for it, would have been to distinguish it from conscious truths of the other senses. And unless men became conscious ^f the very essence of existence they could by making some possible discrimination give names only to distinguish existences inter se. And supposing now, all the senses excepting sight to be wanting, and all objects to vision to possess luit one color, then there would be no oilier existences grounded in the non- ego to discriminate inter se, and the words seeing and color would have been sufficient to d^criminate the parts of man's knowledge. But suppose now that along with the one color, one existence of sound should rise into consciousness, here now is an existence of a diflerent mode, possessing Ja different relation toward the ego from color. . There is, indeed,^o assignable difference within our knowled-e between a color and a sound per se, they are simply differentia, hetera unlike; and their modes of relation to the ego are differenfia: but the difference between hearing and seeing per se cannot be pointed out. The dift'erential mode% of relation, give us the knowledge of the differentia, sound and color. And now, upon the above^ supposition, wc know one sound and one color, and know these two existences to be differ- entia: and to distinguish these two existences inter se by words, two names 24 are necessary. A nameJor the one existence alone, will not answer to enable ns to mention the other. If we should caII the one color, not color might stand for the sound. IJnt suppose now ascent also to rise into conscious- * ness: wc have now three dift'erentia: and if we wish to speak of them, we must have three distinguishing terms, one for each: and so on through* the senses. And hence we see that there will bo five generic names in every lan- guage, which fjas attained to any perfection, to distinguish the five differentia of conscious truths grounded in the non-ego. These names arc signs*of the results of the mind's discriminations by modes of relatioir among conscious truths grounded in the non-ego. A like discrimination is ul so in ado with like results among conscious truths grounded in the ego. But in giving these names, men arc not naming facts, nor are they naming conscious truths per.se; but they are giving names to distinguish conscious truths inter so. Facts grounded in tha non-ego pei se, have no names to dislinguisli them inter se: conscious truths per se have but one common name, to-wit, exis- tence; but conscious truths, which arc inter se differentia, have five names for those grounded in the non-eifo, and five names for those grounded in the ego: each ot the differentia is in langu.tge distinguislied from the others by a name. Tiiese truths spoken of, which are inter se differentia, and grounded in the ego and in tiie non-eso, we will call nominal truths:, because they are the first truths distinguished by differential names. Tiie nominaj. truths, then, are sound, taste, coloi, touch, scent and tlie hearing, seeing, feeling smelling and tasting: all t4>»se are inter se differentia. Wc do not mean) however, tliat these trullis were hisloric.\lly the first truths named. Tlie pro- genitors ol^ur race would be likely to give names to aggregate existences first, as they would come in contact and feel deeply interested in them from the beginning. Bnt philosophically, when atiempting to reduce our knowl- edge to scientific order, nominal truths come up next after conscious truths * and they are the first truths distinguished by differential names. Now proceeding with our inquiry, as w;e have called differential con- scious truths, nominal truths; so the truths gained by diiferentiating nominal truths inter se, we will call primary propositlonal truths: because they are the flrjt ones that can be exhibited in propositions in which the words no NONE and N^Tdo not occur, and in which the subject and predicate are not represented by the same nrime, as red is a coler. And for the present, we will dismiss from our consideration, those truths grounded in the ego, and consider those only, which are grounded in the non«-ego. SuppoSe all the existences ot vision presented to our ^yes for twenty years of our life, to have had but one color, green for instance: and supposing all of the sen.scs to exist in a healthy state, at the end of that period, wc would have the nom- inal truth of color, and some name to diMlnguish it from the nominal truths 29 of the other senses: suppose this name to be color. JVnd suppose that ao- other. existence, RED for instance, should then become a cooBcious truth Now if we should compare this new existence with all the others of which we had any knowledge, excepting green-the first color, we would perceiye that it was not on the same scale of truths, like any of them in aay respect As a conscious truth it is like them all ; for all of them are conscious truths' But as a nominal truth, a further consideration and discrimination, thU new existence has nothing in common with any of them. But if we compare THIS R^ with that GREEN, WC pcrceivc that they both agree in their modes of relation to the ego ; and it was because the modes of relation to the ego -are differentia that the conscious truths of sound, taste, scent, etc , could be discriminated into differentia— into nominal truths. But in the case of red and green, the modes of relation to the ego are not differentia, but similia and hence red and green, as conscious truths, can not be discriminated at all into differential nominal truths; but we must proceed further and discrimi- nate inter se nominal truths (to which both red and green belong, and there- fore the word qolor is applicable to both), into primary propositional truths Red is discriminated from the conscious truths of the other senses in the same manner that green is, and the name color may be applied to both and it sufficiently distinguishes them from the other nominal truths; but it does not distinguish red and green inter ge. And to do.this we must necesswily discriminate colors- This we are able to do. And the reason that wc are rtble to discriminate colors, lies not in iheir modes of relation to the e-o but . in causes, which are differentia forking through mod«s, which are sUn'ilia- the modes of relation to the ego are similia, but the relations themselves are differentia: and to distinguish these relations inter se two names must be used. Red and green, therefore, as nominal truths, are both distinguished in language by the name color; as primary propositional truths, the one is dis- tinguishedbythcnameREDand the other by green. And hence we can ' say that this color, this nominal truth distinguished by its mode, is among truths of the same mode, distinguished by the name j^ed: this color is reix And if we add another color to our list, we must deal wilh it in like manner and similate it with the nominal trullis of color, and. then differentiate thes^' Rimilated nominal truths into primary propositional truths; and so on through the colors. And if we now call color a genus, asTs generaWy done^ by logicians, we will then have species of color. And thus we maV deal with scents, sounds, tastes and feelings. And hence we see that primary propositional truths arise by comparing- and generically similating and specifically differentiating non^inal trutl^ And Ihese primary propositional truths, which as primary propositioaal truths agree in eveiy respect, will .of course, be classed together i e wiU havcft common nmic for each and every .one of the individuals thus alike- 2« just as all Domiual truths inter se similia, will, as nominal truths, have a common name. Take the primary propositional truth red. and suppose two 1 heterical REDS to be before us: now two heterical reds as primary proposi- J tional truths are exactly alike in every respect, starting from the pacts which he at the foundations of them. They are both perceptional facts' both are conscious truths grounded in the non-ego, both are nominal truths* and both are primary propositional truths: but we can carry our discrimin- ation no further. As primary prepositional (ruths, ihey are alike in everv respect in every step from facts: and could we not at the second steft exist- ences grounded in the non-ego, discriminate them into hetera, they would be o us the same thing. And in this manner are sounds, colors. tastJs, scents • and touches dirided and classifled. ' • The nominal truthjof sound arc divided inlo musical and non-musical And the pnmary pi-opositional trull.s of musical Bound are again divided into rythmics, melod.cs and dynamics: these lastare secondary propositional truths. Non-musical sounds too are freqaemly sukclassifled by calling to our m.nd and conncc.inK «-ith them some object which is supposed to pro- duce them, or some stale or leelins of the mind itsell, which certain objects produce; as vocal, nasal, pleasant, dismal, deathly sounds, and soon. But there are, no doubt, thousands of truths ,,orceived by the mind without names to distinguish them For the colors, which are differentia, and the sound! wh^h are differentia and so on. are very numerous, and only the very appre! | ciable and mark«l difterentia receive dis.ineuishlng names Now cons^fotfs I lruths,-nominaUruths. primary and secondary propositional Iru.bs "^°Z our knowledge of those simple existences, which we will have occastn hereiWter^o call facial gregaria. wcasion CHAPTER V. OBDINAI,, C.^RDINAI. AND TKMPORAI, TKITHS. AND TIME AND SPACK ' Having in the last chapter treated of those existences, which we will ^occasion to use again in our inquiries under the nameo fuc .1 gT^aTla we must now proceed to classify still other truths, which enter into our daM^ concerns of life, and from which we continually reason. We hav. a rtadv shown hetera to lie at the very foundation of our knowledgr And altlouS theuNiT IS the tirst ol the series of cardinal lumbers and the SL^ of tf.« system. Jet duality or plurality is necessary to our knowUdl oMh. «!? Without the knowledge of two existence", at least, we coulT not iaveie knowledge of the unit. For. the knowledge of one pring, {roTJZll, relations; and wiUi one existence per se there can be'.o n^meTal ^a "n" Now we have already seen that, differentia receive distingui hinr«a.^o ' But heter., also receive names to distinguish .hem inter se. If we comT.?; one conscious trutU with another, apd cannot discriminate them in o noTn 27 truths, i. e., into differentia, the only way that is' lea for us to distinguish thenrai all bynames, is to mark them first, second, third, etc., and this result is accomplished by distinguishing existences merely into hetera and marking the individuals. These truths, therefore, we call ordinal truths They come to our minds in point of time at an early period of our knowledge- but they may not receive names to set them out clearly for a long time after- wards. Ordinal truths are simply the relations of separate existences as ex- istences and their names aistinguish the individuals inter se. And hence these names may be applied to anything, just as we may call anything of which we have knowledge, an exijtence. And in point of time the ordinal truths or numbers, philosophically considered, must come to our minds be- fore the cardinal truths or numbers. And historically, this appearu to have been the case. We find tjie ancient Jews, Greeks and Komans, using for their notation the first ten letters of the alphabet, which upon reflection will be seen to express much better the ordinal than the cardinal numbers and for which purpose they were most proj^ably used at the first, and for which thev are now with us exclusively used. And after the ordinal numbers or truths are obtained, we have but to com pound or colligate them and name the colligations (for in nature thev will be similia hetera unlike) and we will then have the cardinal ttuths or num bers, Cardinal ttruths, therefore, are coliegations of hetera with a defer- ence, inter se of one, and they are distinguished in language by the names one, two, three, etc. And as each colligation is a colligation merely of hetera the distinguishing name given to any colligation may be given to a like' colligation of thin^ diflfering in nature from the first, as two men two horses, etc. Tke abstract nature and applicability of numbers to any and everything, is owing to t^e circumstance, that they are names of hetera which do not take iato considenuion, in any manner, diflTerentia in nature' but which merely represent heterical existences. When, however we applv these numerical names to^objects in the concrete, the objects must be lieteri cal similia. We can say that a potato and a horse are two existences but we can not place after the word two any dift'ereatial name by which we can express, in the concrete, the numerical sum of a horse and a potato. But again : we have already seen that facts, the one perceptional and the other self-conscional, enter tl>e mind in ^ binary manner, and from their rela turns, acta of the mind itself become conscious truths, known existences Aad conscious truths grounded in the ego may be compved inter se. and from their relations another class of truths may be evolved. If two acts of the mind m the sauM mode and direction, be discriminated, we will have the temporal truths of once, twice, thrice, etc. Whether a man can hear see smell, etc., all at the same time, which is probable, we will not discues ' But that a man can not sec or hear, h e., that the mind cannot act in the same 28 mode and direction in citlier hearing or seeing twice at one and the same time U evident. Place an object before you and look at it. apd then %fter having taken your eyes away fVom it, look at it again, and you will not say that you have looked at it twice at one and the same time. The comparison; Iheretore, of two conscious truths inter se similia, grounded in the ego ^ evolves the temporal truths of once, twice etc. But again: if we resolve existences grounded in the non-ego mto hctera we will, of course, perceive a plurality of existences. And if the modes' of relation to the ego, of two existences so resolved at the sanae time, be the same, we must perceive that the two existences do not occupy thesame WHERE for if they did we could not, at the same time, resolve them mto hetera ' Ued, for instance,which occnpies but one point, can not at the same time be resolved into hetera, into separate existences, into two redr. Heter- ICAL existences grounded in the non-ego, which are related to the cgom like modes, necessarily occupy heterical wheres. Each of these wheres may be but a single point, which can not b^esolved into hetera; but Uie two wheres must be separate, and if they be separate, that which separates them we call sp^ce. Space is a truth which forms a class of truths by its^f alone Wheres are necessarily resolved into hetera, when we resolve exist- ences grounded in the non-ego into hctera, i. e., existences grounded in the non-ego can not be so resolved without heterical wheres.* When we re- solve existences on the other hand, which are grounded in the ego and pro- duced by the ego's action in the same mode and direction, into hetera, we necessarily resolve TIMES into hetera. Time also is a trulji, which forms a class of Uuths by itself. Mr. Hume derives our knowledge of space from color And if a color cover sufficient space to be resolved into two or more somrwheres, space will be evolved from the relaUon of those wheres: but if only a single point of color so minute as to be incapable of being so resolved, be presented, no knowledge of^pacc can be gained from such pomt per se. Mr. Locke obtains all our knowledge of space from both touch and color and dismay also be done in the manner we have" stated. Sir Wm. Hamilton calls space "A native idea ot the mind," which expression seems to have no meaning. , , i r We have now shown how we derive and classify our knowledge ot colors, tastes, scents, touches and sounds, and of acts of the mind itself into h«tera, of ordinal, cardinal and temporal numbers, and of lime and space. And it will be seen th%t existence, not as a class distinguished from other THINGS, but as the state of being in contradistinction to non-entity, stands at the head of our inquiries. Existences are then divided into^perceptional ai.d self-conscional facts, and from ihe relations of thes^ we evolved conscious truths our first class of truths. We then found some conscious truths to be grounded in tl)e ego and others in the non ego, and in each of these classci I 29 we founc; no^iinal Uuths, so called because they are the first truths which receive differentij#. names. From the relations of nominal truths ^nter se, we then evolved primary propositlonal truths, so called because they are the first truths which can be used in propositions in which the words no, none and NOT, do not occur, and in which the subject and predicate terms are not the same name. We then evolved secondary propositlonal truths, and saw that we had exhausted those simple existences which Jiercafter we ♦will call facial gregaria. We then evolved the ordinal, cardinal and temporal num-' bcrs and time and space. And we must still proceed further with our in- miiries before we commence where logicians have U8\ially^ commenced in bating of the reasoning processes. But if the reader will liave patience to follow us in our preliminary inquiries, we believe, he will be able when w^e come to treat of propositions and the syllogism, to understand the whole matter, and to escape from the obscurities and perplexities, which in our opinion, have hitherto suia*ounded those subjects. • CHAPTER VI. CLASSIFICATION OP AGGREGATE EXISTENCES AND OTHER TRUTHS. Having already considered those simple existences grounded in the non-ego, whteh we shall call ^cial gregaria, we come now to the contem- plation of aggregate existences. We may find a color, a sound, a. taste, a touch and a scent," all sifuated in one location. Two existences grounded in the non-ego and related to the ego by Xhe same mode, can not occupy the same where at one and the same time : for if they do, the existences can not be hetera. Thus : two colors can not exist in the same where, nor two sounds, nor tastes, etc., at tho^same time. But the five nominal truths grounded in the non-ego, nevertheless, may all be found co-existing at the same time in the same where and forming thefdcial gregaria of an aggregate existence (Gre- garius, a, um ; gregaria, neuter plural— things in a herd). And by an aggregate existence we mean an existence composed and made up of simple existences; as the leaf of a rose, iron, snow, a stone, water, etc. These aggregate existences grounded in the non-ego possess facial gregaria, some, if not all of the nominal truths grounded in the non-ego. But aggregate existences, besides the facial gregaria, have also capacial gregaria, i. e., capacities fo receive and give effects among themselves. If we move two heterical and aggregate existences towards each other, we find that both can not be made to occupy the same where in space at the same time ; one of them must necessarily exclude from its where, the other, or they both could not remain hetera. This capacial gregarium of aggregate exist- ences is called impenetrability, and is said to be one of the primary properties of matter. And each particle of matter must necessarily have a where in space and without a wh(?re it must cease to be an existence. Impenetrability, . >» 80 therefore, is one of the essential capacial gregaria of aggregate existences : If matter did not possess impenetrability each particle migDl annihilate its neighbor until the earth became a non-entity. And another essential capa- cial gregarium of aggregate existcBces is form or flgur«. But after we have gained a knowledge of matter, i. e., of aggregate existences, ^we readily perceive that in some matter the particles cohero rigidly, while in others they move freely among themselves. This capacial gregarium of the one and 'that of the ether are inter se differentia: and if we distinguish these gregaria inter se we will have the classes, solids and fluids. Then again fluidg may be discriminated by their facial and capacial gre-^ garia: one will not have a like color with another, and their tastes may be differentia: a volume of one may be tried in a balance with an equal volume of another, and their specific gravities be found to differ: heat may be applied, and fluids be found to differ in the degrees of heat necessary, ceteris paribus, to make them boil, etc. And wherever the mind can- discriminate into differ- entia, It will form classes of fluids ; and those which are not to us differentia, may be called by one and the same name. The knowled^ of all classes ot fluids is gained by differentiating theii gregariacither facial or capacial : capa- cial as well as facial gregaria being truths grounded in the non-ego. And when men begin to examine matt^ closely, they find that the particles composing one bulk may be analyzed, i. e., discriminated into differ- entia. And hence they form classes of what they call elementary substances, i. e., aggregate existences, the particle of which can be discriminated into helera, but not into difl'ere'ntia. The ancients knew but four elements, viz : earth, air, fire and water : man has since found a great many more elementary differentia. And every differentiation, that the mind can make, throws new light upon the world and adds new truths to our store of knowledge of the elements. Now the number ot facial gregariff^that matter may possess, so far as we can know, when expressed In the classes of nomln^ truths, is five. Each of these five classes, however, are divided into numerous primary pro- positional truths, which have names, and besides these there are various other classes of which we have knowledge but for which We have no names. But the number of capacial gregaria of matter is found out slowly, one after another: and where the number ends we can not even guess. Each generation to come may find out new capacities of Matter, and when they do, they will ot course make new classifications ^cording to tlie differentia dis- covered. 'We have matter, now, classified by its specific gravity, its attraction of cohesion, its friability, its ductility, its maleability, its compressibility, its effects received and produced among existences, etc. Any capacial gregaria, which are inter se differentia, may produce classes of matter. Chemestry is a suctession of differentiations of elements and compounds, i. e., capacial gregaria discovered by experiment. And what is Yery strange, the mineral ^ i I •n 5 81 enter into compounds in a binary manner, as truths are compounded, so to speak, in a proposition as we shall see by and by. Thus: carbon and oxygen unite and form carbonic acid: hydrogen and nitr<5gcn unite and form amonia: and then the carbonic acid and &monia unite and form the carbonate of amonia. Now the mental process of similating and differentiating hetera, gives us all the classes, which we possess, of the different kinds of com- poficds and elements. The classification of matter by differentiating its capacial gregaria-, so far as it has been accomplished, may be found in works on chemistry and materia medica. And we must perceive that aggregate , existences when stript of their facial and capacial gregaria, are unknown to us. The gregaria are the only things of which we hare any knowledge through the senses. That which lies behind the gregaria are merely infer- ences drawn from the gregaria. Now after knowledge has increased and language ]^en invented to ex- press it, the science of grammar takes its rise. Men begin to similate and and differentiate words. The parts of speech are classified by differentiating Ihe intentions of the mind in using different words, i. e., by the functions of words. The principles of the declentions of nouns and adjectives, and of the conjugations and inflections of verbs arc obtained in the same manner. The knowledge of tense is gained by the discrimination of times into hetera: of modes by the differentiation of manners and so on. The same mental process also obtains in Botany. The botanist differ- entiates, cotyledons, radicles, plumules, etc., and as the plants grow he finds buds, which he in like manner classifies into auxiliary, accessory, adventi- tious, latent and so on, he also differentiates the leaves and give distinguish- ing names to each class. The whole classification of botany, shows, that the human mind has been dealing with every part of the plant by similating and differentiating. And if we look into Zoology, the same mental process meets us at the threshold. Vcrtebrated, radiata, articulata, rumenants, pachydermeta, planti- grade, etc., are classes obtained by the differentiation of truths. And this can easily be shewn to be the case with ethnology, entomology, mineralogy, anatomy and all of the natural sciences. And hence, each of those sciences is also a mental philosophy giying us the classifications of as many truths as the particular natural science contemplates. Accepting therefore the classifications ef the several natural sciences and making them our own we will proceed to consider other truths, wjiich come to our knowledge from other sources. After having obtained the knowledge of space and matter, we may easily get the truth of extension. Extension, indeed, independent of every- thing else has no existence: it is not a consious truth. We speak of the extension of spfaceand that of matter: but had thercexisted nothing extended 32 extension could liave made io part of our knowledge. And whatever is ex- ' tended must be so exteadcd that two points in space, two somewheres, can he discriminated by the mind. And hence extension when applied to matter- means consecutive and contiguous points, which can be discriminated. And in every other sense, the word is misapplied ; and it is thus when we use ex- tension as synonomous with space. The proper meaning of the term exten- sion is the stretching out bf something. And if we take two points and con- sider the space between them, and then remove one of the points further from ihc other, the space between the;n will be extended. So if wc consider a colored point on paper, the enlargement of tUat point will extent the area of the color. A mere mathematical pomf can not give us the knowledge of ex- tension • but two Sathematical points separated from each other, can give us the knowledge of the extension of space. Our knowledge of extension is gained by the discrimioation of heterical points .located In somMhing in ppace or in space itself. The consecutive points must all be in some cxist^- enceof the non-ego: for extension is a truth gained by the comparison of truths grounded in the non-ego. Extension, like time and space, forms or itself but one truth and a class'of tmths, i. e., there may be heterical exten- sions but the hetera are inter se similia; there may be heterical times and heterical wheres, but inter se times art similia, and so of wheres, and there- fore, each makes but one class. But again, if we take an aggregate existence, a piece Of iron for instance, and move it to another palce, we will perceive that it is not now in the same WHERE in which it was before it was moved, it has changed its place in space. And hence the iieteration of wheres occupied at diflfer- ent times by one and the 'same «xistence, gives us the knowledge of that existence's motion. While the same points in an existence remain in the same wheres, no discrimination of any points wn£RES, of course, can be made, and without the heteration of one and the same poinds wheres, no motion of that point can take place. This truth of motion, again, forms of itself a class of truths. But again : w« have in our minds testimonial truths. And testimonial truths ai-e those, which we receive upon the testimony of others without bringing them up from facts for ourselves'. And every witness must testify to that only which has coaie under his own observation, or to a truth which" his own mind has wrought out: or, if a person state that which has been told to him by another, and the dlher but related what he had heard, in order that there may be any truth at all in the story, there must have been some person, whose mind broug.ht tiie truth in question up from facts. For some truths, we are entirely dependent upon the testipi^ony of others: as that Ccesar was assassinated, Columbus discovered America, etc., while there are others, whicii we may gain for ourselves from nature and also receive thera 83 from testimony: as that the sun and moon shine upon China. And respect- ing those truths, which are conreyed to our minds by thetestimony of others, it is to be observe^J that there must always be some analogy in the whole or in the parts, between a truth related to us and some truth of which we already liave the knowledge: otherwise we can gain no knowledge by such relation should there be no analogy existing between the truth, which a friend desires to relate to us, and some truth with ^hich we are already familiar, no con- ception of the truth in his mind can be established by words in our own The king of Siam is said to have laughed when told that water, a fluW, would congeal and become ice, a solid : but if he had had already no knowledge of a solid or fluid, he would liave had nothing at which to laugh: for he could have known nothing about the subject of the conversation. If a traveler should discover in some unexplored country an animal with 0et like those of a cow, a.botty like that ©f a lizzard, and a head like that of a crane hv using these things with which we are familiar K) explain the appearance of the various parts of this newlj^iscovered creature, he could give us a con . ception of his animal as a whole. But should a traveler discover an animal -.4 which in the whole and in the parts, was entirely unlike anything of which . we have any knowledge,.he could not possibly, by language, give usany con- . ception of what hejiad seen. And in order that we might gain any knowl- 1 edge of Puch an animal, we would have to see the animal itself or have a pictupe or sculptured image of it presented to us. ^ But again: we have the knowledge of existences of the imagination ^ These existences are peculiar and require some consideration here. Centaurs' ^ Sphihx, Harpies, Hydras, etc., are -represented to us, while these creatures' really have had no objective existence in nature. Yet the mind per se has no * t power to create from nothing existences of any kind ; even the baseless fabric of dreams is not the creation of the mind from nothing. But if existences ^ of the imagination have no real objective existence, and if the mind can not Thfl?'°I- n''"' """^^'"f : ''^'"^' ^^ *^'^ ^^"^^ ^^ ^* subjective existences? Ihe state of the case is this, a centaur, and all otMer existences of the imagi- nation, though they have no real objective existence in nature as a combina- tion and whole, yet all of them, partially in the parts considered, have a real ' objective existence. A centaur is an existence of the imagination one nart of which is like that of a man, and the other like that of\ Z2 Both of th^ parts separately considered, have a real objective existence in nature The imagination unites these parts and from their combination creates an existence, which has a real subjective existence, but which .as a whole a. unity, has no objective existence. But had the parts, separately considered no objectrve existence, their unity could never have had a subjective exist- fonL n ^°''^'° J?'"'"'^"'' ""^ ancient and modern times have been foim^ in this manner. The images in works of fiction, theGods of Homer II 84 the Metamorphoses of Ovid, and the cbaraclcr of Ilamlei and Othelo are creatures of imaginatioD, which have been collected in the same manner. CHAPTER YII. CAUSE AND EFFECT. As we will have occasion in a subsequent part of this volume to treat ■ of cause and effect, it seems necessary t^ prepare the way by examining the manner in which wc come by the knowledge of these existences. Now we can gain.no knowledge of cause except through effect. We may know arsenic as a metal ; but as a poison, a cause of death to animals, we can know nothing of it without first having the knowledge of the eflect; that thiscapacial gregarium is contained in it, is found out through the effect. We can not vi^objects, which are potential causes, and per se determine such to be their case, a priori; it is some effect of which we tlrst gain the knowledge, that brings to our minds the knowledge ol cause. But the yery instant we Took upon anything as an c%t, we havo the knowledge of cause- for, cause and effect me but counterparts of each other. To under- stand, therefore, what wcmean by cause, it Is necessary to begin TVith the examination of effect. . Now an effect, in general language, is some change^ produced. \V ith- out change there can be no effect. If wc conceive of the earth as having always existed, we can not conceive of its existence as an effect. W^e do not mean however^ that that of which we can not coneeivc, can have no existence : all we mean is that we can have no knowledge of that of which we can not conceive. And if' no changes whatever took place upon the earth, or in the heavens over our heads, we could never gain the knowledge of effect, and consequently we could know nothing of cause. If we cpnsider pure space, we will see that we cai> not conceive of its having had a l)eginning, or of any changes whatever having taken place in its nature, and therefore, we can not conceive of it, as an effect. The knowledge of change must preceed that of effect and cause : and when we perceive that the changa has been produced hy something else than the change itself, we then have the knowledge of •effect and cause. We must perceive, however, that the change has been pro- ^ duced, or we do not come to look upon such change as an effect. Suppose the first inhabitants of earth to have looked upon the moon and to have seen her und*ergoiflg in appearance, continual changes, (and this they could nftt have avoided if they looked up) could they have evolved the truths of eftect and cause fT3m.these phenomena alone? We think they could not. If tie • first changes with which men became acquainted were those of the phases of the moon.*and their minds were not yet familiar with the exertion of any power in nature to produce change, providing they really believed the olOt and full moon to be in rcalitj- changes in the same moon, indicat|^ by 35 phenomenal differentia, the comparison of these differentia would only evolve the knowledge of change. But that this change was the effect of some cause, could not be evolved from such coipparison. Now the simplest change with which we are acquainted, and which wc can perceive to be produced, to be an eflect, is the change ©f aggregate existences in space, i. e., a change of their wheres. Suppose a man should see one ivory ball strike against another and send that other some distance through space ; in such case he would see a change produced, an effect. He would perceive heterical wheres occupied at different times by the one and same ball which was. struck, and also heterical wheres occupied successively by the striking ball : he would also perceive that some ©f the heterical wheres of the one ball and some of tho^e of the other, became, at dj^erent time?, homon (Greek— neuter singular; from homos, a, on— tj^e same). If we contemplate the two balls, we perceive that they are hetera and that their where/4 are hetera; and when the striking ball moves towards the other its course is made up of wheres which are inter se hetera until it strikes, when the ball struck makes heterical wheres. But so soon as the first ball strikes the second one, some of the first one's wheres and some of the second one's wheres become homon, and from the impenetrability of matter, this could «ot b« the case without the second one having vacated those wheres. In this case the change in space of the second ball is seen to be an effect, and the cause is easily perceived. The first ball commenced to move towards the second one until it touched it, and had it proceeded no further, no effect would have been produced upon the second one: but if it go on further some of its wheres and some of those of the second must become homon i. c., the wheres of the second hall at one time and the wheres of the first ball at another time, are in space, homon. Now one instance of change involv- ing such reikions, if contemplated, would give us the knowledge o( effect * and cause. But again, if we ti« one end of a string to a permanent object and attach the other end to the one end of a lever, every point in tliat string will occupy a where, and the wheres of all the points inter se be hetera. The 'end of the lever to which the string is attached will also Save a where, which in reference to any point in the string, will be heteron. If now the stiiag contract, some of the points in the string will take the wheres >of other po'ints and some of the wheres of the end of the lever, and some of the wheres of points in the string, which were at first hetera, now become homon. And hence we see that in all those changes of aggregate existences in space, which we regard as effects and whose causes we understand, we find heterical ex- istences with heterical wheres, and some of the wheres of one and of another becoming hgmon. Change of objects in space is also produced by what is called attraction and repulsion, but what are the causes and modus operandi iU- ajni^!*! 36 in these changes, pliilesopbers have not yet sufficiently explained to us.« The convertiou of hetera into homon among wheres, is the modus operandi in those changes of objects in space, which we fully understand. Take a piece of iron and keep it all the time for a certain period under your eye, and during this period move it with your hand from one place to another! In this case we perceive that the existence moved (the iron) remains one and the same ; but its wheres successively and the times of occupying them can be discriminated, and so also respecting your hand. But some of the wheres of the iron and some of the hand's wheres can not be discriminatecl, they are komon, though the times of occupying them by each successively are never liomon always but hetera. :^ut again, we sometimes see one existence acting upon another, and a constitutional change following such action. Take a hammer and with it strike a grain of corn placed upon a rock, and we will see that a constitu- tional change takes place in the corn. This change too, we could scarcely avoid regarding as an effect the first time that we should witness the occur- rence. And in this case, it will be perceived that two heterical existences come in contact and that some of the wheres of the one and some of the ether become homon : and further that some of the heterical wheres of the^ particles in the grain of corn become homon, and hence the constitutional change. The grain of corn possessed rigidity but this gregarium- was de- stroyed by reducing heterical wheres of heterical particles to homon. On the contrary ignite gunpowder and heterical particles immediately take heterical wheres. * Again, if we take a piece of ice in our hand and it melt and become water, here ft a constitutional change; ice, an aggregate existence, has changea some of its fi:regaria and become water: and in chalking these gregaria, heterical wheres ot particles became homon. And in this case we must perceive that the where of the two aggregate existences, ice and water remams the same for bpth; but the existences possess gregaria inter sedifi-er- entia, and the times of occupying the same where are hetera. And hence when there is during a certain period of time but one where for two differ- ' ential existences, the one must have occupied that where for a part of that period and then^become the other existence. And when we conceive such to have been the case, we can not help conceiving of a constitutional change having taken place. Now in change times can always be heterated and when we can go a step further and heterate wheres, the change is that of place. But when we can go still further and perceive that an aggregate existence has lost some of its gregaria and taken others, which with reference to the first are differentia, the change is constitutional. A piece of iron ahen heated possesses different gregaria from those which it has when cold : this is owing 37 to a constitutional change. It, however, cools again and assumes its former gregaria. • But again, if we take grains of white sand and consider them all to- gether in a pile, we shall have a homogenious aggregate existence i e an existence in which all the particles are inter se similia: and consequemiy the wheres of all the particles can be heterated but the particles themselves can not be diftbrentiated, if now we mix red sand with the pile, we then find in it particles which are not only hetera but also difterentia. -lie pile now therefore, compared with what It was shows change. Thia change, however' is owing entirely to the change in space oP the particles of red and white sand. * • •^ But again, suppose we take an aggregate existence in which all of the particles arc similia, so far as we can perceive, but by subjecting it to a certain process we find that particles which we regarded as similia Miave become plainly differentia, which is always the case in the analysis of compounds here is to us a change of a different kind from any oF the former. - ' And again, suppose we take two aggregate existences, in each of which the particles inter se are similia, but the particles of the one and those of the other are inter se differentia, and we put ^lese two aggregate existences to- gether and find that all the particles of each existence now, if compared with what they were then, arc then and now inter se differentia, but among them- selves they have all became now similia: here again is a change different in kind from any of the former. This change always takes place when differ- ent elements unite aud forn^ compound. The following:, therefore, appear to be the principal changes with which we are familiar, viz: the starting an aggregate existence in an homoni- cal WHERE into heterical wheres, which is a change of place ; the chancre . of heterical wheres of particles into homonical wheres, and vice versa which IS a constitutional change of the adhesion of particles inter se, as in'crush- ing and expansion; the convertion. of similia into differentia, which is the analysis of a compound; and the conversion of differentia into similia which is the synthesis of elements, having chemical affinity fer each other ' Every change which takes place among existences of the non-ego involves theprio- cip?es of one or another ot the above examples, excepting changes in degree And we can readily see that one homonical existence perse can not change' but that the change of any one existence is owing in part to some other exist- ence. Every change is dependent. And as change springs from the relations or existences, within those relations must also be the cause or power to pro- duce change. Sodium persse does not posses the cause of 'soda; nor does oxygen contain it within itself; but from the relations of sodium and oxy-en spring the protoxide of sodnim or soda. And we see that the knowledge^ of Change comes into our minds by comparison: and so dso does-our knowl- • % 88 _ edge of effect and cause. And without the involution of homon and hel#ra, or similia and differentia, or coramensura and iucomensiita, we can not evolve the Knowledge of cause and effect. There is a change in the appearance of the moon ; there is also a change in the state of the atmosphere, by the comparison of these changed, we have hetera aud differentia, but neither homon or similia. And from tliese things per se, i. c., from helera and differentia, or from homon and similia, or from hetera ot homon aud commensura, we cannot evolve the knowledge of cause and effect. If a rock fall from the cliff of a mountain into the valle)% and about the same time the ice bl^ak loose from the shores and float down a river, here also are changes, iSlit they do not'come together anywhere, so as to bring hetera into homon, or vice versa ; similia into differentia, or vice versa ; commensura into incommensura, or vice versa; so that we can evolve from their comparison an effect or cause. Hetera must meet somewhere in homen or vice versa; or similia in differentia, or vice yersa; or commensura in in- commensura, or vice versa; in order to bring to our minds effects and causes. Now of causes there are three classes viz: expended, acting and poten- tial. Causa slriarum of the rocks is an example of an expended cause. Tlie floating icebergs, as believed, striated in their course the rocks. Biit they have vanished and ceased to be causes. The flawing of the water in the liver Is an effect of an acting cause, and gunpowder \inexplodcd is an exam- ple of a potential cause. ' • * . CHAPTER VIII. ^. NAM«S. We come now to the consideration of names. When we reason and use words, we must necessarily sec to it, that our words have some definite meaning, otherwise we will but veer about over subjects at random wilh«ut making comparisons in such a manner as will evolve truths. In the most common affairs of life we reason either well or or ill, and we lead others into our trains of thought and reasoning by the use of words. So much have words to do with reasoning, that Archbishop Whatcly concluded logic, or the science of reasoning, to be entirely conversant about language: a mistake similar to that of supposing the symbols of Algebra to be the only things about which that science treats. But the relations of existences inter j?e arc subject-matter of the science. of reasoning and of every other science. And as words are used to designate the results of these relations, the words them- selves must subjectively bear some relations to each otJier and to the exist- ences which they are used to designate: and so far as they are brought by the mind to jjjay a part in the relations of the ego to the non-ego in rcason- 39 ing, they are the subjects of the science of reasoning. And after what has already been said in the previous chapters, we do not \hing it will be very difficult to undeastand the functions of words in the processes of reasonino-. We have already seen, that hetera lie at the very foundations of »oiir knowletlge. That which 'is so related to the ego, that it may be an object between which and the ego, some truth depending upon such relation may come to our knowledge, we tall an existence. And words when spoken are to the car signs ^ cos:nitions of the per;3on speaking them; when written on paper they arc signs for the eyt. And when existences come to our knowl- edge to be existences by the power of the miad to evolve the relations among whichit is placed into hetera, these heterical existences are known only as lietera, and no one of them is distinguished from another except as separate existences. And when wo consider one of these heterical existences inde- pendently of its relations to others, and we wish to set out a word as the sign of our cognition, we use a name to call to the mind of the hearer or of hhn who sees the word written, one of/ hetera, without distinguishing in any manner this one from others. And hence words, for logical purposes, mav be divided into two classes, viz: names which are used by us to distinguish existences inter se and names used to call to the mind existences without distinguishing theni inter se. To the later class belong such words as existence, being, thing, entity^phenomenou, etc. These non-distinguishing names are few in*number in all languages. And taking up the second class, i. e., names used by^s as signs to distinguish existences inter se, we will notice those few in number which distinguish hetera inter se. Names to distinguish hetera ^inter se are such words as the following: this and that, these and those, once, twice, first second, Cgo and non-ego, etc. ' * But every conscious existence lias a where, wbich it occupies, and the relations of wheres occupied by conscious existences are expressed byprepo- .^itions. The where, however, and the conscious truth which occupies it, are differentia. And we will, perhaps, be bettcV understood if we sub-divide that class of names, which distinguish existences inter se,*into six classes viz: names of homon, of hetera, of similia, of differentia, of commensura and of mcommensura; and keeping this sub-classification in view, we will treat of them somewhat promicuousi3\ Now it must be evident that sometimes a simple word is used as a name, as iron, glas?, ice, etc., and sometimes names are Compound words,*as hydrophobip, etc. All those words, which by grammarians are distinguished as nouns, arc names. Some of tUcse are names of simple exislendfes as red, tnste sound, etc., and some are names of aggregate existences as iron, wood* CDal, ship, etc. And all those words too, which are grammatically adjectives' arc logically but names ©f the gregaria of aggregate existences. In the ex- 40 pression, "A red house," the word red sLowa lliat this facial gregarium is one of the gregaria of the house, and of this facial giegariumrit is the name. And all adjectives of the positive degree when joined to ac^gregate existences, name some one of the gregaria, facial or capacial, which aion*^ with others constitute the peculiar aggregation named by the noun to wliich the adjective belongs. 'In the expression, "A good man," the noun man is the name of an aggregate existence, and the woid 'good,» which i? joined with it, is the name of one ot the capacial gregaria suppo^d to be in the aggregation. "A fusible metal," is an expression of thejsame kind And it is to be remarked that those adjectives which are the names of facial gre garia may stand alone as the n^mes of eillier the subject or predicate of a proposition: while names of capacial gregaria require, generally, in our language, the names of existences in which the gregaria named by them severally, are aggregated, to go along with them when ihey are made the subject of a proposition. We can say that white or red is a color; but wo can not say that a round is on the table; and we should rather say a round tiling IS on the table. And when wc wish to use such words, which are the names of capacial gregaria, as names by themselves in the subject of propo- sitions, we usually change the lorm of the word: thus round is changed into roundness, rectangular ipto rectangularity, heavy into heaviness or weight. The article a or an is continually used in logical propositions and it alwa3>ha8 a significance. This article is tlie name of an heterical relation • itisderirecl from ane; German ein, and means oke. And therefore the expression, "A red house," contains three names viz : house, the name of an aggregate existence; red, the name of one of its gregaria, and a (bne) the name of the numerical relation ot the house. The article tjie, is tl.S name of an homonical relation, and it is used to distinguish homon from hetera- as, This IS the horse which we saw yesterday," "Thou art the man " etc Sometimes the adjective same and also the word self are used alone with the" noun to which the article refers": as, "The same horse," "The gate itself." The articles, however, can not be used alone, either as the subject or predi- cate of a proposition which is concerned about anything else than names. They however frequently appear in propositions along with other names, and their functions, therefore, ought to be understood Prepositions are the names of relations among existences and amon" the wheres of existences in space: as, "The log nnder tlie brid-'e " "In the house. "Over the river," "Beyond the treo..- etc.^ Adverbs are tfte' names ^f relations n'««ar« «««« otherTm^st ^ inter se differentia. If we take ten grains of corn inter se similia and -call to Lth? ' T""" ^"'' '"'°"'" Gamm^randso on, our naming hasUonn,^ to nothing; for so soon as our eyes are turned away from them andreyha^ Changed places, w. can not afterwards tell, which one is Alpha or BeTa r fhin^T r'"""""'- '•""^°'«' *•''«'' "='«' "•' be discriminaUd by us fu^^r" ban into he.era must from a mental necessity, when not numerLlly con! sidered. receive from us a com«oa name. But it may be said that hobse is a common name, yet horses can be discriminated. This is true ^ftten they also receive distinguishing names; aot indeed, to dis-tlnguish the i^dt A !. .' distinguish them inter se; as black horse, white horse^ Arabian hor... the horse With short ears, the near horse, the ofrZ^2 la ike manner color is a common name, yet colors inter se can be discrim- .nau.1 mto differentia, which receive distinguishingnames, and wWchnamt ( ■• 42 Now if a man should place before himself a horse, atr^c and a stona, by examiniDg them, he would perceive, that the one possessed the capacial grega- rium of animation; the other the capacial grxjgaria of vegetation, and the last, capacial gregaria of a different kind from either of fhe former. These three objects, therefore, would be inter se differentia: they are the three aggregate nominal truths, and we may distinguish them inter se by the names animal, vegetable and mineral. And alterwards every object possess- ing the capacial- gregarium of animation and the horse, as aggrecrate nomi- nal truths, would be similia, and therefore it ftiust be called by the name animal. Animals, however, may be differentiated into aggregate primary propositional truths, and so on in a like manner, which, we saw was persucd with those simple existences, which we call facial gregaria grounded in the non-ego. 'And it must appeaj;, that^f every aggiegate existence, with -which ■we are acquainted, possessed the like number of facial and capacial gregaria, •which were inter se sifhilia, aggregate existences could only be discriminated into hetera, they would all be similia and they could have but one compou name. But the facial gregaria inter se differentia are many and the differ- ential capacial gregaria are innumerable; and could we pind an aggregate existence, in which all the facl^ and capacial gregaria exccj&ting one were . like those of gold, yet as it differed from gold in one respect, it and gold ■would be differentia, and consequently it would have to receive a name to distifiguish it from gold and other fhings. Common names, thfireforCj are the names of the individual existences severally, which upon one and the same generalization of existences are similia or commensuray^ A proper name is the name given to a single existence to distinguish it from all others in the unive;-se. And it must be perceived that, besides the capaciai gregaiium of animation, which distinguishes animals, animals are made up of various other gregaria, both facial and capacial, by which -we can easily distinguish them inter se. And after that we have sub-divided them into species, we are still able to distinguish the individuals of the samo species. Take for instance, the species or genus homo, and after that wo have divided this species into the five races, we can easily distinguish the in- dividuals of the same race. Nature is so fond of variety that, in the largest cities two men can'feeldom be found, wl>o are in all respects similia. And this variety of gregaria outpide oi those upon which llie generalization, in respect to which men are similia is made, enables ui. to impose witjji effect proper names upon individuals. Daniel Webster, outside of tliose gregaria whicK m^de him and other men inter se similia, possessed gregwi a facial a«d capacial, by which he could be distinguished and known from others. . City is a Common name, and yet every city, besides the juxtaposition of houses and the jostling of men, has other relations and dissimilar plats and surroimd- 43 ings on the earth by which we may distinguish them by the proper names London, Paris, Philadelphia, etc. ' Correlative names are the names of existences so related to each other that the mention of the one suggests the relation ; as father and son, hus- band and wife, mother and child, cause and effect, king and subject, etc. A concrete name is the name of an existence grounded in the ego and considci-cd with reference to its ground in the ego, or of an existence ground- ed in the non-ego and considered with Reference to its ground in the, non- ego; in other words the existences (for, names in themselves can not be con- crete or abstraqi) distinguished by what are called concrete names, have their locations in the ego* or in the non-ego, assigned to them by the mind when their name rtre spoken, and therefore, they are concrete; -and frpm this circumstance the names of such existences are called concrete. An abstract name is the name of an existence for which the mind assigns no location, but merely views ^the existence sul)jectively without 'determining its ground cither inthe ego or non-ego, as whiteness, fusibility, roundness, etc. The adjecti\ce naii;^es of facial and capacial gregaria, such as white, red, sweet, fusible, combustible, conscious, etc., are geaerally concrete; and when tl^e existences for which tliey stand are to be viewed in the' abstract, we change these names grammatically into nouns: as whiteness, redness, blackness,, consciousness,. etc. We may however use abjective names to denote abstract existences, as white is not black, i. e., whitenesS is not blackness. Names have been divided into positive and negative. This division, however, is made altogether from the combination and appearance of words] and notYrom the func.tipns of words as names. The division made by Aris-^' totle into defiaite and indefinite is a much better one: as definite white, red, man, horse, etc. ; indefinite not-white, not red, not man, etc. Definite names] then, are names of individuals S-eparately, or of the individuals severally of a class; and indefinite itumcs are the names of anything not denoted by the definite name, whi^h is always part of the word used as an indefinite name. The truth is that such 'names as not red, not man, nothing, non-entity/ etc.] can haVe no existence hi any language^ independent of propositions,' they spring up in propositions, and in order to i*nd.erfctand ^hejp, we will have to treat of propositions. There is also another set of names, such as blind, mute, deaf, etc., which have been called privitives; they certainly exercise tlie functions of names, but we can understand them much better afler hav- ing trcaied of propositions. It has been usual with writers on logic to treat explicitly of names and their divisions, and we have said this much by a kind of duress, although after names have been divided itito names of hetera, homon, sifiiiiia. differentia, commensura and incommcnsura, we dceuTthe other divisions of no great importance. i. y..i^» ^^l^i ^^ ^®^™^ necessary, at the end of this chapter to notice briefly, what we regard as erroneous in the chapter on names in the work of J. btuart -MiU on logic; not because we wish to find fault with Mr Mill more than others but because Mr. Mill is one of the strongest writers upon logic iiT the English language, and the futility of the subject is, therefore best shown from his work. On page eighteen, of the edition pubM*hed by Harper & iiros., he says, "A general name Is familiarly defined, a name which IS capable of being truly aflBrmed in the same sense of each of an in- definite number of things. An' individual or singular name, is a name JI.^i^A''A°"i^^ capable of being ,truly affirmed in the same sense of one luininf^^f !^T.°^>^.5 same pafre, '«A general name is one which can be predicated of each individual of a multitude; a collective name can not be predicated ot each separately, but only of all taken together." Now upon the foregoing, we would remark that a name can not be affirmed of any- thl?^ii^''K7^''X.^''P^^?^*''^ affirmation is contained in a proposition, and that, which is affirmed in any proposition, can not be a name, as we wil see TnH^v^ ''TW^n'^.^\*?^ propositions in chapters X, XI, XII, XIII, XIV and Xy. Mr. Mill, m his explaination of names has all the lime hkd in llV^^hr «^°tr^^^J^' ^,^ '^^y »ay. the universally received hypothesis that, in FhXnrn'^fn^.LP^^^ tT '' "*^'°^'^ ^' "^^"i^d «f t&e subject, or tha^ the hing denoted or connoted, to use a term of Mr. Mill and the schoolmen by he predicate term is affirmed or denied of the thing denoted or connoted by the subject-term ; a theory which we hope to be able to show hereafter to be entirely erroneous, and wLicfi has led M?. Mill and other eminent write^ into erroneous conceptions of names. But again on the same page as ^- • fore. "A concrete name is a name which stands for a thing ; an^ abstract I!^Sp J^«/«^°;« which stands for an attribute of a thing." lid hence the hP? .Stv*° T'^""^^ ^^ V^^^' '^ ^^^ ""^^ ^f NOTHING, unless an attribute be a THING of a THING. But on page thirty-two he tells us that, "When we have occasion for a name which shall be capable of denoting whatever wo?^.?fnr°°lw''l?^"^'^'^ ^'^^ non-entity or nothing, there if .iTa Sly a word applicable o the purpose, which is not also, and even more familiarly taken ma sense, in which it denotes only substance^'. But substances aro T.^\lt^r' 'r'''' f "^"^^' %'^'^ ^^'°i ^'"^ '^ ^«'po^"^ ofTmusri^ said c^p or« '/^^^l"^? ^^'^ ^''*''- ^^^ •^^«" we speak of an object, or of a thing kmror'lZfL^Zfr '^PP^^''^ K"^'^^ ^ substance. There seems to be ^a Kind of cpntradiction in using such an expression as that one thine is mere- ly the attribute of another thing." From this, it seems tharMrMilPs defi- nitions of concrete and abstract names ought to hav^read: a concrete name lnd,Tn'''^*'^.'.\?^^' for a substance; aS abstract name is Tname, wh^^^^ at?ribute« .?. tTi^".''i?^/ substance: for, otherwise, if both substanieTand attr butes are to be called things, then a concrete name, according to Mr foT}^eteullr^^^^^^ V^ '^'' ^^^°Se of words in his senten?^s S^.* T^nf "^ ^^*^' ^' White also is the name of a thing, or rather of things '» Mr. Mill, we presume would not go so far as to call white a subsUnce bit would connsider it rather as an Wibute of a substance Yer in X^^^ sentence he tells us that, "Whiteness, again. Is the name of a Wality or at tribute of those things" (whites). That whiteness is the attribute of wh^k IS certainly strange enough. But he would probably say that whiiene^U not \^c attribute of white, but of white thinL i!^. L7,^«"llV !rJl^?.TJ* not t^o attribute of wb^^^ ^^l =oZ^l d?nVtt^ean%;'^^^^^ :«^i •* *"*^- --- -^ ««» If .*vii nrc oav Buuw IS wniic, milK is wnite linen 18 White, we do not mean to be understood that snow, or linen, ormilk is a • ■ ■ i5 color. We mean that they are things having the color" (white is their attri- bute). "The reverse is the case with the word whiteness; what we affirm to be whiteness is not snow, but the color of snow." Well, whiteness then is the name of the color of snow, but such being the case what is white the nanie*offrtien we ray snow i« white? It may be answered that white is the name of snow itself and of all white things, as Mr. Mill has said pre- viously. Well then, if such be the case, what is snow the name of? Mr Mill's language is merely a jargon. But Mr. Mill proceeds to divide names* into connotive and non-connotive, and this division he considers of the most importance, *'And one of those which go deepest into the nature of langua""e " "A non-connative term is one which signifies a subject only, or an- attribute only. A connotatu;e term, is one which denotes a subject and implies an attribute. By a subject is here meant, anything which possesses attributes Thus John, London, England, are nanie« which signify a subject only. None of theic names, therefore, are connotative. But white, long, virtuous, are connotativc. The word white denotes all white things, as snow, paper' the foam of the sea, etc , and implies, or as it was termed by the schoolmen con- notes the attribale whiteness. The word white is hot predicated of the attri- bute, but of the subjects, snow, etc.; but when we predicate it of them we imply, or connote that the attribute whiteness belongs to them." Now in the above sentences, the misconception of the .meaning of propositions first spoken of by us, is commingled with the confusion respecting concrete and abstract names, which we noticed a moment ago. We do not wish to fill our l>ook w ith strictures upoa the works of others, which is apt to be regarded at best as gqneorious. The best way to cure errors is to bring forward the truth and let it be examined. And we repeat the remark that all the flivis- ions of names, after that they have been divided into names of homon hetera, similia, diflereniia, commensura and incommcnsura, are of but small iuiportancc for the purposes of explaining the reasoning processes. These six classes lie at the foundation and are used in assisting the undesUnding in drawing its conclusions; the other classes are useful, if useful at all merely for tlie purposes of distinctions in mentioning things, but they do not assist but ratlier impede, the progress of science. * CHAPTER IX. classification of niOP08ITION8. In the previous chapters, we endeavored to obUin classifications of those objects with which we are familiar, and to treat of names used to mark and distinguish truths. And it must have been observed, that what former writers have called attributes we call existences, and when these existences co-exist, we name them grcgaria. Among most logicians, and especially among the schoolmen, what they call attribute* aire said to inhere in a sub- stance. But of this substance in which attributes inliere, we hare not been able to gain any knowledge whatever independent of the attributes. And we regard the name ATTRiBirrE as calculated to mislead, and therefore we do not it at all. Aad a substance stripped of gregaria is unknown to us ; independ- ent of tlie capacial gregaria, we know nothing o^ the ego, or of any mind ; and stripped of facial and capacial gregaria, we know nothing of matter! And the gregaria, of which we know something directly, may with as much 46' # propriety at least be called c«Islences, as those things which our Ihoughls, IVom our kuowledge of orcgaria, lead us to suppose to be in sonic manner, we know not kow, the Ciiuscs between the ego and nou-ego, of those gie- garia. We are able to say with confidence that one tiling per se can iTot be a cause, i. e , no piiangc or eftect can come out of it. We are able to say witii cpial confidence that red, white, sweet, etc.,have not always been to us exist- ences, but that wiih us they had a beginning; and therefore we conclude that our mind in and of itself must be something", and that there are otlur somethings, whose relations to tha-niind ' caiKse these existences, which wo call red, sweet, etc. ' m ^ Now when men were forming language, they were endeavoring to dis- tinguish by the names, which they hit upon, certain truths which had come to their minds. But if their names do not point out clearly to our minds, -well defined truths, we lay them aside vid endeavor to supply their places •Witli more suitable instruments. And it must appear evident to every one that had any person attempted to compose a treatise on logic in the infancy ■ of language, iu-order to have- succeeded in stating what is now known about it, he would have liad to ruu away ahead of his generation in the knowledge of things, apd to have invented and explained terms which have cost the human intellect ages of labor to furnish to us. But happily for us the labra- lorfot' thought has been vigorously operating for many a thousand years before we have been called upon to enter tile arena of mind. Instruments for slampinir truths have been prepared to our hand by nations, each inde- pendent of the others. And although language always has been and always Avill be behind the wants of a people who push their inquiries- beyond the already occupied fields of knowledge; yet the advance usSually proceeds with so gradual a pace, that ihere is not much dilficulty usually, in forming the language chart of the newly discovered territory. Now in the prcceediug pages, we endeavored to show how we obtained and classified the 4ruths of which we treated: we also applied the names used for distinguishing them. At the same time, therefore, that we were tracing the processes of the mind in gaining knowledge, we were^ilso fur- nishing and setting down the signs by which 'to distinguish the knowledge obtained. And if words, as it has been said, are the forts established To guard and keep mental ittquisitions, we should expcCt a .writer, who puts his truths carefully into. groups for future use, to fprtify them witli proper terms, as he passed along. This we have endeavored to do.ns well as we were able ; and then we took a view of these names or forts. We must proceed, there- fpre,.tv:> connect those names, or forts,' together and consider the; results! This is done by the use of propositions. A proposition, in general, we define lo be the result of the.^jomparison of exigences made by. the mind and expressed in words; and under this » • 47 general defiuition of proposition we make two classes of propositions-? iz: logical and conclusional propositions. A log'ical; proposition is one in uhich llwe result of the Comparison between two existences made immediately by the mind is expressed in words; a conclusioual proposition is one in ^ which the comparison between Iwo ormore existences is mado immediately * by means of a particular existence or existences and Uie result of the com- parison is expressed in wftids. The sun is an existence, fire burns, snow.. is white, etc., are example of the first class. In each of these propositions there is a mental comparison immediately made between tt*vo existences, and tUo result ol the comi^rigpu is exprensed in words. The expressions; the sun is and the sun is an existence, arc equivalent : fire burns, is equivalent to fire js the-cause of burninjr sensations: fire itself is, the efiect of chemical aftlnities. And hence every proposition fujly stated requires a subject and predicate, i.e., .a name to distinguish the truth upon which the mind fim looks, and also a name to point out the trutli connected with th€ first in comparison. The comparison m^iy frequently, by a mode of speech, be expressed by using the n:uuc of the subject only with a verb: and in such cases the other exis- tence compared is suggesteind iHink-s etc. Tliis is also the case when the first existence is looked upon as thesuL- joct upon wlkieh some efiect is produced: as beauty fades, water runs, leaves fall, etc. But all such propositions m.iy be made by wording them'diflfer- ently to- set out a subject, a predicate aud a copula, i. e., m each of which propositions, two well denned truths shall appear, the one as subject and tlio other as predicate, with a copula to express the result of the comparison. The verb used. in our king u age, as the copula, may always be made to be some part of the substantive verb to ue; as snow is whi^e. Kow respecting the meaning of this copula, in propositions there hiis been much dispute among authors. When we say that the sun is, we. mean that thS sun exists, is an existence, /ibis, indeed, is the primary meaningof the verb to be. But besides tiiis meaning autiftns tell us that it has another; a3 when we say John is a man; they luil us we use the copula is merely as the sign of predication. And alt)iQugh in the pi^oposition, the sun ia, tliey tell us 18 is a pretiicale of itself, yet when a name is placed after it, it' theii passes Us preuicablc.qualHy over to that name. All this is certainly some- what obscure. For, when we take from the verb to be its primary significa- tion and cail it a sign of predication, what tlo we mean by this expression? We mean, say our authors, that the copula aflirms one tUiugpf another. But I do not ace that any more 4 ight has been thrown upon the subject, by the change of phraseology. When we say that ice is frozijp water, according to 43- tklseiplainatJan, we afflr^ frozen water of ic, when in truth ft-ozen ^^^^^^ and ice are the same tkm«, ^d therefore, in truth, we affirm ,t8.lf of he subject. Bat if il be explained by saying lliat the copula shows tha the subject possesses the predicate, •r that the predicate belongs to the subject. as It is usually done, we answer that this explaination explains nothing. For according to this doctrine, ice possesses froze* water, or frozen wirier belJngsto U^etamere jagon of words. But it is said ;«That the ernploy- ment of it (the copula) a» a copula does not necessarily include the affirma- tion of existence appears from such a proposition as this, »A centaur is a flctioD of the poets.' where il can not possibly be m^fhled that a centaur exists, sinee the proposition itself expressly asserts, llmt the thing has no real existence."-J. Stuart Mill. To this we answer, that a cenUur has areal existence, nor does the proposition assert the contrary. Its existence, how- ever, is grounded in the cg«. as the proposition asserts, "A fiction of the poets." Although modern logicians have arrived at more certain conclusions, io very many respects, yet in their expositions of propositions, they are as much at lault as the ancients. TXve truth is that the verb to be as the copula in propositions, maintains its primitive meaning in every Instance, nor can it be shown to have any other 4n any case. We may. Indeed, say that it is merely the sign of predication, but when we come to •xamine closely Ihis expression, we will lind it to be merely words without knowledge. Such expressions as these, snow is white, John is a man. leaves arc green, etc.. were brought into use before philosophy had made a beginning; they are natural, short and convenient modes ef expression and explicit enough for the wants of mankind in communicating thought in a general manner; the philosophic interpretation of them, however, by writers upon logic, we re- gard as erroneous, iiut wc must defer the further consideration of the copula until we come to the interpretation of propositions, when we hope to give a full and clear explainalion of the whole matter; and we have merely advert- ed to the subject here, for the sake of order, and to put the reader on his guard against what we consider errors. From the supposition that in all propositions there is something affirmed of llie subject io c^tain cases, and something denied of the sub- ject in other cases, writers l>ave classified propositions into affirmative and negative. But this classiflcation, in our view, is unscientific and built upon a sandy foundation. Every proposition, indeed, expresses a discourse of the mind, which may be denied or contradicted. But if we place before our m4cd a single existence either simple or aggregate, red for instance, as the subject of every proposition must be, we can deny nothing of that existence: if we say anything at all about it, we must make an affirmation. Take the two propositions, John is well, and, John Is not well: and if we consider the one as a reply to th« other, there will, indeed, l)e a denial ; JhU coDtemplatitig ^ '49 either one of them as indepeadent of the other, and it contains an affirma- tion. And further, if this appear obscure, we may ask ourselves, whether both expressions are really propositions, and if they are, then they must have something in common: proposition must be the genus of which each is a species. If they be differentia, and yet in some generalization similia, they must have been differentiated from the higher class in which they were similia. But if we say that the ene affirms something of something, and the other denies something of something, as is done, they then have nothing in common, excepting that each has a subject and a predicate, i. e., one existence before and another aften the copula. But if the names of the two existences compared in propositions be set down, as may always be done, and we dis- tinguish the one from the other by calling the one the subject and the other the predicate, this is merely a classification of the terms, and terms alone do make a proposition. The classification of terms, therefore, can not be the thing in common, which unites all propositions in a common class. But if some propositions affirm and others deny, these things (affirmation and de- nial) are differentia, and there is nothing left in which the propositions can agree excepting the classification of terms. In the two propositions "A pear is a fruit," and, *'An apple is not a pear," we consider that there is no denial in either case, both are affirmations ; though this doctrine will, no doubt, sound strange to those inaoctrinated from the books upon logic. They affirm, however, results which inter se are differentia. This doctrine will bo easily understood after that we have treated of the interpretation of propo- sitions. What .we consider, therefore, the proper mode of classifying proposi- tions is by the differentiating of the results affirmed. We dedned a logic^ proposition to be the result oT a comparison made immediately by the mind between two existences expressed, or aflirmed, in words. Affirmation, we consider, is the very thing in common in all propositions; but the results affirmed are differentia. And these results, we find, may be discriminated into six classes, and therefore, we make six classes of propositions, viz : homonical, heterical, similical, differential, commensural and incommensural propositions. It is not necessary that we should take up each of these classes and give them further attention here; for we are only classifying preparatory to a thorough investigation hereafter. Some things have to be merely stated at first, so that the explainatioa when it coi^es, may be understood. Now each of the above classes might, apparently, be subclassified into aimple and complex propositions. A simple proposition; then, would be one in which one subject is compared with one predicate, as "John is a boy." And a complex proposition would be onf in which one and the same subject is compared with each of two or more predicates; or in which one and the smm predicate is compared with each of two or more subjects; or in which tMseiplalnallon, we affiri^ frozen water of ice when ^-^'^^'^J'l^^ and ice are the same tkiog, and therefore, in truth we affirm «elf of the sobjecl But if it be explained by saying that the copula *1>«^» ^^*J^/^f ?£ p---a the predicate, •r that the predicate belongs to the sUb aet. a. It is usually done, we answer that this explaination explains nothing. For, according to this doctrine, ice possesses frozen water or frozen w^r Lungs to icet^a mere Jagon of words. But it is said ;'That the employ- ment of it (the copula) at a copula does not '«^.^«'*"»^.;;"^^",^;;J^^, "f .^T tion of exiatence appears from such a proposition as this. *A centaur is a fiction of the poets.' where it can not possibly be Uniflied that a centaur exists, since the proposition itself expressly asserts, llmt the thing baa no real existence."- J. Stuart Mill. To this we answer, that a cenUur has a real existence, nor does the proposition assert the contrary. Its existence, how- ever, is grounded in the ego. as the proposition asserts. "A fiction of the poets." Although modern logicians have arrived at more certain conclusions, io very many respects, yet in their expositions of propositions, they are as »ucb at fault as the ancients. The truth is that the verb to be as the copula in propositions, maintains its primitive meaning in every instance, nor can it be shown to have any other in any caee. We may. indeed, say that it is merely the sign of predication, but when we come to oxamine c osely Ihis expression, we will find it to be merely word, without knowledge. Such expressions as these, snow is white, John is a man. leaves arc green, etc.. were brought into use before philosophy had made a beginning; they are natural, short and convenient modes ef expression and explicit enough for the wants of mankind in communicating thought in a general manner; the philosophic interpretation of them, however, by writers upon logic, we re- gard as erroneous. But wc must defer the further consideration of the copula until we come to the interpretation of propositions, when we hope to give a full and clear explainalion of the whole matter ; and we have merely advert- ed to the subject here, for the sake of order, and to put the reader on his guard against what we consider errors. From the supposition that in all propoaltlons there is something affirmed of the subject io c^tain cases, and something denietl of the sub- ject in other cases, writers Ivave classified propositions into affirmative and negative. But this classification, in our view, is unscientific and built upon a sandy foundation. Every proposition, indeed, expresses a discourse of the mind. wWch may be denied or contradicted. But if we place before our mlcd a single existence either simple or aggregate, red tor instance, as the subject of every proposition mutt be. we can deny nothing of that existenec: if we say anything at all about it. we must make an affirmation. Take the two propositions, John is well, and, John is not well : and if we consider the one as a reply to th« other, there will, indeed, be a denial ; IhU contemplating > '49 either one of them as independent of the other, and it contains an affirma- tion. And ftirther, if this appear obscure, we may ask ourselves, whether both expressions are really propositions, and if they are, then they must have something in common : proposition must be the genus of which each is a species. If they be differentia, and yet In some generalization similia, they muBt have been differentiated from the higher class in which they were similia. But if we say that the ene affirms something of something, and the other denies something of something, as is done, they then have nothing in common, excepting that each has a subject and a predicate, i. e., one existence before and another aflen the copula. But if the names of the two existences compared in propositions be set down, as may always be done, and we dis- tinguish the one from the other by calling the one the subject and the other the predicate, this is merely a classification of the terms, and terms alone do make a proposition. The classification of terms, therefore, can not be the thing in common, which unites all propositions in a common class. But if some propositions affirm and others deny, these things (affirmation and de- nial) are differentia, and there is nothing left in which the propositions can agree excepting the classification of terms. In the two propositions "A pear is a fruit," and, ''An apple is not a pear," we consider that there is no denial in either case, both are affirmations ; though this doctrine will, no doubt, sound strange to those inaoctrinated from the books upon logic. They affirm, however, results which inter se are differentia. This doctrine will be easily understood after that we have treated of the interpretation of propo- sitions. What .we consider, therefore, the proper mode of classifying proposi- tions is by the differentiating of the results affirmed. We defined a logic^ proposition to be the result of a comparison made immediately by the mind between two existences expressed, or affirmed, in words. Affirmation, we consider, is the very thing in common in all propositions; but the results affirmed are differentia. And these results, we find, may be discriminated into six classes, and therefore, we make six classes of propositions, viz : homonical. hetcrical, similical, differential, commensural and incommensural propositions. It is not necessary that we should take up each of these classes and give them further attention here; for we are only classifying preparatoiy to a thorough investigation hereafter. Some things have to be merely stated at first, so that the explaination when it copies, may be understood. Now each of the above classes might, apparently, be subclassified into simple and complex propositions. A simple proposition,' then, would be one in which one subject is compared with one predicate, as "John is a boy." And a complex proposition would be on/i in which one and the same subject is compared with each of two or more predicates; or in which one and the Mun^redicate is compared with each of two or more subjects; or in which 50 two or more subjects are compared with two or more predicate!. What, how- ever, is called a complex proposition is really a single propoBition expressed and one or more others understood, as "John is good and wise," equivalent to "John is good and John is wise." Again, "John and James are good and ■wise," is equivalent to "John is good and John is wise and James is good and James is wise." "John is not good," is a simple proposition of a different kind, and "John is neither good nor wise," is a complex proposition of ffee same kind. And "All the Apostles were Jews," "All the boys in the house are barefooted," etc., are complex propositions. The classification of propo- sitions into simple and complex, however, is not a classification of propo- sitions, as such, but rather a division of them according to the number of propositions expressed and employed in a set of words which contain but one verb. But again, propositions have been divided into pure and modal, as "Brutus killed Ca?sar," (pure) and "Brutus killed Caesar justly" (a modal proposition). This division of propositions is made merely from the appear- ance given to propositions by the wording of them, and it is not a division of propositions, as such, at all. The sentence "Brutus killed Cicsar justly," contains a result which will be exactly expressed by another set of words, as **Th€ killing of Coesar by Brutus was just"; a pure proposition. The divis- ion has no foundation, whatever, in the nature of propositions, but rests en- tirely upon the wording of them. But again, propositions have been divided into univ(*rsal or general, as "All men are mortal"; particular, "John is mortal"; individual or singular, "A man is mortal" ; and indefinite, "Some men are strong". We, however, reject these divisions, as divisions of propositions, as such. The words Ai*l, EVERY, SOME, etc, jolncd to subjects or predicates qualify them and make Ihem a certain kind ©f subjects and predicates, but the aftlrmalions is made in Buch propositions, just as it is, where these wortls are wanting. These words, therefore, qualify the results of comparisons only by their qualifying effect upon the existences compared in propositions, the manner of making the affinnation is iu no way affected by them ; thfy belong to subjects and predi- cates and not to the result affirmed which is the essence of propositions. The sub-classification therefore, which we will make, is into categori- cal and hypothetical propositions. A categorical proposition is one in which ji certain result is expressed as actually existing in the relation of existences, as RED is a color, red is not green, etc. An hypothetical proposition is one iu which a certain result is supposed to exist in the relation of existences, for the purpose of drawing some conclusion from it; as "If a sheep be a horse, (hypothetical) a lumb is a colt" (conclusion). This wh#le phrase would be considered hypothetical by writers upon logic. Tlie hjTiothesis, howe\'er, lies in the first proposition, "If a sheep be a horse," the latter «en- 51 teuce is not hvpotl.etica), but a categorical conclusion, which cxpressee a result flowing actually from the hypothesis; but the hypothesis being false the conclusion dcpenJing upon it must be false also. Now before leaving logical propositions, we must say a few things about subjects and predicates. Subjects may be divided into simple and aggregate. A simple subject is a single existence per se, as "Red is not gseen," here red is a simple primary propositional truth. An aggregate sub- ject is an aggregate existence, as "Iron is hard." Here iron is an aggregate existence made up of certain facial and capacial grepari a entering into a kind of fasciculus, which gi*egaria are the things in fasciculo for which the subjective term stands and which it distinguishes. Predicates are divided in like manner. This is all that we need say at present respecting subjects and predicates: when we come to unravel the meanings of propositions, we will liave to consider subjects and predicates more fully. And this brings us to notice logical conclusions, or conclusional propositions, about which we will say but little at present as they will be treated again hereafter. A logical or ratiocinitive conclusion, as already said, is a proposition in which the result of comparisons mediately made by means ol certain ex- istences, is expressed in words. In a logical proposition the result of the comparison made immediately between two existences is expressed in words f but in a conclusional proposition thercsult is not derived from the immediate comparison of two existences, but mediately, as A is equal to B, C is equal to A, and therefore C is equal to B (a conclusion). In the last proposition, which is a conclusion, the comparison between C and B.isnot immediate, but mediate by the means ol A. This distinction between logical propositions aild conclusional propositions is important to the clear understanding of logic: for it is evident that a conclugion once gained may be made the premise in a subsequent syllogism, and unless we understand this distinction, we will not know how to get to the bottom of the reasoning process. All those propositions which have been denominated modal, by writers are conclusional propositions, as "Brutus killed Ca?sar justly" is a conclusion! And much of what we have already' said about logical jpropositiona, will apply to conclusional propositions, we need not therefore, repeat it. Propo- sitions, which are called disjunctive, ali^o, arenot logical propositions proper, but conclusions, the premises of which are often not mentioned: as "John is either a knave or a fool," is not properly a logical proposition, but a conclu- sion drawn from some premises, which are found in and can be made out of John's actions. What have been called hypothetico disjunctive or dilematic propositions, also, are cooclusious, as we will more fully see and explain hereafter. In this chapter we have endeavored to classify propositions so that we may be more ea.?ily understood in our subsequent inquiries. All truths, and 53 I especially those about logic, are so interlinked that we are obliged to draw, sometimes, upon those whose explaination has not yet been given in order to accomplish the work on hand. And the subject upon which we have been ^ engaged and which we must yet consider more closely, has been misunder- stood, as we believe, by all writers heretofore upon logic. I I CHAPTER X. ! HOMONICAL PROPOSITIONS. j We have defined a logical proposition to be the result of a comparison between two existences made immediately by the mind and expressed in words: and a conclusional proposition to be the result of comparisons be- tween existences made mediately and expressed in words. We will first give pur attention to logical propositions. And the result expressed in every legi- ' cal proposition will be either a truth or an error. If our faculties be in a perfect state and exercised in the right manner, the result will generally be a truth : but if our faculties do not act in a legitimate and sufllciently vigorous manner, we will obtain an error. In every instance, therefore, it is always necessary, in order to obtain a truth by comparison, that we should have an adequate knowledge of each of the two truths compared in logical proposi- tions. We have already shown that all existences may be compared one with another, and that knowledge is a result brought out of the relations oL exis- tences. To show, indeed, how the mind possesses the capacity in itself to compare is no part of our undertaking; but that it actually does compare among tlie existences which are the subjects of its cognitions, and hence i gain knowledge by the comparisons, we think, has been sufficiently shown ] already. j Now when the mind has gained knowledge and clothed this knowledge with words, i. e., given it as it were, a body to render it visible to others, Ih© knowledge gained, indeed, is thus made appreciable to others, but the opem- tions of the mind in gaining that knowledge, leave no trace behind. And did every proposition clearly exhibit the two existences compared, and also the result or truth gained by their comparison, propositions would need no interpretation, for each one would fully interpret itself. But Ihe men who commenced language, were seeking merely for an instrument of utiliry^ in the common affairs of their lives, in which clearness of detail and precision , of expression were of less importance than general availability and dispatch. And therefore, in every language, the truths which are really compared in propositions ai-e sometimes but dimly shadowed forth, and the result of their , comparison always but obscurely shown by the form of the words. And this N makes it necessary, in order to obtain a thorough insight into propositions, to show what the two truths compared really are, that the result of their com- ' parlson may be clearly perceived. To this task, therefore, we now proceed; and we will comineucc with the cxamiaation of homoaical propositions. Take the proposition "Ked is red," and let us endeavor to clearly set out the two things compared and the truth, which is the result of their com- ] arison. And fir«t, we must observe that an existence which is absolutely' the same existence can not be two existences, and that one thinf, per se can not be comparcd^at all : two existences must always be found in every propo- sition. We must also observe that when we have the knowledge of an exis- tence, we can always make some discrimination respecting that existence: for wiihont some discrimination we can have no knowledii^e. Plurality of ex- istences is necessary to our knowledge of anyone; and, tkerefore, absolute oneness or identity is not within our knowledj^e: every truth of which we have any knowledge is evolved from relations. I3ut how then can we say that "John is John," or what is equivalent to this, "John is himself"? In order to understand this it is necessary to recollect that some truths ara •2:rounded in the non-ego and others in the ego. It we look at a tree, the relations between the tree and the ego bring to our knowledge an existence (a tree) grounded in the non-ego, and also an int(;rnal existence grounded in the ego. Now simple existences can only be discriminated by their wheres, by their times and by their effects. Many effects upon the mind are inter se similia; thus if we look at an inkstand to-day, and to-morrow look at it ao-ain : both* to-day and to morrow it will produce etlects upon the mind exactly similar^ yet these effects will not be the same, they will not be homon, for they can be discriminated by their times. But similar effects upon our minds can only be discriminated by their times: and where there can be no hetcration of times made, there can be but one and the same existence grounded in tlio ego, similarity is lost in identity. And we must always recollect that by the ego, we mean my mind for me and your mind for you: For should I and a thousand other persons, at one and at the same iilstaut of time, look at an object and be affected by itx'xactly alike, 3'et to n\e only one of these effects would be gfbunded in the ego: and all the efl'ects upon the minds of the others in respect to myselt would be grounded in the non-ego. Similar tfuths, therefore, grounded in the ego, which can not be differentiated, but whose times can be heterated, are not one and the same, but separate exist- ences: they are hetera. But with respect to truths grounded in the non-e^o, though their effects upon the mind may be exactly similar, or to change the form of expression, these truths may exactly resemble each other, yet if their , WHERES can be heterated, they are not the same but separate existences. If three men receive mental impressions exactly similar, yet any person can heterate the wheres of these effects and therefore the effects are not the same. Dissimilar truths grounded in the non-ego, or in the ego, can be discrimi- nated into differentia, they can be differentiated ; but similar truths grounded in the non-^go, whose wheres cftn not be heterated, are to us the same. It 53 especially those about logic, are so interlinked that we arc obliged to draw, sometimes, upon those whose explaination has not yet been given in order to accomplish the work on hand. And the subject upon which we have been engaged and which we must yet consider more closely, has been misunder- stood, as we believe, by all writers heretofore upon logic. CHAPTER X. HOMONICAL PROPOSITIONS. We have defined a logical proposition to be the result of a comparison between two existences made immediately by the mind and expressed in words: and a conclusional proposition to be the result of comparisons be- tween existences made mediately and expressed in words. We will first give pur attention to logical propositions. And the result exprifssed in every logi- cal proposition will be either a truth or an error. If our faculties be in a perfect state and exercised in the right manner, the result will generally be a truth : but if our faculties do not act in a legitimate and sufficiently vigorous manner, we will obtain an error. In every instance, therefore, it is always necessary, in order to obtain a truth by comparison, that we should have an adequate knowledge of each of the two truths compared in logical proposi- tions. We have already shown that all existences may be compared one with another, and that knowledge is a result brought out of the relations ot exis- tences. To show, indeed, how the mind possesses the capacity in itself to compare is no part of our undertaking; but that It actually does compare among the existences which are the subjects of its cognitions, and hence gain knowledge by the comparisons, we think, has been sufficiently shown already. Now when the mind has gained knowledge and clothed this knowledge with words, i. e., given it as it were, a body to render it visible to others, the knowledge gained, indeed, is thus made appreciable to others, but the opem- tions of the mind in gaining that knowledge, leave no trace behind. And did every proposition clearly exhibit the two existences compared, and also the result or truth gained by their comparison, propositions would need no interpretation, for each one would fully interpret itself. But the men who commenced language, were seeking merely for an instrument of utility in the common affairs of their lives, in which clearness of detail and precision of expression were of less importance than general availability and dispatch. And therefore, in every language, the truths which are really compared in propositions are sometimes but dimly shadowed forth, and the result of their comparison always but obscurely shown by the form of the words. And this makes it necessary, in order to obtain a thorough insight into propositions, to show what the two truths compared really are, that the result of their com- parison may be clearly perceived. To this task, therefore, we now proceed; 03 md we will commence with tlie cxamiualion of homonical propositions. Take the proposition '*Ked is red," and let us endeavor to clearly set tut the two things compared and the truth, which is the result of their com- arison. And fii«t, we must observe that an existence which is absolutely the same existence can not be two existences, and that one Ihinf, per se can not be compared^at all : two existences must always be found in every propo- sition. Wc must also observe that when we have the knowledge of an exis- tence, we can always make some discrimination respecting that existence: for without some discrimination we can have no knowledge. Plurality of ex- istences is necessary to our knowledge of anyone; and, tkerefore, absolute oneness or identity is not within our knowledge: every truth of which we have any knowledge is evolved from relations, liot how then can we say that "John is John," or what is eqtiivalent to this, "John is himself"? In order to understand this it is necessary to recollect that some trutlis ara grounded in the non-ego and others in the ego. It we look at a tree, the relations between the tree and the ego bring to our knowledge an existence (a tree) grounded in the non-ego, and also an int(;rnal existence grounded in the ego. Now simple existences can only be discriminated by their wheres, by their times and by their effects. Many effects upon the mind are inter se similia; thus if we look at an inkstand to-day, and to-morrow lo^ok at it again ; both' to-day and to morrow it will produce effects upon the mind exactly similai* yet these effects will not be the same, they will not be homon, for they can be discriminated by their times. But similar effects upon our minds can only be discriminated by their times: and where there can be no heteratiou of times made, there can be but one and the same existence grounded in the ego, similarity is lost in identity. And we must always recollect that by the ego, we mean my mind for me and your mind for j-ou: For should I and a thousand other persons, at one and at the same iilstant of time, look at an object and be affected by it exactly alike, yet to n\e only one of these effects would be gfbunded in the ego: and all the eftects upon the minds of the others in respect to myselt would be grounded in the non-ego. Similar (tilths, therefore, grounded in the ego, which can not be differentiated, but whose times can be heterated, are not one and the same, but separate exist- ences: they are hetera. But with respect to truths grounded in the non-e^o, though their effects upon the mind may be exactly similar, or to change the form of expression, these truths may exactly resemble each other, yet if their , WHERES can be heterated, they are not the same but separate existences. If ' three men receive mental impressions exacily similar, yet any person can heterate the wheres of these effects and therefore the effects are not the same. Dissimilar truths grounded in the non-ego, or in the ego, can be discrimi- nated into differentia, they can be differentiated ; but similar truths grounded in the non-%o, whose wheres cftn not be heterated, are to us the same. It we should see a rock of a particular shape and color to-day iuone place, and to-morrow see a rock exactly similar in another place, the only thing whicii would enable us to know that these two rocks are not the same, is that their present wheres are hetera. If we should find out that tht first rock was no longer in its wonted place, and we could not tell the where in which it now is, we would most likely conclude the second one to be it. Respecting simi- lar truths grounded in the ego, therefore, the heleration of their times alone destroys the identity: respecting similar truths grounded in the non-ego, time being the same, the heleration of their wheres destroys the identity! The power of the mind to heterate depends upon the time and space. And now we look at John and receive a mental effect, and again look at him and receive a similar effect, the times of these effects can be heterated, and hence there are two similar existences grounded in the ego, wliich can . be compared siith each other. But if we project these existences and ground Ihera in the non-ego, at the very time we last looked at John, we knew^f but one where for these two subjective existences to exist objectively, and hence no heleration, objectively, of their wheres can be made; and, therefore, as they are subjectively similia, they are objectively to us homon: and henco we can say that John is John, or that John is himself. The mind can pIso gain a truth grounded in the non-ego'and afterwards recall it by what w^e •call memory: and as often as the mind does thus recall one and the same 4 objective truth, so many subjective truths inter se similia, but not identical, will pass through the ego, any two of which may be compared and projected! And respecting the projection of truths from the ground of the ego into that ot the non-ego, we have already seen heretofore, how existences are divided by the mind into those grounded in the ego and those grounded in the non- ego. And hence the meaning cf the proposition "John is himself," is tTiat John, grounded in the non-ego, and iiimseij.-, grounded in the non-ego are the same thing; John and John who are subjectively hetera are objectively homon. We may say that John and himself are the same thing, or that John . and himself exist identically, or that John exists as himself: whatever itay be the words and their syntactical relations, the two subjective existences, each of which we call John, are objectively the same, and what is affirmed by the proposition, is homon. None of these expressions, however, mark in ^ words with enlire fullness the whole of the mmd's operations, but merely state or set down the existences compared and affirm the result of the com- parison. And in a large class, of propositions, all of that class, which w'e have called homonical, the result of the comparison made by the mmd is homon, homon is the thing affirmed. This is always the case in those propo- sitions which defined words, i. e., in which the meaning of a word is ex- plained by some syuonkn or equivalent expression: as taithfulibss is fidelity. 55 i. e., the meaning of the word faithfulness and that of fidelity are homon The following propositions are similar to the one first spoken of: "Sun is the name of the orb of day;" "Death is the name ot the etid of life;" "Term is a name given to each df the names which distinguish the existences com- pared in a proposition;" and so on. All of these propositions are homoni- cal, homon is affirmed in each one of them. Such propositions as the one above have been called verbal, because the existences compared in them are words. And according to the old but erro- neous system of predication, in such propositions, one name is predicated or affirmed of another. One name, however, can not be affirmed of another, uof canone existence be affirmed of another; the only thing that can be affirmed, in such propositions as we are now treating of, is homon. In those propositions, also, which arc called real, in these, which explain the nature of the thing defined, homon is the thing affirmed; as "A triangle (the thing signified by the word) is a figure having three sides and three^angles," "Ihe eye is ^ physical organ by which we see," "A primary property of matter is impenetrability," and so oo, • But in the proposition "John is John," which we considered a little while ago, we notice that both the subject and predicate are aggregate exis- tences, and that each one is compared with the other in the aggregate as a totality. Now when the subject is an aggregate existence, and U^is viewed as atotality, andiillof itsgregaria are taken collectively, the predicate must also be compared in the aggregate in all homonical propositions: for an aggregate existence, as a totafity, can not be the same as a simple existence, a gregarium, and vice versa. But there are homonical propositions in whicli the subject, in appearance, would seem to be an aggregate existence viewed as a totality, while the predicate is very plainly a simple existence, a gre- garium : we must therefore examine such propositions. AVe must always keep in view that in every simple proposition, two existences and only two are compared: in logical propositions these two ex- istences are immediately,,compared, and in conclusional propositions they are mediately compared. These two existences may be, each of them, sim- ple, aggregate, or collective; yet there can but two enter into the comparison in the proposition of which the result is expressed in words. And one of the difflculUes in the way of understanding propositions, is to ascertain what are really the two existences and the nature of each of them in the proposition. , This difficulty has not been overcome by any writer upon logic, heretofore, with whose work we are acquainted. Now when we say that Snow is white, or. that Iron is fusible, we might believe that snow and iron, aggregate existences, are compared in' to- tality, with their predicates respectively: this ho-wever, would be entirely erroneous. And in order to ascertain and clearly exhibit by the wording of 56 t]i£ proposition, tlie two things wliich are really compared, we have to stale the proposition thus; One of the capacial gregaria of iron is fusibility, a proposition in whiclf a like result is obtained as in the other, and in which two simple existences, which arc the things really compared distinctly appear. And if the .proposition be stated so that the horaonical nature of it also shall clearly appear, it will read thus; One of the capacial gregaria of iron and lusibility are homoH. And in ail homonical propositions in which the sub- ject is an agffregate existance and the predicate a simple one, it is only one of the greuariaof the aggregate existence, that is compared. In the proposi- tion, ditaline was ambitious, wiicn the things actually compared are clearly set out it will read Ono of the capacial gregai'ia of Cataline was am- bition, i. e., one of the capacial gregaria of Catalin«r and ambition are homou. Wlien we say Red is red, the result of the comparison is easily seen, because we plainly see that both subject and predicate are simple exis- tences; but when the real subject is covered up by a term which signifies an aggregate existence, and the predicate is simple, we are misled. And hence in such propositions as Ironjs fusible, writers have said that the predicate is affirmed of the subject, or that the predicate iscpntmned in the subject and so on, all of which expressions not only give erroneous notions of the nature of propositions in general, but per se they are utterly false: for the existence which propositionally is called the predicate is com- pared with the subject and the result of such comparison is'what is atlirmed in every proposition. And although fusibility is one of the capacial gregaria of iron, and it is contained in this aggregate txistence,yet this aggregate ex- istence in totality is not 'the subject of the proposition -Iron is fusible, but this capacial gregarium of iron is the subject. We have already shown that in every proposition two subjective existences, i. e., existences grounded in in the ego are compared: and in the proposition Iron Is fusible, twx) fusi- bilities are sujectively compared, and subjectively they are similia: and then they are objectively located as homon in the aggregate existence iron, and this is the result of the comparison in the proposition Iron is fusible. Now as there are but two classes of subjects, simple and aggregate, and so also of predicates, it would not be necessary at present to say any- thing further respecting homonical propositions were there not sometimes set down the words all, evtry, most, some, the whole of, none,^oth, etc., alonir with subjects and predicates: but homonical propositions in which these words are either expressed or understood need a further investigation. And when we say that All iron is fusible, which writers have called a uni- versal proposition, what do we mean by the words All kon ? As iron is an aggregate existence, let us first examine a simpler case; take the proposi- tion All red is red,* i. e.. red and red are homon. Now almost any one will say that this proposition is self-evident, because were the predi6atc anything 57 else than red, it could not objectively be the same thing as the subjept, which is red. 'Now this explainalion can*easily b6 applied to unravel the mysteries of the proposition All iron is fusible. For this proposition may be thus stated, Oneof the capacial gregarium of all iron and fusibility are homon. And from this proposition, it must appear, that were fusibility lacking in an aggregate existence, that existence could not be ipon. Fusibility is a neces- sary gregarium in any aggregate existence, which we distinguish by the name, iron; and consequently it must exist in this piece, that piece, and in all pieces of similar aggregations. The word all standing before iron does not indicate that the mind must have made what is usually called an induction, i. e., that the mind from a great number of l^tances has determined the laws of nature to be uniform, and therefore this piece and that piece will fuse. The discovery of the capa- cial gregarium, fusibility, in one single piece of iron, if by this gregarium we distinguish an aggregate existence from' others, and mark the distinction by the w>rd iron, will enable us to say with certainty and^ruth that All iron is fusible; for in doing so, we merely state that one of the necessaiy gre- garia of an aggregate existence, which we distinguish by the name iron, and fusibility are homon. . That there may be other gregar/a in the, aggregation, of which as yet we know nothing, does not change the case at all. Suppose a person to be taken into a large room in which there were four kinds of balls upon different shelves around the apartment, and he be required to give distinguishing names, which would enable him to speak afterwards about the bulls, respecting merely their tastes and colors. lie would take up the first one at hand, and perceive that it was of a red color and had a sweet taste, and therefore he would name this ball A. Thpn every ball in the room that was red and sweet, as balls of color» and tastes, which are inter se similia,. can not be diflerentiated, must be called A from a men- tal necessity. And by the name A, they are afterwards distinguished from those that are blue and sour, which might be called B, and from those which are while and bitter, which might be called C, and- so on. But so soon as he had given the name A to distinguish the first ball of a red color and ss^'eet taste from others, all balls of a red color and sweet taste must be called A, and if so, could he not immediately afier naming the first ball, have said with perfect certainty and truth that all A is red and all A is sweet? And it afterwards, a red ball should be found that was sour, it would not be an A, but it must be called by some other name. But an Indian, before the discovery of America, might have said that all men are red, for he had never seen any man of a different color, yet his assertion would not have been truQ. The ancients also, might have said and did say, that all swans are white, yet such is not the case. And the error in both these ca^es lies in taking the gregarium of a particular object or objects and making this gregarium in our mind, one of the necessary gregaria to dis- tinguish this object from others, when ^t is not so: there were other things red besides Indians, and other things white besides swan's, when animals were distinguished by names: the color was not one of the gregaria by which these objects were necessarily distinguished. But we have said that aggregate existences are distinguished inter se by the facial and capacial gregaria co-existing. And hence did one aggre^ gate existence contain similar facial but not similar capacial gregaria with another, the two aggregations would not be similia, and they could not be in- telligently distinguished by the same name. A distinguishing name is r. word taken at pleasure to distinguish existences inter se; and when It sUnds for an aggregation, any one of the gregaria Bine qua*)n, can not bo lacking, and the aggregation be called by the same name as an object in which it exists. Charcoal and the dinmond are said to be, as elements, similia, yet the gregaria differ and consequently we can not speak of each intelligently and use the same name. • But how then, say you, is it that % black swan and a white one may both be called swans ? Simply because they are differentiated into^ swan's irrespective of their colors, just as red and white, as we have seen, are first diffeientiated into color, amd then distinguished inter se, by the names red and white. All men are mortal, is a proposition of the same kind as All iron Is fusible. Mortality is one of the capacial gregaria sine qua non of man, and a living being not subject to death would not be a man. Ihe proposi- tion All m'en are mortal, however is a very different one from. All men are mortals- the first affirms homon of mortality and one of the cappcial gre- garia sine qua non of man; the second affirms man and one of the aggregate existences called mortals to be homon. AH men are animals, and. All sheep are animals, are similar propositions, and they may be. thus interpreted: man and one species of animals are homon, sheep and one species of animals are homon. ' . . . .., But to pursue further the effect of the word all in propositions, if when man was first, placed upon the earth, he had lived to the age of tcn| thousand years without a death occurring, and if during that period he had invented language and distinguished himself by the name man, it is plain that mortality would not have been in his mind one of the capacial gre- garia of himself: he would not at least have known this by direct observa- tion And if during this time, no constituttonal changes among external objects had come to his knowledge, it is evident that he would have known 1 nothing at all about the capacial gregaria of objects; but all the names inl his language would have been signs to. distinguish simple existences inter se, and aggregations of facial gregaria. And therefore all the aggregate exis- tences now classified by their capacial gregaria and marked by distinguish- i 69 • ing names, would have remained unclassified. And then each one of the facial gregaria, whic^^was a sine qua non of any class, would have been a necessity in order that any object might have been called by the name given to individuals of the class. Names, of course, under the circumstances would have been few in Bumber. But suppose now, that at the end of the period above spoken of, one of the human species had died, here would have been to mankind a new truth learned by observation. And were this instance of deatU then made known to all the living, all subsequent deaths would not have been new truths, but other instances of similar truths. And although non simile est idem or non similia sunt idem, objectively, yet subjectively similia are the same thing if time be* left out of tho question. And hence respecting the knonrlcdge of truths in the mind, the recurrence of similia are regarded and often spoken of as other instances of the same truth, Although they ar^not homon i)ut similia; their times arehetera and therefore the truths are similia, but were their times homon, the truths also, would be subjectively homo% Now if we have gained the knowledge of one individual of similia, we have gainod all the knowledge we will ever have of tho similia, except- ing their number or instances. And therefore after pnc death had occurred, the question would have been, men being similia in those gregaria which to- gether make the object distinguished by the name man, is death one of these capacial gregari^ That it is could have been proved to men under the above circumstances only by a process of reasoning which we shall develop hereafter. (See book 1, chapt. xxii.) But so soon as it is established to be such, it is a sine qua non of man and hence we say that death and one of the capacial gregaria of all men are homon. And as aggregate existences are composed of certain facial and capacial gregaria, which are the very things which distinguish them into classes of similia, when any oi^e of these gre- garia sine qua non is known and given a name, it may be made the predicate of an homonical proposition, in which the word all names the sum totum of the aggregate existences for any one of which the noun placed after all . stands as the name. And hence that all iron is fusible, when fusibility is once in our minds a sine qua non of iron, is a necessity of our miyds. It may TJe said that fusibility is not a gregarium sine qua non to distinguish iron from other things; for gold and other metals possess it. This is true; but go one step back into the class of things called by the narne metal, and we will find fusi- bility to be one of the distinguishing gregaria, and in subclassifications this . gregarium must pass int^ each of the subclasses;- for they, each of them, under the name metal possessed It. And hencei by adding the words all and EVERY to the name of an aggregate existence and then making the term the subjective one of an homonical proposition with a simple existence as the predicate, we show this simple existence named in the pr^icate to be one of the gregaria sine qua non of the aggregate existence named in the subject. eo All gold is proof against the effect of nitric acid, i. e., one of the capacial gregaria sine qua non of g»ld, and proof against tlA^ffect of nitric acid are homon. But we must now examine the function of the word some when placed before the name of an aggregate existence in a proposition. Take the propo- sition Some ink is red, i. e., one of the facial gregaria of some ink and red arehomon. Now it must appear that the facial gregarium here mentioned is not a sine qua non of ink, but that it is one which compared witli, some other color, enables us to differentiate inks. Some therefore, as it names the^part of a whole, shows also by being pjaced before an aggregate existence in homonical propositions, that the gregarium, which appears as a simple exis- tence in the predicate, is not a sine qua non of the clHIs of aggregate exis- tences distinguished by the name which appears in the subje'ct and named by the noun after some. * • ' * * We do not deem it pecessary to pursue the subject of homonical propositions further at present. If the reader will carefully stud> what has been said already, we think he will be a^le to follow an* understand the arguments, which we will -advance hereafter. We will, however, set down several homonical propositions in the language that is used in common dis- course, and the reader can change the phraseology, so aa to make the result aflSrmed appear plainly to be homon: Some men are black-eyed; All fowls lay eggs ; All gold is maleable ; God is love ; An apple is an apple ; A straight line is the shortest distence between two points in space; Ice is frozen water; Schuylkill is the name of a river in Pennsylvania; Washington died at Mount Vernon ; We are living in the nineteenth century of the Christian era; Columbus discovered America A. D. 1492: Shakespeare was a dramatic author; Sophocles wrot^ ^dcpus Tyrannus; Newton discovered the univer- sal law of gravitation. CHAPTER XI. - ^ HETERICAL PROPOSITIONS. Having Seated of homonical propositions, we hope, with partial suc- cess, we,come now to speak of the second class, which we hare called heter- cal propositions. And heterical propositions affirm results, which are directly the opposite of those affirmed by homonical ones, and consequently the twa classes £\re differentia; and when a proposition of the one class is spoken with reference to the other, it denies the affirmation made by the other. If any person affirm that A is B, i. e., Ihat A and B are homon, and another person reply that A is not B, i.e., that A and be are hetera, the latter makes and aflSrmation contradictory of the affirmation of the former and vice versa. " Now if we take two twenty dollar gold pieces which are inter se 61 jsimilia, and lay them before us, any person will say this piece is not that one. But the two pieces being inter se similia, if you hand one of them to a per- json, and then take it again and put the two together, and ask the person which one lie had in his hand, he can not tell. How then does any one know that this piece is not that one, i. e., that the two pieces are not homon, but hetera? Simply because the wheres of the two pieces at the same time can be heterated. But is not th« proposition. This piece is not that one, an independent propo- sition, i. e., a proposition expressed without reference to any other? If it is such, tlien it can not contain a denial or negation of the subject, as it is generally supposed, but it positively affirms this piece and that piece to be hetera. You can not numerically count pieces of money without hcterating them, and you can not express in words the heteration of them without using an heterical yroposition or propositions. What is the difference between These two pieces are separate existences, and This piece is not that one; leav- ing the wording out of the consideration ? The difference is this, the former propositien never could have been put into words at all, without the latter one having first been menially at least eiuntiated: the latter proposition must preceed the former in the mind, or a knowledge of the former never could be gained: in eflect, however, the two are alike. The former proposi- tion may be resolved into This piece is an existence and that piece is an exis- tence and the whole expression is exquivalent to This piece is not that piece 1. e., thi8 piece and thatpiece are hetera. And every heterical proposition may,' in effect, be exactly expressed by the use of two homonical ones, by placin<^ the distinguishing names of hetera, this and that, befcre their subjects: two homonical propositions may also be condensed into one similical or com- mensural one; or they may be differentiated or incommensurated, in. differ- ential or incommensural propositions, as we shall see hereafter. But there must be an heteration of existences in the mind before any proposition wlwt- ever can be expressed; for we have already shown that the process of heter- ation lies at the very foundation of knowledge. And this process of hetera- tien can not be a negative process; it must be positive or it would amount to nothing, and its positive character can not be expressed but by an affirma- tion. This has been overlooked, heretofore, by all writers upon logic. Be- cause the panicle not is found in the proposition, it has been universally believed that the predicate denied something of the subject, or that the predi- cate was denied of the subject; a proposition, which follows legitimately enough from an other, which is that when this particle is omitted, something is affirmed of the subject, but both of these suppositions are untrue. The predicate is no more affirmed or denied of the subject in, propositions than the subject is of the predicate; the two existences are compared, the one with the other, and that which is affirmed, in all cases, is the result of the comparison. It is impossible for the human mind to affirm or deny one 62 cxistancc of another ; all that we can do is to affirm some relation existing between existences. One and the same existence of the non-ego can not sustain heterical, similical or differential relation to the ego in an homonical time; for it it could, we could have no knowledge of identity. When we lay, thereiore, that A is not B, we do not mean that A does not exist, or that B does not exist, for both must have an existence .grounded in the ego at least, or we could not put their separate names down on paper; but, by A is not D, we mean that A and B exist heterically, that A and B are hetera. The particle, NOT, therefore, in propositions, stands as the sign of hetcrution made by the mind, but the result of the heteration is positive, and it is affirmed in all propositions containing this particle. And we lay down this rule: That whenever the wheres ot existences grounded in the non-ego can be heteraled in an homonical time, and whenever the times of existences grounded in the e^o can be heterated, the heterical relations of these existences are expressed in heterical propositions. In homonical propositions we saw that the wheres of the two existences compared, could not at the same time be heterated. When we say, John is John, the subject and predicate subjectively have the same where, but not an homonical time: John and John objectively have the same whereat the same time, and therefore, objectively they are homon. But the objective John and the subjective John are hetera because their wheres at the same time can be heterated; and John and John are subjectively hetera because, though, their wheres are homon, they can not have an homonical time. And, thercfforo, homonical and heterical propositions contradict each other, when their sub- jects arc similia in every respect, and their predicates similia leaving the particle not out of the consideration. • Now in heterical propositions, we make no account of the similarity or dissimilarity of existences; all we care about, is to be able to heterate the wheres of existences grounded in the non-ego at any given time, and the times of existences grounded in the ego, and then we affirm hetera. And hence if we place two white marbles before us, the color of the one and that of the other being perfectly similia. yet we say that the color of the one is not that of the other, i. e., the color of the one and that of the other are hetera; for the wheres of these colors can be heteraled. When, however, we look at A (one) marble and say The color of this marble is white, or to use the short expression. This marble is white; the color of the marble and wiiitp: sub- jectively have the same where, but heterical times; but when we project these subjectively heterical colors which are inter se similia, into (he objective marble, they both have the same where at the same time and therefore, we affirm homon. Now we have, heretofore, divided subjects and predicates into two 62 classes, simple and aggregate. And of simple cjistences, some become the gregaria of aggregations, others do not. Time and space are never gregaria. And we must have observed that it is the relations of simple existences or of aggregations in time and space, that enable us to affirm homon or hetera; the power of the mind to heterate depends upon time and space. When we say tbat this apple is not that one, we apparently compare one apple with the other immediately: the existences, however, which are immediately com- pared, are the wlieres of the one and the other at the same time. But when we say subjectively, An onion is not a peach, this proposition is more than heterical and it belongs to the differential class, which we will treat of hereafter. If, however, we say this peach is not that onion, we heterate the wheres and affirm hetera, and tliis is shown by the words this and that And if the reader will bear in mind, that whenever he can heterate the wheres* of existences at the same time, or sulyectivelj heterate 'the times of subjec- ive existences, the proposition may be iieterical, we think he will be able to detect heterical propositions, whenever he may find them in books or couver sation, by some words which distinguish hetera. We will set down a few heterical propositions for practice: Philadel- phia is not New York; The Pacific Ocean is not the Atlantic; My hat does not lie on the floor; The birth-place of Washington was not Boston; This hand is not that one. CHAPTER XII. 8TMILICAL PKOPOSITIOXS. When treating of homonical propositions, we shawed that absolute identity makes no part of our knowledge; that in all homonical proppsitions» the exisU^nces compared are always subjectively hetera; that heterical results in the order of time always precede our knowledge of identity, an«i are the v very first results obtained ; that the knowledge of the existence of any simple existence is dependent upon hetera; and that unless heterical results can be obtained, chaos reigns supreme. If I see a horse to-day and to-morrow see the same horse again, nevertheless, subjectivel}', I have seen two distinct horses; and when viewed as existences grounded iu the ego, I distinguish them by heleraling their times, but when projected onto the ground of the non-ego, the heteration of their times does not distinguish them and as I can not heterate their wheres at the same time, I caji not distinguish them at all, but pronounce them to be homon. But suppose that sulgeclively I consider heterical existences and can not further discriminate them, and objectively also I heterate the existences but can distinguish them no further, then we call the existences similia. And Jience when we can heterate subjective existences, but can proceed no further, tlic existences are subjectively similia, and when we can heterate objective 64 existences but can distinguUh themno further, tbe^xistences are objectively similla. And, therefore, objective bomon is always subjective similia, but not always vice versa; for subjective similia may also be objective similia. Subjective homon can not be expressed in a proposition, i. e., two acts, feel- ings or states of mind can not be one and the same, they must be beiera, and one thing per se can not be compared. Take the proposition This orange tastes like that one, i. c., the tastes of this one and of that one are similia. Now the sensations of the taste of the one and of the other, as existences grounded in the ego, arc similia, and when projected onto the ground of the non-ego, each one is a gregarium of heterical objects whose wheres can be heterated, and therefore, objectively.the tastes are similia. We need not proceed further at present with similical propositions. We will subjoin a few examples for practice: This apple tastes like that one; John is like his father; Time is like a silent river. CHAPTER XIII. DIFFERENTIAL PROPOSITIOJTS. We proceed now to the consideration of the fourth class ef proposi- tions, namely, differential propositions. And when two subjective existences can be discriminated by anything besides their times, the existences are sub- jectively differentia. The effect produced upon and within the mind by red is different in kind from the effect produced by green, and hence the two effects are not only hetera subjectively, but also differentia. And existences, which are subjectively differentia, must necessarily, if each have a corres- ponding objective ^istence, be also objectively differentia. But ho# or why it is that the mind is able to discriminate between red and green,subjectively, we do not sufficiently understand. The two objects, which produce severally these different effects upon our minds. Sustain in some manner different re- lation to the ego: they are other different elemeitary principles, or the one is composed of more or differently arranged gregaria than the other. Let this be as it may, for logical purposes it makes no differtncc to us; every person will distinguish subjectively and objectively red from green, and consider them to be things differing in kind — differentia. We have already stated that subjects and predicates of propositions are either simple or aggregate existences. And when both subject and predi- cate are simple existences, the differentiation clearly appears. That red is not green ; will easily be seen to be a differential proposition. The iign not does not indeed of itself indicate whether the existences have been differen-* tiated or meiely heterated. But hcteration can easily be distinguished from differentiation, if we look at the terms of the proposition. In the heterical proposition, This red is not that green ; we see that the terms are particular names, the names of individual existences, and that the distinguishing heteri- 65 hetericiil names, this and that are joined wiih the common names, red an I GRKEN, and thus making red and green the names of particular inlividuaN: Wliile in tiie differential i)r<>poftilion Ued is not green, red and green are unlimited common names. Tlie name red stands for this red, tiiat red and for any red, and fo also with green ; but when we say tliis red, or this or thai green we mean an individual. And lience in heterical propositions, Ihelerni:* are individual names, Ahile in differential propositions, they are unlimitfd coainion niimes. And we may assert with truth that*all red is not green: though this proposition, from the custom of our way of speaking, seems to imply that some red is green, and to avoid the effects of language upon our mind?* it is usual and better to siy that xo red is green. We are accustomed to say with truth that till men are not black, i. e., one of the gregaria sineqn.i non of man is not black, i. e., black and each of the gregaria sine (pia non of man are differentia, and therefore, by implicaliou wo afflrm that some ir.ca are, or may, be black. And hence the custom of language, when we say that all red is not green, would lead us to inter that we meant, some red is grcin, i. e., that some red and green are homon* In every r roposition, therefore, in w hich the particle not occurs, and the subject and predicate are simple exis- tances, if the teims are unlimited common nomes, the proposition is differen- tial, it they are particular names the prooosiijou is heterical; :is John is not (.'liarles. And this is tilso the case when both the subjectl ami preilicate are aggregate existences, as a man is not a horse. Is a differential proposition ; This man Is not that e measured, for in measurement there must lie siome coincidence anil not mere separation, and differentia, as differentia, can not be measured, for they can have nothing iii common which is measurable. ^^imilia, therefore, are the only results, which admit of c' as long as that one I. e., the lengths of the two sticks are commensural, and thus we can compare n»any of the similia of nature and obtain commensural results. We do not lUem it necessary to enlarge upon the subject ol commensural propositions, as we coneluded that tliey will be easily under-^to«>d, and they will als«i be illuslratid along with the iuhers hereafter. We must here observe, how ver, that homon is at the bot- tom cf them. Wi»en we say, this red is as red as that reil, the a8 iikd an«i THAT red are houion, and by stating two homonical propositions with tin* word AS between them, we will readily see, how tw« hom»)nical propositions merge into one commensural one: Thus, this red is red, as, that red is r«f«l. In the first pr(»position, the subject and p:edicate are objecliontly homon, and so also with the second proposition, and the word as shows that the two are commensural. W<' will sulijoin a tVw examples (or practice: The day WHS as dark as niixhl ; this candle shines as bright as thul one; she looks as fresh as the rose; it is just as sweet as honty. x^-; — /. 6? CHAPTER XV. IXCOMMKNRCUAL PROPOSITIONfl. We come now to the consideration of incommensurable propositions, the last class of logical propositions. And in incommensural propositions, the existences compared are similia in kind, but they differ iu decrree or quantify. \^hen we say that this candle shines brighter than (hat one, we mean (hat there is an excess of brightness in the one compared with the other. The two are not differentia, as wliite and black are, bi.t there is a difference, an excess, in the one over and above the brightness which exists in the other. The difference In the specific gravity of bbdies is expressed in incommensural propositions, as ijold is heavier than iron, i. e., the specific gravity of gold and (hat of iron are incommensural. This excess in one of the existences compared is some times shown by the use of an adjective name in the comparative degree. There are, however, three ways of expressing the exc(»sg in words, viz., A is larger than J5, li is less than A, ai.d B is not so large, or not as large as A. Now when we say (hat snow is white i. e., one of the facial gregaria of snow and white are nomon, we l.K-ate the gregarium, white among the other gregaria, which make up snow, so when we say that ice is colder than water, we locate the existence, which would t)e named by the adjective name In (he I osiiive degr^H? in the subject ice, ami by adding eh or mohk (o (liis adjecdve name, and thus marking an excess, we locate hIso the excess in the subject. Take first (he case of the comparison of simple existences, this red is retler than (hat red. Now leaving kh off of the adjective name and we will have HEKoiiE TiiKM,(his red is red, an homonicnl proposition. And in (he propo- sition (his led is reder than that red, we retain the homonical red— the predl- eate of the homonical proposition, and add, v.n to its name to snow an excess al»ove the retl which follows after tuan, and which is ihe predicate of (he in- (ommensural |>rop<.sllion. Hut as (he predicate of the luunonical proposition, was hn-aied objectively in the subject (.f the proposition, i.e., it and tne subj<^ci were found (o be homon, so (he excess ridded lo it in the incommensural pro- poslilon must be located with il in the subjeei of the incommensural uroiH.- situui. *^ * In the incommensural proposition, this red is less reil than that red, however, the «lecremenl is li»CM(ed in the subject and conwquenlly the excess IS in the |»redicate. And In the pro|)08ition, this red is not so red as tlint red, the f-oKii) aijfl THAI. KKD are h« mon, i. e., the degrees o[ red suujeciively (oinmensural are objectively hcmion in ti.e predicate of the incommensural propo.sitiop, and the particle ^'(»T^h<^ws that the degrees in the subject and those in the homonical predicate are ineommensuial. In the commensural pr as rcti as that red, the last (rtOREi>s, which are h'>mosi- lions as; John is the strongest man in the house. This proposition at first sight would apfjear to lHt>ng to a seventh class of propositions, but on exami- nation, it will be found to In? merely an homonical proposition collected into a conclusion from several incommensural <»nes, and it may be thus staled, the strongest man among t lit men m the house and Jidin are homtm. And so ulso, Sampson was the strongest man of whom we have read, is an homonical propositiou. Hercules was stronger man Sampson, is an incumiuensural pro- position. And all propositions, in which there are superlative names, are homonical. We g.ve the following examples fur practice: Winter is colder thau summer; the elephant is m«)re intelligent than the as"* ; dogs are nwue taithfui than cats; c<»ws are more useful than rabbits; the bite of a rattle- snake is mme dangenms to man than the atingof the wasp; Honey issweeter thansuirar; the m>le of the nighleni'ale is more plettsaul than ihht t»f the ei\»\v : x-f.. ^/., CIIAPTKH XVI. PROi'osiTioNs i»uo.Misd lo ex'st for the sake i>f argn ment. We will therefore, now give ^ome further attention to the terms and c<»pula of pro|M»siiions ol all the foregoing classes. Ami lookinir back to the nominal iruihs groundid in the non-ego, of I G9 which we spoke at the beginning of our iiirosligalious, anJ supposing that all objects had had the same color, cojld we have called this nominal tiulh A (one) color? We have already shown that the unit is a numerical re- lation and that our knowledge ot Ills envolved from duality or plurality-. And in the five nominal truths mentioned, we have hetera, from which the knowled;«:e of first, SECOND, thikd ^kc, might have beeu evolved. JBut we have also shown that when numbers, the names of the individuals of hetera, or of commensural colligations of hetera, are applied to existences, and the name to distinguish individuals otherwise than helerically, is spoken or written after them, the name so spoken or written must be the name of similia, a common name. We may hi^ve a horse and a dog and the two aro existences. But exisienck is not a name given lo distinguish existencea inter se, and should we write any name, which does distingui:>h existences inter se alter the word two, we will find that two will not apply unless the existences be inter ss similia. Horse and dog are dillerentia, and their names distinguish them; neither of these names, therefore, can be written after two so as to express lo us the numerical sum of a horse and a doir: as hetera existences, two may l>e applied to them, but not as ditterentia. And respecting the nominal truths, as tiie are inter se difterentia, two could not be joined with any name, which distinguishes them as nominal iruths. But if oxic be the name of a numerical relation, as we have shown when it is applied to a dirt'erential name, there must be more than one thiu'^' (lislinguished in like manner by the same name; there must bo similia; otherwise the ihing distinguished oy such name could have no numerical re- lations to other things, except as hetera, which in language do not receive differ- eulial names, which afterwards become Ihecommou names of similia. And therelore, when we say. An existence, by this expression we show that we have in our mind one of several or many existences, i. e., one of hetera, and \\heu we say a dog, the expression shows that we mention one of similia. Looking then at the nominal truth, (oi.oii, could we say that, this is a (one) color? We think not. We could say this is color, or this is an exis- tence, and that is sound; but a color, as a name, not only distiuiruishes color from sound, taste, d'C, but it also points out some one of similia, as colors. And hence a or an before a name, in homonical propositions, makes them (luasi similical ; as this town is a Philadelphia, i. e., this town and one of the IMiiladelphias are homon, and in effect, this town and Philadelphia are simi- lia. The proposition This town is Philadelphia; is an homonical pr«po8itioa but the placing of a before the predicate makes the proposition tnoiigh ho- monical still, quasi similical, there being but one Philadelpnia in our mind, and this t<»wn not being that one. And all names excepting proper names, used as terms of propositions point out among other things, a numerical relation inter similia. In the 70 l.omonlcal proposilion, John U Joh.. ; neither of llie ierm=i p>inl out a nu- merical relation; but in the homonicail prop:)sitiou J .hn is a man; i. c.,Joha anil a (one) man are homon, ihe predicate term i oin'.s out a numerical rela- tion, and as it stands lor tl»e 8ame object as John, when John is brought among the similia of which it is one, among these objects. John has a numerical relati»m, he is a man, one of the simiiia named man. Now bringing before us again the name color, i.»* these existed a reil and A green, we would tJien have two colors and we could say that reer names anil we coi hi not say, this is a red, or that is A green, though we could say this is a red color antl that is a green color. Jiut hi the homonical proposition Ukd is a color; uki> is brought from pri- mary proposili«»nal truths into noiuinal truths, and among nommal truths, it is one 4.f the simiiia, a color, i. e., ukd and a (o.ie) color are liomon. Hut if HKD be A color, ho^ can we fully distinguish m every respect this existence liiim others by words, when Ae have it in our minds, olherwiiC than by cal- ling it a ukd color r And hence we see that every term of a proposilitm, which is made up of more than one name of simple existences, |>oinls out the results of several relatims, ami the numerical relation among simiiia pointed out by the term, is called the extension ot the term. Passinir on now to the consideration of terms, which are the names of aggregate existences, take the piopoj-iiion, »now is while; i. e., a gregarium iiflinow and a white color are honwui, and we see that wuitk is brought into and fasciculated among other gregaria in snow by an homonical pro- p».8ition. Again, Snow i- cold, Snow will mell, iVc, are all hom(»nical pro- p«»sitions, and the prwlicftes of all these i roposii ions are located, lasciculaled in sni)W. We may say While is in snow ; i. e., the where of a wiiitk and thai of snow are homon. Cold is in snow, The capacial gregarium of melting is ia huow; all those gregaria co-exist in snow, i. e., a fasciculus of certain grega- ria and snow are homon. And if by homonical propositions we fasciculate simple existence^* in an aggregate one, can we not in like manner bring together aggiegate existences? When we say. The audience was intelligent, we have done so. John is mlelllgent, V\ illiam is inlelligen:, Mary is intelli- gent, A:c. ; but John was one of the audience, William was one, A:c. And when a name, as t'le term of a proposition, stands for an aggregate existance, the gregaria taken together in iasciculo constitute what is called Ihe comprehension of the term. And in the ditlVrential proposition, Stone • is not iron, the comprehensions <»f the terms, stone and iron, i. e , the gregaria of the one and those of the other, arc compared in fa-sciculo. Smon. If a, b, e, d and e be th ; simpU' existences, the grogaria of an ajr^re- gate existence, and A be the name of the rascioulat'd gregaria, we may then sajr according to the custom of lani^uai^e that A is a, A is b, etc. And if we wish to locate A in a some wiiekk, wliich shall be distinu'uished from other WUERES by words we m;*y say; A upon the tabb; is a. And if the where is n«»t ycl sufficiently distinguished, and we may say, A \ pon the table in the house; and still further, A upt>n thr table in the Iidusc of Jfdm Sliles on front street between Walnut and CMiestnut streets in ll>e city of I'hlladelphia is A. 15ul again, take the proposition, John's book is on the table; and we see that the ftubjcct of tliis proposition i> a fasciculation of the subject and jjredicale of the proposition, Tiiis book is the property of John. We do not consider it necessary to explnin tlie terms of propositions further: but the copula i» yet to be examined. Now in tlie propositions, I am; 1 exibt, or I am an existence: we must see that the attirmalion is made in the pres>ent tense, granuaatieally. And in the proposition, I was, Did exist, or Was an existence; the affirnmtion is also made at the present lime, but tlie time of existence spoken of, is the past. I was- an existence; may be rendered, The lime of my existence of which I spvak, and past time are hoiaon. C*idumb u iljscovered America, A 1). 1493; may be rendered The time of the discovery of America by Colum- bus aiui A. D 141)2 am homOn, etc. And whatever may be the tense of tha Vfirb, the existences are always compared and the attirmation made at the present lime. But respecting what is called tlur potential mode by gram- marians, as John may be a scUidar; the verb itsrlf imprus ::apacial gregaria; the cspacial gregaria of John and those of a scholar aresimilia; and iu the pro|MH»ition, John might have been a scholar; the capaeial gregaria are rc- fered to as having existed in past time. « Now in all propositions, we say that the c«>i)ttla is, means exists But take the propositicm, Nothiug is nothing; and if is nicans exj»f>, what Is it that does exist, for nothing can nf)t be an existence? But we say lUat it U the rdalion l)elween the suliject and predicate that exists. But still it will l)e asked the relation f>f what, when we say Nothing is nothing? And in order to nnderstand this, it is necessary to consifler how we came by the name no- thing. Take the proposition This is nothing, i. e.. This tl^ng and no-tl»ing are homon. Now if the subject this tiiixo, means st^me thino and the preilicate x«»thino, means no thing, how can the two be homon ? If we con- ceive of a witch, an old ]u\f of a woman, with a beard, ruling a broomstick, aubjectiveh this is some thing, but obj( clively it is nothing, and therefore, 73 we can say with truth that this some thing grounded in the ego, is upon the ground of the non-ego nothing; this is nothing. "Kom.— "Peace, peace, 3Iercutio, peace; Thou talketh of nothing." "Marc— True, I talk of dreams, wlilcb are the children of an idle brain, begot of nothing but rain fantasy.'* Now had man gained the knowledi^e of only two objective existences and had he called the one a, not a would have been a name sufficient to dis- tinguish th(* other, and he then could have said pointing to a This Is a and pointing to the other, This is not a; for if it be not a, it must be the other ex- istence. Both these propositions then would be homonical viz: This is a this and a arc homon ; This is not a, this and not a are homon. But if lie' wished to show a, and not a to be differentia, or to affirm helera in a proposi- tion, he would have to say, a is not not a, i. e., a and not a are hctera, or a and not a are diflereutia. But if there were four or Ave existences known to man and he should distinguish one of them by the name a, and then pointing to another he should say, this is not a; not a, would not distinguish any one of the remaining four from the others, and consequently not a would be indefi- nite. And hence when there are two existences or but two modes of exis- tence, and the one is named a, for instance, not a may be used as a definite namefortheother. as truth, not truth-error; faculty of vision, not faculty of vision-blind; hearing, not hearing-.ieaf. A:c. Bat when there are more than two existences or modes of cxistance, .not, i;k, i.x dis, Arc, joined to names makes an indefinite name. But suppose that we had the knowledge of but two existances which were inter se differentia, and we should give to each of them a separate name as iiED and green for instance, we would then say red is not green. But not oKEK^^ if it be any thing, must under the supposition, be red, and we could say, not green is red, i. e., not green and red are homon. But if we had a knowledge of three diflereutia, red, white and green, for instance, and we should say that red is not green, not green would stand f\)r either red or WHITE, and would b« indefinite. J5ut what definite existence Is meant iu the casl^by not (jueen, would be indicated by the subject of ihe proposition. RKi), and hence red and the not (4Rkkn are homon. And if not grekx and RED be homon in the proposition, red is not oreen, red and green muht be diflereutia: for in this proposj.irm, red and not green are homon, and in the proposition, green and not red aie homon, green is, and red is; the homoni- cal proposition, red is green, however, is not true, and the slmilical proposi- tion, red is like green is also untrue, and hence nc see how homon lies at the loiindAtion of ail propositions; and we see also that the pai tides not and NO, belong always to the subject or predicate and never to the copula. We have yow g(me far enough, perhaps to make our n«:ws of proposi- li or < the sign in commensura, just as in mathematics. 1st. A & B are homon, C & A' are homon, /. G=B. i 2d. A & 6 are hetera, C & A are hetera, .*. C & B are hetera. 84. A=B, C=A, .-. 0=B. A>B C>A .•.C>B I AB C>Aor CB 5th. A and B are homon, C and A are hetera '.C and B are hetera. 6th. A and B are homon C=A •.C=B. 7th i A and B, are homon, CA .•.CB. 8th. A and B are hetera, C and A are homon, .C and B are hetera. 9th. A and B are heterft, C=A .•.C=BorCB. 10th. A and B are hetera, C>A I orCA, .•.CB, orAB : .•.CB ;or AB. 16th. A>B orAB : C A, if it be so and therefore 2d^ 1st. And without the power to syllogise the car- penter could make no use of his foot-rule, the shoemaker no use of his last, the 81 farmer no use of his half-bushel ; no one could put into a pile one cord of wood ; and no one; could tell without first having knocked his hat oft'.whether the door in his house was high enough to let him enter without bending his body. The process of syllogising is used by every person in the daily vocations of life, and it always has been so used from the creation of man. But notwithstanding the almost constant use of the syllogism by all men, the process itself has been misunderstood both by the friends and the encmies_of logic. The opposers of logic have represcnied that if the syllo- gism be a true process of reasoning u cd by us in matters about which we reason, men could not have reasoned at all before the time of Aristotle, who is regarded as Die true expounder of logic; which is argument is analogous to the lollowing; If the wheels of a wagon turn upon the principles of the lever before these principles were understood men could not have driven wagons. The contempl, ht>wever, which the oj.noseis have heaped upon logic, and of which its innnds complain, is not owing to the want of a syllo- gistic process in the mind, but to the circumstance that the friends of logic have been neither able to explain this process, nor to refute the objections of its advisaries. For the explaination of the syllogism, most of the writers upon logic have relied upon the Aristotlean dictum de omne et nullo— what ever can be predicted of a class can be predicted of any individual of that class— and Jieuce tiiey say that the middle teim must always be distributed in one of th« premises by being the subject of a universal affirmative or the predicate of a negative pn^prosilion, which in our opinion amounts to nothing so far as the syllogistic process itself is concerned. For a class is nothing else than several individuals inter se similia, or but one individual difl^erentiated from nil other things; and hence the dictum asserts merely that whatever can be predicated of each one of similia can be predicated of any one of similia; and although this is true, it is but a part of the whole truth. If we have be- fore us several marbles, the colors of which are inter se similia, we may with equal truth, turn the dictum th3 other way, and say that whatever can be predicated of the color ot any one of the class, can be predicated of the color of each op.c of the class, for the reason that the colors are inter se similia. And for the same reason and for none other, to-wit, that the indi- viduals are similia in the respect in which every one or any one is spoken of, or joined with a certain predicate in a proposition, does the dictum mean anything: that there actually are in nature similia, difterentia, commensura and incommensura, is the foundation of the dictum, and yet a syllogism may be constructed of homonical or heterical premises. And from the notion Ihat in every syllogism tha middle term must be be distributed in one of the premises, i. e., stand for a whole class of individuals eo nomine et innumero; while in truth it is never does so stand, but always rcprestiuts an homonical 83 individual, or an individual of similia, or of commensura, the friends of logic have been overpowered by their own logic. And hence the friends of logic have conceeded to its adversaries, that in every legitimate syllogism, the con- clusion contains nothing which is not emplyed and virtually asseited in the premises. For say they we reason from generals to particulars, and what is trje in general is true in particular — dictum deomni et nullo. And although J. Stuart Mill was able to see that Aristotle's dictum was only adapted "to ex- plain in a circuitous and paraphrastic manner the meaning of the w^ord class." Yet he too along with the rest was overpowered by the dictum. And hence he says "It must be granted ihat in every syllogism considered as an argument to prove the conclusion, there is a petilio princlpii. W aen we say all men are mortal, Socrates is a man, therefore Socrates is mortal, it is unanswerably urged by the adversaries of the syllogistic theory, that the proposition, Socrates is mortal, is presupposed in the more general assump- tion, all men are mortal ; that we could not be assured of the mortality of all men, unless we were previously certain of the mortality of every individual man; that if it be still doubtful whether Socratee, or any other individual you choose to name, be mortal or not, the same degree of uncertainty must hang over the assertion, All men are mortal; that the general principle, in- stead of being given as evidence of the particular case, can not itself be taken for true without exception, until every shadow of doubt which could affect any case comprised with it is dispelled by evidence aliunde and then what remains tor the syllogism to prove ? That in short, no reasoning from generals to particulars can, as such, prove any thing; since from a general principle you can not infer any particulars but those which the principle itself assumes as foreknown. This doctrine is irrefragable." Now this "irrefragable doctrine" is owing to a misconception of the nature of propositions and of their combinations in the syllogism. In the first place it is not true, although it has generally been conceeded to be so, that there is nothing contained in the conclusion, which is not implyed in the premises. In the syllogism, A and B are similia, C and B are similia, therefore C and A are timilia, we have indeed the existences A and C in the premises, their relation, however, to each other, is neither expressed nor im- plyed in either of the premises, but it is evolved from the combination of the premises. And if it bo meant that by the combination of the premises the conclusion is implicated, this indeed is true, but this certainly can not be urged as an objection, for it is of itself an approval of such combination for the purpose of gaining a result, which we can not obtain without such combination. In order to understand this matter clearly, it is necessary that we enter into an elaborate explanation of the syllogism. We have shown heretofore that when the existences really compared in any proposition are clearly set out by the wording of such proposition, the ttrms of the proposi- 8a tion may be ♦ransposed ; as all men are mortal, i. e., ono of the gregaria sine qua non of man and mortality are homon, and by transposition, mortality and one of the gregaria sint qua non of man are homoa. And hence when a proposition is so worded that the terms may be transposed (and every pro- position can and ought to be so worded when it is considered in a scientific view) it may be combined with another proposition worded in like manner, in any one of the four figures ; and therefore, an explanation of the syllogism in any one of the sixteen modes of any figure, will be an explanation of the like numbered modes in aU the figures. V\e will commence our examination, therefore, with mode 1st in iho paradigms in which the first four kinds of propositions were used. Take the syllogism. All snow is white or snow is white. The foam of the sea is white, therefore the colors of enow and of the foam of the sea are similia, i. e., snow and the foam of the sea are similia in one facial gre- garium— color— which facial gregarium of snow and that of the foam of the sea^ have each of them been differentiated from tho other four nominal truths into color; but inter se they could not be differentiated, and therefore they are similia. But we have heretofore shown that fcetera lis at the very foundation of our knowledge. Suppose then that we look at the color of paper, and without any reference to discrimination say— this is— and having turned our eyes away from it, look at the same paper again and say- this is; now is this the thing which, we have said, is, when considered as grounded in the ego, the same thing in both cases? certainly not; and why not? Simply for the reason that their times can be heterated, and the power of our minds to heterate, gives us the knowledge that then and now are hctera and that an existence grounded in the ego five minutes ago is not sub- jectively the same existance grounded in the ego now. But if two existences can be heterated only, the two must be to us inter se similia; and therefore when we have said, this is, and that is, if we can discriminate no farther we must say, this and that are similia, and merge the two homonical propo- sitions into one similical proposition. Returning therefore to the premises. Snow is white. The foam of the sea is wbite, the heterical whitks are similia we can discriminate them no farther than into hetera, and hence the conclu- sion must follow that the color of snow and that of the foam of the sea are similia. But when we say. Snow is white. The foam of the sea is white, therefore the colors of snow and of the foam of the sea are similia, we must recollect that the hetericai whites, which are subjectively similia, have, each of them, an objective where, and therefore they are also objectively similia, while if we should project them into an homonical where, they would be objectively homon. The above premises, therefore, contain four subjective existences, two of which the heterated whites, are subjectively and objectively similia; objectively however, there aie but two existences in the 84 premises to wit, the color of snow aud the color of the foam of the sea; Mud objectively the s\'lIogism in mode 1st, in the conclusion locates these "objec- tive existences, as similia in their respective wiieues. Mode 2d, if we consider the four hetcrcical existenoci of the premises merely subjectively, they would not bring us into a conclusion; but two oi the subjective existances must be considered as occupying an homonical where in an homonical time; they must be objectively homon. When we say 1st and 2d are hetcrn. 3d and 2d are hetera, therefore 1st and 3d are hetera, the two subjective 2ds must be referred to an homonic:d where at an liomoui- cal where at an homonical time; but Isl and 3d, cuiiiun be homon for they are not compared with each other In either of the premises, Imt they are brought together by means of 2d, and if 2d and both 1st and 3d, be hetera, as stated in the premises, 1st and 3d must also be hetera. It may, however, be said that in tiiis mode the conclusion does not follow from the combination of premises; tor, if we put before us three objective existences, marked Isl 2d 3d, we can saj tirst is not tiiird, without comparing each of these with second. This is true; but it is the distinguishing terms, 1st aud 3d, which enable us to jump the middle existence. Suppose we apply our nose to a rose and say This (1st) smell is not that scent, we then apply our nose again and say, This (2d) smell is not the 1st smell, therefore 2d smell and that scent are hetera. In this case the 1st smell, which is the middhj existence appears twice suhjectivol}^ but we refer these t v^ 'Uyeciive existences to au homoui. cal where and time, aud therefore th.;> ...o homon, and without this middle existence we could not gain the conclusion, that second smell, and that l^L SCENT, the homonical scent menti(mcd in the tirst premise, arc hetera. In mode 3d, each of the premises is a conclusion drawn from a former syllogism: as A is white, B is while, tLerefore the colors of A and U arc similia, (mode 1st); A is white, C is white, therefore the colors of A aud C are similia (mode Ist); and from these conclusions we form the premises, A and B are similia, C and A are similia, and hence C and B are similia~con- clusion. Mode 3d needs no lurther explanation. Mode 4th is somewhat more diflicult. When wc say, sweet is not sour, bitter is not sweet, we are apt to look back at the words sour and bitter, and as these words distinguish dilierentia, we see from the terms that sour and BITTER are differentia, and hence we are apt to infer merely difTerentia from the premises. When we say, A peach and a pccir are differentia A potato aod a pear are difieientia, we will naturally say, A potato aud a peach are differ- entia, which- indeed is true, but it is uotTHKUEFOUE true, it does not follow from the premises. Xo categorical concluaiou can he legitimately drawn frem these premises, the conclusi.m which really does follow, is that a potato and a peach arc cither diflerentia or similia. Tliis will easily be seen if we treat a peach and a potato merely as hetera and call the peach first, and th« pota o second: then diBpiissing from our m-ind those differential names 'we say, Ist and a pear are differentia, 2d, and a pear .are differentia and '^1; do now see from the terms Ist and 2d whether they be diffe^mia or not th« conclusion follows ligitimately in our m-inds from the premTe and W ce color of this marble is white, the color of this marble and Uie coirof THATone are hetera, therefore the color of that one. let it iTj^Trl" and the white in the first marble, are hetera.. Snow is white snow and oJer are hetera, therefore the color of snow and the color of. paper ^"^^^^^^^^^ ' "^Thr 'tH^^'T.' ''^" '" ' ^^^^^' ^"^^ ^^-^-^ colors'areTetera ' greater difficuUie? W,''""^ "'^^''^* " •"'' ""'' '''"^''''^ '^ '^^^'^^^^^ <^-tain thT^lnnt r ^ ° """'"^ this apple is sweet, that pear tastes like f.i Tr' 'f '^""' ''''' ''^"' '^'' conclusion, therefore, that pear is sweeU f^lows fiom the premises, though this conclusion is an homonicTl propos 1 tion The taste of this apple and sweet are homon, the taste of this apl andtha of that pear are similia, therefore the .weet in the apple Ld^^^e e .1^ -' r''^' similia; but similia have a common name, and therefi^ ion t tt'ih nr'"."'" ''""' '^ ^^"^' '^^'^'-^^ - -y ^- the conct! 8.on,lhHt Uie pear is sweet, i. e,. that the taste of the pear and sweet are hon.oo. Now if we examine the above syllogism closely.'^.^e wm see that [n he premises there are subjectively four heterical existences, to w ^ t Tl " aste of this apple; ^nd. Sweet; 3d, The taste of this apple; ;nd 4^^^ The U se of n.at pear; three ot Which subjective existences are objectivel/homoo 1 HE TASTE of that PEAR only, is located in an heterical where with referTnce Z^^^^r^T' '/ '*''!'" '^'^ '' ''''' apple,.sweet, aud the tLe of thi Xectiv^er^r f'-'"'^ '^"'^^^'^^'^ "' ^^^ premises subjectively; but. bjectly hese three are homon. But the swee.^. mentioned in the concl^^on- ril '" -v '' ^Tr ^''' ^'^^ "^^ '^''' '^ '''' ^''' P^«°^>«e. tUey are ob- jectively snml.a, and because they are similia they have a common na^ and wc say This pear is sweet, i. e., one of the gregaria of t^rpear a^ son one of these similia appears ioeated in one of the objective wAeres iXrhtrj" ' "' the premises, as the other one .f the similia was locZ m the ^ther ^HERE in the other premise. In mode first we saw that of the" ZTiT::^''^'^^^^^ ''^^ - the firs, premise w re 11^;?! V^^ ""''' homon; in modes ^h and. nth thb tw6 subjective existences in one premise and one of the SHbiective ' exisences in the other premise, are objectively homon. . Aad we ^uLt sl^; e«r J r '' "^";'"^'^'!' The sweet in,this apple and .l-k, ta^« iothat pear aie s.miha; and dress it in common language, viz: That pear is sweet, ii 86 «b4 then combiDe tbit cooclution witb tbt bmnoiical proposition {of tbe aboTe prtmises, and we will bt in mode flrtt, and will fi^ain tbe other premise fit the abore tyllof ism as the conclusion : The taste of this apple is sweet the taste of that pear is sweet, therefore the tastes of the pear and apple are •imilia. And to make the matter still clearer, we may suppose three persons whom we will call k, B and C, t9 be sitting in a room with two apples in their hands. A tastes both of the apples and says secretly to himself, "this apple is sweet and that apple is sweet," and then drawing the conclusion in mode Ist, he says aloud, '*this apple tastes like that one;" B then tastes one of the apples and says, **this apple is sweet;" well then says C from what A and B aay, *^the other apple is sweet also." But hitherto we have not used what are called universal propositions for either of our premises, and when general propositions are used in mede 1st, it is then, that a petitio principii is supposed to occur. We did not dis- cuss this matter when treating of mode 1st, for the reason, that we desired t» get the reader further along in the knowledge oi some of the other modes* so that he might be better prepared for such discussion. When we say, all men are mortal, Socrates is a man, and, therefore Socrates is mortal, it is said that the conclusion, Socrates is mortal is implyed in the first premise. All men are mortal. The difficulty in this syllogism is, indeed somewhat below the surface, but if we set clearly before us the existences, which are really com- pared in the premises, the solution will be more easily obtained. All men are mortal, or iu equivalent, Han is mortal, shows that one of the capacial gregaria sine qua non of man and mortality are homos; Socrates is a (one) Man, shows that the existence called Socrates and one of the existences called man are homon; and therefore Socrates, who is hom(»nical witb one man, and other men are similia, in mode 1st. The simile, mortality, exisU in every object, which may be called man, but Socrates, I. •., the object designa- ted by that name, may be called a man, and therefore this simile exisU in So- crates; for MAN is the common name of similia. In the foregoing syllogism let us write the premises and conclusion thus: Socrates and ▲ man are ho- mon. One of the gregaria sine qua non of man and mortality are homon. Therefore the gregaria sine qua non of man and the gregaria of Socrates are similia, and One of these gregaria of Socrates then must be mortality, Socrates must be mortal. Suppose we look back to what we have called nominal truths, where we saw that when an object of vision arose into conciousness we called it COLOR, to distinguish it from conscious truths of the other senses ; and sup- pose that the first object of vision should have been the color, which we now call red ; red then would have been called color, to distinrilflh it from con- scious tmths sf the ether senses. Then suppose green to have arisen into consciousness, green too would have been called soler, to distlnguisn it from 87 objects of the other senses, and then red and green, as color, as distineuished from objects of the other senses, are inter se similia, and therefore each of them is a color. Now, if we collect into an hemonical proposlvion the rery thing, which enables us to differentiate objects from other things into colors, to-wit, visibility, we will say. All colors are visible, or iU equivalent. Color is visible, i. e.. Color and visibility are objectively homon, and if we then add That red is a color, i. e.. Red and one color are homon, it will follow that the object called red and visibility are similia i. e., red as au object distinguished from conscious truths of the other senses is distinguished in the same man- ner as other colors, to-wit, by being visible. And we must perceive that the first premise gives visibility as the ground of different Ution from the con- scious troths of the other senses, the whole of which ground lies partly in the visual faculties and partly in external objects, that is, in the relation of these, and it gives also color m the name to distinguish that part of the ground lying in external objecU; and hence color and visibility are objective- ly homon. The second premise Ukes one of the subjective similia so diff- erentiated, and pronounces this similie and red, a color further distinguished among colors to be homon ; and hence this simile and any other simile are similia (non simile est idem) and red as a color and visibility, when located in the same where, are homon, for similia have a common name and when their wheres are homon ical, they are objectively homon. Again, suppose we Uke several sticks, each one of which we dot with differently colored dots in such manner that by looking at the sticks when thus dotted, we cannot by the dots discriminate one stick from another, and suppose that each dot on any stick can be discriminated from any one of the other doU one the same stick, and to distinguish the dots inUr se, we call one A, another b, c, d, Ac. Now letting the doU in the aggregate be the very things, which distinguish the sticks before us from other things, we will call these dots, in the aggregate, in fasceculo. A. But supposing that by the lengths of the stieks we are able to distin^ish the sticks inter se, we will call a particular stick B, another C and another D. Now we can say that one of the dots of every A is a, I. e., one of the dote of any A and a are ho- mon. But B, this particular stick, which I now hold in my hand and men- tion by the name B, is a (one) thing, whose aggregate dots are called A. i. e. B and one of the A's are homon, therefore any one of the A»s excepting the ▲ which I hold In my hand and mention by the name B, and the A which I hold In may hand and which is the same thing as B, are similia; and hence the homonical a which wo find in any A excepting the A, which is also B has a simile, a dot like itself, in the A in my hand which I may call also B* B is A. • It must be confessed that the exposition of this matter is soms what difficult; and heretofore all logicians have failed to understand the trite state 88 cf the case, but by tliinkin- pear that the predicate, a color in the first premise, and the predicate, a COLOR in the second premise are inter se homon, or similia; the middle term therefore is faulty, not because it is not distributed, but because two existences are used which do not appear to be inter se similia. The fourth rule, therefore, laid down by writers, as a guide to keep us upon the true process of the mind in syllogising correctly, we conceive to be, not only of no value, but erroneous. The fifth rule given, is that No term must be distributed in the con- clusion, which was not distributed in one of the premises. "All quadru- peds are animals, a bird is not a quadruped, and therefore a bird is not an animal." This conclusion is evidently erroneous; and it is quite clear that those, who were engaged in the constiuctioa of this rule, saw, independently of the syllogistic process in the premises, the error in the conclusion, which from the appearance of the words in the premises might be supposed to fol- low legitimately. The proposition, "All quadrupeds are animals." means simply that each quadruped and one animal are homon, and. when we add that a bird is not a quadruped, i. e., that each bird and any quadruped are differentia, it does not follow that each bird and any animal «re differentia^ what fallows legitimately, is that each bird and the animals homonical or similical with the animals inaluded in the predicate of the homonical pro- - 91 position "all quadrupeds arc animals'* are differentia. For bird and animal are brought into the comparison in the conclusion by means of an homonical existence or similical existences, wi*h which they were each of them com- pared in the premises. We stated in our first rule that each existence, which appears in the conclusion, must be compa'ed in the premises with the same middle existence or with two existences inter se simiMa or commcnsura. And in the obove premises quadruped is compared with one animal, and quadrupeds being iater se similia, bird is then compared with one of these similia, and tlie conclusion must be that the animal compared in the homoni- cal proposition and found to be one of the quadrupeds and every bird must be diffireutia, but nothing can be infered respecting any other animal, except it be a simile, than the animal spoken of in the first premise, which was homonical with quadruped, lied is a color. Green is not red, are premises ju^t like the former, aud from them ',t follows that the on« color hemonical with RED and green are diflerentia. The fifth rule ther.efore is of no value in our system, it is erroneous and falacious as a grade in the syllogistic process. The sixth rule given, is that From negative premises you can infer nothing. This ru'e in our system has no meaning, for, we do not admit that there is any such thing j»s an independent negative proposition. But calling such piopositions, which have no, none and not in their negative, th# rule itself is not true, it is o ily true that we can not infer a categorical con- clusion. From the premises "A fish is not a quadruped, A bird is not a quadruped," it legitimately follows that a fish and a bird are differentia or similia (mode 4tb). The seventh rule s:iven is that if one piemise be n^igatiye the conclu- sion must be negative. This rule in our system means nothing. Now in stating every homonical proposition, such as All men are mor. ta), we must be careful to see whither the predicate be one of the gregaria of the subject or not;4"or if it be not, and it be represented by an adjective uame in order to make the proposition clear, some noun must be placed after it, or understood for adjective names which are not the representatives of grega- ria, are the names of existences standing as a class by themselves. When w« say "All gold ia precious," we mean that all gold and one of the things es- teemed of value amon^ men, are homon ; the proposition therefore should be slated this; All gold is a precious thing, and then we can add that All gold is a mineral, and it will follow that the mineral homonical with gold is a precious thing. Mr. Hamilton gives as the second rule, that "The subsump- tion must be affirmative," and he illustrates this rule by the following ex- ample; "All colors are phj^sical phenomena, no sound is a physical phenome- na;" "Here" says he, "the negative conclusion is false, but the affirmative, which would be true— all sounds are physical phenomena— can not be in- ferred from the premises, and therefore no inference is competent at all." .') i, 92 (page 289 ) After what we have said heretofore, I thick, it will be very easy to see throufifh Hamilton's mistake. When we say that "All colors are physi. cal phenomena," we mean that each color is a (one) physical phenomenon and when we add. No sound is a color, we mean that any sound and any cobr are differentia, and therefore we can infer, not that no sound is a physical phenomena, but that all physical phenomena homonical with colors and sounds are differentia. We have gone far enough perhaps, in this direction to make ourselves understood by the reader. Before leaving this chapter, however, it seems necessary, that we should make some remarks tending in another direction. It is the uni- mous doctrine of logicians hitherto, tliat one of the premises at least must be what they call a universal proposition, otherwise no legitimatt conclusion can be drawn. And hence, if we should take a stick and apply it to a table aid find the lengths of the stick and table so be commensura, and then apply the stick to another table and find the stick to be longer than it, and we should then make the following statement; lsttable=stick, 2d table2d table, this would not according to the received doctrine be a legitimate syllogism. But if this be not a legitimate syllogism, what is ii» General propositions are necessary at all to enable us to syllogise, excepting 3«^hen we wish to syllogise with gregaria or a gregarium sine qua non of ob- jects. When we say all A is b, i. e., one of the gregaria sine qua non of A and b are homon, no B is b, i. e., the gregaria sine qua non of B and b are differentia, it follows that A and B are difterentia. In such cases as these general propositions are necessary; but such cases from but a part of the in- stances, in which the syllogistic process is used. And from the consideration no doubt, that general propositions are always necessary in order to be able to syllogise, J. Stuart Mill, concluded that the syllogistic process was not realy inferential reasoning. He says "In the above observations it has I think, been clearly shown, that, although there i? always a^rocessof reason- ing or inference, where a syllogism is used, the syllogism Is not a correct analysis of that process of reasoning or inference; which is, on the contrary (where not a mere inference from testimony) an inference from particulars to particulars: authorized by a previous inference from particulars to generals and substantially the same with it; of the nature, therefore, of induction " Now when we tell a friend that the heighth of a stove in this room is com mensural with the heighth of a stove in the other room, which latter stove the friend has never seen, and thatithe heighth of this stove is three feet and then ask him from these data to tell us the heighth of the stove in the other room, If he does not syllogise and on the syllogistic process make an infer- ence, I^houia like to know in what other manner, by what kind of induction, he would be able to solve the problem. 93 CHAPTER, XIX. EXPLANATION OP SYLLOGISM CONTINUED. Having explained the syllogism, in which the first four classes of pro- positions are combined, we come now to give some further consideration to the syllogism combining the first and second and fifth and sixth classes of propositions. And of the manner, in which the first and second classes of propositions are combined in the syllogism, we have already said suflScient; it is to the manner of combining commensural and incommensural proposi- tions, therefore, that we will more especially direct the attention of the reader. In our explanation of propositions heretofore, we observed that, similical and differential propositions spring from homonical propositions; we showed this to be the case also with commensural and incommensural propositions. Homon is at the bottom of all propositions; helera are at the bottom of all knowledge; and the power of the mini t© heterate depends upon time and space. We must also perceive that, homonical propositions, which are col- lected into heterical, similical, differential, commendural or incommensural ones, must in every instance have a local reference in the subject or predicate; for, in every proposition there is a comparison between two existences, and if these two existences be considered merely heterically, they can not sub- jectively be homon; to be Lomon the subjective hetera must be located in an homonical where at an homonical time. We have already seen, how we come to have the knowledge of existence; and after this has been obtained, we may say indeed, that this grounded in the ego and one existence grounded in the ego are homon; but when the one existence is grounded in the ego, it is located there in the same where with this, and at an homonical time; and the one existence and the this refered to must also, irrespective of time and space, be subjectively similia, otherwise the bringing them into an ho- monical where at an homonical time will not make them homon. An object may be heard by the ear and another seen by the eye; irrespective of time and space they are differentia, and although they may subjectively be located in the same where at an homonical time they do not become homon. And where we say. This is an existence, and then again. That is an existence, the first existance and the second one are hetera, and if they can not be discrimi- nated further they are similia. Existences, however, is a name, which does not distinguish existences inter se. But if we say, This is white, and then again, That is white, as while is a name, which distinguishes existences inter se, if the first ching and the second thing be not similia, in the respect of color the word, white has been misapplied to one or both of ihem. 94 Kow in commensural and in incommcnsuial propositions, the things compared are always similia, yet commensural and incommensiiral propo- sitions are not derived from similia but from homon. If we take a cerlaiu stick and say, the length of this stick is oke (tlie unit) i. e., the length of thi," stick and ONE are homon, and we then go to an other stick and say tl,c length of this stick and one arc homon, if the lengths of the two sticks be not commensura, ONE has no definite meaning; and we can give a definite meaning to one only by taking some homonical thing as" the unit of men urement. If then w« make the length of a particular stick the homonical thing by which to define one, and apply this length to another stick, and wc can not discriminate the lengths of the two, we may say, the length of ll,c first stick, the homonical thing which we have made the unit of measurc-- menl, and one are homon, and as the length of the second stick when com- pared with the first cannot be discriminated from it, we must from a mental necessity call it ONE also. The length ol the first stick and one are homon, the length of first stick and that of the second are commensura, therefore the lengtu of second stick and one are commensura; but commensura must «l necessity have a commoa name, and hence the length of second stick must be called one, and length of second slick when not compared with another and one are homon. And if we combine this propo.silion, with the homoni- cal one which gave the unit of measurement, we will have length of fiiNt stick and ONE are homon, length of second stick and one are homon, there- fore engths.of first and second sticks are commensura, since one and one (not wiceone) are commensura, 1=1; and hence the length of any stick which may be called one, will be commensural with the first stick. If how- ever, the length of first object<2d and 2d<3d, then lst<3d, and we ha.e hree heterical objects, which are inter se incommeusura, and we may con- w v^ ph"? ^"r^^"'' """■"''"'" !»'<•'"'. l-ut 4th<5th. therefore lst<5tb, but 5 h<6th, therefore IsKCth, ana therefore 1st or any of one of the objects after 1st, is less than 6th, and so on. Here then we have six objects inter so mcommensura and as they are similia in kind, each of them in a like man- ner has been diflerentiated from other things, and they have a common name distinguishing them Irom other things in kind; but this name does not dis- tinguish Uiem inter se. And if we name them 1st, 2d, 3d. &c., these distin- guishing terms merely distinguish them heterically inter se, but they do not show the incommensural relations existing among them, and therefore by Uie use of such terms, we can not show any results further than heterical, which we may hare obtained by comparing those objecU inter se. There is therefore only one possible way for us to form a language by whsse terms we may be able to show the results of the minds coutparisons among com ' mensura and incommensural objects. Alter that we have gained the knowl- edge of the homonical thing, which we establish, as .he unit of measurement 95 in an homonical proposition, we may apply this homonical unit to a second object, and if the homonical thing be measured just twice upon the second object we may arbitrarily name twice one, two, and tl^cn twice one and two will always be in our minds commensura, and two will show the resnit of the comparison between any object named two, and the homonical thin- called ONE. And by naming thrice one, TmiEE, four times one, four, and so on, we will buf e the cardinal numbers applied to similia. One, then will be a common name for all objects, which are inter se similia and inter se com- mensura; and so also will 2, 3, 4, &c. But 1, 2, 3, 4, &c., distinguish incom- mensura inter se, and show by the relations of the homon inter hoteia the incommensural relations existing among similia. And these arbitrary sign, ol commensural and incommensural relations may be applied to any similia in nature, by taking an homonical simile as the unit of measurement; they may be appi led to lengths, to heats, to colds, to w-.-ights, to volumes &c It is >he peculiar perogative of mathematics to develop and carry out these principles. But we must see that the unit of measurement, in all cases, is the pre- dicate of an homonical proposition, and then commence commensural and incommensural propositions. And the syllogism with commensural and in- c.mmensural propositions, is used in every branch of mathematics from the beginning to the end. And as the demonstrations, in mathematics depend upon definitions, it is necessary to consider the manner in wliioli we svllo- gise upon those definitions. We have, heretofore said, that all definirions whiQh state directly what a thing is, are contained in liom«nicaI propositions •' this IS the case id mathematics, and as geometry affords us sufficient illustra-^ tion of our subject, we will confine our remarks to it. Geometry, it needs not to be shown here, treats of relations in space, and hence A point is a position, a where in space, i. e., a maihematical point and a where in ipace are homon. A line is the cause of consecutive points in space. A strairht line 18 the course of consecutive points in a uniform direction in space 1% a straight line and a course of consecutive points in a uniform direction in space are homon. And again, the portion of space included between two lines touching each other at a given point, and an angle are homon. Aniin the portion of space, which being included by two straight lines touching at a given point, which point being taken as a center and a circle described is a quadrant .f the circle, and a right angle are homon. and so on. All the foregoing definitions, and all of the direct definitions upon Which in geomAry demonstrations are constructed, are contained in homonical propositions But when we say, an acute angle is an angle less than a right angle, w. do not directly define an acute angle, and therefore the proposition is an incom- mensural one, and so also when we say, an obtuse angle is greater Ui«ii « right angle. And it must be observed that line is a common name for simi- -M««^. 96 lia and that straight line is also a common name for similia, line being a renus ©f wiiich straight line is a species ; and so also with angles &c. But atler the definitions in geometry, then lollow what arc called . axioms. These axioms are contained in commensural and in incommensural propositions, the bottom of which, as we have seen, is homon. But the com- mensural and incommensural propositions which contain axioms are founded more immediately upon the syllogism. The axiom, that. Things inter se similia,*which are equal to the same thing are equal to each other; is obvi- ously th« condeasation of a syllo^rism into a commensural proposition. Let the length ol a cerUin stick be the homonical unit of measurement and call this length one; one then will be a common name tor all lengths commen- sural with that of the stick. Now if we apply this stick to another, which we will call A, and they be lound to be commensura, we will say, A and 1 are commensura, A=l; and if then we apply the first stick to a third one which we will call B, and find them to be commensura, we will say, B and 1 are commensura, B=l; then we have the syllogism A=l, B=l, therefore A==B. And all the axioms of geometry are founded immediately upon the syllo- f istic process, though homon is at the bottom of the whole thing. If equals be added to equals, the sums will be equal, is very plainly founded on the syllegism. If A=B, as they are commensura, we may call each of them— three; and is A' =B', as they are commensura, we may call each of them— two; then if we apply the homonieal unit of measurement to A, we find that thrice one and A are commensura and so also of B ; and if we apply the unit to A', we find that twice one and A' are commensura andjso^also with B' • then A-|-A' must be equal to five times one, or five, and B-fB'= five lim'es one, or five; and we have the syllogism, A+A' =5, B-f B' =5, therefore A+A' =B-f-B' . So also when we say that magnitudes, which being applied to each other coincide throughout their whole extent, are equal, this axiom ii founded upon the syllogism: and in this case we cojie closer to the homon at the bottom. Suppose wo have before us a certain object called A, and an- other called B ; if now we represent the magnitude of A by A, and that of B by B, we must theh say, the magnitude of A and a are homon, and the mag- nitude of B and b are homon; but it a and b cannot be discriminated other- wise than heterically, if they coincide, they are commensura, a=b, and each of them may be called d. and we have m. of A=d, m. of B=d, therefore m. of A=m. of B, But if in the above case a and b can be incommensurated, we would have m. of A and a are homon, m. of B and b are homon: but aoked one, are in ca- pacity differentia; given a certain number of points in space, a line that can run through all of the points, and a line, that can run thi^ough only some of them, are inter se differentia. 8 ^ « B '» *■ Let, therefore, A B C, be a straight line and let a represent its uniform course from A to C; then a straight line and A are homon. But let A B D be another line, whose course from A to D is represented by b, then A B D and b are homon. Then if a and b be homon, or similia, ABC and A B D will be similia. But the circumstance that the point at D in b can be dis- criminated from any point in the C(mrse a, and that at A and B, a and b co- incide, shows that the courses a and b are differentia. Then the capacity of thie line A B C, and a are homon, and the capacity of the line A B D and b are homon, but a and b are differentia; therefore we have, capacity of line A B C and A are homon, a and b arq differentia, therefore, capacity of line A B C and B are difterentia; but capacity of line ABD and b are homon, capacity of line ABC and b are difterentia; therefore ABC and ABD are differentia; A B C however, by hypothesis, is a straight line, therefore A B D is not a 98 straight line. And from the foregoing demonstration, we can easily see* how the syllogism underlies the proposition tiiat two straight lines cannot inclose a space; for, a space inclosed is a space surrounded by consecutive points, and if we lay down one straight line, another straight line touching the first one In any two points, cannot diverge from it, but must coincide with it in ita whole course; but a course, a mere uniform direction can inclose nothing. "We have gone, we hope, far enough, to show that the axioms of mathe- matics are founded upon the syllogism, and leaving the axioms, therefore, wc will give one illustration of the principles of our system of reasoning from a simple proposition in geometry. Take the proposition that the sum of the angles of a triangle are eqial to two right angles. C B Let DEC be tlie triangle and prolong the side DE to A; and from the point E draw EB parallel to DC, then from previous syllogisms we know that the angles CDE and BEAare commensura; we also that the angles CEB and DCE are commensura. But as CDE and BEA are commensura, we may call them by the common name A; and as CEB and DCE are commensura, we may call them by the common name B; Then either CDE or AEB is an A, and either CEB or DCE is a B; and we may call CED, C; then AB and C and the sum of the angles of the triangle are commensura. But the sum of all the angles that can be formed at a given point on one side of a straight line and two right angles are commensura, the angles A, B and C are the sum of the angles so formed at the point E, therefore A, B and C together, and two right angles are commensura. CHAPTER XX. ENTHYMEME, SORITES AND DELEMMA. Having explained in the previous chapters the manner in which the syllogistic process proceeds, wc do not deem it necessary to elaborate much upon the Entymeme, Sorites or Delemma. When either one of the premises of a syllogism is expressed and the other understood, the expressed premise with the conclusion is callen an entymeme; as Iron will rust, therefore the plowshare; will rust, or The plowshare is iron, and therefore it will rust. In Bttch cases, it is easy to supply the premise, which is understood. Any per- 99 son* well grounded in the principles of the syllogism, will have no difficulty in managing the enthymeme. Now when a conclusion has been legitimately drawn from premises, this conclusion may be made a premise and combined with either of the for- mer premises, and another conclusion may then be drawn; and then this lat- ter conclusion may be combined as a premise with the first and so on. When we continue to syllogize in this manner, the chain of syllogisms is called a Sdrites; as, A and B are similia, B and C are similia, therefore A and C are similia; but C and D are similia, therefore A and D are similia; but D and E are similia, etc. And this process may be pursued with any of the modes and figures, which we have given in the preceding paradigms. Thus: A and B are similia, B and C are difterentia, therefore A and C are differentia; but C and D are similia, therefore A and D are differentia; but D and E are differentia, therefore A and E are differentia or similia etc. Now we stated in a previous chapter that there are five objective nominal truths, and If we lei A stand for one of them, B for another and C, D and E for the others severally, we may syllogize upon them in the following man- ner: A and B are hetera, B and C arc hetera, therefore A and C are hetera; but C and Dare hetera, therefore A and D are hetera; but D and E are hetera, therefore A and E are hetera; and therefore A, i. e., the thing distin- guished by the name A, and taste, or sound, or feeling, or color, or scent are homon. And this shows us the manner in which we come to use disjunctive propositions; they are conclusions of syllogisms. The sky is either clear or cloudy, why ? There arc two states, capacial gregaria, of the atmosphere, distinguishad inter se by the names clear and cloudy; one of these states now exists, therefore it is either clear or cloudy, i. e., the present state of the at- mosphere and either clear or cloudy are homon. And when we say that Men are either black or white or ta^ny; this is a conclusional proposition drawn in the same manner as the one above: though there might be men of neither of tuese complexions, for aught we know. And in the conclusional propo- sition just given, that which is really affirmed is that one of the facial gre- garia of every man and on« of the three colors a*mely, black, white or tawny, are similia. And as similia have the same name, the color of any man and black or white or tawny are houion. Again: Iron and glass are hetera, hetera are divided into two classes, namely, similia and differentia, therefore iron and glass are either similia or differentia. Now by the combination of dfsjunctive cunclusional propositions in premises, we form the basis of what is called the Dilemma; thus, A and either B or C are similia, i. e., A and one of the two are similia, but either B or C, i. e., either one of them, and D are similia, therefore A and D are similia, therefore A and D are similia. And it must be noticed that there is an ambiguity in the use of the correllatives, either, or. In the first instance / 100 A and either Bor C are siinilia, we mean that A and one of the two are^imi- lia, while A and the other may be differentia for aught tnat is disclosed by the proposition ; while in the latter instance, either B or C and D are similia, we mean that Band D are similia and also that C and D are similia. And it is this ambiguity in the use of the correllatives, that makes the dilemma kind of trap by which men are caught betore they are aware ol it. Now if we set down before us the propositions, A and either B or C are homon. but either B or C and D are homon, and be careful not to be mis- led by .the ambiguity of the correllatives, we can easily see by censidering these propositions how we come by such hypothetical enthymcnes as the loUowing; if A and B are homon, A and D are similia, and if A and C are liomon, A and D are similia; but A and B or C are homon, therefore A and D are similia; (mode Ist). But taking again the two disjunctive propositions A and either B or C are homon, and D and either B or C are homon, and tak- ing'the correllatives in both instances to meam one ot the two and not the otOier, we will have for conclusion that A and D are either similia or differen- tia, if A and B are homon, and D and B aie homon, A and D will be simi- lia; and if A and C are homon, and D and C are homon, A and D will be similia; but it A and C are homon and D and B are homon or A and B are homon and D and C are homon, A and D may be differentia. Again ; if we take the propositions A and either B or C are similia; E and neither B nor C are limilia, it will follow that A and E are differentia. Now it i* evident that we may take any categorical proposition and put into a hypothetical form. Take the proposition, Ice is cold, and we may gay, If ice is cold; but from this latter expression, we expect some conclusion © follow, and we state the proposition in this hypothetical manner tor the purpose of drawing some conclusion, and therefore we give it. this illative wording. And in such cases we always take one of the premises of a syllo- gism and sUte it hypothetical ly. Take the syllogism, Rainy weather is wet weather, it IS rainy weather, therefore it is wet weather; now we may state the second premise hypothetically, If it is rainy weather, aed draw the con- clusion, It is wet wes^her, leaving the first premise unexpressed. We call such arguments hypothetical enthymemes ; and those expressions of argu- ment which have been commonly called hypothetical syllogisms, are merely hypothetical enthymemes stated first, and then throwing off the hypothesis, the enthymeme is stated again categorically, t© show that the conclusion does not only follow logically, but alao that the premises, from which the conclusion is drawn, are actual. Thus if A and B are similia then A and C are similia; but A and B are similia, therefore A and C are similia. In this example, the conclusion introduced by thbkefore does Jiot at all depend upon the expression, if A and B are similia, then A and C are similia, but upon, A and B are similia and another premise understood. In the syllo- 101 gisnf, A and B are similia, (J and B are similia. therefore A and C are simi- lia, any person, who looks at it, und grants that C and B are similia, will readily go farther, and grant that, if A and B are simtlia, if such be really the case, then A and C sre similia, and when you convince him that really A and B are similia, the hypothesis is thrown oft', and be acknowledges that A and C aiL' .similia. In such cases the conclusion is not drawn from the first hypothetical eulhymeaic — if A und B are similia then A and C are similia, but from A and B are similia und the other premise, Band C are similia, «n- dersto.»d. If Socrates is virtuous, thcji he merits esteem; but Socrates is virtuous, therefore lie merits esteem; why? The viituoii>j merit esteem. So- crates is virtuous tlierelore he merits esteem. We do not consider it necessary to go into an elaborate discussion upon such mutter, we will, however, sub- join a note. Note.— It is strange that neither Arch' ishops Whately nor Sir Wm. Hamihou were able lo sound to the bouom of what they call hypothetical pr<»posilions, nor be able lo perceive the true nature of the dilemma "A hypotheiicHl proposilion," says Whaiely, "ia defined to be two or more catt^ troricals united by a copula (or conjunciion) ami the different kinds of hy- pothetical prjjpositious are named fr»)m their respective conjunctions: viz; conditional disjunctive, causal &3." And agrain; ''A conditional proposition has in it an illative foice, i. e., it contains two and only two categorical pro- ])ositious, whereof one results from the other (or lollows froni it)." And a«.^ain, "A disjunctive proposition may consist of any membei of categwri- cals." That a proposition may be the sutyect of another prjposilion is very clear; as that John is a scholor, is not denied; but (hat one proposition ma}' be a dozen propositions is certainly very strange. Sir Wm. Hamilton adopt- ing the explanation of Krug says(patj:e 108) ''Alth(mgh, llierefore, an hypothe- tical judgment appear double, and may.be cut into two different judgments, it is nevertheless not a composite judgment. For it is realized through a simple act of thought, in which if and then, the antecedent and consequent are thought at once and as inseperable. The proposition if B is, then A is, is tantamount to the proposition, A is through B. But this is as simple an act us if we categorica!ly judged B is A, that is, B is under A. Of these two, neither the one — If the sun shines, — nor the other, — then it is day — if thought apart from the other, will constitute a judgment, but only the tw'o in conjunction." Now the above is a misconception of the nature of proposi- tions, aj;d it arises from the erroneous noticms entertained by Hamilttm and others respecting predication. Suppose in the above example given, we leave the if and then out, we will then have, the sun shines, it is day: Nmw Mr. Hamilton would admit that here are two propositions, but would answer that although there arc two. yet it is not shown in any way ihat the one is connected or dependent upon the other without the words ip and then. Very well ; take the propositions A is B, C is B, A is C, and witliOUt the word tuekkfoke, before the last one, it is not shown by words, that this is the con- clusion of a syllogism. And if the words if and then possess the magic •|)ower to merge two propositions into one, we may use them also to merge a syllogism into a proposition, thu«; if A is B and C is B then A is C, which according to Mr. Hamilton would be merely an hypothetical proposition. For when we say if A is B and C is B, we expect something to foUow and 102 we perceive thai A is C, does follovr, and hence we mav iPimrd .11 .. : ilton's erroneous notions of what'hP pu11« . « 1 ^, *^ ^'!'^^^ ^ ^^- ^'^^^ him to misunderstood enthe^ whir h^^^^^^ hypothetical proposition led page246,followinrEs:rr?Ha^i;J :;L^tr'^^^^ ^>» position invo ve onlv the ri.nnrri.t »? ' • ^'/""^^^^ei, an hypothetical pro- consequent, it til! 1?,1 ow t^at'in;'l,ypmY,!ucal"'Jr'iir:'i"' """ "' " ''"8'" more ihan tliree but of 1p«« Tltn., h..lL^!? '. , ^J^""Ki8'n consists not of sense, this is aclualh the case O , M.u*"'."' "h"""'' *,""• '" » 'iK'-'on^ acnteness have viewed t le livnotheMr,, iln'' """'^' '"'".^ ""gicians of great andoriwoproposiUons Thi'iii ? ^^ Ld?-nrdr;iSSH^^^^ other; if one^be! tl SI^Ts °s XbJi ,'„- '-^^^ '""-" '"' ""= the other hand, he ex stance orlnXl,"'"'^'^- , ^" "'esubsumption,ou these notions comprisef?sexpresslv it.'^fr'' "'."■'"".""" °'' '"« "tlnr of affirmed or expressly denfedmHnlliMMvnfi *" •' ","* "f '^'""^''P'' «^P>-i'8slv- different significance from what il„». «l "^' "] "'" 8"'>s"mptiou, a whollv of reality, or unreal iiva.ul h. lil ''*P ""'^ enounced as a conditioli tion left untouched nd concerning wr"""' """ '"'""° ^^""^ "'« sub,ump- conclusion declde^^ buins a c "ar«1:ter a to.f.'iL' ^ iV"' '""' ""'"""""' '^"^ what it presented in theXrinnint •• Tht! fvl? ' itterent m the end from fromEsser. And hence fror,h!„,,,!l''iL ''''P '*''*''"" Hamilton obtained have before us a hat and a b o„m fwWcI. v,rT"'"'' "^ "'' .""PP""' """ *-■ rate existences) and wrsav ifX h« u „?,Th''?P''''''"," ''»P'>'« •»"' "^P"" are separate existences- hut the 1ml L„?,.i^^'"""™' ""^ ''""'"'' broom are separate existences? we 'mKiumntion to ^'i,''';"'''"' '""'='""= "'" '"" "f« and this third term Is en^olved be^fuse t re°,H™ .'."'".^ '■'"^"^!' "'"•'' ""■"'■ eether in the relation of lealou^nd conseo" 'f "' ,'' '»* «""?""» 't^nd to- they are asserted to be reahties and HFvf ?«•!?> fi •'•j"."'* subsumption they sumption we take the sumo Hon to he «^>n»i w "■? '"1"^ ""=" '" "'« ^''^ syllogising, we prove thafthi h., ; "."k ''°J ""'• "'"' V H'ie method of Ihesumptfon Itha,,'nish1n^.U? ""' «"« broom, just as we supposed in ability a^ Hamilton should have bee^ T°"! "■" TV,'- ^""'"'"S ""d natural nonsenseof the German In wh!tH u m'"*^'"' ""btle and trifling he and Whatley are also'in the dark '^^'"1!' '*"" D"e»'»« "l>i'".matic in the predicate and as th.if« .nmh- ."° '» /"una, both in the subject and disjunclire form, they maV also a™ n'°"'?^ f ?" ''yPO'hetical form ind of a disjunctive. If x is\ i7(x ?s eXr^R l^' be denominated Hypothetico- is prohibited eitherV natiri or by'^poS.iJe'tr/"'"' ".'"""^ Pi"'""''^"' " e^t^r I o^rgSn" t,rJt"x I^MtT '""' "^ ^ ' <> - ""y - ' either B or C f H. and thereh^e x is ei ..5r k'' '^T^^' "'? P^''<^e»«-A is errors respecting Dilemmati^ nrnnn.wl """":' ^ <"" C Hamilton carries his ' syllogismr; bulle w~t irit^ZTrther. '"'° """*' ''^ *""'^ Dilemmatic 108 CHAPTEK XXI. ™E StNOULAK HO.V0XICAL SVLIX)GISM. ...orouSr mr;^,;-''t;f "sf it;ir ™ :f„ ^-^ :-'"'-" -"^ for us to show the further apnl.cati.! ,f tiis pro es ,. Ihe' " '"' ""'""" kuowledge. We have already shown that Irouftre'^'i^i^^r;!,"', wrr' mon.cal propositions, as premise., we may caIn «i„,il7» ,?" ^""" the conclusion. And if we reoresont „",i , -r commensura in .vim wu lepieseut aggregate existences hv K f n v t and »ny simple existence by A, we nnv Ti.m. ft.,-™ ""''.\°^ B, O, D t &c., ..otnonical propositions, alA., whic:i,?r:vlTa;;;.:rr:d;rt..r'r'- "' Ther.:fore similia ,'^'-<'««:'>"" "J « «■'-{ A are homo,.. Therefore simiiia •• .. k ""? ^ ""-' """"»• Therefore simiiia ( - .. y "" t T """""• Therefore simiiia' " •' F an t " """""• A 1 " I P and A aie houion And so on, which i« a continued syllo-rism or Soritc. A „ 10-1 upon time and space; but respecting the ego per se and the non ego per se, homon is homon irrespective of time. And hence if we talie an object as time can have no heterating effect upon it, a thousand years from to-day, it will be homon; and alti\ough time has been personified and endowed witli capacial grcgaria by the poetg, it must be evident that time per se has noth- ing in it, to produce any ef!ect uptm the ego or non-ego. But as time has no capacity to heterate or differentiate objects, it we affirm that this where is a where of pure space, i. e., this where and one whereof pure space are homon, and that where and a where of pure space are homon, it must follow tli^il this where and that where are similia. If time per se can neither heterate n«r dilferentiafe, any two wheres of pure space are now, always have been, and always will be, Similia, so long as pure space and pure space are homon ; and so also with every other object &o far as time per se i« concerned. But we may ask ourselves, has space any capacial gregaria to aflect •bjects occupying it? And by the artificial production of a vacumm, we are able to decide upon reflection that here, in this instance, is a space, which has no capacity to interfere in any manner with objects occupying* it, were aiy object in it. But if hwmon is homon, if space is space, this particular vacuated space and an}'^ other where of pure space are similia, they cannot be differentia, aLd hence no space can heterate, differentiate or iucommensuraie objects occupying it. We have therefore eliminated time and space, as agents, from our consideration; but before proceeding farther, we must explain some terms, which we will have occasion to use hereafter. If we take any homon, this homon to-day, will be homon a thousand years hence, so far as time and space are concerned, we will, therefore, call this homon an homonical homon. But if we take another homon, a like case will be with it, and to distinguish thc^ second liomou from the first, we will call it an hetcrical homon ; an homonical homon and an heterical Lomou will then be heiera. Again; If the homonical homon and the heterical homon be inter se similia, we may call the heterical homsn with reference to the homonical homon, a similical homon. An homonical homon and a similical homon will then be similia. Again; If the homonical homon and the heterical homon be inter sc differentia, we may call the heterical homon with reference to the homonical homon, adifferential homon. An homonical homon and a differential homon will then be differentia. Again; If the homonical homoaand th(/heterical homon be comraen- aura, we may call the heterical homon a commensural homon. An homoni- cal hom«n and a commensural homou will then be commensura. But again; If the homonical homon and the heierical homon be in- commensura, we may call the heterical homon, an iucommensural homon. An homonical homon and an incommeusural homon will then be iu- commensura. ♦ 105 The following list will show the terms and the manner in which ihey distinguish objects: ... i_. H«)moniCHl homon- a } , ^^^- Homonical homon-a )" ''''"^'»" hetera. 2^^ Homonical homon — a ) Heterical homon— b j" q,i Homonical homon — a) . ... "^^ Similical homon— a' p""'''*- A.,. Homonical liomon- a / .-a. *"*• Differential homon-b [ ^'^ rentia. Homonical honum — 2 } Commensural honioa — 2' f oth. r^ . . - r ^commensura. Qjlj Homoniciil homon — 2 ) Iucommensural homon— 3 ) '"^ommensura. Now with the above terms, the following syllogisms which we call singular homonical syllogisms, because one premise at least in each mode is homonical, maj' be constructed: MODE IST. The homonical hoinon a, in the place— b to-day, and the homonical homon— A, in any where a thousand years hence, are homon. The homonical homon— a', in the place— c to-day, and the homonical homon— A \ a thousand y^ars hence in any where are hoinon. Therefore the homonical homon— a, in any wheire a thousand years hence, and the homonical homon a, in any where a thousand venra benco, aie similia, . MODE 2d. The iiomonical homon— a, in the where b, to-day, and the homonical homon— a, in any where a thousand years hence, are homon. The homonical homon— a, in the where» b to-day, aod the hetericlU homou c, in the where— d to-day, are heiera. Therefore the homonical liomon— a, in any where a thousand years hence, and the hettrical homon c. iu anywhere a thousand years hence, are hetera. mod£ 3d. Tlie homonical homon a in the where b to-day, and the homcmical ho- mon A In any where, a thousand years hence arc homon. The liomon cal homon a io the where b to-day, and the similical ho- mon A' in the where c today are similia. ,.j^ Therefore, the homonical homon a in any where a thousand yefiff hence, and the similical homou a' in any where a thousand year* hence, aie similia, \ mode 4th. The homonical hom^n a in the where b to-day, and the homonipal homon a in any where a thousand years hence are homon. 106 » The homonical homou a in the where b to-day, and the diftVrential homoD c in the where d to-day are differentia. Therefore the homonical homon a in any where a thousand years hence, and the differential homon c in any where a thousand years hence are differentia. MODE 5rH. The homonical homon a in the where b to-day, and the homonical ho- mon A in any where a thousand years hence are homon. The nomonical homon a in the where b to^ay and the commcnsural homon a' in the where c to-day, are commensura. Therefore the homonical homon a in any where a thousand years hence and the commensural homon a' in any where a thousand years hence are commensura. MODE 6th. The homonical liomon a in the where b to day and the homonical homon a in any where a thousand years hence are homon. The homonical homon a in the where to-day and the incommensural homoD c in the where d to-day, are incouimensura. Therefore, the homonical homon a in any where a thousand years hence, and the incommensural homon c in any where a thousand years hence, arc iocommensura. After a careful study of the above mode in the singular homonical syllogism, the following reasoning, we believe, will appear obvious. If we let a homon, always be homon in our minds, and we make this homou a SIMILE, i. e., it the homon a in the where b, have a simile in the where c, and another in the where d and so on, each one of these similia must have a com- mon name, and no matter if their heterical number be infinite and the points Ib[ time of some be in the past, of others in the present, and of still others in the future, yet we have no hesitation in belicvinj; that each one must be an a, tor if it should not be so, homon would not be homon ; and that the really aame thing ihould not be the same thing is absurd and impossible. But the homon in our minds has a simile in the minds of other men, and hence wc believe without a doubt that two beings like ourselves a thousand years hence all colors, which they will know any thing about, will be visible, i. e., color and visibility will be to them homon. The same thing is the same thing, hom«D is homon, no matter about the modifications of time and space. Color and visibility are homon, visibility and visibility are homon. Therefore, color and visibility are similia (mode 1st) as the must be, if the risibility, in tke first premise and that in the second be objectively hetera; and two ob- jectively heterical existences, one in each premise, must always be found in the premises of every syllogism. And hence the general proposition that all colors are visible, is established beyond a doubt by the syllogistic process. 107 The proposition that all sounds are audible, or that sound is, has been, and ever will be audible, is established in the same manner. And thus we may deal with all the homonical propositions in which both the subject and pre- dicate are the simple existances, which we have called facial gregaria. That all red is red, that all sweet is sweet, or that all white is, has been, and ever will be white lo human beings, nobody doubts, because a contrary supposi- tion is not only inconceivable but impossible, unless similia and differentia are homon. ' Let us now turn ouf attention to capacial gregaria, and we will first notice figure or form. It is a proposition not worth discussing after what has already been said respecting homonical propositions and space, that every a^igregate existence must have some figure or form. But were ten milliens of forms inter se differentia known to our minds (and about thin^i unknown we cannot reason) and we should give a name to distinguish any one figi re or form, each other figure, which was a simile of the figure named must receive the name given to the homonical figure, which name now be- comes a common name for all similia. If for instance we distinguish from other things any round ring by the name CIRCLE, then any round ring thus distinguished from oth2r things, has been, is aud always will be a circle First round ring aud a circle are homon, second round ring and first are similia. Therefore sec(>nd round ring aud a (one) circle are homon. And 8 » also with squares, cubes, triangles, parallelograms, jr'the BIN0T7LAR HOMONICAL SYLLOGISM, which WC have just been discussing, seiems to be what J. Stuart Mill considers the true type of induction, when he de- fines induction lo be "the operation of discovering and proving genera! pro- positions." Mr. Mill, however, like all other writers upon induction, leems to have had no definite conception of the thing for which he was on the look- out, and he would not have been able to have identified it, if he had found it. In one place induction is "the operation of discoverinf^ and proving general propositions;" in an other it is "generalization from experience;" in an other it is "that operation of the mind by which we infer that what wc know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects;" and again, "to ascertain what are the laws of causation which exist in nature; to determine the effects of eyery cause, and the caiises of all effects, is the main business of induction ; and to point out how this is done is the chief object of inductive logic." Mr. Mill is an able writer, but his logical induction is, in a great measure, an ignus fatuus. CHAPTER XXII. , THE PLURAL HOMONICAL SYLLOGISM. , „• ,,. .^ ; ._, Having shown in the last chapter how we generalize from experience, and also how in certain cases we may select a simple homonical existence and prove it to be a sine qua non by the singular homonical syllogism, we must pursue the syllogistic process still further and show how wo reason by the Plural Homonical Syllogism, if we put two balls before us, we will say that they are hetera, i. e., that the one is not the other; if, however, we turn our eyes away from them for a few moments, or cover iheix^ with our hand, and then we remove it from them and look at them again, we will say^ no that they are the same balls. But by this expression we do not mean Ihali the one and the other are homon, for we know that inttr se \hey are hetera, but what we really mean, is, that the two balls under our eyes then aie the identical balls under our eyes now, i. e., the two balls then and the two ballrj NOW are homonical hetera. And before proceeding further, we must again explain some terms, which we will have occasion to use in our future inquiries. We hare already seen that time aud space per se have no capacity to heteratt, differentiate or incommensurate objects in time and space, that sub- jectively two, but objectively one homonical ball te day, so far as time and space per se are concerned, will be objectively homon, to-morrow and for- ever; we will therefore call such homa, homonical homa. But if we take subjectively two other balls, which are objectively hemon, they are related to themselves in like manner as the first two, we will call them heterical homa: Homonical homa and heterical homa will then be hetera. A^ain, If two homonical hetera be inter se hetera to-day, so far as time and space are concerned, they will remain hetera, and therefore we will call them homonical hetera; but if we take two other hetera, they also will remain hetera, and to distinguish them from the first two, we will call them hewrical hetera: Homonical hetera and heterical hetera will then be hetera. Again, If twe homonical lietera be inter se similia to-day, so far as time and space are concerned, they will remain similia inter se, and therefore we will call them homonical similia ; but if we take two heterical hetera inter se similia, they also will remain inter se similia, and to distinguish them from the first two, we will call them heterical similia: Homonical similia and heterical similia will then be hetera. Again, If we take two homonical hetera inter se differentia, they will remain differentia, and we will call them homonical differentia; but if we take two other hetera inter se differentia, they alse will remain differentia, and to distinguish them from the first two, we will call them heterical difier entia: Homonical differentia and heterical differentia will then be hetera. Again, If we take two homonical hetera inter se commcusura, they will remain inter se commensura, and we will call them homonical commen- sura; but if we tak6 two other hetera inter se commensura, a like crise will be with them, and to distinguish them from the first two, we will call them heterical commensura: Homonical commensura and heterical commensura will then be hetera. Again, If we take two homonical hetera inter se incommensura, they will remaim incommensura, and we will call them homonical incommensura; but if we take tw* other hetera int-er so incommensura, a like case will be with them, and to distinguish them fr«m the first two, we will call them lU heterical incommensura; Homonical incommensura and heterical incom- mensura wfll then be hetera. « Again, If we take two hetera inter se similia, they will remain inter se similia, and we will call them homonical similia; but if now we take two heterical similia, and the homonical similia and heterical similia be inter te similia, to distinguish the heterical similia, we will call them similical bimilia: Homonical similia and similical similia will then be similia. Again, It we take two homonical similia and two heterical similia, and the homonical similia and heterical similia be inter se differentia, we will call the latter differential similia; Homonical similia and differential similia will then be differentia. Again, If we take two homonical differentia and two heterical differ- entia, and the one of the homonical differentia and one of the heterical differ- entia be inter se similia, and the other of the homonical differentia and the other of the heterical differentia be inter se similia, we will call such heter- ical differentia, similical ditterentia: Homonical differentia and similical differentia will then be similia. Again, If we take two homonical differentia and two heterical differ- entia, and the homonical differentia and heterical differentia be inter se dif- ferentia, we will call such heterical dift'erentia, differential differentia: Ho- monical difl'erentia and differential differentia will then be differentia. Again, If we take two homonical commensura and two heterical com- mensura, and they be inter »e commensura, we will call the latter commen- sura, commensural commensura: Homonical commensura and commensural commensura will then be commensura. Again, If we take two homonical commensura and two heterical commensura, and they be inter se incommensura, we will call the latter, in- commensural commensura: Homonical commensura and incemmensural commensura will then be incommensura. Again, If we take two homonical incommensura and two heterical incommensura, and the one of the homonical incommensura and one of the heterical incommensura be inter se commensura, and the other of the ho- monical incommensura and the other of the heterical incommensura be inter se commensura, we will call the heterical incommensura, commensural incom- mensura: Homonical incommensura and commensural incommensura will then be commensura. Again, If we take two homonical incommensura and two heterical incommeusura„and they be inter se incommensura, we will call the latter, incommensural incommensura: Homonical incommensura and incommen- sural incommensura will then be incommensura. 118 The following list will show the terms ♦nd their relations: ^ Homonical homa a.a. Ij^Qm^ Homonical homa a.a. f ' JJomomcalhomaa.a..U^j^,j.^ ** Hetcncal homa a. ' a. ' ) 9 ST°°'f *i '•™-l-* K K* f differentia. ^' Differential similia b.b. ) ^rt Homonical differentia a.b. Ift;-,;i;- ^^ Similical differentia a.'b.' p^™*"* - Homonical diffcremia a.b. Ugtera 13 P'^*^^^ ^°°^' o'H incommensura. ^- Heterical differentia c.d. i 'i*^''^^*- ^^ Incom. com. 3.3. J g Homonical comensura 2.3. { ^etera.U ^ZilTcoT^I^" [ commenaura. Heterical commensura 3.3. ) Com. incom.-i.d. ) ,''*H«monicalincomens'a2.3. ^ ijetera 15 ?°"- i^.^*^^- 2-^' j. incommensuru ^' Heterical incem'ensura 3.4 f "*'**'^'' ''' Incom. mcom. 6.6. S 8 S^°?*°'^*^. ^^ M-^^^'* *•*; ^ similia. ^' Similical similia a.a.' i Now the following paradigms will show the syllogisms, which may be constructed with the foregoing terms, which syllogisms, as they have one homonical premise at least in each mode, we call plural homonical syllogisms. Mode First.— The homonical homa a.a. to-day, and the homonical homa a.a. a thousand years hence, are homonical homa; The homonical a' a to-day and the homonical homa a. a.' a thousand years hence are homonical hotoa ; Therefore the homonical homa a.a. a thousand years hence and the het<>rical ht>ma a. a.' a thousand years hence, are similical homa. Mode Second— The homonical homa a.a. to-day, and the homonical homaa.a. a thousand years hence, are homa; The heterical homa a. 'a.' to- day and the homonical homa a.a. to-day, are heterical homa; 1 heretore, the homonical homa a.a. a thousand years hence, and the heterical homa a. 'a.' a thousand years hence, are heterical homa. Mode Third.— The homonical hetera a. 'a to-day, and tho homonical hetera a a. a thousand years hence, are homonical hetera; The homonical hetera a. a. to-day, and the heterical hetera b.b. to-day, are heterical hetera; Therefore, the homonical hetera a. a. a thousand years hence,*and the heteri- cal hetera bb, a thousand years hence, are heterical hetera. ModeFourth.— The homonical similia a.a. to-day, and the homonical similia a.a. a thousand years hence, are homonical similia; The homonica similia a-a. to-day, and the heterical similia a. a.' to-day, are heterical similia; Therefore the homonical similia a.a. a thousand years hence, and the hetericjil similia a. a.' a thousand years henco are heterical similia. Mode Fifth.— The homonical differentia a.b. to-day, and the homonical differentiaa.b. a thousand years hence are homonical differentia; The ho- monical differeatia a.h. to day, and the heterical differentya c.d. to-day are haterical differentia; Therefore the homonical differentia a.b. a thousand years hence, and the heterical diffcicn^ja c.d. a thousand years hence, are heterical differentia. 113 Modo Sixth. — The homonical commensura 3.2. to-day, and tke homon- ical commensuTa 3.2. a thousand years hence, are homonical commensura; The homoDical commensura 3.3. to-day, and the heterical commensui:a 3.3. to -day are heterical commensura ; Therefore the homonical commensura 3.3. a thousand years hence, and the heterical commensura 3.3. a thousaud years hence, are heterical commensura. Hode Seventh. — The homonical iacommensura 3.3. to-day, and the homonical incpmmensura 3.3. a thousand years hence are homonical incom- mfusura; The homonical incommensuru 3.3. to-day, and the iieterical incom- mensura 4.5. to-day are heterical incommensura; Therefore the homonical incommensura 3.3. a thousand years hence, and the heterical incommensura 4.5. a thousand years hence, are heterical incommensura. Mode Eighth. — The homonical similia a.a. to-day, and the homonical similia a.a. a thousand years hence, are homonical similia; The similical similia a. a.' to day and the homonical similia a.a. to-day are similical similia; Therefore the homonical similia a.a. a thousand years hence, and the similical similia 'a. 'a,' a thousand years hence are similical similia. Mode Ninth. — The homonical similia a.a. to-day, and the Jiomonical similia a.a. a thousand years hence are homonical similia; The homonical similia a.a. to-day, and the differential similia b.b. to-day, are differential similia; Therefore tlio homonical similia a.a. a thousaud ye*^ars hence and the differential similia b.b. a thousand years hence are differential similia. Mode Tenth. — The homonical differentia a.b. to-day and thehomon]cal differentia a.b. :i thousand years hence are homonical differentia; The homon- cal differentia a.b. to-day, and tbe similical differentia a.'b.' to-day are similical ditferentia; Therefore the homonical differentia a.b. a thousand years hence, and the similical differentia a. b.' a thousand years hence, are similical differentia. Mode Eleventh — The homonical differentia a.b. to-day, and the ho- monical differentia a.b. a thousand yeurs hence are homonical difterentia; The differeniial differentia c.d. to-day, and the homonical differentia a.b. to-day are differential differentia; Tiierefore the differential differentia c.d. a thous- aud years hence, and the homonical dift'erentia *;.b. a thousand years hence are differential differentia. Mode Twelfth.- The homonical commensura 3.3. to-day, and the ho- monical commensura 3.3. a thousand years hence, are homonical commen- sura; The commensural commensura 3. '3.' to-day, and the homonical com mensura 3.3. to-:day, are commensural commensura; Therefore tlie commen- sural commensura 3. '3.' a thousand years hence, and the homonical com- mensura 3.3. a thousand years hence, are commensural commensura. Mode Thirteenth. — The homonical coyimensura 3.3. to-^ay, and the lioraonical commensura 3.3. a thousand years hence are homonical com- mensura; The incommeusural commensura 3.3. to-day, and the homonical commenaura 2.3. to-day, are incommeusural commensura; Therefore the in commensural commensura 3.3. a thou.sand yeais hence, and the homonical commensura 3.8. a thousand years liecce, are iucommensural commensura. Mode Fourteenth.— The homonical incommensura 3.3. to-day, and the homonical incomraensur 3.3. a thousaud years hence, 'are homonical ihcom- uieusura; The commensural incommensura 3.'??.' to-day, and the homonical incommensura 3.3. to-day, are commensural incommensura; Therefore the commensural incommensura 3. '3. a thousand years hence, and the homoni- 114 cal incommensura 2.3. a thousand years hence, are commcusural incom- mensura. . Mode Fifteenth.— The homonical incommensura 2.8. to-day, and the homonical incemmeusura 2.3. a thousand years hence, are homonical incom- mensura; The incom^ensural incommensura 5.6. to-day, and the homonical incommensura 2.3. to-day, are incommensural incommensura; Therefore the incommensural incommensura 5.6. a thousand years Jience,and the iiomonical incommensura 2.3. a thousand years hence, are incommensural incommensura. If the reader has carefully studied what we have called the singular homonical syllogism in the proceeding chapter, the plural homonical syllo- gism will not need to be specifically explained. And any person can see thac we are not necessarily limited to two homa or helera; we may take the ho- monical homa or hetera a, b, c, d, e, &:c., and deal with them in like manner as we have dealt with two homa. Now if we take any simple existence in nature, any one will allow that this simple existence and itself are homon ; and any one will agree also that so l«ng as this simple existence and itself arc homon, it and itself can not be hetera, and consequently it can not be a simile of itself, nor can it and itself be differentia. And in a previous chapter we have shown that, when wc look upon nature, we gain our knowledge of cause, in the first instance through effects, which arc manifested by changes. And from what we have said already, it must appear, that a homon per se can not change: whalev..r it may be, so long as it exists, it is the homonical homon. If then we take any sine qua non, impenitrability for instance, this sine qua non isimpenitrability to- day, always has been and always will be, homon is hoinou. Now if we place before us an ivory ball, wu hare no dowbls in affirm- ing that one of the capacial greguria sine qua non of lhi& ball and impenetra- bility are homcm; and it we put before us another ivory ball, we will make a ike affirmation respecting it, and therefore the first and second balls are similia. And if the first gregarium be located in the homonical where 15, and the second one enter the homonical where B, the first one must take an heterical where. For, in the respect of impenetrability the two balls are similia; and therefore the homonical similia a. 'a. to-day, the one (a) in the homonical where B,and the other (a') in the where C,and the homonical sim- ilia a. 'a. to-morrow in any where are homonical similia. But respecting the homonical sifnilia a. a. to-morrT)vv, if the second (a) be in the where B, i. e., if the where B occupied to-day by the first (a) to-morrow be occupied by the second (a.), the second (a. ) must have a simile in the first (a), and the where of this SIMILE, and the where B must be hetera. Ikit if (a.) the first sine qua non be displaced necessarily from the where B by the entrance of the .second (a.) sine qua non, is nof what has happened in a single instance sufficient to establish beyond a doubt that, whenever any w^hekk is occupied by an a and another a' enters this where, the first a must be displaced? So long a.s homa are homa, this mu^f be the case in any part of space at any point of lime. 115 And if this be the case with the homonical similia a, 'a., must it not always be the case with all similical similia? And if we call this displacement of one impenitrable object by an other, a law, it must be evident that this law is uniform, i. e., this law and an uniformity are homon. And in a like man- ner we might treat of elasticity, of fluidity, of rigidity, lubricity and so on- And so lone as homa are homa and similia are similia, we can not doubt of the uniformities in all instances. But again if we take two differentia, oxygen and hydrogen for instance, we may reason upon them in like manner and with perfect exactness. For, oxygen being an elementary thing, so long as oxygen is oxygen, as homon is hoinon, any particular oxygen will contain all the gregaria of any oxygen, i. e., each gregarium of a particular oxygen will have a simile in any and every other oxygen: and so also with hydrogen. And hence if any homonical pro- cess unite them into water in any instance, a aimile of this process will unite ihem into water in every instance. So long as homa are homa, similia similia and ditterentia differentia, we can not doubt that a result brought out of the homonical differentia a.b. by the homonical process d, will have a simile of that result brought out of the similical ditterentia a.'b. by d', a simile of the homonical process d. And hence we must conclude that The laws of nature are uniform; is a proposition which is established in our minds by the syllo- gistic process. The result of the homonical differentia a.b. by the homoni- c.mI process d and A are homon: The homonical ditterentia a.b. with the ho- numical process D and the similical ditterentia a 'b.' with the similical pro- cess d' are similia; Therefore the result of the similical ditterentia a.'b.' by the similical process d' and a are similia. We have now said all that we deem necessary to be said at present while treating of the syllogism. We have given the syllogistic process a much more thorough analysis than it has received heretofore by writers upon logic, and we h«)pe that our labors thus far will enable philosophers who shall come after us to see clearly the manner, application and use of the syllogism. We, however, must proceed further, and treat of induction, a subject, which, we are confident, has not been understood by writers upon that subject. lnducii«)n, therefore, will occupy our attention in Book II. BOOK II. •■:#» ,1 ^'H , CHAPTER I. MISNAMED INDUCTIONS. The processes of the mind concerned in induction, in our apprehend- sion,have not been understood by any writer upon logic, with whose works we are acquainted. Bacon is said to have been the author of the inductiye philosopliy ; but his Novum Organum shows the necessity of such a philoso- phy scientifically constructed rdther than the actual construction in a methudical manner. His remarks, as far as they go, are not systematically arranged, and therefore they arc often obscure; and from this reason with others, his suggestions, though frequently of the greatest importance, have not led his successors to glean from his aphorisms the true principles of in- duction and to work them into a scientific and methodical system of inductive logic. That Bacon iiad in view a better and greater systena of philosophj than subsequent writers have made out of it seems to me to be certain. The aids fbr the understanding, about which he speaks so frequently, are suggested here and there in the second book of the Organum, but without any scientific theory to cement und make his remarks understood. History and experi- ments, without the knowledge of the inductive processes and their applica- tion can not aid the understanding in gaining certain knowledge of nature's laws; and these processes, as far as treated of, arc not brought out in a scientific manner in the Organum. Men have always had nature before them but the method of interrogating h«r has not been understood And though Bacttn made a grand beginning at explaining this method, yet most subse- quent writers have not only, not improved upon Bacon's work, but have underated the val'te of such method. There is no subject about which more erroneous notions prevail among philosophers, than about the subject of the inductive processes themselves; and these notions, in our opinion, are grounded upon erroneous notions about the syllogism. Philosophers are not at all agreed, about what pro- cesses, when pointed out shall be called iaductive; and hence results, which are entirely owing to the syllogism, are often claimed as inductions, induction having some vague and unexplained meaning. The better way, however, to show what results are owing to the syllogistic process, is to explain the syllogism, and then the reader himself can make the application to any case, which may arise; this we have endeavored to do heretofore. And the better way to show what results are owing to the inductile processes, will be to explain these processes. But before doing this, from the manner in which the subject has been treated by authors heretofore, it is neeessar}-, in order to be well understood by the reader, for us to show some things, which have been called inosition, which may be constructed upon this sine qua non. All those truths, which we have called nfmiinal truths, are each of them, a sine qua non of themselves; aud hence there is no indiiction in establishing the truth of the proposition that, every color, in any place at any time, is a color, but the tr.Uh of such proposition is estab- lished by the singular hMm(»nical syllogism, as we have shown heretofore. Neither do we consider induction to be the collecting of a stUllcient number of in.stpnces to wanaiit us in believing that the instances, which we Imvo seen, are fair specimens of the class. We should think strangely of a man, who, after having been ijiformed that the name island distinguishes a portion of land entirely jsurrounded by .vater shouUI start on a tour to examine this and that island, until he had a snflleienl number of instances collected to warrent the inference that, all islands sire surrounderiod of time and hold its relations in our miud. By the where [of ourselves and the where of other objects in space and their relations inter I se we are also enabled to locate a particular where in space and preserve its relations in our minds. And although we may not always be able to point out the precise point of time, in which a given eftect begins to take place, we can generally come near enough to that period fi)r the purposes of heterical induction; and so also we can come sufticiently near to the precise where in space of a given eftect. Simple heteration is sufficient to bring us to the poMil ot time and the point of space of any given effect i nder consideration of tl»e inductive processes. And when we have the period of lime in which any given eftect took place, as the cause of that effect must have been inter se synchronous and have touched upon some homonical point of that period of time, no aggregations before or since that period could contain the causal gregaria of that effect. If the .Enead was written in the age of Augustus, no person, who lived and died before that age, or who has been born since, could have written it. And hence if we know the period of time in which any given effect took place, all aggregate existence, which have not an ho- nionrcal time with that period, are immediately heterated from the causes of the effect by our minds; and this is heterical induction. For, when we have tlu<.wn out'those exisfmces, which could not have been the causes, we have before us other existences, which may hare been the causes, and by casting out the former we have led in or inducted the latter. And were there but two ag-regate existences in esse at the period of time of the effect, as there must have been heterical gregaria concerned in producing it, we would know by the heterical inducti.m of aggiegations by their times alone that, these two existences contained the causal gregaria of the effect. But although the heteration of objects from the time in which any given effcHJt takes place, by throwing out many aggiegations which could not contain causes of the effect, narrow the field in which the causes are to be found. Yet there are afterwards so many aggregate existences in esse synchronous inter se and having times homonical with that of the eftect, and any of which, therefore, so far as time is concerned, may have been causes of the effect, that after that we have determined the hom »jiical timeof the effect and determine also what existences have limes homonical with this, we are still unable to tell which of these contemporary existences con- tained acting causes in the present instance. We have, therefore, to proceed farther and heterate the wheres ot objects from the homonical where in which the effect took place. Although this be an easy matter in s >me n - stances, vet in olh-rs it is attended with great difficulties. If we f^eci an ob- ject in motion by heterical impenetrabilities, if a ball be started by the impact 12 of some other objecf, every object, wliichal llie homonical vime of theeffeci's beginning, was outside of the honionical where of impact, i. e., whose where and the where of impact were hetera, can be immediately heterated by the mind from the causes of the effect. And so also, from the very nature of compounds, we know that, the iuirredients compounded must come in contact or tliey wt.uld not enter into compounds together. And aiihogh we can not tell but that other existences than those in- gredients which enter into compounds, may havo something to do with ihe compounding of those ingredients, yet if the action of these other existences be always constant at all times and places, whenever and wherever a given effect IS offereJ to our senses, for all practical purpose** their action mnv be omitted in our considerations without any error to our principle* or results. Thus; although we may nor be able I . het.-rate tlio space, which bounds and limits the capaciai gregaria of the n.>rtli polar star, from the spacu- in whieh pine sh.svings are burning, yet if the influenee of t .e n.irth star be constant whenever and wherever shivirigs and tire are found upon our earth, for nil practical purposes we may omit this inttiience in our considerations Mud s,ek after other nggregafi >ns, whose capaciai gregaria we can delcrnnnc and limit in space; and if their space and the space in which shavinirs are burn ing be hetera, wo may immediately heterate those other agirngatins from the causes of the effect. And hence, wlienever, for instance, we'' find soap, we feel assured that no ingredients outside ot those which hav,. eome in contact, can c.ntain the causes of soap, or at least we may look for and receive a^ causes, if not all of the cau^^es, scmie capicial s^regaria conlaineu in the in- gredients, which have come in contact when soap came into existence as an effect. But in numerous instances, for the purposes ot the hefeiical induction of aggregations in space, we must follow Bacon's rule of varying the circum- stances, i. e., we must find what capaciai gregaria of aggregate e'xistences are within the homonical time and place of given effects in one and the other in- stance of similical effects. Sometimes by observation upon numerous instan - ces of similical effects in nature, we are able to heterate aggregate existences from others containing the causal gregaria ; and very frequently we can do this by experiment. If, in the consideration of compounds for instancy, a chemist can analyse and find a certain portion of water to contain the primary aggre gallons, oxygen, hydrogen and sulphur, in one inMance, and in anothor in- stance, he find a j ortion of water to ct>ntain oxygen, hydrogen and poiasium he may then, by the latter instance, heterate sulphur from the sine quibus non of water; for, in the latter instance, water occurs wiihout sulphur being in the homonical space of the effect: and by the former instance he can heterate potasium from the sine quibus non of the effect. But it is not quite clear from the above analysis of the chemist, that both potasium and sulpliur can l)t* absent from the water; for, oxygen and hydrogen may not unite, for any- ihiijg we yet know, into the c(im,)ouud of water, wiihout the presence of riihor tne one or the other of these substances. Hut if Ine chemist find a l)()ilion of water containing only oxygen and hydrogen, he may liien heterate all (Jther aggregations IVoin the sine quibus non ot water. 15ul neither oxygen iinr hydrogen can be lieterater()posi- tion; whatever is absent from the homoiiical time or i)lace of a given effect, and the causes of that effect, arc hetera. CHAPTER V. ITOMONICAL INDITTION. In the previous chapter we explained the modus operandi of the mind in separating those aggregate existences, whose gregaria can not be causes of a given effect from other aggregations, whose gregaria may be the causes so far as time and space are concerned, i. o., their times and wheres fulfill the conditions of causation. In the present chapter we must show the process of the mind in determining what aggregations fulfilling the conditions of time and space, and the aggregations containing the causal gregaria are homoni- cal hetera. Although we may heterate all other objects from the homonical place of a given effect at the time the efiect took place, excepting a, b, c, yet it is not certain that a, b, c, each of them, contain the causal gregaria of the given effect, nor is it certain which of them do contain causal gregaria. Three men may have hold of a rock when it begins to move, and yet one of them may have done all the lifting. And supposing that lye, sand, sawdust and adipose tissue be put together in a kettle and boiled, and soap be the result, which of these ingredients contained the causal gregaria of the effect? We might, no doubt, heterate some of these ingredients from the causes in the manner pointed out in the last chapter, but our object now is not to find existences, which in relation to the causes of the eflfeet are heterical, but to find the aggregations, which are homonical with these containing the causes. And in order to find the homonical aggregptions we must again follow Ba- con's rule of varying the circumstances Suppose we take lye, sawdust and sand without any adipose matter and boil them just as spoken of above, and 15 ■ find that no soap is produced, we may then conclude that adipose matter was a sine qua non of soap in the first experiment. And hence when we wish to ascertain whether any one of the aggregations, fu'filling the condilionsof the lime and place of a given efiect, be a sine qua non of that effect, we first as- certain, if possible, all the aggregations fulfilling' those conditions, and then we find an other case having all the aggregations as before, excepting that aggregation, whose gregaria as sine quibus non, we wish to try; and if in the latter caee the effect is not produced as in ihe former one, then this uiTJiregalion left out of the latter case was a sine qua non of the effect in the former c.ise. Thus; if in one case we find the aggrega- tions fulfilling the conditions of the time and place of the effect a, to be a, b, c, and d,and in an other case we find a, b and c without d in like condi- tions as befo«'e, without the effect a, we then have the data from which to niake the houu)uical induction, that d was a sine qua non of a. Tliat the sun is a sine qua non of day may be proven by taking the case of a bright (lay and a case in the same day, when the sun is eclipsed by the interposition of the opaque body of the moon, or when the earth ret^olves and takes us away from the sun. And it is no matter which of the tw<; cases, one of which contains all the airffrejrations and Ihe other all excepting one, come under our observation first. If a, b, and d, be found in ct;rlain conditions, and then e also come into those conditions ajid then the eflect a immediately commence, all the data of tWe two eases requirerl are furnished. Before the sun rises, we have the aggregations, a, b, c, . .p without day; when the sun rises we have ihe aggregations a, b, c . .p and the sun, and then it is day. And if we can find cases by which we can thus try successively each one of the aggregations fulfilling the conditi(ms of time and space, we may find, by homonical in- duction, all of the aggregations containing all the causal gregaria of any given effect. But we must be sure that the case, in which the effect does not . occur, contains all the aggregations excepting the one, which we are trying as to its being a sine qua non, and which, the ease, in which the effect fol- lows contains. Thus; if the case, in which the eflect a, follows, contain the aggregations, a, b, c, d and e in an homonical time and place, and we wish to see whether a, was a sine qua non of that eflect, we must find a case in which 1), c, d and e are found in a similical time and place without the eflect. If there be more aggregations in the case in which the efl'ect does not follow, i, e, if there be b, c, d, e and f in the case without the effect a, and a, h, c, d and e without f in the case where the eflect follows, as the effect adoes not follow in the former case, the additional aggregation f vvouid not vitiate our inference respecting as being a sine qua non in the latter case, unless some effect due to f should prevent the effect a in the former case. If a, b, c, d and e be found to make a compound in the condition g, and b, c, d, e and f M 4 16 remain but a mixluic in the rondilion g, we may infer a to luivc been a sine «iua non in the former case, unless f he a pi eventing cause in tlie latter one. But for entire certaint}^ it i>; neec^IKFFJli:\TIAl. IND! . 1 1 >\. We have already seen that tlie h')ni.>i,i>;il :i mm-I :hc hoin-i n. ;il .i, through their times ;ire hetera, are in -|.:ii<' homon. i. r, ih, \ ;iif in the same where at any given point of lime W-' liavc il-. -en ih -t p,,. liomonicul a and the heterical :,. Ihongh ,. : linic^ i,i v Im :,. m >ii, ure hetera in space, i.e, one a, !»ai a certain wh. iv and llir ."h.r i. his an other certain where, both of whirh whercs may be ...ciipi.-.l ai ihc Mn. linir. We have also seen that hetera lie at the foundaii«.n <>f «■ -i -i! i .a, and that things inter se similia, and also things inter se difVereniia. am-i be inter ><• hetera; and hence either similia or «lifrerentia arc the e.-m-'-^ ol .v. ry etbci. The homonical a, and the helerical a, arc i it< r -e h tet.i, ih.y are also inui- se similia, hut a, and b, are hetera and thev aic also inter se (liMVrenti i. Now as,the gregaria of aggregate existences aretne causes of .11 ( II, • k and as there must be heterical gregaria concerned in the production of ,v( ly effect, and as the heterical gregaria concern<'d nui»*t be inter se slmiiia .»r difterentia, it is the province of ditlerential induction l.. eliminate those -re- garia, which, with reference to the causal gregaria of an etVect existing in either of the aggregations in the homonical time and place of such ert'ect.are differentia. And in order to do this, we must first make helerical and homou- ical inductions of aggregations, (we may then also make heteric^d inductions of gregaria, which is as far as Bacon pushed induction) and then we must make differential inductions in the method about to be explained. And in order to understand the matter thonuighly, let us approach the subject by first clearing the way. Suppose we take two aggregate existences, whose gregaria we know, and suppose the gregaria of the first aggregation to be, a, b, c, d and e and no more, and the gregaria of the second aggregation to bj a, b, g, h, i, and no more, and suppose that in an homonical lime and place, bv heterical and| homonical inductions of aggregations, a certain eflict, whicii we will call a, to spring from thes^ helerical aggregations: then we can not 17 tell, whether the effect a, sprung from the similia a and a, or b and b, or from the differentia a and b, b and b, or c and i «S:c. But supp«)sing the efi'ect to have sprung from but two heterical gregaria, these heterical gregaria must be located, one in each aggregation, and not both in the same aggregation, oth- erwise the effect would spring up in a single aggregation and the two ag- gregations would not be sine quibus non in the homonical time and [lace of such effect, as we may have determined to be the case by a previous homonical induction, and without a previous homonical induction of aggregation , differential induction of causal gregaria can not proceed. Hut suppose we take five aggregations, whose gregaria we know, the the gregaria of the first being a, b, c, u aud e, and no more; those of the second a, b, c, d, and f, and no more; those o*" the third a, b, c, e and f, and no more; (hose of the fourth a, b, d, e and f, and no more; those of the fifth a, c, d, e and f, and no more. Now we can conclude, by heterical induction, that the effect, which springs from the first and second aggregations, is not caused by the similia e and e, for e does not exist in the second aggregation; and the effect which springs from the first and third, is not caused by the similia d ant! d; aud the effect, which springs from the first and fourth, is not caused b}' the similia c and c; and the effect, which springs from the first and fifth, is not caused by the similia b and b. If now the four effects be inter :»e similia and in view of the above state of the case, we look upon the second aggregation, we conclude by heterical induction that, in that aggre- gation e was not a sine qua non of the-eflect, which sprung from the combi- nation of the first and second aggregations; and hi^nce a simile of it is not a sine qua non in any (»ther aggregation, which may combine with a simile of the first aggregation and produce a siiuilical effect. And in the.othcr instan- ces, we may eliminate by heterical induciion, d from the third aggregation, c from the fourth, and b from the fifth. We have not been speaking above of any other effects than these aris- ing from the given combinations of the given aggregations, whic. by pre- vious heterical and homonical inductions we know to dc the aggregations containing the causal gregaria, and the gregaria ef each of which aggrega- tions we know also. There may, for all that yet appears, however, be other aggregations containing causal gregaria of effects, which, with reference to the given effects spoken of above, are similia, and yet the causal gregaria of the other eff'ects, with reference to the causal gregaria of the given effects, may be differentia. But suppose there be other aggregations containing other causal gregaria of an heterical effect A, these other causal gregaria, with reference 'to the causal gregaria of the homonical A, the effect above spoken of, must be either similical differentia, in which case the heterical ett'ect is but another instance of like causes, i. e., the causal gregaria of the homonical A being the Inunonical diffe»entia, a in the first 18 aggregation and fin the second, for instance, if the causal gregaria of an heterical A',Aand A» being inter se similia, be similicalditferentia, the causal gregaria of the heterical A' are the similical differentia a' and T; or the causK.'^ gregaria ot the heterical A, with reference to the causal gregaria of the ho- monical A, must be differential differentia, i. e., the causal gregaria of the homonical A C being the homonical differentia a and t, for instance, the causal gregaria of a heterical a, may be the differential differentia e and g, lor instance for aught that yet appears. But in no case, the causal gregaria of the homonical A being the homonical differentia a and f,can the causal gregaria of an heterical A be,with reference to the causal gregaria of the homonical A.similical similia; for the similia a and a, b and b, or d and d, &c., to be similical similia with the homonical differentia a and b, is abgurd and impossible. But supposing the causal gregaria of an homonical A, to be the difftr- entia a and f, may not the causal gregaria of a similical A, be inter se similia, such as k and k, y and y, or z and z ? Now it we contemplate the causal gregaria of the homonical A, and those of the similical A, im the two a's are inter se similia in every respect, and as each oi the causal gregaria of bollj a's is not an aggregation but a simple gregarium. the effect produced by n and f inter se can not be a simile of an effect produced by a and a, inter se, so long as homon is homon, and similia are similia; and if a can origin;ite upon a* a simile of the effect, which f originates upon a, then a and 1 must be intir se similia, which is absurd. If a certain vibration of the uimospliere in con nect.on with the aparatus of the ear produce a certain soun^., then a simile of that sound, the aparatus of the ear remaining the same, can not be produced but by a simile of the given vibraUou. But in the case considered above, the causal gregaria in the first iii- ilance being by supposition the differentia a and f, and in the second instance the similia a and a, one of the causal gregaria (a) in the first instance ami one (a) in the second are inter se similia; that no effects inter se similia can spring from such sets of causal gregaria, is evident. But an effect, an ho- monical a, having sprung from the causal gregaria, the homonical differentii a and f, may not a similical A, spring from the similia, gandg? In the first instance a originated upon f, an homonical effect A, and we see that g cannot originate upon f, a simile of A, unless a and g be inter se similia; but in the first instance, by changing the mode of expression without affecting in any manner, the result, f originated upon a, the homonical effect A, and g cannot originate upon a, a simile of A, unless g and f be inter se similia; but a is an liomonical gregariura and g is an homonical gregarium, and inter se they are differentia. Now two gregaria inter se differentia can not in their action be inter se similia unltss similia and difl'erentia be inter se similia, which is impossible. And if a cannot act towards f, as g acts towards g, and if f can- not act towards a, as g acts towards g, the results of the actions betwcin » 19 and f, and between g and g, can not be inter se similia. And an homonicHl effect a, having sprung from the homonical differentia a and f, we may rea- son in like manner respecting the effect, which must spring, if at all, from the differential differentia g and h. So tuo if an effect spring from the similia a and a, no similical effect can spring from the differentia a and b, c and d, &c., nor can a similical effect spring from differential similia as b and b, or c and C&c. Ot the differential elements of the alphabet, no other two can be conjoined so as to produce the sound resulting from ab; and so it must be throughout nature. And hence it must appear that effects inter se similia in every respect must be produced by similical gregaria, either similical simi- lia or similical differentia; differential similia or differential differentia can- not produce similical effects. And therefore if two or more aggregations come into the homonical time and place of an effect, we first find by heterical and homonical inductions of aggregations, the aggregations from which the effect sprung, then we look for other instances containing a simile of one of the aggregations from which a similical effect sprung, i. e., we vary the cir- cumstances, and by doing so we are often able by heterical induction of gre- garia to eliminate certain gregaria from the differential aggregations combined with the similia of the other aggregation in the given instance; then we pro- ceed farther. And it must be remembered that two gregarial similii cannot exist in tlie same aggregation. Thus; iron possesses hardness, and there is an ho- monical hardness in this piece and an heterical hardness in that piece, and inter se the homonical hardness and the heterical hardness are gregarial similia; but there cannot be two hardnesses in an homonical piece of iron; all the gregaria in a single piece or particle of iron are inter se differentia. Now when effects are produced between two aggergations, these aggregations either disappear in a measure and merge in the effects, as in chemical compounds, or the effects, which our senses witness are grounded in one of the aggregations or in both. When oxygen and hy- drogen unite and form water, the two aggregations, in a measure merge in the effect— water, i. e., although the weight, impenitrability, &c., of the sepa- rate elements remain as gregaria of the compound, yet some of the gregaria of each element seem to have disappeared and to have merged in an effect, whese gregaria with reference to the gregaria of either of the elements are differentia; but if we apply oxygen to steel, we witness an effect grounded in the steel. Having now cleared the way, as we hope, we may proceed t« diff- erential induction. Suppose then, that we take a certain aggregation, which we will call A, and that we apply the aggregation B to it, and we find a certain effect x to spring up; we then in like coniitions apply to A, or to a simile of A, the ag- gregaliim C,and flndeitherno effect or the effect y, then it is certain, A and A 20 being homon or inter se simil lain every respect, that the causal grcs^ariura of x existing in b has no simile existing in C, i. e., that each of the gregaria of c and the causal gregariuin of x existing in B are inter se differentia. ' Suppose then, that we can discover in B the gregari.i a, b, c and d, for instance, and that we can also discover the gregaria a, b, c and d, in C, then we know that neither a simile of a, nor of b, nor of c, nor of d, was the causal gregarium, in B or in similia of B, of x, which sprung from the horaonical time and place of A and B. And letting the capitals A, B, C, D, &c., be names to dis- tinguish aggregations inter se, and the small letters, a, b, c, d, &c., be names to distinguish eftects inter se, we may make the following tables to assist the understanding. 1st. A and B produce a A and C produce b A and D produce c A and E produce d A and F produce e A and G produce f tfec. 2d. B and A prcnluce a B and C produce g B and D produce h B and E produce i B and F produce j B and G produce k »kc. Now in the first set of instances in the homonical time and wince of the effects, if we desire to find the causal gregaria of a, which exist in B, we see that gregaria, similical with the causal gregaria in B of the effect a' do not exist in C, nor D, nor E, &c., and hence wherever we find ag.euarium' in C, D, E&c, which has a simile in B, we know that this similical Vcjra- rium in B and the causal gregarium. or each of the causal irrcgaria ii^ B? it- there should be more than one causal gregarium in B, are inter se ditferen'iia. And in the second set of instances we may deal in like manner with the gre- garia of A. And after that we have differentiated, by differential inductron as in the manner now explained above, the gregaria in B, which are not the causal gregaria, from the causal gregaria, we may dismiss the non causal gre- garia from our consideration and look further into the matter. The case, however, may and does occur in chemistry, where two a"-, gregations will not produce an effect without a third aggregation being brought to bear upon them, and then differential induction is rendered still more complicated and difficult. Suppose that A, B and C, produce the effect a, and that A and B produce b, A and C produce c, and B and C produce d then it is evident that the causal gregaria of a existing in A and each of the gregaria in B are differentia; for, if the causal giegaria of a in A, have simi- lia in B, then B and C would produce a without A. And in like manner it is evident that the causal gregaria of a in A and each of the gregaria in C are differentia, and the causal gregaria of a in B and each of the gregaria in A are differentia, and the causal gregaria of a in B and each of the gre 21 garia in are differentia. And hence the proximate causal gregaria of a must be in b and C, or in c and B, or in d and A. Now if A and B really produce no effect at ail, and if B and C produce no effect at all, it is evident that tne proximate causal gregaria are in c and B. And if c be a permanent effect, wa may then deal with c and with B in the manner abore given; but if c be evanescent we are not able to manage it in that manner. If nitric acid and platinum in an homonical time and place produce no effect, and if silver and platinum in like conditions produce no effect, but nitric acid dis- olve silver, i. e., nitric acid and silver produce an effect, which we will call c; and if nitric acid, silver and platinum produce an effect, which we will call a, then it is evident that the causal gregaria of a lie in c and platinum, and we must, if possible, inquire into the gregaria of c and also into those of platinum by differential induction as explained above. But suppose, as before, that A, B and C produce the effect a, and that A and B actually produce b, and A and C produce c, and B and C produce d, if is then uncertain whether b and C, c and B, or d and A produce a; and if the eflects, b, c, and d be evanescent and not of a permanent character per se, so that we cannot examine them, we can make no inductions respecting the proximate causal gregaria of a. If, howtver, b, c and d be of a permanent character, when A and B have produced b, we can try b with C, and >.o of c and d; and in tiiis minner we can differentiate the gregaria of c and d fVom the causal gregaria of a. When four elements enter into a compound in a binary manner, diff- erential induction is easy. When A and B produce a, and C and let us form two tables as before: 1st. 2d. A and B produce a B and A produce a A and C produce a B and G produce a A and D produce a,&c. B and H produce a, &c. Now in the first set of instances, as B, C and D, each of them along with A produce a, A remaining the same or a similie of A being in each instance, the respect, in which B, C and D are inter -se similia, is the causal gregarium of a, existing in B, in C aud in D, &c.; and in the second ?et the respect in which A, G and H are inter se similia, is tlie causal gregarium of a existing in A. And if A and B produce d, and then d and C produce a, we may make a similical induction respecting the causal gregaria in d and in C in the manner shown above. And if A and B produce d, and C and D prodace g, and then d and g produce a, we may continue our inductions in like manner, and so on. In differential induction the respect in which aggresraiions, one of which contains causal gregaria of a given effect aud the others not, are inter se similia, and the causal grtgarium in the one causal a^^i^reLraiiou are inter ie differentia; in similical induction, the respect in which ajji^reirutions, all uf which contain causal gregaria of a given effect, are inter se similia, and the causal gregarium of the given effect in any one of the aggregaiions c<.m pared are inter se similia. And if two aggre^r.-aions containing causal gre- garia of a given effect and compared in the manner abfive stated bo inter se similia only in one respect, that respect is the causal gregarium of flie effect existing in each of the aggregations. The principle ot similical induction may be summed up in the following similical proposiiiou ; whatever gregaria in similical conditions produce similical effects, are inter se similia. CHAPTEH VIII. INCOM.MEXSl'RAL INDUCTION. We have seen heretofore that, commensura aud incominensura are relations which have an homonical standard, and therefore when these terms are applied to aggregate existences, or to gregaria, they are applicable only to those existences, which are inter se similia. Thus: a mav be equal to n\ i.e., a=a*, or art to differential and similical inductions. In differential induction, which presupposes homonical induction of aggregations, we look directly at the gregaria of aggregations, and having applied these aggregations severally to a common substance, or to substances entirely similia inter se, we note the gregaria, which are inter se similia in two substances, one of which along with the substance A for instance, will produce the effect Z, while the other along with the substance A will not pro- duce a simile of Z, and then we differentiate those similia from the causal 28 gregaria. Sugar and soda, for instance, will both dissolve in pure water, these capacial gregaria of the two substances are inter se similia; but when vinegar is applied to soda it will foam and boil, while when applied to sugar it will not; the capacial gregarium of being held in solution, therefore, is not in soda the cause of the ebulition witnessed when it is put into acid. In the first book of this volume we spoke of facial and capacial gregaria; we called the color, the taste, the feeling, the smell and the sound of objects, their facial gregaria, because they present such appearances to our senses. In realityi however, all these things are capacial gregaria; and the only difference Is, that facial gregaria are perceptional facts immediately noticed by the mind, while our knowledge of what we have called capacial gregaria is derived from a comparison of perceptional facts. Thus, if I apply sugar to my tongue an effect is produced immediately between the sugar and my organs of taste; but if I put a lump of sugar in water, 1 see the sugar and the water and I may see the sugar dissolving; I, indeed, make an induction in every Instance to arrive at the knowledge of capacial gregaria of aggregations. Now in making differential inductions, we always arrive at the knowledge of similical gregaria in various substances by observing the facts which spring from them when applied to similical substances. Thus, supposing our or- gans of taste to remain in similical conditions during a certain time, and during this time we taste two substances and find their tastes to be exactly alike: if now we find the one when taken into the stomach will net as an emetic and the other as a cathartic, we feel assured that the qualities, the gregaria which are similia in regard to our taste, and the gregaria, which produce in the stomach differential effects, must be inter se difffjrentia. And so we may try any two or more substances with pure water or with any other thing, and in this manner determine similical gregarial, and if then we apply these substances to some other thing and And differential effects, we may differentiate the similical gregaria from the causal gregaria of a given effect. Differential induction does not, indeed, determine what gregaria are causal gregaria, but it merely determines what gregaria are not causal gregaria. And this it does n©t only in respect to a particular instance but in respect to all instances of similical effects. In the compli- cated workings of nature, however, laws are frequently antagonistic, and when one prevails over another, the prevailing one must always be considered the cause of the ensuing change which takes place, while the abrogated law, as it were, is not the cause although it is often called so. And in order to make the subjects of differential and similical induction clear, it is necessary to speak of this matter here. If, for instance, two men with rope and pullies be raising a rock and the rope break and the rock fall to the ground, we are apt to say that the breaking of the rope is the cause of the rock's falling, while in truth the causal gregaria of the rock's falling are in 29 the earth and rock, and the rope has 'nothing to do with it; though the rope, before it broke, was a cause of the rocks rising. Every change, indeed, is an effect, and when a certain positive phenomenon is going on it is being or hag been produced by certain causes, some of which may cease to act and then the phenomenon disappears, in which case we are accustomed to call the cessa- tion of the cause of its production, the cause of its disappearance. We are accustomed to say that the want of wat«r is the cause of the death of a fish up on the land. That, however, which is heterated, the absence of a thing the want of an aggregation or gregarium, can not be the cause of anything. Certain laws may be kept in operation by certain gregaria of aggregation?^ and then certain phenomena exist; take away one of the aggregations, the taking away of which is truly an effect, and although we may properly call this taking away of the aggregation the reason of the cessation of the phe- nomenon, yet it is not the cause of such cessation. That only which acts can be a cause. And hence although there may be and is plurality of causes of similical effects, i. e., the causes of similical effects are hetera, yet simili- cal effects can not be produced by differential causes. And hence, although many aggregations, which as aggregations are inter se differentia, may pro- duce similical effects, yet when we come to the causal gregaria of similical effects, the causal gregaria will always be similical. And therefore, the causal gregaria of similical effects being inter se similical, we at once know that, of two aggregations, one of which produces the effect and the other not, the gregaria which are inter se similia and the causal gregaria are later se differentia. In similical induction we compare together different aggregations, each of which we find to contain causal gregaria of similical effects to ascer- tain in what they agree. And if they agree but in one respect, this respect we know must be a causal gregarium: for the causes of similical effects are inter se similia If they agree in several respects, we can not tell which of the similia are causal gregaria, and we should try by differential induction to difierentiate some of these similia from the causal gregaria. Thus: if A, B, C and D will, each of them, with G produce similical effects, and if they all agree in several respects so that we can not tell the causal gregarium in either of them, we may find as aggregregation in which some of the gregaria existing as similia in A. B, C and D, exist also, and yet the aggregation along with G will not produce the effect. That crystaline structure is not the causal gregarium of the doublwrefraction of light is clearly proven by differ- ential induction, although all substances which have hitherto been found to cause the double refraction of light, have been crystaline ; and therefore, if we knew that they did not agree in any other respect, by similical induction, it would be proven, that double refraction depended upon crystaline structure alone. Crystaliae structure may, indeed, be one of the cansal gregaria exist- 30 ing in all substances, which refract light in this manner; but it is either not a cause at all. or at best it is not of itself the cause, since all crystaline sub- stanc«9 do not cause double refraction. Differential and sirailical inductions aid each other in the search after causes, and neither of them should be ne- glected in any case, if they can be applied. Incommensural and commensural inductions also aid each other in science. That the oscilations of the pendulum are cau&ed by th« earth, i. e., that the earth contains causal gregaria of these oscilations, and also that the earth contains causal gregaria of the gravity of terestrial objects, was proven by incommensural induction ; and then Newton by commensural induction proved the earth to contain also causal gregaria of the motion of th« moon, and established what is called the universal law of gravitation. It does not seem to me to be necessary to speak farther upon the six methods of making inductions which we have endeavored to exhibit in the previous pages. These six methods of induction with the aid of ratiocination exhaust the powers of the human mind in drawing logical conclusions. And whil« treating of our subject in the first book, we saw that hetera lie at the founda- tions of knowledge and that homon is at the foundation of propositions; and we must now see that homon is at the foundation of all induction and that ttie homonical syllogism, sustains the truths upon whicli every induction proceeds. But before passing on to further considerations it seems necessary to make a few remarks upon the methods of induction which have been set out by J. Stuart Mill, and in doing so we will not go into a lengthy discussion, as we believe that the student who has mastered the preceding pages of this book, will be able with but few suggestions, to perceive, what we consider, the errors of Mr. Mill. Of Mr. Mill's method of Residues, we shall merely remark that when we have subducted, from any phenomena, what by preri- ous inductions and ratiocinations we already know to be due to known causes, we proceed with the residue by some one or other of the six methods, which we have given, and that there is nothing peculiar to his method of residues, so that it should be considered in itself a particular kind ©f induction. In what Mr. Mill calls the method of agreement there is the mixing together and confounding ot what we have called heterical induction with similical induction. The axiom upon which-Mr. Mill considers this method to rest, to-wit: "Whatever circumstances can be excluded, without prejudice to the phenomenon, or can be absent notwithstanding its presence, is not con- nected with it in the way of causation," is applicable only to heterical induc- tion, yet Mr. Mill endeavors to apply his method of agreement to infer caus- ation from the agreement in respect to the presence of some antecedent in 81 every case from which the effect arises, which can be done only by similical induction. Mr. Mill's method of Difference corresponds with what we have called homonical inductions, though his exposition of it has not been satisfactory to our mind. What Mr. Mill calls the Joint Method of Agreement and Difference, we regard as an intermixture of homonical induction with erro- neous views, which indeed, have reference to differential induction, although Mr. Mill had no conception of such method. It is, indeed, quite evident, that if A will produce a certain effect and B will not, the causal gregaria ex- isting in A have no similia existing in B, and if now we could examine every substance which will not produce the given effect and find that thej all agree in not containing some gregarium which is contained by A, there would be a strong probability, and nothing more than a probability, that this gregarium was a cause of the given effect. To pursue such a method, how- ever, would be to depart from true induction and in the labyrinths of nature it is entirely impractical, and of very little value could it be done. On the other hand if we have but two cases, in one of which the effect springs from A, B and C, while in the other, viz: A and B, the effect will not be pro- duced, although we may never be able by experiment to remove and again replace C, yet the two cases furnish all the data necessary for making the homonical induction that C contains causal gregaria of the effect. We con- clude that there is nothing in Mr. Mill's Joint Method to make it a particu- lar kind of induction and further that a great part of hi« doctrine respect- ing it is erroneous. Of Mr. Mill's method of concomttant variations, we will only say that he does not make any reference to what we consider to be the true principles involved in the matter, but treats of cases, some of which are to be deter- mined by commensural and others by incommensural induction. We have been very limited in our remarks upon the methods of Mr. Mill, as we desire in this book to take the afllrmative and not the negative side of questions. Our object is to build up and not to tear down. And we propose also to make this book as concise as possible and not fill and enlarge it with criticisms. We may dismiss the subject of the inductive methods here, hoping that the reader will be able to understand the matter. CHAPTER XI. HYrOTHESES. In the previous pages, we have dealt only wivh those principles which are brought into view by the comparisons of truths which have been derived from actual facts And in the investigation of nature, our object must always be to find out what actually exists and how it operates, and not to assume certain hypotheses and from them determine how nature should exist and 32 operate. He, who would gain any scientific knowledge of the phenomena of nature, must investigate and not make assumptions. When we hav« really gained any new truth in nature, we do not rest the evidence of that truth upon an hppothesis; but in regard to all certain knowledge, we apply the saying of Newton "Hypotheses non fingo." Yet it is natural for man to form theories, and these theories often direct his energies towards valuable results. And for the purpose of stimulating the mind to investigation an hypothesis may be laid down, aid in many instances for that purpose an hy- pothesis must be resorted to. No man, whose object is to search after truth, will take the trouble of investigating anything unless he expects to find out whether something which he has in view be true or not. A scientific hypothesis, therefore, is a subject stated for debate, in which arguments pro and con can be brought from actual facts in nature. If by ratiocination and induction founded upon actual phenomena, the hypothesis can be proven, that closes the debate and the hypothesis is converted into a truth, the evi- dence of which does not at all rest upon the hopothesis. And hence when we have laid down an hypothesis, our object must be to prove or disprova it from actual phenomena. But from nature we can prove only homon or homa, hetera, similia, differentia, commensura and incomensura; and there- fore, scientific hypotheses may be divided into homonical, hetera, similical, differential, commensural and Incommensural hypotheses. In heterical hypotheses, which seem to be the most convenient to be treated of first in order, we may make a supposition respecting the heterical existences of a phenomenon; or granting its homonical existence, we may lay down an heterical hypothesis respecting its causal grecjaria as sine quibus non of certain effects. Thus: as a simple example of a supposition respect- ing the heterical existence of a phenomenon ; suppose we see a certain horse in an enclosure to-day, and to-morrow we see a horse in another place so much like the former that we are uncertain whether it be the same horse which we first saw, we may make the heterical hypothesis that, it was not the same ons, i. e., this horse and the one we first saw are hetera, and then we must look for the evidence to prove the hopothesis. And if by investigation we find that the first horse has been continuously and is now in the same en- closure, we have proven the hypothesis to be a truth, whose evidence does not rest upon an hypothesis, but upon actual relations of time and space. And a similar example might be given to illustrate homonical hypotheses respect- ing the homonical existence of a phenomenon : we need not, therefore, speak of this again under the head of homonical hypotheses. But suppositions re- specting the causes of phenomena are also useful to excite endeavors, and we may make heterical hypotheses respecting causation. If the aggregations A, B, C and D be in the homonical time and place from which springs the effect R, we may suppose, for instance, that D is not a sine qua non of the 88 R; and to prove our hypothesis we find another instance of the effect R, from which D was absent in time or space. And again : respecting causal i^regaria, if the aggregation A along with Z will produce a given effect, and Balso along with Z will produce a similar effect, and we can perceive that A possesses gregaria, which B does not, we may heterate those gregaria con- tained by A, but not by B, from the causal gregaria of ths effect produced by A and Z, and thus prove the heterical hypothesis respecting those gregaria, if we have made one. And we have already, no doubt, gone far enough to soe that heterical hypotheses, respecting the existence of any phenomenon, to be worth anything, must be succeptable of proof by simple heteration, and that heterical hypotheses respecting causation must be proven by heterical induction. Homonial hypotheses also respecting causation must be proven by homonical induction; and until they are so proven, they are not, of course, to be received as really true, however useful they may be in stimulating in- quiry. Homonical inductions, indeed, are best and more frequently made by experiments than by observations upon nature in her undisturbed processes offered gratuitously to our senses, and therefore we would more frequently resort to experiments to prove any homonical hypothesis. If, for instance, we should suppose that, it is the equsil pressure of the atmosphere upon un- equally balanced columns of water, which force the water up the shorter arm of a syphon, we could make experiments from which an homonical induction of the real cause could bo brought out and the hypothesis proven. That there is an ether pervading all space and causing light by its vibrations, however, can not be proven by homonieal induction, aud if ever proven, (and without being proven the hypothesis amounts to nothing) it must be proven by simil- ical induction. An homonical induction can not be made in any case, unless the existence of aggregations containg causal gregaria can first be proven. If, for instance, we suppose that the aggregations A, B and C, produce x, when we do not know, whether or not, A really has an existence, we can make no homonical induction in the case; for although we should find that B and C alone will not produce x, that is no evidence of the agency or exis- tence of A in the former case Homonical hypotheses respecting causation, to be useful in increasing our stock of knowledge, must be susceptible of proof by homonical induction. And no hypotheses respecting the existence of an aggregation containing causal gregaria can be thus proven. We may also make differential hypotheses respecting causal gregaria, and for their proof we must resort to differential induction. We might sup- pose, for instance, that the quality of dissolving upon the tongue and the causal gregaria of the taste in common salt are diflerentia; and by examin- ing other substances containing this quality, we could prove our hypotheais. And in the examination of nature, as differential inductions, though they do niSt jJrovfe w^at the tiausal gregaria are, assist very much itt making aimilical itfductions, so differential hypotheses should be assumed and tried that we may have every help in unravelling natures complications. In similical hypotheses we assume that, the causa! gregaria of certain phenomena, whose causes we wish to ascertain, and the gregaria of certain objects, with which we are familiar, are similia: and if their effects can be sboWn to be inter se similia, we prove the hypothesis. Thus; if we find a particular color upon white paper, we may assume that the aggregation whatever it might have been, containing causal gregaria of such effect, was similar, in respect to its causal gregaria, to some object with which we are, familiar; and if the object wtth which we are familiar will produce upon the same kind of paper the same kind of color, we prove the hypothsis. If all the planets contain the quality of attracting iron, they, each of them, possess gregaria similar to the lode stone. And if we could make ourselves certain of the existence in any place, of an ether, whose vibrations would produce light, we could prove the ethereal hypothesis. Respecting incommensural effects, we may make three suppositions, viz: first, that the times and spaces being commensura, the increase of the qiiantity of gregaria in a certain obj«ct incommensurates the effects; second, that times and quantities being commensura, the incommensural efftcts de- pend upon incommensural relations of space; and third, that spaces and quantities being commensura, the incommensural effects depend upon incom- mensural relations of time. And having made our hypothesis, we must then find the proof by looking into circumstancei varied in these respects, and in which Ihe effects occurs. But in making our hypotheses, these hypotheses must have i-eference only to what object or objects contain causal gregaria of the incommensural effects, which we witness. And we have remarked several times already that, in the cases from which an incommensural induc- •6on can be made, we are to deal only with similia, commensura and inc«m- inensura being relations inter similia. And ihe hypotheses above spoken 'of must be proven by incommensural induction. After having ascertained that certain objects contain causal gregaria of given effects, we may make ^!iyp"Dtheses respectinsr the relative increase or decrease of the effects to the ■ times, spaces or quantities of causal gregaria. But these hypotheses can not '^e verified by induction, and unless they can be verified by mathematical calculations, they are merely guesses. We are frequently obliged to make ''mathematical calculations respecting the laws of variation in the effects de- peHcting upoh incommensural spaces and times. That gravity varies inversly as the square of the distance is not an induction, but a truth found out by the application of mathematics to actual phenomena. Thai the spaces passed oVer in successive commensural times by falling bodies are in the relation of ''ih4 odd ntrmbers 1, 8, 5,7, &c., is a truth of the same kind, i. e., it is found 35 by making calculations of what actually oceurs, as observed, in this respect, when bodies fall without being impeded. Respecting commensural effects, we may make hypotheses in the same manner as respecting incommensural effects, and we must seek for the proof in like manner. We do not consider it necessary to make further remarks upon hypotheses. Every hypothesis respecting causation must b« proved by induction ; hypotheses respecting iheT^stioos of quantities, times and spaces are to be dealt with by ratioci nation. We have now completed our view of ratiocination and induction, so tar as we propose to treat of them in comnK)n language. And we may well consider of what value these speculations may be to the cause of science. And merely as a speculation we regard the previous pages as not ontirely unworthy of study ; but we hope yet to show, that practical results of the grandest kind may be expected to follow from a knowledge of the principles therein set forth. To gather up an exhibit these principles in formnlae, and to apply them to the actual phenomenon of nature will be our object ii^ Book III. -k T> /-: lib - k BOOK III. CHAPTER I. SIGNS IN RATIOCINATION. In the two previous books we have examined the foundations of rea- soning throughout and have endeavored to explain, by the use of common language, what we have considered necessary on the subjects of ratiocination and induction. Common language, however, is not the appropriate vehicle of recondite ecience. Without the assistance of symbols, which form a pe- culiar language, Algebra, which consists of syllogisms with commensural and incommensural propositions, could not have been brought to any great perfection. These commensural and incommensural propositions, with the syllogisms constructed upon them, however, have been expressed and wrought into Algebric formula?, which can be transformed in various ways, and there- by unexpected and grand results can be brought to our apprehension. And it may be useful to inquire whether the other four kinds of propositions also can not be expressed in symbols and reduced to formulne, which may be formed into a complete system of abstract and exact science. That such complete system of science may and will be constructed in the future by the genius of man, the author of this treatise believes; and it seems to him to be not an unworthy undertaking to make a beginning at its construction, "Which may be an incentive to call to the work others of more favored cir- cumstances and greater learning. The construction of such system will, therefore, be attempted in this book. And we will commence with simple propositions. ^ Let the sign !r stand for an homonlcal comparison; then, ^a, will be equivalent to the proposition in common language, a and a are homon. Let the sign v stand for an heterical comparison; then ava will be equivalent to the proposition in common language, a and a are hctera. Let the sign || stand for a similical comparison; then a || a, will be equivalent to the proposition in common language, a and a are similia. Let the sign H- stand for a differ- ential comparison; then an-b will be equivalent to a and bare differentia- Let the sign = stand (as in Algebra) for a commensural comparison; then, a=a will mean that a and a are commensura. Let the signs > and < stand (as in Algebra) for an incommensural comparison: then, a>a, or ai Let the sign, || a indicate similical homa (( (( U II V # IL ii < {< ({ t( (C k t> il {( CI (C i( (( (i 11 (4 (I (( t( C. The premises in mode 5th reduce as follows: (f.) f. 8. • A. And as T.8. A are homon i. e.. A A A V A A T. 8. T. 8 'AX C V A. in the first premise and __* '_ in the second premise A, A A A A A A Tl^ _^ ^'^ the comparison between C A A A, - (g.) A A ^ V A A and A makes the conclusion ^^ ^^ _^ A V C. Tlic premises ill iv.odes) 8 reduce as Inllows: A V A ^ \' V A V T. !^. T. S. T.S. A.B V V A'..B\ 1-ii., prtnuise, *iil, ;>i(.n)i"e 11k' c.onclnsi'M], ('. 8. A.B A A T. \ V CD. Now pronnsiiionR ciiluT (8) nr (III) iiiidcilrHs 'hv nonchisidns in modes 1, r>, G ami 7, ;um» proposilion ciThiT (4) or (IV) und(Mli«'.s llie coiicliisionH it) mouis, 2, 0, 4, 8, 9. 10, 11, 12, 13, 14, 15 and 16; |V.r, bimilia. diireiontia, com- luensiiiu aul iiicominoiisura arc alst^ iieiera. (hiv kno\vii'd;rt' ot lielera and conricqucnily <.t" lioinon dcpiTds upon tinif and .space; but our kiio\vled;ie »>f simiiia, diircrciiha, cninuunsiua .wul incomnicn lu a does not depend upon lime and space, but upon t(»e .i::«euHria M' agjnre:.;alir>ns. And these substrala of our kno\vled«:^e are lo be ii.cpnred int?) (Vom other groiinils. rn.vn^K ii Sli^NS IN IKDITCTION. In heterical induction of air»jreiratious, we find two or mt)re instances oi" similical effects, and we u<%e one of the iniitanee^ to eli^ninate some of the airgregalions fVoni Uie sTrie qr.iUu8 non in another instance. Tlje ugffrega- tions of the two or more ini.t'incei>* may be synehrontjus or.they ma}' not b< . An observation mode in the lime (»f Htuner, if correctly made, is as valuable for one of tiie instauces, as one ma(ie to-dav, although the a;rgregat ions which caiue under observation then, may have ptssed away into other forms. And in making experiments, tiie times of ilie experiments are not homon but hetera. But the aggregations brougltt together in any one instance of an ob- servation or experiment have homonical times. And when we view ametallc globe, for instance, of the diameter of six inches, we consider it as occupy- ing an homonical WHERE, thougii the wheres of its particles be heter*. And so also, if we bring the aggregiitions A, B, C, D, &c., in contact with each other, we may tlien consider, the result as an aggregation of aggrega- tions and as occupying an honn)nioal where. Now if we let the last letters of the Alphabet, v, x, y, z, stand for eft'ects, and let the sign U stand for cau satioii, then in view of what hns been said above, we will have the proposition. A A (1.) V V T. S. A A A..B..C..I). V V A'..B*..C' 2: V V T.S. U X II X' And as x and x' are similical effects, they can be produced by simili- « cal hetera and in order lo have similical hetera EO nomine etin numero, we must dismiss D in the first term Irom the sine quibus non of the effect x. We may then find another instance and have the proposition: (!•; A A T. S. V V T. S. V V '.^. s. A"..B" A '..B'..C' 11 V v T S. U X" •••••• 11 •••••« ..X' And this proposition enables us to heterate C. Tiie heterical induc- tion of irre-Niria mav be represented in the same manner. Take the proposition (2.) A A T. S. A .. B V V T.*S. A A V V T. S. f A A • T. .->. C .. B' a..b..c..d e..f..g .h a..b..c. e..f..g..h n U X ••••• 11 •«• X' l|:l 9 Now as B II B', Ihejr will contain a like number of similical gregaria and Jience by looking at C, d can be eliminated from the causal grega- lia in A. Homonical induction is llie reverse of heterical induction. Take the proposition respecting aggregations: (3.) A A T. S. V V T. 8. A A T. 8. A..B..C » V V V V T. S. K- B'..C' X n 0. or Now H8 we desire to have similical effects, i. e., x and x', they must bo prmluced by similical lietera, eo nomine et in numero, and by looking at the terms, we see that A must be added to the second term, i. e., that A was a sine qua non of the effect x. In differential induction we first clear the way as much d* possible by heterical induction of gregaria and then take the proposition: A A T. S. A. .B a..b..c..d i.k.&c. n (4.) V V T. S. V V V V T. 8. A A T. S. C. .B H..b..e..f i..k..&c n X H- 0, or y. And now as B !| B', their gregaria are similical differentia; aad if A || C, we should have had similical eff-cts; but as the effects are differentia, their causal gregaria in A and in C are differentia: and hence the similical grega- ria in A and C may be differentiated from the causal gregaria, i. e., a and b and the causal gregaria of x in A are differentia. Similical induction is the reverse of differential induction; lake the proposition. 10 A A T. S. A. .B a..b..c..d i..k..&c. U (5.) V V T. S. V V V V T. S. A A T. 8. C. .B' a..b..c..f i..k..&c. 21 X II X' Now as X II x', tliey have been produced by similical gregaria, and as B 11 B', we must find similical gregaria in A aufl C, and we find a and b in both; therefore the.se gregaria, or one of them at least is a causal gregarium. We must notice, that in »ur propositions for making heterical and honiouical induetiens, wv rej*resent the aggregations by the signs between the terms, merely as lietera. This mutt necessarily be the case; for, v»'e are eliminating and aggregating hetera by those processes. In differential and similical inductions also we must represent the aggregations by the signs, raerelv as hetera. For, if A..B It and A i| B, we know by ratiocination that eimilical similia will produce simi- lical effects; and if Ai+6, we know that similical differentia will produce similical effects. But in the al>ove inductive propositions, B i| B' and Ah-C, as aggregations, and we desire»o find in A and C, the respects, the gregaria inter se similia and to make an inference respecting them and this can be done only by using the heterical signs between the terms. In incommeusurl induction, there are three cases; 1st, times and spaces being commensura, the quantities are incommensura; 2d the times and quan- tities lieing commensura, the spaces iU'e incommensura; 3«1 the spaces and quantities being commensura, the times are incommensura. Let us suppose that we witness the effect in B and B', tken: A V T. 8. A..B X... A V T. 8. ,y V V T. 8. U ..X' -.>j 11 13 A V T.8. (7.) = V A'..B' X. .. t.. . . X' ^.l (8.) < V = V T. 8. il A.B V V V T. S. < A.B' X ^. •2^ X' Commensural induction brings a simile of one of the aggregations, irhich we hare determined by incommensural induction to contain causal gregaria of a given effect, an4 some other aggregation, about which we are uncertain, into relations commensural with the relations between the aggre- gations, which we know to coatain causal gregaria <>f such effects. And these relations are threefold, hence : ^. s. (9.) ic V =^ V T. S. • ^'.H. A.B 21 X = V • V V T.8. C.B' X' M Which proposition brings C and B' into commensural rclalions with tlie relations of A and B, and when that is done we'find the commensural effect, and hence, as B || B', we cenclude that C contains similical gregaria with A. If we should take the second term of psoposition (8,) as the first term of an inductive commensural proposition wc will have: u (9.) = V = V T. ^. fs'. A'..B' = V ' VV T.8. C.B' U r X' U X" If we cannot thus bring'the aggregations, which we are investigating, into commensural relations as above, and find commensural effects, wc may yet frequently, by mathematical calculations, find what would be the effect, if such commensural relations were realized; and this will answer the purpose. CHAPTEK III. HKTERICAL IVDUCTION APPLIED. In the two previous chapters, we have given formulae, which, when carefully considered and fixed in the mind, will assist the understanding in investigating nature. Observations and eitperiments must furnish the data but the inferences to be drawn from those data must be dictated by a sound philosophy. And the formulae, which we have ^iven, will not only aid the mind in making proper inferences, but also in lookiag for the kind of instan- ces, from which alone legitimate inferences can be drawn. And in applying the foregoing principles, it will not be necessary for us to bring the cases noticed into the exact form of the formulae, as the reader, who has mastered ihesulyect, can easily do that for himself We wish merely to show the utility and impsrtauce of the subject, by illustrations from cases in which these principles have led to scientific discoveries, though the investigators, perhaps, were entirely ignorant of the processes heretofore explained. And it will not be necessary to furnish many illustrations to show what may be expected to follow trora a thorough knowledge of these processes by the scientific men of the world, who are engaged in the several departments of science. Our illustrations may be taken from any department of Knowlcdgt for our principles apply to every branch of science. We will commence with heterical induction. Among all the varieties of material forms, which surround us in the world, chemists have been able to find fifty-five elementary substances, i. t. Substances whwe particles are inter se similia. And from some or other of these elements, mineral compounds, vegetable organisms and animal or- ganizations are produced. Now nature^s bbratory can be entered, in the first instance, only by indjjction ; we cannot commence with the simple ele- ments and reason a priori, or a posteriori, without first having made indue- if 13 tions. There is no evideaoe, about which we at present know Anything, to establish any belief, that what now are called elements, are really compounds; and when we find the number and kinds •f elements, which, from any eom- pound, or oro:anization, we conclude, that we have all the sine quibus non and because none other are present, i. e., ky heterical induction. But be- cause a certain number and kin*is of •Itments^are found in certain instances, or even in all instances known tons, v?c are n«t certain that each one of them is a sine qua non of th« -iven effect ; althouijh this false kind or reason- ing per enumerationem simplioem is still employed by writers upon the physical scieiccs. In the organiEations of animals we lind an animus or life principle vis vitffi, and this princii^le has been said to possest and exert a force sui generis upon the elements and to impart to them, wh«u taken into the stom- ach, an unusual action. And although this life principle exists in all ani- mals, yet the theory respecting it? force on the elemeats (and it is nothincr bMt a theory) has recently been disproved in a measure at least in the mos^t satisfactory manner by heterical induction. It has been shcxwn that hard boiled albumen and muscular fibre can be dissolved by adding a few drops of muriatic acid to a decoction of tli« stomach of a dead calf, precisely as in the stomach of a living animal. This one instance heterales the vim vita- from the sine quibus non, and leaves the stomach t act upon chemical prin- ciples in dissolving the food; and if the known principles of chemical trans- formation do not yet sufficiently account for digestion, it must be further in- quired iito. Physiologists have also attributed the foimation of formic acid oxalic acid, urea &c., in the body to the force of the ris vit^e- yei each of these can be formed in the lakratory of the chemist, and con^quently it is proved that vis vit«e i- not a sine qua non. True heterical induction thus dispells mystic tkeories and opens the true road lor inquiry. Chemists have contended that vegetable !5bre in a state of decay which IS called humus, is absorbed by plants ai.d is necessary to Ui^ir growth- yet this humns can be separated by heterical induction. For, although 'this humus IS present im most soils, yet "plants thrive," as we are informed by Dr Leibig "in powdered charcoal, and may be brought to blossom and bear fruit If exposed to the influence of the rain and atmosphere; the charcoal may be previously heated to redness. Charcoal is the most 'indlflerent' and most unchangeable subsUace known; it may be kept for centuries without Change, and is, therefore, not subject to decomposition." Now one suck case •fljust cited from Dr. Leibig, who rea^ns more philosophically than mo.i chemists, completely hetorates the absorption of humus from the sine qoibus noD. Leibig contends further, that humus merely furnishes carbonic acid for the atmosphere surrounding the roots and stafk of the plant, and that thii U carbolic acid is a sine qua non. This, howewr, cannot be proved by heteri- cal induction, which is the oqly subject that concerns us at present. We find that several kinds of opium contain maconic acid, and from the examination of such kinds alone wilh(iUl a true philosophy by which to test nature, we w(mlderroMwously conclude maconic acid t(. be asiuc qua non of opium as an anadyne and soporifl'r, but there are other specimens of opium, which do not contain a trac(! of tiiis acid, and yet thry produce similical cttectr*. By heterical induction also, wr establish the truth, that volition and the mind's command of the nervous apparatus are not sine quibus non of nutrition in animals. For, in those parts of the body, which have been para- lyzed and which, llierefore, are destitute of feeling and not subject to the mindB control, nutrition still proceeds without inlerrupiion. Oxygen may be condensed into a liquid by pres>iure, in which state it posses those grega- ria, which distinguish a liquid from a gass; Hiid yet in either state its actions upon other substantts are inter se «iuiilia; and those distinguishing gregaria some in the nne and suiiie in the Mther state, can be heterated Irom the causal gregaria of the effects of oxygen. Wen«*ed not illustrate further. CHAHTEU IV. HOMONFCAL INDUCTION APPLIED. We have henM<»fore obst*rved that heterical induction does not deter- mine causes, but merely clears the way si* tliat homouical i* duction can be made more easily applicable io any given case. Now we find that animals having lungs respire the atmosphere, and so long as respiration continues, the circulation i)f the blood and life and heat exist, but let respiration be prevented and denlh ensues; by honionical induction, lhercf»re, the atmos- phere IS one of the causes of life and heal in ^uch animals. And upon ex- amination of the atmosphere, we find it to contain frequently carbonic acid, water, some earthy matters and oxygen and nitr(>geu. The earthy matters, carbonic acid and water can be removed from the causes of the etfecls of respiration by heterical induction; but if we remove the oxygen, these effects immrdialcly cease, and hence it is certain that oxygen is a sine qua dou. And by heterical induction we can remove all elements from the sine quibus lum ot the growth of mamihalia excepting those contained in milk; for the health and grt)wth ot the young may be promoted by milk alone. N«w we find milk to contain caseine, a compound containing a large proportion of nitrogen; sugar of milk, in which there are large quantities of oxygen and hydrogen; lactase of soda, phosphate of lime, common salt and butyric acid. Is each of these elciuents a sine qua non ? A horse may be kept alive Qpon potatoes, in which the quantity of nitrogen is small, but he does not thrire, and if deprived of all food containing nitrogen, he dies. Mammalia cannot Htc withonlH salt, nor can any one of the consiiluenis of milk be wanting 15 for any threat length of time without a marked influence upon tiie healtli of the animal. Experiments showing such truths furnish the data for homoni- cal inductions. Plants cannot grow if either hydrogen or carbonic acid be wanting, and hence, these art* sine qui bus nun. And aixain, we see that if tiie blood be taken from animals, the imme diately die; that blood is a sine qua non, is therefore evident. We see also by heterical induction that food taken into the 6*omach is not a sine qua non to the life of the foetus; nor is the respiration of atmosphere; but after'birtli both these things by ht)monical induction are sine quibus non. Nt)w blood is composed of fibrin© and serum, and eacii of these has been analysed, and they are found to be isomeric, i. e., the constituents of the one and of the ether are, not only similical diilermtia, but also by weight commensural in- commensura. It has been found also that if the blood be deprived of any one of its constituents, the health suft'ers; eacn one, therefore, by homwnical induction is a sine qua non. We can prove also by homonicai induction that light is a sine qua non of the growth and health* of reiretables; for, other things being equal, they will not dev^lone in dark cellars or caves. Most plants contain organic acids in combination with bases sucij as potash, soda, lime or magnesia; and hence it has been concluded, (but it is onlv probable and not an induction) that an alkalino base is a sihe qua lum of growth of plants. The way to prove it is to make an experiment and have all other things, found in th« soil and atmosphere where the plant grows well, present excepting these ba.ses; it the plant will tht-n not grow, we have mad'e an ho- ;nonical induction. In many of the sterile soils on the coast of South ' Anu-rica, crops of grain will not grow at all; but it guano l>e put upon those soils, they then yield abundant crops; her« is an hommiical induction respecting guano And certain soils, which are entirely barren, may be rendered fertile by put- ting quick lime upon them. Soils also destitute of alkalies and phosphates will not grow certain plants, but if these be added, the plants then thrive • upon them ; here is an homonical inducti(m. Homonical inductions respect- ing the hecessary constituents of soils for raising pl-iuts may readily be made by comparing a productive with a barren soil. We take the following analy- ses from Dr. Leibig's agricultural chemestry. A, repreHenis the surface soil • and B the subsoil. One hundred parts contain : Kina''' ""''"'" ''^''"'"''''"'^^ • 95,m 95^180 • Protoxi^.i;*a*nd*p;;oxid; of iron '.v.* '. .'.V. V.V.V. JS^' l^^ Peroxide of manganese ^' , ^'^^ Lime in combination with silica '..'.'. on^s '^^n a^;- Magnesia in combination with silica .' oVjlj n ml Potasaand8 sand 94,724. 97,340 Alumiua 1,638 0.806 Protoxide and peroxide of iron with maiiiranese 1,960. 1,201 Lime 7 1,028. 0.095 Magnesif". a trace. 0.095 Potash and soda * 0.077. 0.112 Phosphoric acid 0.024. 0.015 CKpsum 0.010. a trace Clorine of the >all 207. a trace Humus 512. 0.135 100,000. 100,000 Tiie above soil produced luxuriant crops of lucerne and sainfoin and all other plants wh(»se roots penetrated deeply into tlie ground. Now from these two cases, it would appear that in those plants receiving their norish- ment from the subsoil, humus was a sine (|ua non; while gypsum is inilieated as a ^ine qua non in the surface soil. W we taktt muscular tibrine, which contains wuter, and let it be ex- posed to a moist atnmspiiere, pulri fact ion takes plac;; but if the fibrine be dried and ihen exposed t** a diy atmosphere, no such result takes place. Hence water or hydrogen, is a sine qua non of the putiMfaclion. So also yeast, wheu :;omplelely dry, possesses no power to produce fermentation. Now yeast possesses a soluble and an iusoluble substance, and the insoluble substance may be thiowu out of the sine quibii« non of fermentation by heterical induction; but the soluable part when exposed to the atmosphere produces fermentation, but when the atmosphere is excluded no such result takes place. An aqueous infusion of j'east may be mixed with a solution of sugar and preserved in hermetrically sealed vessels without undergoing the slightest change, but if exposed to the atmosphere fermentation immediately begins. Hence the soluble part of yeast and the atmosphere are proved to be sine quibus non of the fermentation which ensues in such cases. Sever.al kinds of vegetable fibre, if kept secluded from oxygen or hydrogen, do n*>t decay, but when oxygen and hydrogen are present decay commences; each of « i: those, 11)01 efnre, is a sinf qua iion of :,ucl» decay. Oiker bodies do not decay wilhout the presence of a free alkali, and in sueh cases alkali by homonical induction is u sine qua non. The juice of grapes expressed under a receiver filled with mercury, which compUtHly excluded the air, luble in iilkali. After differentiating we find carbonate of lead and copper to agree in the gregarinm of entering into firm combination with animal tissues; and vital organs thus rendered calous and intlexible can not, of course, perform their functions, and hence death must ensue. We do not, however, give the above as satisfactory inductions; the dat;; are insufficient ;!nd some of tlieni may not be correct. Chemists have not been fymiliar with the inductive pro- cesses and they htwe not looked for data in view of making diJfereutial and similical inductions, and hence they liave not furnislied us with the reqwisitc ground- works. As another case to illustrate the principle of similical induction we may inquire into the causes of the doub)'^ refraction of light. Some of the gregaria of the carbonate of lead, winch substance causes double refraction, are the following: Carbonate op Lead. —It is a transparent snbsrance, it is of crv«taline structure, jts crystals nvv, of tlie rhombohedral torm, it is insoluble iu wnln It is soluble in acid, it is soluble in alkali. The following are some of the gregaria of Iceland spar, another sub- stance causing double refraction : IcEi^\ND SpAii.— If is a transparent substance, it is of crystaline struc- ture its crystals arc of the rhombohedral form, it- is insoluble hi water, it i^ soluble in acid The following are some of the gregaria of one species "of diamond, which causes double refraction: Diamond.— Jt is a transparent substance, it is of crvslnline structure lis crystals are of the rhombohedral from, it is ins.duble in water, it is soluble' in acid. Witli the foregoing double refracting substances we may compare the following substances, which do not refract light in that manner. The follow - ing are some of the gregaria of a species of diamond which causes single refraction : Diamond.— It is a transparent substance, it is of crystaline structure. Its crystals are of the octohedrai form, it is insoluble in Water, it is soluble in acid. , i*wt ^ The ftdlowing are some of the gregaria of pure rock salt : Rock Salt.— It is a transparent substance, if is of crystaline structure, Its crystals are either of the cubical or octohedrai form but sometimes pris- matic, It IS insoluble in water, it is soluble in acid. The following are some of the gregaria of pure borax: Borax.— It is a transparent substance, it is of a crystaline &lruchire Its crystals are either of the prismatic or octohedrai form. " • Now after using differential inductions we find the substances causing double refraction to agree in having their structure made upot rhombohedral 22 crystals. And from this it would appear that the form of the crystal causes double refraction ; but our data are again insufficient for a satisfactory iuduc- ti(»n. There are fourteen difTerent forms of crystals entering into the struc- ture of diamonds and onl}' two of which, the oclohedra and cube, so far as we can learn, cause single refraction. The subject needs further examina- tion with more full and m»re certainly correct data. Fesnel explains, deduc- tively, double refraction by assuming that the ether in double refracting sub- stances is not equally elastic in all directions. This is, of course, merely aa hypothesis, and the evidvnce by which it can be inductively proven is not furnished by double refracting substances. Newton concluded, probably per euuinerationem simplicem, that c«mbusiibility was in some way a cause of retraction and then reasoning a posteriori he conjectured that water and the diamond would be found to contain combustible elements; and his 3on- jecture has been verified. But we have gous far enough to illustrate the principle of similical induction. CHAPTBli VII. INCOMMENSURAL INDUCTION APPLIED. We have seen, heretofore, that there are three cases of incommensural inducti'^i, having reterence to three 'kinds of relations between the causes and their ef!*ects. And if we commcRce our illustrations with incommen- sural quantities of certain objects, which we are examining for the purpose of determining their relations to certain incommensural effects, we will soon see the utilit}^ of this method from the dailj' necessities of life. On making our fii*te9 in the stove, we need but admit a small current of air and then a greater one to convince us, by incommensural induction, that the atmosphere is connected, iu som« manner through causation, with the combustion going on in the stove. And we need but increase the inhalation of oxygen into our lungs to find out, that certain phenomenal effects in our system are depedent upon the respiration of this gass. 'The incommensural quantities of the sun's rays falling vertically and obliquely upon equal areas in different lati- tudes, must also convince u^ of their relations through causation with the earth's temberature and vegetation. And in every branch of agriculture, horticulture and floral training, the case of incommensural inductions tr.om the relations of quautity may be made by a little ingenuity. I extract the following facts from Prof. Liebig's agricultural chemistry: "The employ- ment of animal manure in the cultivation of grain and the vegetables which serve for fodder to cattle, is the most convincing proof that the nitrogen of vegetables is derived from ammonia. The quantity of gluteu in wheat, rye and barley, is vory different; these kinds of grain also, even when ripe, con- lain this compound of nitrogen in very different proportions. Proust found Fi'iuch wheat to contain 12.5 per cent, of gluten; Vogel found that the I 23 BurvariaQ contuiued 34. per cent; Davy obtained 19. per cent, from winter and 24. from summer wlieat; from Sicilian 21. and from Barbary wheat 19. per cent. The meal of Alsace wheat contains, according to Bous^ingault 17.3 per cent, of gluten; that of wheat grown in the 'Jardin dcs Plautes' 2G.7 and that of winter wheat 3.33 per cent. Such great differences must by ow inoj to some pause, and this we find in the diflerent methods of cultivation. An increase of animal manure give.s rise not «nly to an increase in the num- ber of seeds, but also to a most remarkable difiereuce in the projHution of the substances containing nitrogen, such as tlie gluten which they contain. * * * * ^ One hundred parts of wheat grown on a soil manured with cow-dung (a manure containing the smallest quantity of nitrogen) atfordtd only 11.95 parts of gluten and 64.34 p^rts of amylin or starch; while the same quantity grown on a ^il manured with human urine, yielded the max- imum of gluten, namely 35.1 per cent. Putrified urine contains nitrogen in the forms of carbonate, phosphate and lactate of aramrtnia and in no Other form than that of ammonical salts." :^'ovv, in the above facts, granting the soils and atmospheres to have been in all other respects inter se similical and commewural, there is a fair incommensural induction respecting ammonia. In another case of incommensural induction, we have seen that, ceteris paribus, the spaces between an object contaiijing causal ^fregaria and the itcnm- meusural effects are incommensural; and we will now pioceed to give a few simple illustrations of this case. It is said thatGalil«o, perceiving that the chandeliers suspended in a church, when se4 in motion, vibrated long and with uniformity, was led by these phenomena to invent the pendulum. With this instrument a great many persons have since experimented; and the phe- nomena(^f it« vibrations are found to be incommensura in diflerent latitudes and localities. A pendulum of about 39 inches, wliich vibrates seconds in the latitude of New York, will not vibrate sixty times in an iiour of corn- mensural time on the equator; and there is a marked difference in the time of the vibrations of tlie same pendulum iri the valleys of the Amazon and on the liigh peaks of the Andes. The farther you remove the pendulum from the earth's center of gravity, the fewer will be its liibratlons, ceteris paribus And hence we learn from these incommensural relations of spaces between the earth and the incommensural effects, that the earth contains causal gre- garia of these phenomena. Again : The surveyor,from the incommensural illa- tions of spaces between his compass and a c riain hill and incommen.>ural variations of the needle from the true meridian, concludes that the hill pos- sesses causal gregaria of these variations. The incommensural relations of the spaces, between the moon and the waters on different parts of our earth, and the tides, furnish also the data from which to make incommensural in- ductions; and although the tides, on the opposite side of tj^e earth from the moon, might seem at first thought, to destroy the force of these data, yet when 24 wc reflect that the earth is interposed between the moon and those tides, the (lata remain in their validity. The reader will understand that in incom- mensural induction from incommensural relations of space, we are seeking merely for some object which contains causal gregaria of the incommensural ottectsj no matter what may be the characters, in other respects, of the in- coaimensural effects in their relations inter se. Thus: if we try the posi- tively electrified end of a cylinder with the knob of a charged Leyderi jar ;uid find the cylinder to b^ repelled, and then we try the negative pole of the cylinder and find phenomena of an opposite character, by incommensural relations of sp:jcc and the incommensural effects of each kind inter se, i. e., mcommensural similia b(»th these sets of phenomena, though inter se differ- entia, are proved to have a dependence upon the knob of the jar, i. e., the knub contains causal gregaria of both lhe.se sets of phenomena. We will nww give a few illuitralions of the case in which incommen- sural inductions can be obtained from incommensural relations arisons between the two, we would be able to drjuv, from the in- commensural eftV'cts perceived in the ores, conclusive incommensural induc- tions of the cause from the incommensural relations of times, had we never thought of the cause before. For, granting that all other things are similical and commensural in the two sets oC phenomena excepting the times of ex- posure to the atmo«pher3, and ihe (luantities of atmosphere being commen- sura in commensural limes, no object whatever, excepting the atmosphere could have incommensurated the effects witnessed in the oxyilized ores. A hound by instinct .as we call it, makes a kir.d of inverse incommensural in- duction concerning incommensural effects from incommensural relations of lime, or we, ar least, may make it for him, when he is pursuing the trail of a deer. Each tread of the deer deposits in the soil a certain effect, and these effects immediately after the treads in similical soils are, no doubt, very nearl}- commensural inter se, and which the atmosi)here with the soil cftmences to diminish, leaving at incommensural intervals of time from the point from which they were made incommensural effects. When the hound, therefore, strikes a rather old track, not having a scientific kpowledgeof the relalions-of time, space and velocity, and no means, in the present case, of judging of the last, he is not very animated in the pursuit, not expecting to find the deer for some time, although it may have lain down within forty rods from the point where he struck the trail. But as he moves on, he perceives incommensura; he then increases his speed, and finding the degrees of the incommensura, or differences, to increase rapidl}', he becomes warm and boisterous, proclaim- ing as he goes the state of his expectations, in relation to time of coming up 25 ■with the cause of these iucommeasural phenomena. Should a man buy two pair of boots inter se sirailia, and walk in one pair over a given road for six hours a day for two months, and then in like place and manner walk in tiie second pair for four months, and observe the incommensural effects and times, he would not hesitate to make an incommensural induction. We need go no further with illustrations. It must hare been noticed bv the reader that when we are cousiderin"- incommensural effects inter se, our comparisons havj reft?rence to nolhiuj^^ else than quantity, i. e., the effects inter se are quantltively incommensura. It will be noticed too, that drops of water inter se commensural falliuirat in- tervals of one second for one year, and commensural drops falling in like manner for half a year, produce incommensural effects from the incommen- sural quantities of cause. And when a:i aa:grogation exerts from itself in- fluences through space, as iu the radiation of heat for instance, an object nearer and one more remote from the focus of influence, providing the objects be inter se commeusura, Mill receive incommensural quantities ol the influence in commensural times. And hence, laying aside the interference of cause*, the quantities of causes and effects are prop(»rtional. The assertion that ettects -are proportional to their causes, however, must not be understood to mean that such is the case absolutely and without limit, as we will better understand hereafter. CHAPTER VIII. rOMMENSUP.AL INDCCTION ArPIJED. Commensural like incomiuensural induction deals only with effects, which are inter se similia. And we take a certain case, in which we have heretofore determined a certain object to contain causal gregaria of a specific effect, and having determined the time space and quantity in this case, we endeavor to ascertain what objects, over which we may have no control, con tain similical gregaria with reference to such similical effects, from the rela- tions of the time, space and quantity of the case in which the object is under our control to the time, space and quantity in other caees of similical effects in which the objects containing causal gregaria are not under our control. And in commensural as in incommensural induction there are three cases. Let us commence oi.ir siiuple illustrations with the commensural relations of space. Suppose, for instance, we had made experiments with a certain ivory ball and found that when we let this ball fall forty feet upon iron of a smooth surface, it rebounded a certain number of fe«l; when we let it fail upon marble in like manner it rebounded a certain other number; and when upon brass in like manner a certain other and so on : and in all these experiments vfd will suppose the plates of the different metals and minerals with which we experimented to be quite thick and placed upon solid granite rock. The 26 rebounding of the ball is the elFoct in the ball witnessed by us, of which the space througli which it rebounds is the quantum: and some of the causal gregaria of this eff'ect are in the ball and the others are in the objects -upon which it fell. Suppose now, after this, we find a mass of metal, of a 'kind unknown to us, underlain with granite and we let the same ivory ball fall upon its smooth surface forty feet and observe iti rebounding, and we find this effect to be commensural with that obtained when it wa's let fall upon marble; then as the ball is the same and other things are equal, the commen- sural relations of the spaces fallen through by the ball in the two cases to the commensural effects, convince us by commensural induction, that this new metal contains, in the respect to these similical and commensural eff'ects .similical and commensural causal gregaria witli those contamed in marble.' And should this new metal be so situated that, we could not approach to it so as to examine it closely with our eyes or feel it with our hands and the ball used bean heterical one, but similical and commensural with the first, the result would be the same. Again: Suppose we make experiments with a certain magnet and find that if we attach the one end of a small string to the north pole of a magnetic needle placed at a certain distance from the magnet and the other end to a weight, which the magnet, when the magnetic needle is at right angles to it, will just be able to draw on a certain surface until the needle points directly towards the magnet, this drawing of the weight then mny be taken as the (luautum of the eff-rct: it we now take a piece of ©re and situate the needle with weiglit attached on the same surface as 'before and a commensural effect be produced, we conclude by commensural induc- tion, having our eye on the commensural relatiors of the spaces in the two cases and times being supposed commensural, that the magnet and ore con- tain similical and commensural causal gregaria. Again ; if we make a fire in a stove and hold a thermometer at a certain distance from it and read the degrees to which the mercury rises in a given lime, this rising of the mer- cury will be the quantum of the effects; if then we go to a heap of quick lime witJi water thrown upon it and covered up with earth, and we place the thermometer at a commensural distance from it and find the quanta of eff-ects t ) be inter se commensural, we conclude that the heap contains similical and commensural gregaria, respecting such eftecls, with the stove. Secoiid Case.-ir we take the down of the goose and find that a certain quantity will be attracted through a certain space in a given time by the prime conductor of an electrical machine, and we then take a commensural quantify of the down of the swan and find it to be attracted through the same space in a commensural time, we conclude the latter substance to contain similical and commensural causal gregaria with the former. If a weight be attached to a baloon and the baloon then ascend a given distance in a c*ertain time, and we then attach the same weight to another commensural baloon r27 and 111.- secoiul one make the sm\c distance in a commeiisural time, the two bulootis contain similical and coniuunsura j^regaiiu. . Tiiird Ciise.— If we charge a certain Levilon Jar to its capacity and measure tlie space throu-h wliich a spark from tlie knob can be miide to pass so as to ignite sulphuric elher and then wu dischar«re a spark of the jar commensuraily ciiarged thr(.ugh tiie same space into ellier of alcohol and find commensural elfects, times being equal, we conclude tlie two ethers to contain similical and c Mumensurul causal gregaria with reference to such effects. VV(. need not illustrate farther. If ihe reader will bear in mind that all elfects arc produced by heterical causal gregaria, som«i of whicii are in the objects in which we witness the effect, and some in another object, numerous examples, from which commensural inductions can be made, will suggest them.-elves to his own mind. And it is evident that if we can not always find commensural relations, we may yet make our inductions iu many cases by tlie commensural relations ot mathematical ratios. By taking a piece of iron, for instance, to incomiiien^uhal distances from the earth's sup- face and rinding the ratios of its Aveigiilsand distances, we rind that grarity varies inversely as the square of the distance; we tiiid also that the matter • tends to move in straight lines with a force equal to its we4ght multiplied into its velocity; and tliereforc, near the surface of t!ie earth if we pioject a stone of a certain weight iu a horizontal direction with a given velocity, we can calculate the late the n7oon and find its ratios to be com- mensural witii the ratios of our experiment with the stone, we conclude by commmensural induction, that the moon and the stone C(mtain similical causal gregaria. In this manner Xewton extended gravity to the moon, aud it has since been exientled to other heavenly bodies; and it is supposed, by iuductio per enumeraiioaem simplicem, to exi.^t throughout the universe. CHAPTER IX. THE DENOMINATK UNIT. Tho.se Avho have mastered the principles of books I and II, and of the pre- vious chapters in this hook, (whicli in the last four chapters we have emleav- ored to render more easy for the understanding by giving simple illustrations with sensuous objects) vrill be able now to proceed furtner with us in our still deeper inquiries into nature's piocesses. In our previous inquiries, ex cept in similical and differential inductions, we have dealt mostly with ag- gregations, and have not given much ot our attention to gregaria, from whicli only, tho.se relations, which are called the laws of nature, can be evolved And wo have seen, heretofore, that homon per se makes no part of our knowl- edge, but tnat we gain our knowledge «)f homon by means of helera; but our knowledge of similia and of differentia is not predicated upon hetera alone, 28 but upon siinilical and ditferential relations of gregaria; and if we can deal with these gregaria so as to discover the laws of causation by which they act, v,« will have to enter nature's mysteries in this regard by getting hold of re- lations existing inter gregaria. Now, nature is more accessible iu some points than others, and her relations of quantities are most easily compre- hentled by us; we will, therefore commence to evolve the laws of gregaria by investigating their quautitive relations. But for this purpose we need denominate numbers, which have an homonical standard of measure; and space is the only thing from which we can gain such denominate and homonical unii. We will, therefore, treat briefly of the denominate unit In this chapter. If the hand of a clock, when it ticks once, posses from a to b (Fig. 1.) in the small circle of the diagram, while a body on the larger circle passes from c to d, we may take the well known equation in natural philosophy S t: V = T in which relations the space from a to b may be made the denominate and homonical unit of measure; and if this unit will apply twice to the space from c to d then 2 . V= — = 2. 1 The space from a to b may be made also the homonical unit of measure for a steelyard, a barometer, a thcrmomeler, steamguage, momentum, dry measure, I'quid measure, money and throughout nature. Then let V stand for velocity, S for space, T for ttme, W for weight, and M for momentum, and take the following equations in natural philosophy: 6. 1. o 3. 4. 5. 8 VW M V = — W S M V = — f^ - VT T = — W = — M T V V Now if Y in equations 1, 2 and 3 be equal to V in equations 4, 5 and 6 as it may be, and we take the value of V as given in equation 6 and put it for V inequations 1, 2 and 3; and we take the value of V as given in equa- tion 1 and put it for V in equations 4, 5 and 6, we jvill have the following equations: 7. 8. 9. 10. 11. 12. MT SW MT aw 8 M 8 = T = W=— ^ M = — = — M S W T W M S w iSi 29 Gravity, in » body above the cartli's surface, is noLhin- else tban the tendency of the aggregation (o fall to the earth, and the quantum of spare occupied by incommensural a-grogal ions inter se .iniilical, Avhich is fourd by multiplying together their lengths, breadths and thickness, is in propor tion to the quantum to this tendency to fuH. If we take two pieces of lead inter se sim.l.cal, but occupying inco.nmensural spaces, the piece occupvin- the greater quantum of space at commensural distances from the earth's center of ^^ravity will possess a greater quantity of gravity than the other. Now by experiments it has been ascertained, that gravity above the earth's sur ace, vanes inversely as the square of the distance from the eartli's center or direct y as the ratios obtained by dividing the square of the radius by the square of the distance from the eartli's center to the body above the earth's surface. And hence let G stand for gravity, r for radius, Q for .luantity of matter and ^ for the distance of the body from thoearth's center, and *ve will have the following equations: G- 13. Qr^ 82 14. 15. Q = S^G S2= I " ^0w If S in equations 1, 2 and 0, be equal to S in equations l:J. 14 and la, as It may bo, and we substitute the value of S as ijiveu in equation 2 for S m equations l;U4 and 15, and the value ef S as given in equatint into the fcu'm of (a — b) (a'-i-f-'ib-f-b-); arid the denominator is also a multiple of (a — b), and il mfy be put into the form ot (a — b) (a-i-b). and then ue will have i SI :3. X- X (a— b) («-|-l»; Now from this equation we inny liavc (a5i-fab+i.^) 0Xa--fOX»»b-f-'>xl»'2 4. x=— X =: - — -1. (a+b) (OXa-f-OxlO Or we niav have •' (a-«i-|-ah-fl)5J) (a2-f;i!,-fi,.) a,,'^ ;^m • (a-i-b) •> (a-fb) 2a 2 How are those iucoiiunensural results lo be explained r Now as 1 is the raiio of the numerator lo the denc.minalor and also of the (lei.omi- nator to the numerator, as ii always is when tlie numerator and denominaior ure absolutely eummen.Nura; thus 4 8 — = 1,— =1,— — 1, etc. 4 8 And it iseviden: that in ecuialion 4 we have taken the fVaetinn a-hb and mnliij)lie than the dent.mi- nateunit: it is ai.u. evident thai the rtifterenci' between i. «i>d i , will be a jrreater quantity with refeience to the denominate unit, than the diffeienee between t^ and N, while their raii«>s a»e eommen^ura: thus ^-:- i, = i^ and ^"^;'-^'7^!J"'"-"'^^' t>»^^2-^-;ll and 1^-1^ = ;^ and l/Vi^. "And the greater the decrease ol the numerator and den.innnalor, while their ratios Temainc.mim^nsuia.the le^s wdl be their (lirtere;:ee in nnnierieal value com- pared with the denominate unit; and hence the dilference between the numerator and den(»minator mav become infinitesmal and the ratio all tlie time remain the same, i. e.,0-0<0, while 0-0=1, results, which can only be true or infinitesmal quantities in their relations to our minds. And if bv we mean ah^.Iutely nothing: at all, 0^0 is nothing, 0-0 is nothino- at>d 0x0 IS nothing; and it by oc we mean something without limit, aX od is not within our conceptions, nor is oc- oc. Jiuf although we can not conceive of absolute existences, and of course can not deal with them intellieently vet we can conceive ot finite relations as beintr absolutely commensural and in- commensural and hence if we have equation 4 or ", a> rdiove, we mav con- 33 ceive of (he r lationsof a — b in the numerator and in the denominator as absolutely commensinal, and of a and b as ab-*(dutely c<»mmensura, and then the relations contained in a— h a-b will de^lroy each otlu-r and this fratrlion will liave no relation t«» otlVr towards the other factor, i. e., its refations will be a nonentity and it need not be con- sidered, but if a — b in the ilenominaror be an intiuitesmal quanity and a— b in llie uumeral<»r b** an absolutelv co-umensural nifinilesu»al (luanlity, a-b a-b will absolutely equal 1, tlie denominate unit ; and we have seen in the pre- vior.s chapter, that the denominate unit is the space which is the homonical standard lor the measurement of lime. Now wlif-never any numi>er is mul- tiplied by 1 the number is laken one lime, i. ^., ii.«> value is not afteclid; and wlieiiever a number is multiplied by al)so;u!ely nothini:, i. <•., not touched ar !Ul, its value is not aff.'Cled; and he .ci' any n'lmber multiplied by absoIu;<'iy nothin:; will rcmai;i In tlic same relations, as when il is multiplied by liie I .lio nf twf) numbers, uhysc ditt'crence is alisolutely nothing; and tlufrefore in equaii<»n 4 w«- lauitiplieci both numt-ra'or and denom.iia'oi by an infini- u'smai quanlit\ , which prodnred product-; whose diffeienee was not al^o- Intely noihinij thonirh taken t'» be so, while in equation 5 w multiplied by the r-.'i«» wf two numbei>, wh.)se ^.lifierence was ab^oluiely noihing, and iience the incommen-nial resul'.s. And -loon the ^up{>osi:ion wiih wliici' wolarted, i. e., iii:il a was absolutely ecjUal to li, ((piaiion ,") rontains liie Hue p'suit. Now from the the t'orogoing discus.siim it vvil' appear that, ihesymlxd niay be made to make its appearance in every ratio by factoring and sup- jjosing the ditiereiice between ihe numeraior and denon»ina>or <»* one of the factors to he le.ss lUan any t-ssii;;nable quantity: llius the ratio of 4 is V,. which may be etpial to a — vi b X . -2' when the ditVerence between a i»nd b is less than any assignal»le (|Uantity and we multiply bv iheir ratio; but if we multiply by flu' quantities themstlves we wiii hiive 4 i.e., we will l.ave 1 instead of i.>. To iliusirate bv fio;ures let i/g-— X^ 4 and if' 4—4 abs(dut«ly and we multiply by their ratio we will have H — ^Xhz ~}2^ or if we mulliplv in, we will have 4X1 4 4X2 8 but if 4'a!id 4 be reduced to infinitesimilly small quantities and we muhiply in we will ha^'e ' ^l. H' we will have or if 4 and i be made enormously large quantities }o' = =1. * And hence the symbol — . as lesiuais. aiul ^^- X is Its rociprocal; i\m\ tlic nilio of llif'y(M-a(i(.s is 1 • lims — -^ —-=1 Mild — -^ —^-1. i. e., tjjf iriiio of ratios, wliich :uo reoiprocail. is nhf.ivs flK- .!(noinn.:!i(' in.ii • and luMicc the iruc slirnificancc o[ (» ^^ — and -- '* '' i^ i:Ui.) of if(;i|»roca| ratios, •li" wo take the iiiiiiiit(-iiP.allv wf will have 4. x=— =-l ; <> l>i»f l>y taclorino- a.'jcJ cunt'cHin::: \\r wiji haw 8. a-fl) a — b H-|-b *J:i X— X = — ■-•--■ -/:. i\ — b a — b a—b Now if by \\v mean al»solulily uoihiui,' th<'M \=''2:\ and X 2st 2a — =- . i. c, — wil! be the true ratio of x to 1 ; and if by we mean an ih- 111 X tinilesmal quantity ii»en x-= a and — =— , i. p., -? will be ih.- true ratio of x 111 to 1; but tlie two values of x are inconinieMsura, L e., in the fust rase it is finite and m^ tlie seooml il is intinite: and we wjll haw tl-e proposition (a — b)- 10. x= and by inakin<; a=-b inlinitesiinallv we will ^^^"^'^ ^^- x=— , this last equation may be bialed tiius — «=— 3a2 X V, I •< ■> •».4 :5i and if by we mean absolulejy nolhinir we wili liavc — _— , i. ...^ _ ^vill be X 1 1 llie true ratio of 1 to x, and if by we mean an iufinilesmal liieii x=-0 and we will liave —:=.— ; but the two values of x are incommensura, i e ia the X , , - first rase il is finite and in tne second it is iniinilesmnl : ar.d we will hav<- tlie proportion X:l::0:1, xXl=^Xl=0. And from the above we see 1 1 that — , or — -, or — , or — , may be a ratio and may liave a ratio. And we 1 a (X X iiiayhave—-, and -=-; and henee — or — may be a ratio and may liave a ratio, and they and their ratios are the reciprocals of each o;i>er ^ow the whrde oljject of differential calculu^j is to determine the ratio 01 rates, i. e., to determine the ratio of ratios; for rale and ratio, when applied tomouoQor mei(M.se, arethesamethinj;. And the ratio ol' nno eonsiant b 34 number to another is easily found by the ordinary principles ol Arithmetic; it is easy also to find the ratio of rales of the moveiuents of two bodies, when their rates are uniform, i e., when each one for itself makes commensural spaces in commensural limes; but when the rate of one is uniform and the rate of the other |)roceeds upon some law other than Hiat of uniformity, i. e. when it does not make commensural spaces in commensural times, a case is j>resenied for the difierential calculus. Let us then examine the f^)llowing Theorem in the calculus: "The rate of variation of the side of a square is to that of its area, in the ratio of unity to twice the side ot the square." This is the enunciation of the Theorem as given by Prof. Loom is; as we consider, however, lliat this enunciation is incorrect and does not set out (drarly ihe matter to be proven, we will irive the followin«^ in its stead: The rate of variation «)f the side of a scjuare is to the rate (»f variatiwn «»f the cor- risponding area, in the ratio of unity to twice the side of the unvaried square -|- the variation of the side. Let a.b. (Fi;r. L) be e Fi^rure 1. f tjie side oi the s((nare a, b, c, d and a, and sup[)ose jl^.^ ^.^j^^ j^^ ^^ elouiiated to e in one second of lime, b e will then be its increase and the corresponding;: increase of area will be the space l», e, f, «r, d, c, b: c let h=b e, and g=bef«j:dcb, then h==increase of the side, and .i:=th(' corresponding: increase of area. Now ash = the increase of the side in one .second, III*' rate f»f this increase will h be =- — a d fT I and as ^ = lhe correvpondinir increase of area, its r:\le of inerea>(' will iS 11 g h be =-. — ; and the ratio of these rates will be -. = — . 1 1 1 ff Now let X = ab— Ihe side of the s(piare abcda, and y = ae— the side of the square aefira ; then y — x = h, and yi— x-=g, and consequently, h y— X y — X 1 1 ^r y'Z-x'i y-x y-fx y+x But v-fx^2x-}-h, and tlKMefore: h 1 11. — = . g 2x+h 15ut as the value of ^ depends upon the value of h, if we make h an infini- lesimal (and we have seen in 2>J that the ratio of infinitesimals is the same as the ratio of appreciable qnuatities sprini|:in5 from them by multiplication) we will have: 1 12 = . 2x-f0* and hence for infinitesimal viiilations we have: b:g::l:2x. Note. To treat specially of mathematics is not our object in this work, nor do we wi.sh by criticising to offer refutations: but as the under- III 35 standing of ratio is imp<>itant and as ih,. calculus treats spcciallv of this Sn ' a'"'! r "'''n ""'?'' ""f ""'' foundations must be acceptable to every Slue ent Ana from the above demonstraiion it will appear to everv refleclin- reatier tliat the ideas entertained bv many teachers i,r the calculu*^ that h-" IS not the true ratio of 'die race r>f increase ..f ihe side of a square 'to the rale <»t increase of tnecorrespondinir area, but that in order to Lret at the true ratio we must reduce h and or to infinitesimal quantities, so .hat their difer- r'?H!'/vv?iVK;r /'•''" •^"y assignable (|Uanlily, supposinir that thereb/the moneoi^^ '"'''*'' ''' '"""" ^'*"' "'*'^" '''''>' ^^•^■^*.^'»^Ht>l<' M".->ntity, i. . Acrain lake the Theorem: The rale of variath.u of the d-M- of a cube s to llie rate of vaiiatnm of the correspond in": .solidity, in the ralio of unilv to the square .>f the varied edge -^ ihe prndnc^t of the varied and in vn ie | edges + the square of the unvaried edge. Let h = th« variation of ed" e an corresponding variation of solidity; and !el v -_- ed.ro of vari(nr n ' x = edgeol unvaried cube; then ' ' 36 or and X h la. — : V — X g y3-x3 ya-f-yx-f x-^ If within this equation y=x to wMhin less than a:)v asM-nable dillerence 1. nnd g will become infinitesi.nals and we will have ' 1 14. — = : :Jx-* and hence for infinitesimal variations h -cr. . i .-u-' ir ii.,. , j i i ;„.,:. , 1 .• • •••.»i t ai lai luny, II . LT: : 1 :o\'. 11 t hc (M (^C' be decrcas - ingiusfeadof increasing x>y anfl we will have 'Micas 1 _ -»> >:-}' ■ -h ^•* — = ' — , and when x — v — — g \3-y8 _jr yxii When the motion or variation of one bodv or thin- is unif, rm ind another body or thing makes commensural increments of Vncrease idecn' t"^^^ , the 1 Mter bmh or iV.i nl- vanes in Arithmetrical progression; and in order iV^ehtio, ? ratios of the variations we must divide the ratio of spacVma le bv tl e fl is object in a given l.me by the rati, of the space made bv ihc sicond o jecf n aeonmensural time. Let h = space made in five ininutA b a ''ob ee five min iL wi'tirjhe e ^^+' '"" '"f ----'' ''+2d for thi ihinl and so o n>or cessive mi^^^^^^^^^ commensural increment of increase of .1 i„ .,,!. suc- h then - = ratio of the first objects variation, and letting S stand for the sum of the terms iiUhe second objects variation, -^ .-. ratio of second object' variation and ~ = ratio of these ratios. IJut'' letting n = number of term. Md 1 = last term, aiul h will be e,,,ml u. I,„, an.l 1-=: | — I „ ,,.,.| honce- l 8 J ' s. bn 2b IT). S fa+l ] a-hl I In I 3 j ii 2b Hut l=a-!-(u — l)d, and hence; 1«. — = -, and when n — 1 17. b 18. — =— h b — rr — . and if we rediuje h and S to intiniiesimals, 8 a b — , ilierefore, is the true ratio of the objecis' variations •0 a a at the infinitesimal poinl from which they Degin to v;;iy. a a The cipiation — = irives the ratio of Ihe first term in an Arilh- 1 a-Hn-l)d metrical progression to the last term cons'der-.'d. If the reader does no fully comprehend this and the follownig paragraplis, let him lUrn to some mathematical work uj)on Mie subjejts. If oiie «d)Ject vary uiMfoimly and another obXect vary in such manner that the successive values made in commensural times are in proportion to each other, i. e., the lern^s have a «:onsiant rati'), the latter object's variations are in (Jeonutrical piogiessioii ; ami we find the ratio of these object^■,' vari- ations by dividing the raiio wf the one by the ratio of the other. Using the letters as in the |)receding paragraph with the addition of r for the constant ratio, and relying upon the leatlers knowledge of mathematics we will have: h bn bn('-l) 20 — — — . Hut when i>.=-1 we will have S ai» — a a(r» — 1) /W 1 • r-1 h b l» — = — , and conse(|Ueiitly — will be the U'ue ratio of these S a . H objects' variations at the zero point Oi varying. The equation a a '22. — = gives the ra'io o." .he first teim to the last term considered. 1 ar»— 1 If an object varp in Ariih-net'-ical p-ogressio i and another by Geo- metrical progression and we use cap' d lei eis i.i the Geome lical equation for th« sum and first 'erm we wl| have I ••+> 1 ; I n s [21 |r(a-;-l)-(a+b)]H S l.—A 2(lr— A) r— 1 37 We have gone far enough, perhaps, up ,n the suh.ject <,f ratio CHAPTER XL TKANSFOKMATfON OF I'R(HM)s[TFONS. If we take tlie three (list. net proposilions- A I. A V A A '^ S T S T S A A A V A A TS TS TS A A A V A A TS TS TS ura A ^ A V \ \ T 8 T S r s •> o. Via < i *■ ir we lake the distinef propositions 4. A A A \ \ A T S T S T S T S l\s T S A A A V T S i' S A V r S c ii — i\ •^ < b b ==. by uniting them into one we may have A V A \ TS AV TS •». TS A jft =■■ bj . « II - ^s ^ n- ... .^^ , ^ ^ . 7. T S .ij-_c ==-< b+d axe ==< bxd A V ^ V A V T S T S T S A < > < T If we take the commensural propositions t^ ,, A A TS ^^ V TS »• TS a V. < b d V T^ AV is? A A \ A TS ^ V fh T S , a — d by using „.e .„,„ Of eonunensura ,„„nha. „f «!„,„,) I,, „.-„,';., ,„^. terms wc; may liave A ^' ,\ * AV TS TS TS 10. , from which we may have 11. II 1ft == b! „ d " c A V TS A V TS AV TS 12. axe == bxd and A V TS 13. A V TS a-j-c AV TS A V TS 88 A V TS = b+d AV TS II a e = = b d If we have any number of incommensural propositions as the follow- ing: AA A A T S A V T S 14. ^s , n < b we may derive from them AA TS b A A AV TS T S , < c A A A A T S A \" T S T S , etc. c < d A V A A A V T S T S T S A A TS a-fd A A V T8 a-f-d aXd A < AV TS aXd AV TS 17. a A A TS AV TS a d A And if we have any number of incommensural propositions as the following: \ A A A TS AV TS 18. TS — - a ^ b we may derive from them A V TS 19. 'l^S AV TS A A TS d TS e aV TS < TS f A .'X TS A \- TS ptr» etc. a-fb+c+d+e-ff a < < < a+b+c+d+e+f By setting down all the signs in our transformations, we are able to integrate or re.solve the complex propositions into th«ir simple and primitive ones without any difficulty; but there is still another object of more importance in doing so, as we will see hereafter. Now we have shown hereiofore, that both incommensural and com- mensural propositions contain only relations inter se similia, and as we have used the letters a, b, c, etc., not to distinguish kinds of things, but merely to distinguish the quantities of similia, proposition 6 may be translormed into 39 20. A V TS a-fc TS out the sigus of equali,^ 8o5 inenZtv befwZ^l'' ''•'"»f<"-™^J ''J' "Hking their stead the sign of similia^ ^ ^ between the terms and inserting i° ^imi.ia'l^n^ diff^J'nl^'S tk^e fhe';;;^^ tlafV^SnT''^'' '''^""«"''" 21. and ^ b c AV TS oo Take the propositions Av TS TS d AV TS H-H- By unitin.jr them we will have AV TS b fl 23. TS H- 24. % unitinfT we will have a b' AV TS II H- A V TS a' b ^" %iB^'S»-S^=;:-z,siu-' ■- 2«. AV TS II TS A A A V A A T S T S T S ~"r ~~" ~7;, % uniiinor them we have 07 A V TS A V TS A V TS ' ' ' a II I! a" a' depeud?u;or,i':ra!;7:ptr:l;:,i" ''':''''•; •"^"''•' <=«p»^"v -> '--ate a single remark further - n thkt u . !•« Y^r'i*"'!?'' "," IT''" *^"'"'k'' '" >""ke hoih see the bell and hear its i, „„. in L T " "• ". ''*^" ''e struck, we can cupies an h.,m,.nical space b« the or^a"^''';"'"'^"' ''"""; "''"« "'* ''*" <'c "ccupyheiericul spaces; and t e sminj "<' '' "'•"■" " """' "*" ^'^"""^ Uo uot come to .he''mind throui^'^. ^trVtc^Vriuh^o!.^!?' t.'.'i^e'^^'i 40 appiMeutly in the case homonic&l time and spaces yet the spaces are really hetera, and they eaable the mind to heterate. Take the hetcrical propositions r/^A A^ AA T S T S T S . By uniting them we will have b A b' 28. a A A A V A A TS TS« TS a' 29. T S T V ^v S TS VV a VV a' b b' Bui if we should transpose the terms of the first of propositions 28 and then unite it with itself we would have 30. aY, aa TS TS a a aV :n Take ilie propositions A A A A A A T s r S T s aV TS a a A A TS rs ^% a a b A b ^4 n And by uniting them we have 32. A A TS a b a b Hut if we unite the first of the propositions 81 with itself we will have ^ 33. A S a a aa TS AA AA TS .a a Now from the few examples given above anv one with moderate capacity can see how to unite and transform simple propositions into com- plex ones and obtain all the varieties of propositions having the varieties of signs between the terms as set down in Chapter First ot this book and to place the appropriate siijns over the T's and S's, we need not therefore deal lurther with this matter. Now we have seen in Hook I, that in every case of causation some homon is converted into hetera or vice versa; some si m ilia are converted into differentia or vice versa; or, some commensura are converted into incom- comensura or vice ve versa: and if we compare the simple propositions with the complex ones derived from them in thu proceeding transformations, on comparison of the signs of the S's over the terms we will see, that in the transformations given the heteration of space has occurred. In those trans- formations of propositions, however, the heteration of space mav have been made merely by the mind; but if we suppose a, b, c, etc., to' be material 41 • M tlM- toieir.Mnnr comi.lex i)n)posiri.,ns re be causes h. llr .-Vb ' P' '^^^•' •>t lime and a liomoo ot space over ihe i.m.L .m^\ "s iMake a li..m(,n :;4. .' A •A A 'J'S V — We ,„ny ut-al will, ,,r„„„»i,iou,s T and S iu a similar .uannc-r. lor JiZ w;«i;i l,av,!" •' '"" ""■ """^ '"■ I""l"->i"u H and 1.., vs.an.l f^ l\s fj; :{.">. Ami if in this proposition we d have •anire \ jnio \ between Ihe leinjs we will A A ao. TS AA must lifpnSr and ^ :::'.T^:' 'V^ ^ ''^^\ '»-^^^"- ^- effects inter se nu,st he differentia C^^ clifte.entia the effects other, and we will have '' ""^ "* '"^ ''^'''^' '»"*» >• f"'" "»« 37. A^ A • A A T 8 r s r s X H- y ' io^/r;^:Lte„)i' ;?'°e: ^::zz^--^ - ^^"' "- •• m effect diff'er- 4% AA AA AA TS TS TS 38. . z A z Let us now take propositions 23 and go through all the transforma- lioDB, which the reader will now readily understand a' H- b' U TS a b' II H- aV TS a' b U H a b' ^l 1! H- TS X II X n A A TS A A TS A A TS X A X 2X AA TS AV TS AA TS X II X U AV AV AV TS TS TS a' b Produce by heterating space between objects in terms towards each other. By homouating space between objects in terms. By homenating space between terms. By heterating space between terms. By heterating space between objects of terms. ^ AA TS a A A TS a A V TS H- A V H- Icrni • Jieteialin^r space bolween oJ»iecK o( TS h A A TS !»' '■-H.e,. z i'::;:r :„:;l '.".rr;:; r; "-^^ --' -" ""» -"^ <- coml,i„a,i„„s in l>.oposi,io^ ^ !\^ j ',, v ^^ ■«'-" "f frrcg..,!,. and of U,ei,. c".. >-evolvecl,,;poi,uou errors r ,0 r '"""' """»"« "»• "■"""' l-""osop|,y, to „a,e experh .e , s „ adel^ "mlanu.nlal principles in „„.,ral •-necl in iig,.,, electric ,y an! itT Bn "7"."'^""'^'« ''^-'"^ "«'"ally ob- fmc.Uy in geuing .„c amlun. 1 f p'r ."'r' '" """""• '""^ '-^"-' fore .he scienlific world, have com, el !,i ' ' '" "' '" '"'«=« •''«'» »>«- tl.e subJecMs abrnpllv broken offZm '"" '" ''"'' '"-"•''= "'"'""«'' tl.e science ,o the invLi.a,,^„ „, Z'ZT '""T^''' "'* "PP'i^ability^f "'at 1.0 has made many v;i I « uiclve i^ " ?'"""-"*'' "'« """'"^ «'"'»'* be left for ano.her work and ,r Ze ',' '" "'"""' ''='""'=^- "■""^" '""^t s<.ould ever come. The pres n Lui n ,. f """' '^"•'="'"^"'"«''«. if such l^arrisin, circumstances 'and 1 ffie^„ri': "" '" '"""" ""^-- •"<•• "-'t "tlierwise than that numerous eVror, „ , """'" '"' ^'^l''^^^'^'' 'o be 'n.e.se the reader will ex ."e « dlh n "'"'" ^""'"^ "W-" "> "• vesli„-ated the work and expres:ed.h,.i '"'""'^'' "'^'" ^''••'" ''uve io- bet-er prepared to judge :reM,;rr:t"'' " ""^ '""'"•^ «'" "« pie e a work on natural vmosoZtl^ Z,^^'"' ' " '""'"'P' '" «»■»- and reasoning exhibited in this b.H,k ' P'""^'l"<^^ "^ experimet:l TUI KNU. J