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Charles S. PeirceLogic, Considered as Semeiotic

An Overview of Charles Peirce's Philosophical Logic,Constructed from Manuscript L75

Version 1

Analytical reconstruction by

Joseph RansdellDepartment of Philosophy

Texas Tech University Lubbock, TX 79409 USA

[email protected]

Version1ofMSL75isaspecialeditorialconstructiondesignedtobereadbydefaultasasinglelinearsequentialtext.Itisnotahypertextdocumentproperbutuseshypertextonlyasatoolformanagementofthetextforthepurposesofonscreenpresentation.

FortechnicalreasonstheMSistoolargetopresentasawholeonasingleweb"page"(i.e.asasinglecontinuousdocumentunit),andsoitispresentedhereintenconsecutiveparts.Itshouldbeunderstood,though,thatthesepartshavenosignificanceasregardsitsorganizationandmerelyreflecttheneedtobreakitintosmallerunitsfortechnicalreasonsonly.

Thedocumentisorganizedbysuccessivelynumberedmemoirsandsections.Theupanddownarrowheads

atthetopofeachmemoirorsectionmoveyou,respectively,tothebeginningofthepreviousandthefollowingmemoirsorsections,sothatyoucanjumpthroughthedocumentinasequentialorder,forwardorback,inthatwayifyouwish.

Thetitle,"Logic,ConsideredasSemeiotic,"iseditoriallysuppliedbutechoesPeircehimselfinrelatedcontexts.Peirce

sometimesusedthespelling"semiotic"instead,andeitherspellingisjustified,givenhisvariableusage.SofarasIknow,Peirceneverspelleditas"semiotics".

PleasereadtheEditorialIntroductionifyouarenotalreadyfamiliarwiththisspecialreconstructionofthetextanditsrationale.

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BEGINNINGOFTHERECONSTRUCTEDTEXT

FinalVersionMSL75.345

Milford,Pa.,1902,July15

To the Executive Committee of the Carnegie Institution,

Gentlemen:

I have the honor respectfully to submit to you herein anapplication for aid from the Carnegie Institution in accomplishingcertain scientific work. The contents of the letter are as follows:

1. Explanation of what work is proposed.

Appendix containing a fuller statement.

EDITORIAL NOTE: By the "Appendix" Peirce means the entirelist of 36 proposed "Memoirs," including his accompanyingdescriptions of their contents: thus he is referring by this towhat we are treating here as the body of the present work,which we have supplemented extensively from the draftmaterial.

2. Considerations as to its Utility.

3. Estimate of the Labor it will involve.

4. Estimate of Other Expense involved.

5. Statement as to the Need of aid from the Carnegie Institution.

6. Suggestion of a Plan by which aid might be extended.

7. Estimate of the Probability of Completion of the work, etc.

8. Remarks as to the Probable Net Cost to the CarnegieInstitution, in money and in efficiency.

9. Statement of my apprehension of the Basis of my claim foraid.

Final Version MS L75.346349

SECTION 1

EXPLANATION OF WHAT THE PROPOSED WORK IS

Some personal narrative is here necessary. I imbibed from myboyhood the spirit of positive science, and especially of exactscience; and early became intensely curious concerning the theoryof the methods of science; so that, shortly after my graduation fromcollege in 1859, I determined to devote my life to that study;although indeed it was less a resolve than an overmastering passionwhich I had been for some years unable to hold in check. It hasnever abated. In 1866, and more in 1867, I ventured upon my firstoriginal contributions to the science of logic, and have continued mystudies of this science ever since, with rare interruptions of a fewmonths only each. Owing to my treating logic as a science, like thephysical sciences in which I had been trained, and making mystudies special, minute, exact, and checked by experience, andowing to the fact that logic had seldom before been so studied,discoveries poured in upon me in such a flood as to be embarrassing.This has been one reason why I have hitherto published but a fewfragments of outlying parts of |347| my work, or slight sketches ofmore important parts. For logic differs from the natural sciencesand, in some measure, even from mathematics, in being moreessentially systematic. Consequently, if new discoveries were madein the course of writing a paper, they would be apt to call for aremodelling of it, a work for mature reconsideration. Still, as far as Iremember, no definitive conclusion of importance to which I have

ever been led has required retraction, such were the advantages ofthe scientific methods of study. Modification in details and changes(very sparse) of the relative importance of principles are thegreatest alterations I have ever been led to make. Even those havebeen due, not to the fault of the scientific method, but chiefly to myadherence to early teachings. But what has, more than that cause,prevented my publishing has been, first, that my desire to teach hasnot been so strong as my desire to learn, and secondly, that far fromthere having been any demand for papers by me, I have alwaysfound no little difficulty in getting what I wrote printed; and |348|when the favor was accorded, it was usually represented to me thatfunds were sacrificed in doing so. My first papers, which have sincebeen pronounced good work, were sent to almost every logician inthe world, accompanied in many cases with letters; but for tenyears thereafter I never could learn that a single individual hadlooked into them. Since then, I have had little ardor about printinganything. Now, however, being upon the threshold of old age, Icould not feel that I had done my best to do that which I was putinto the world to do, if I did not spend all my available forces inputting upon record as many of my logical results as I could.

Therefore, what I hereby solicit the aid of the CarnegieInstitution to enable me to do is to draw up some three dozenmemoirs, each complete in itself, yet the whole forming a unitarysystem of logic in all its parts, which memoirs shall present in aform quite convincing to a candid mind the results to which I havefound that the scientific |349| method unequivocally leads, addingin each case, rational explanations of how opposing opinions havecome about; the whole putting logic, as far as my studies of it havegone, upon the undeniable footing of a science.

COMMENT to L75.349 by Ransdell (Rev. 7398)

From the beginning to the end of his career Peirce had ashis goal the establishment of logic as a science, and"establish" should be understood here in two senses: first, inthe sense of showing or demonstrating some things about itwhich would make it rationally plausible to regard it in thatway, and second, in the sense of persuading others to thiseffect such that it actually came to be publicly identified assuch, institutionalized appropriately in universities, and soforth.

As regards the first aim, what needed to be shown wasboth that its subjectmatter is essentially public, which isthe primarythough not the onlysense of the dictum "allthought is in signs" that runs like a leitmotiv throughoutPeirce's work, and that it can be understood methodically, inthe manner of science generally. "Methodically" does notmean "algorithmically": Peirce did not think of scientific

method in terms of a mechanistic procedure of generating orvalidating truths, but rather in terms of the exercise ofjudgment in following complex cyclical and selfcorrectiveprocedures involving hypothesis, deduction, and induction,the lastmentioned of which he regarded in terms of testingrather than generating general propositions.

To understand Peirce's logic and philosophy of science,though, it is of the first importance to take due account of asecond sense of "establish" which he, as a working scientisthimself, knew to be at least as important as considerations ofthe sort just mentioned above. For he also understood thatthe establishing of a science is not a matter of an ingenioustour de force of demonstration by an individual in a book orarticle, as philosophers are usually inclined to conceive it, butmeans rather the actual establishing of a shared practice ofinquiry by a community of inquirers with common andoverlapping concerns. This second sense of "establishment" isespecially relevant here; for Peirce regarded this applicationto the Carnegie Institution as presenting the real possibility ofestablishing logic, in a broad sense which includes what wenow call "philosophy of science", as an institutionallyrecognized scientific field on par with the hard sciences byappealing to his own scientific peers in the hard sciences torecognize it as such by supporting him in gathering andpresenting it systematically as foundational work in the field.

Contrary to a continuing misconception, Peirce was not anunknown figure in his time as regards academicians in generaland scientists in particular, and had quite an impressivebacking for his application by way of letters ofrecommendation from important academicians, of whom agood many were in or connected in one way or another withthe sciences, and the board of referees to whom he wasappealing was a similarly prestigious board composed largelyof people in the sciences. (Transcriptions of these letters arecurrently being prepared and will be made available here atthe Arisbe website in the near future.) The attempt, thoughunsuccessful, was not quixotic: indeed, there is reason tothink it would have been successful had it not been forextensive clandestine activity aimed chiefly at discreditingPeirce's character rather than his plan. This is discussed in alittle more detail in the Editorial Introduction.

FromDraftAMSL75.2129

What I desire aid in doing is in bringing before the world the

result of my researches into logic.

I began the study of logic in 1856, and it has been my principaloccupation ever since. Twice, I have made determined efforts todismiss the subject from my thoughts; but the bent of my mind issuch that I did not succeed in doing so for more than a few monthseach time. It was, however, not until 1861 that I ventured upon anyserious original research; so that, subtracting distractions, fortyyears' work is about what my results have cost me.

These results have never been published. It is true thatfragmentary papers mostly upon relatively unimportant topics haveappeared; but the whole forms a unitary system to such a degreethat no part which seems to have any importance can be set forthseparately in a manner to do it justice, either in respect to itsmeaning or in respect to the evidences of it. I will explain how thiscame to be the case. In May 1867 I presented |22| to the Academyin Boston a paper of ten pages, or about 4000 words, upon a NewList of Categories. It was the result of full two years' intense andincessant application. It surprises me today that in so short a time Icould produce a statement of that sort so nearly accurate, especiallywhen I look back at my notebooks and find by what an unnecessarilydifficult route I reached my goal. For this list of categories differsfrom the lists of Aristotle, Kant, and Hegel in attempting much morethan they. They merely took conceptions which they found at hand,already worked out. Their labor was limited to selecting theconceptions, slightly developing some of them, arranging them, andin Hegel's case, separating one or two that had been confused withothers. But what I undertook to do was to go back to experience, inthe sense of whatever we find to have been forced upon our minds,and by examining it to form clear conceptions of its radicallydifferent classes of |23| elements, without relying upon anyprevious philosophizing, at all. This was the most difficult task I everventured to undertake. This list is fortunately very short.Corresponding to Aristotle's Substance, there are two conceptionswhich I call Being and Substance, but corresponding to his nineAccidents I find only three, Quality, Reaction, Mediation. Havingobtained this list of three kinds of elements of experience, (forBeing and Substance are of a different nature,) the business beforeme was the mixed one of making my apprehension of three ideaswhich had never been accurately grasped as clear and plain aspossible, and of tracing out all their modes of combination. This last,at least, seemed to be a problem which could be worked out bystraightforward patience. Such was the teaching of all the logic Iknew, that of Aristotle, of the Greek commentators, of |24| the11th century thinkers, of the great scholastic doctors, of themodern French, English, and German logicians. Long after, when Ihad developed the only effective methods of doing the one thingand the other, that is, of rendering my apprehension clear and offinding the forms of combination of the categories, I ascertainedthat the latter was from the nature of things, not to be compassed

by mere hard thinking, that it was necessary to wait for thecompounds to make their appearance, and patiently to analyzethem, until the list down to a certain point was complete. But, notthen knowing this, after years of fruitless effort (I will not say theywere wasted, since they gave me great training,) I said to myself,this list of categories, specious as it is, must be a delusion of which Imust disabuse myself. Thereupon, I spent five years in diligently,yes, passionately, seeking facts which should refute my list. Never inmy life have I been more thoroughly in earnest |25| than I was inthat long struggle. It was in vain. Everything that promised to refutethe list, when carefully examined only confirmed it. The evidencebecame irresistible. Then that in which I had failed must be feasible.

EDITORIAL NOTE: Peirce apparently means that he failed infinding the forms of combinations of the categories. His pointseems to be that these cannot be ascertained a priori. Thusin a draft version of his comments on Memoir 5 he says:"These three categories are compounded in a multitude ofways which can only be apprehended through experience.They cannot be built up by an act of pure thought. Some ofthese forms of composition have to be carefully examined inorder to obtain distinct conceptions with which to build atheory of logic."

But it never proved so; and at length I learned why it could notprove so. To this solution I was guided by the very categoriesthemselves. Then began the long work of collecting the compoundsand analyzing them into the categories. This work is of its natureabsolutely interminable. It involves a logical doctrine which cannever be completed. But it was now worked up to the point at whichthe general method of research could be made evident to everymind.

But by that time, I had reached a mode of thought so remotefrom that of the ordinary man, that I was unable to communicatewith him. Another great labor was required in breaking a path bywhich to lead him |26| from his position to my own. I had becomeentirely unaccustomed to the use of ordinary language to expressmy own logical ideas to myself. I was obliged to make a regular studyof ordinary ideas and language, in order to convey any hint of myreal meaning. I found that I had a difficult art to acquire. The clearexpression of my thoughts is still most difficult to me. How awkwardI am at it, this very statement will in some measure show.

All this will explainnot distinctly, that would be impossiblewithout going into details, yet in some vague way,how impossibleit was that any fragment of the truth that it has been granted to meto perceive should be adequately represented by itself. Hence, it isthat I have been quite grotesquely misrepresented. I have been

called a hedonist, I who from the beginning of my career to this day,have not written one single piece of a general nature which did notsufficiently show that I regard pleasure, not as most do, as a smallsatisfaction, but as quite no rational satisfaction at all. One Historyof Philosophy sets me down as a typical sceptic, though Kant'scriticism was, so to say, my mother's |27| milk in philosophy. I havebeen called a modern Hume, because Hume denied causalityaltogether, and I, after calling attention to the fact that all men setsome limits to causality, endeavored to define these limits. BecauseI pointed out the insufficiency of existing logical algebra, and haveused algebra as an aid in explaining the logic of relations, it hasbeen assumed that I regarded logical algebra as the whole, or chief,part of logic; although, in fact, I have protested earnestly againstthe exaggerated importance attached by many to this instrument oflogic. At almost the same moment, one eminent philosopher wasreferring to me as a sort of Bchner, while another was calling me apure Schellingian. I am supposed to be opposed to Hegel at allpoints. Indeed, I do think that Hegel's processes, if regarded asproofs, are quite the most absurd reasonings that ever were or couldbe. But as to his main doctrines, which were reached by him beforehe ever lit up his dialectical procedure, I think there is a good dealof truth in them. |28| I think that metaphysics, as it has beenhitherto, has mainly consisted of pretty wellgrounded truthsenormously exaggerated, till they become monstrous falsities; andHegel's opinion that they are all onesided amounts to the samething. My main objection to Hegel is that of all exaggerators he isthe most errant; and that he carries onesidedness to its lastextreme. In my view, there are seven conceivable types ofphilosophy. Three greatly exaggerate the importance of some one ofmy three categories and more or less underrate the others. Threemore somewhat overrate two and almost utterly neglect the third.The seventh type does nearly equal justice to all three. Hegelianismis one of the first three. But the category which it exaggerates is theone most commonly overlooked; and for that reason there is arelative wholesomeness in it. Vera used to say that whileHegelianism was rejected, it had more or less filtered into andpermeated all thought. Very well; dilute |29| Hegelianism bydiminishing the importance it places upon mediation and byrecognizing the due significance of the others, and you havesomething like the truth.

From Draft B MS L75.39

That which I desire aid in doing is to bring before the world theresults of my researches into logic.

I began this study in 1856; and it has been my principaloccupation ever since. I cannot lay claim to the slightest merit forthe constancy with which I have pursued it, since it has been anuncontrollable impulse. On the contrary, it has been necessary for

me at all times to exercise all my control over myself, for fear thatmy mind might be affected by such unceasing application to aparticular subject. When I have found myself in a solitary situation,and there was not a daily round of duties to occupy me, I have haddesperate struggles with my logic. It has kept me poor; but myexperience is that there is only a small proportion of mankind whoare able to make the earning or gaining of money their leadingmotive. At any rate, I am sure that I am not one of that class. I haveexperienced |4| extremely little encouragement. It was more thanten years after I published my first papers that I became aware inany way that anybody but myself and the printer had ever lookedinto them. I have thus had every reason except one for abandoningthe pursuit. Twice I have made determined efforts to do so; but mybent was too strong.

Though I began the study as far back as 1856 and spent almostall my time reading at that time the German philosophers andAristotle, it was not until 1861 that I ventured upon any seriousoriginal research, and not until 1866 that I was far enough advancedto offer anything for publication. It is therefore the results of aboutthirtyfive years work which I desire to present.

Merely fragments of the work have been published, andrelatively unimportant parts, which moreover cannot be properlyunderstood when standing alone. A striking |5| example of how I ammisunderstood is that while one of the histories of philosophy setsme down as a sceptic, a sort of Modern Hume, as I have been called,I note that one of the greatest living philosophers ranks me as a pureSchellingian. Both [of] those classifications cannot be true; yet theyboth come from most competent and careful critics.

I shall be asked why I have published so little and in [so]fragmentary a way. I answer,

1st, that I have had extreme difficulty in getting what I wrote onlogic printed. My boxes are full of unprinted MSS on the subject ascarefully written as anything I ever wrote. Only those things couldbe printed which could pass as relating to some other subject, andthen only if they were made so brief as to be almost unintelligible,or else worked up so as to answer the purposes of popularmagazines.|6|

2nd, that even so, I have not been able to learn that as many ashalf a dozen persons have ever read any paper of mine, no matterhow I had dressed it up.

3rd, that during all these years the vast volume of my results hasbeen such that it has not been easy for me, with my aptitude for thesubject, my personal interest in the discoveries, and my incessantstudy of them, to hold them all in my head at once in an orderlymanner; and the difficulty of the task of arranging them in a lucidand convincing manner is such that several years of exclusive

devotion to that task would be requisite for its accomplishment.

4th, that up to within a few years [ago], new results werecontinually coming in in such profusion as to leave me no leisure toset forth old ones.

5th, that I have no natural gift of making myself understood, andmy thoughts appear to me in a garb so |7| foreign from the ordinaryways of thinking that it would be a difficult matter to translate theminto the language used by readers.

6th, the chief reason remains unmentioned. In May 1867, as theresult of two years of unceasing application, I published a paper often pages which was either entirely mistaken or was one of the mostimportant of philosophical generalizations. Several years nextfollowing were largely occupied in tracing the matter out into itsdevelopments. But here such difficulties were encountered thatwere so great that, although my original result still seemed evident,I began to think that some undiscovered error must lurk in it andthat I was the victim of a selfdelusion. Almost persuaded that thismust be so, for a considerable series of years I was continuallyscheming to discover some downright refutation of my theory. Butevery inquiry I made which promised |8| to lead to such refutation,turned out in the end to afford only new evidence of its truth.Finally, I discovered that the real reason of my difficulties lay not inmy generalization, but in a view which had been accepted by alllogicians without serious question. I now returned with energy to myoriginal position which I adopted, with the utmost advantage as asort of skeleton of my whole logical doctrine. It brought great unityinto the whole subject, but at the same time kept it far remote fromthe ordinary highway of men's thoughts. Since that development, ithas been absolutely impossible to present my views on almost anypart of logic separated from the whole.

7th, notwithstanding all I have said, without referring to earlieressays, I have twice within my later years written a whole bookupon logic. The first was offered to a publisher; but notwithstandingthe recommendations of his readers, he declined it; and I have beenvery glad he did. |9| The other was a very large work, done withmuch care. However, when it was done, I found it to be written toomuch from its own standpoint. It did not examine opposed opinionswith sufficient sympathy and understanding; there was an offensivetone throughout; it was unconvincing, and utterly unworthy of thetheory which it had the honor to defend. I have since thought muchand experimented much upon how the book should be written. I cannow write a treatise which shall restrain every assertion in it withinthe limits in which it shall be absolutely convincing, which shallnotice everything of importance that has been said on each topic,and shall meet every issue squarely and fairly.

From Draft C MS L75.6064

What are the researches of which I speak?

They are the work of my life, that which I seem to have beenput into the world to do. I was born in 1839, and brought up in ascientific circle. I began to be initiated into the methods of physicalscience before I was ten years old; and it has always been methodswhich have chiefly interested me. By 1856, I was alreadysystematically studying logic, in its broad sense, beginning with theCritic of the Pure Reason. I continued my reading diligently, passingto Hegel, Herbart, Aristotle, the scholastics, Berkeley, Hume,Leibniz, etc. I first began serious original research, parallel to myreading, about 1861, and began to publish in 1866. From 1856 untilthis day my passion for the study of logic has been so intense that noother motives could prevail, although the amount of encouragementthat I have received has been so |61| small that I have mostly beenin a desperate depression. Several people have at one time andanother given me aid in pursuing my studies. I can never forgetthem. In each case, there have been solid results, as I shall show, inthe proper place. I have, however, published very little, becausethere was no sort of encouragement to do so. During the greaterpart of my life, the chairs of logic at the universities have beenoccupied by men bred in theological seminaries, devoid of any idealof progressive science, penetrated with formalisms, examiningnothing with real exactitude. This fact naturally brought along anentire situation sufficient to discourage me from troubling a printerto set up what no man would read. What little I could print had to bebrief and fragmentary. I must select subjects concerning which whatI had to say would be intelligible without previous studies.|62|

But my studies were continued almost without interruption.Whatever distractions from my solitary position I might seek, acertain amount of work upon my logic was a daily need. Myperseverance was no merit, any more than my perseverance inbreathing. The result has been that by this time I have built up suchan elaborate system, that the task of undertaking to explain it is oneof the utmost difficulty.

It is, however, now a good many years that I have had this taskunder systematic study. Twice I have actually written treatises onlogic. The first was rejected by the publisher, I am very happy tosay. The second, a more ambitious performance, I myselfcondemned. Finally, last year some friends offered to buy of me thecopyright of a few sections of such a work; and I wrote several,amounting to about 200,000 words in all, which if the funds had not|63| given out, would have grown into the convincing book which Ishould recognize as somewhat worthy of the great theory it wouldattempt to expound.

What I desire is to divide my researches into a number of heads,say from a score to two dozen in all, and to set forth my

investigations of each together with an exhaustive criticalexamination of everything of importance that has been said or couldbe said against my results. Each such paper would be complete initself, except that it would suppose an acquaintance with thosewhich had gone before. The different memoirs would range from20,000 to 100,000 words each. Probably it would require, on theaverage, some ten weeks to prepare each. During the last year Ihave worked faster, it is true; but I hurried more than I ought tohave done. If I lived to complete the plan, as there is every reasonto expect that I |64| should under the enormous stimulus whichassured aid would give my vitality, the whole when completed wouldmake a large treatise on logic, somewhat the largest ever given tothe world. It might be something like a million words. When I speakof the number of words, I mean that it would when properly printedoccupy as much space as that number of words of ordinary matterset up solidly. A good deal of it would contain formulae, diagrams,etc.

From Draft A MS L75.2933

But what would be the contents of my three ponderous volumesof logic? I answer, in the first place, in reference to the expectationswhich would be roused in uninstructed minds by the word "logic,"that it would contain a theory of scientific reasoning and also atheory of the reasoning of practical men about every day affairs.These two would be shown to be governed by somewhat differentprinciples, inasmuch as the practical reasoning is forced to reachsome definite conclusion promptly, while science can wait a centuryor five centuries, if need be, before coming to any conclusion at all.Another cause which acts still more strongly to differentiate themethodeutic of theoretical and practical reasoning is that the lattercan be regulated by instinct |30| acting in its natural way, while[the] theory of how one should reason depends upon one's ultimatepurpose and is modified with every modification of ethics. Theory isthus at a special disadvantage here; but instinct within its properdomain is generally far keener, and surer, and above all swifter,than any deduction from theory can be. Besides, logical instinct has,at all events, to be employed in applying the theory. On the otherhand, the ultimate purpose of pure science, as such, is perfectlydefinite and simple; the theory of purely scientific reasoning can beworked out with mathematical certainty; and the application of thetheory does not require the logical instinct to be strained beyond itsnatural function. On the other hand, if we attempt to apply naturallogical instinct to purely scientific questions of any difficulty, it notonly becomes uncertain, but if it is heeded, the voice of instinctitself is that objective considerations should be the decisiveones.|31|

The methodeutic utility of logic is still further limited by the factthat the reasonings of pure mathematics are perfectly evident and

have no need of any separate theory of logic to reinforce them.Mathematics is its own logic.

Furthermore, the three normative sciences, esthetics, ethics,and logic itself, although they do not come under that branch ofscience called practical, that is, the arts, are nevertheless so farpractical that instinct in its natural operation, is perfectly adaptedto their reasonings after the subtle analyses of which these sciencesthemselves take cognizance have prepared the premisses.

It follows that the only reasonings for which a science of logic ismethodeutically useful are those of metaphysics, and the specialtheoretical sciences, of the physical and the psychical wing. Physicalscience has hitherto done well enough without any appeal |32| to ascience of logic. But at this moment questions of a logical naturehave arisen which nothing but a scientific logic are likely to settle.Witness the controversy between those who are about Poincare andthose who are about Boltzmann. Witness the still more difficultquestion of the constitution of matter. To my prevision physicsseems to be entering a period when such questions will bemultiplied.

How much the psychical sciences have suffered from the lack ofan exact logic can be understood from my memoir on the methods ofresearch into history by means of documents.

In metaphysics the dependence is much stronger yet, but it is ingreat part masked by the circumstance that metaphysics is utterlydependent upon logic in a different way which the categories ofKant and even those of Aristotle illustrate. Namely, metaphysicsregards the universe as thinking, as representing, and all the logicalrelations are repeated as meta|33|physical relations. Metaphysics ishardly more than a corollary from logic. Now metaphysics affectsphysics and the physical sciences most intimately, even more than itdoes the psychical sciences.

Thus the methodeutic utility of the science of logic, although itis beyond price, is pretty narrowly limited.

End of PART 1 of 10 of MS L75

Queries, comments, and suggestions toJoseph Ransdell Dept of Philosophy

Texas Tech University, Lubbock Texas [email protected]

http://members.door.net/arisbe/menu/library/bycsp/L75/Ver1/L75v101.htm

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MEMOIR 1

ON THE CLASSIFICATION OF THE THEORETIC SCIENCES OF RESEARCH

This will be a natural classification, not of possible sciences, butof sciences as they exist today; not of sciences in the sense of"systematized knowledge," but of branches of endeavor to ascertaintruth. I shall not undertake to prove that there is no other naturalclassification of the sciences than that which I give; and this, beingmerely an introductory memoir, cannot have the same convincingcharacter as the others. Every unitary classification has a leadingidea or purpose, and is a natural classification in so far as that samepurpose is determinative in the production of the objects classified.The purpose of this classification is nearly the same as that ofComte, namely, so to arrange a catalogue of the sciences as toexhibit the most important of |351| the relations of logicaldependence among them. In fact, my classification is simply anattempt to improve upon that of Comte; first, by looking less atwhat has been the course of scientific history, and more at what itwould have been if the theoretically best methods had beenpursued; second, by supplying the shocking omissions which Comte'srage against nonsense led him to commit; and third, by carryingdown the subdivision as far as my knowledge enables me to do. Itwas necessary for me to determine what I should call one science.For this purpose I have united under one science studies such as thesame man, in the present state of science, might very well pursue. Ihave been guided in determining this by noting how scientistsassociate themselves into societies, and what contributions arecommonly admitted into one journal, being on my guard against thesurvival of traditions from bygone states of science. A study to whichmen devote their lives, but not, in the present stage of developmentof science, so numerously as to justify exclusive societies andjournals for it, I call a variety of science. That which forms thesubject of the narrowest societies and journals, so that any studentof any part of it ought to be pretty thoroughly informed about everypart, I call a species of science. That branch of which the student ofany part is well qualified to take up any other part, except that hemay not be sufficiently acquainted with the facts in detail, I call a

genus of science. If the only new training necessary to pass from onepart to another is a mere matter of skill, the general conceptionsremaining the same, I call the department a family of science. Ifdifferent sorts of conceptions are dealt with in the different familiesof a depart|353|ment, but the general type of inquiry is the same, Icall it an order of science. If the types of inquiry of the differentorders of a department are different, yet these orders areconnected together so that students feel that they are studying thesame great subject, I call the department a class of science. If thereare different classes, so that different students seem to live indifferent worlds, but yet there is one general animating motive, Icall the department a branch of science. Of course, there will besubbranches, subclasses, etc., down to subvarieties; and evensometimes subsubdivisions. To illustrate, I call pure science andapplied science different branches, and call mathematics and thespecial sciences different classes; I say that general physics, biology,and geology belong to different orders of science. Astronomy andgeognosy are different families. Thermotics and electrics aredifferent families. Optics and electrics |354| are now differentgenera. Entomology and ichthyology are different species of onegenus. The study of Kant and the study of Spinoza are differentvarieties of one species.

Of course, the execution of this useful but ambitious design can,in the first instance, notwithstanding all the labor on my part thatseemed economically recommended, be but a sketch. It will havefully attained all I hope for if it is respectable enough to meritserious picking to pieces in its smaller and in its larger divisions.Indeed, I may say of all these memoirs that what I most desire is thattheir errors should be exposed, so long as they lead to furtherscientific study of the subjects to which they relate. The relation ofthis present memoir to those which follow it in the series is that itgives, from a general survey of science, an idea of the place of logicamong the sciences. I will here set down the larger divisions of thescheme as well as I remember it (not having the notes in mypossession). But it will be the discussion which will form the chiefvalue of the memoir, not the |355| scheme itself. Nearly a hundredschemes given hitherto will be criticized.

A. Theoretical Science

I. Science of Research

i. Mathematics

ii. Philosophy, or Cenoscopy 1. Categorics [= phenomenology or phaneroscopy] 2. Normative Science a. Esthetics b. Ethics c. Logic [= semiotic] [philosophical grammar]

[critical logic] [philosophical rhetoric] 3. Metaphysics

iii. Idioscopy, or Special Science 1. Psychognosy a. Nomological or General Psychology b. Classificatory . Linguistics . Critics . Ethnology |356| c. Descriptive . Biography . History . Archeology 2. Physiognosy a. Nomological or General Physics . Dynamics 1. Of particles 2. Of aggregations . Elaterics and Thermotics . Optics and Electrics b. Classificatory . Crystallography . Chemistry . Biology c. Descriptive . Astronomy . Geognosy |357|

II. Science of Review, or Synthetic Philosophy (Humboldt's Cosmos; Comte's Philosophie Positive)

B. Practical Science, or the Arts

EDITORIAL NOTE: Bracketed material in the above scheme iseditorially supplied as a clarification. Josiah (Lee) Auspitz hasobjected, though, that the simple identification of logic in thebroad sense with semeiotic (also spelled "semiotic" by Peirce)is not correct. His reasons for this are not clear to me and Ibelieve the currently prevailing opinion is in agreement withmy own view that they are supposed to be identical; but LeeAuspitz is a careful and talented scholar and his dissent isworth taking special note of. Perhaps he can be persuaded towrite up a critical note to that effect which we can add to thepresent presentation by including it through a hypertext link.This invitation applies to anyone else as well who wants totake exception to any of my editorial interpretation here orsimply wants to add something to it by way of commentary for

further elucidation: write it up as a criticism or commentaryand we will put a hypertext linkbutton for that note in thetext itself, thus making it an addendum to the presentaccount.

FromDraftEMSL75.206207

This [classification] would be restricted to sciences as theyactually exist, with some little provision of what is sure to bebrought about soon. It would consider sciences, not as "systematizedknowledge," but as organizations of research, as they live today. Myclassification of the applied sciences, or arts, not having been verysuccessful, I should probably not attempt to go into that subject.Moreover, such studies as Humboldt's Cosmos, and Comte'sPhilosophie Positive, although they are really studies of science,would not fall within the scope of my classification, which wouldthus be limited to the theoretical sciences. My classification is quiteminute; but its leading divisions are: mathematics; philosophy or, asBentham calls it, cenoscopic (i.e. based on universal experience);and idioscopic, or special science. The last falls into two parts,psychognosy (embracing psychology, linguistics, ethnology, history,etc.) and physiognosy |207| (embracing physics, chemistry, biology,astronomy, geognosy). I divide philosophy into three parts, thecategories, normative science (esthetics, ethics, and logic,) andmetaphysics. Geometry and the science of time form a connectinglink between metaphysics and idioscopy.

In constructing my classification, I have carefully studied thereasons alleged for nearly a hundred other systems; so that thecritical part of this memoir would be extremely laborious. Yet as mypurpose is not to advance anything for which I cannot produceconvincing proof, such criticism must be carefully and respectfullyperformed throughout all the memoirs.


MEMOIR 2

ON THE SIMPLEST MATHEMATICS

This is that mathematics which distinguishes only two differentvalues, and is of great importance for logic.

From Draft E MS L75.207

This is the system which has a scale of values of only twodegrees. Since these may be identified (in an application of thispure mathematical system) as the true and the false, this systemcalls for somewhat elaborate study as a propaedeutic to logic.


MEMOIR 3

ANALYSIS OF THE CONCEPTIONS OF MATHEMATICS

Such are number, multitude, limit, infinity, infinitesimals,continuity, dimension, imaginaries, multiple algebra, measurement,etc. My former contributions, though very fragmentary, haveattracted attention in Europe, although in respect to priority justicehas not been done them. I bring the whole together into one system,defend the method of infinitesimals conclusively, and give manynew truths established by a new and striking method.


My work in this direction is already somewhat known, althoughvery imperfectly. One of the learned academies of Europe hascrowned a demonstration that my definition of a finite multitudeagrees with Dedekind's definition of an infinite multitude. It appearsto me that the one is hardly more than a verbal modification of theother. I am usually represented as having put forth my definition asa substitute for Dedekind's. In point of fact, mine was published sixyears before his; and my paper contains in very brief and crabbedform all the essentials of his beautiful exposition (still more perfectas modified by Schrder). Many animadversions have been made byeminent men upon my remark, in the Century Dictionary, that themethod of infinitesimals is more consonant with then (in 1883)recent studies of mathematical logic. In this memoir, I should showprecisely how the calculus may be, to the advantage of simplicity,based upon the doctrine of infinitesimals. Many futile attempts havebeen made to define continuity. In the sense in |209| the calculus,no difficulty remains. But the whole of topical geometry remains in

an exceedingly backward state and destitute of any method of proofsimply because true continuity has not been mathematicallydefined. By a careful analysis of the conception of a collection, ofwhich no mathematical definition has been yet published, I havesucceeded in giving a demonstration of an important propositionwhich Cantor had missed, from which the required definition of acontinuum results; and a foundation is afforded for topicalgeometry, which branch of geometry really embraces the whole ofgeometry. I have made several other advances in defining theconceptions of mathematics which illuminate the subject.


MEMOIR 4

ANALYSIS OF THE METHODS OF MATHEMATICAL DEMONSTRATION

I shall be glad to place early in the series so unquestionable anillustration of the great value of minute analysis as this memoir willafford. The subjects of corollarial and theorematic reasoning, of themethod of abstraction, of substantive possibility, |358| and of themethod of topical geometry, of which I have hitherto publishedmere hints, will here be fully elaborated.


[This memoir] will examine the nature of mathematicalreasoning. Logic can pass no judgment upon such reasoning, becauseit is evident, and as such, beyond all criticism. But logic is interestedin studying how mathematical reasoning proceeds. Mathematicalreasoning will be analyzed and important properties of it broughtout which mathematicians themselves are not aware of.


I have hitherto only published some slight hints of mydiscoveries in regard to the logical processes used in mathematics. Ifind that two different kinds of reasoning are used, which I |210|distinguish as the corollarial and the theorematic. This is a matterof extreme importance for the theory of cognition. It remains

unpublished. I also find that the most effective kind of theorematicdemonstration always involves the long despised operation ofabstraction, which has been a common topic of ridicule. This is theoperation by which we transform the proposition that "Opium putspeople to sleep" into the proposition that "Opium has a soporificvirtue". Like every other logical transformation, it can be applied ina futile manner. But I show that, without it, the mathematicianwould be shut off from operations upon lines, surfaces, differentials,functions, operationsand even from the consideration of cardinalnumbers. I go on to define precisely what it is that this operationeffects. I endeavor in this paper to enumerate, classify, and definethe precise mode of effectiveness of every method employed inmathematics.


No science of logic is needed for mathematics beyond that whichmathematics can itself supply, unless possibly it be in regard tomathematical heuretic. But the examination of the methods ofmathematical demonstration shed |91| extraordinary light uponlogic, such as I, for my part, never dreamed of in advance, althoughI ought to have guessed that there must be unexpected treasureshidden in this quite unexplored ground. That the logic ofmathematics belonged to the logic of relatives, and to the logic oftriadic, not of dyadic relations, was indeed obvious in advance; butbeyond that I had no idea of its nature. The first things I found outwere that all mathematical reasoning is diagrammatic and that allnecessary reasoning is mathematical reasoning, no matter howsimple it may be. By diagrammatic reasoning, I mean reasoningwhich constructs a diagram according to a precept expressed ingeneral terms, performs experiments upon this diagram, notes theirresults, assures itself that similar experiments performed upon anydiagram constructed according to the same precept would have|92| the same results, and expresses this in general terms. This wasa discovery of no little importance, showing, as it does, that allknowledge without exception comes from observation.

At this point, I intend to insert a mention of my theory of gradesof reality. The general notion is old, but in modern times it has beenforgotten. I undertake to prove its truth, resting on the principlethat a theory which is adapted to the prediction of observationalfacts, and which does not lead to disappointment, is ipso facto true.This principle is proved in No. 1. Then my proof of grades of realityis inductive, and consists in often turning aside in the course of thisseries of memoirs to show how this theory is adapted to theexpression of facts. This might be mistaken for repetitiousness; butin fact it is logically defensible, and it also has the advantage ofleading the reader, step by step, to the compre|93|hension of anidea which he would not be able to grasp at once, and to theappreciation of an argument which he could not digest at one time. I

will not here undertake to explain what the theory is in detail.Suffice it to say that since reality consists in this, that a real thinghas whatever characters it has in its being and its having them doesnot consist in its being represented to have them, not even in itsrepresenting itself to have them, not even if the character consistsin the thing's representing itself to represent itself; since, I say, thatis the nature of reality, as all schools of philosophy now admit, thereis no reason in the nature of reality why it should not havegradations of several kinds; and in point of fact, we find convincingevidences of such gradations. It is easy to see that according to thisdefinition the square root of minus 1 possesses a certain grade of|94| reality, since all its characters except only that of being thesquare root of minus one are what they are whether you or I thinkso or not. So when Charles Dickens was halfthrough one of hisnovels, he could no longer make his characters do anything thatsome whim of a reader might suggest without feeling that it wasfalse; and in point of fact the reader sometimes feels that theconcluding parts of this or that novel of Dickens is false. Even here,then, there is an extremely low grade of reality. Everybody wouldadmit that the word might be applied in such cases by an aptmetaphor; but I undertake to show that there is a certain degree ofsober truth in it, and that it is important for logic to recognize thatthe reality of the Great Pyramid, or of the Atlantic Ocean, or of theSun itself, is nothing but a higher grade of the same thing.

But to say that the reasoning of mathematics is |95|diagrammatic is not to penetrate in the least degree into the logicalpeculiarities of its procedure, because all necessary reasoning isdiagrammatic.

My first real discovery about mathematical procedure was thatthere are two kinds of necessary reasoning, which I call thecorollarial and the theorematic, because the corollaries affixed tothe propositions of Euclid are usually arguments of one kind, whilethe more important theorems are of the other. The peculiarity oftheorematic reasoning is that it considers something not implied atall in the conceptions so far gained, which neither the definition ofthe object of research nor anything yet known about could ofthemselves suggest, although they give room for it. Euclid, forexample, will add lines to |96| his diagram which are not at allrequired or suggested by any previous proposition, and which theconclusion that he reaches by this means says nothing about. I showthat no considerable advance can be made in thought of any kindwithout theorematic reasoning. When we come to consider theheuretic part of mathematical procedure, the question how suchsuggestions are obtained will be the central point of the discussion.

Passing over smaller discoveries, the principal result of mycloser studies of it has been the very great part which an operationplays in it which throughout modern times has been taken fornothing better than a proper butt of ridicule. It is the operation ofabstraction, in the proper sense of the term, which, for example,

converts the |97| proposition "Opium puts people to sleep" into"Opium has a dormitive virtue". This turns out to be so essential tothe greater strides of mathematical demonstration that it is properto divide all theorematic reasoning into the nonabstractional andthe abstractional. I am able to prove that the most practicallyimportant results of mathematics could not in any way be attainedwithout this operation of abstraction. It is therefore necessary forlogic to distinguish sharply between good abstraction and badabstraction.

It was not until I had been giving a large part of my time forseveral years to tracing out the ways in which mathematicaldemonstration makes use of abstraction that I came across a factwhich a mind which had not been scrutinizing the facts so closely|98| might have seen long before, namely, that all collections are ofthe nature of abstractions. When we pass from saying, "Almost anyAmerican can speak English", to saying "The American nation iscomposed of individuals of whom the greater part speak English", weperform a special kind of abstraction. This can, I know, signify littleto the person who is not acquainted with the properties ofabstraction. It may, however, suggest to him that the popularcontempt for "abstractions" does not aim very accurately at its mark.

When I published a paper about number in 1882, I was alreadylargely anticipated by Cantor, although I did not know it. I howeveranticipated Dedekind by about six years. Dedekind's work, althoughits form is admirable, has not influenced me. But ideas which I havederived from Cantor are so mixed up with ideas of my own that Icould not safely undertake to say exactly where the line should be|99| drawn between what is Cantor's and what my own. From mypoint of view, it is not of much consequence. Like Cantor and unlikeDedekind, I begin with multitude, or as Cantor erroneously calls it,cardinal number. But it would be equally correct, perhapspreferable, to begin with ordinal number, as Dedekind does. But Ipursue the method of considering multitude to the very end, whileCantor switches off to ordinal number. For that reason, it is difficultto make sure that my higher multitudes are the same as his. But Ihave little doubt that they are. I prove that there is an infiniteseries of infinite multitudes, apparently the same as Cantor's alephs.I call the first the denumerable multitude, the others theabnumerable multitudes, the first and least of which is themultitude of all the irrational numbers of analysis. There is nothinggreater than these but true continua, which are not multitudes. Icannot see that Cantor has ever got the conception of a truecontinuum, such that in any |100| lapse of time there is room forany multitude of instants however great.

I show that every multitude is distinguished from all greatermultitudes by there being a way of reasoning about collections ofthat multitude which does not hold good for greater multitudes.Consequently, there is an infinite series of forms of reasoningconcerning the calculus which deals only with a collection of

numbers of the first abnumerable multitude which are notapplicable to true continua. This, it would seem, was a sufficientexplanation of the circumstance that mathematicians have neverdiscovered any method of reasoning about topical geometry, whichdeals with true continua. They have not really proved a singleproposition in that branch of mathematics.

Cayley, while I was still a boy, proved that metrical geometry,the geometry of the elements, is nothing but a special |101|problem to projective geometry, or perspective. It is easy to seethat projective geometry is nothing but a special problem of topicalgeometry. On the other hand, since every relation can be reducedto a relation of serial order, something similar to a scale of valuesmay be applied to every kind of mathematics. Probably, if theappropriate scale were found, it would afford the best generalmethod for the treatment of any branch. We see, for example, thepower of the barycentric calculus in projective geometry. It isessentially the method of modern analytic geometry. Yet it isevident that it is not altogether an appropriate scale. I can alreadysee some of the characters of an appropriate scale of values fortopical geometry.

My logical studies have already enabled me to prove somepropositions which had arrested mathematicians of power. Yet Idistinctly disclaim, for the present, all pretension to having beenremarkably successful in dealing with the heuretic |102|department of mathematics. My attention has been concentratedupon the study of its procedure in demonstration, not upon itsprocedure in discovering demonstrations. This must come later; andit may very well be that I am not so near to a thoroughunderstanding of it as I may hope.

I am quite sure that the value of what I have ascertained will beacknowledged by mathematicians. I shall make one more effort toincrease it, before writing this second memoir.


I now pass to a rough statement of my results in regard to theheuretic branch of mathematical thought. At the outset, I set up formyself a sort of landmark by which to discern whether I was makingany real progress or not. Cayley had shown, while I was, as a boy,just beginning to understand such things, that metric geometry, thegeometry of the Elements, is nothing but a special problem inprojective geometry, or perspective, and it is easy to see thatprojective geometry is nothing but a special problem in topical geom



MEMOIR 5

ON THE QUALITIES OF THE THREE CATEGORIES OF EXPERIENCE

An analysis and description of three irreducibly different kindsof elements found in experience and even in the abstract world ofpure mathematics. This memoir rests upon observation of theexperience of every day and hour, this observation beingsystematized by thought. It is proved, beyond doubt, that there areno more than the three categories. The list was first published byme in May 1867, but has since been repeatedly subjected to theseverest criticism I could bring to bear upon it, with the result ofmaking it far more evidently correct. The categories were originallycalled "quality", "relation", and "representation". The question ofnames and other terminology for them still somewhat perplexes me.I am inclined to call them "flavor", "reaction", and "mediation".


[This memoir] will show that all that is before the mind asperceived, imagined, supposed, rejected, etc, has three kinds ofelements and no more. These are the qualities of feeling, reaction,and mediation. [EDITORIAL NOTE: Notice that elements of the firstkind are qualities of feeling and not simply feelings.] Great pains willbe taken to make these three conceptions perfectly clear and vivid.


My aim in this paper, upon which I have bestowed more laborthan upon any other, beginning two years before my firstpublication on the subject in May 1867, is far more ambitious thanthat of Kant, or even that of Aristotle, or even the more extendedwork of Hegel. All those philosophers contented themselves mainlywith arranging conceptions which were already current. I, on thecontrary, undertake to look directly |103| upon the universal

phenomenon, that is, upon all that in any way appears, whether asfact or as fiction; to pick out the different kinds of elements which Idetect in it, aided by a special art developed for the purpose; and toform clear conceptions of those kinds, of which I find that there areonly three, aided by another special art developed for thatpurpose.*

Editorial Note (by Ransdell):

Does anyone know what Peirce is referring to asregards these special arts? If you have any ideas onthis let us know and we will post it here as anannotation. You need not have the "definitive"answer to this to post your comment here: the ideais just to get some cooperative work done on thisand on other such questions as might arise,proceeding at a leisurely pace and in the manner ofa scholarly dialogue.

Let me know at [email protected] and I'llpost your response here:

COMMENTS & RESPONSES:

(1) Bo Larsson: August 15, 1998

(2) Jeffrey Downard: June 19, 2007

In my present limited space, I cannot make myself clear, stillless convincing. Yet I will give such hint as I can of the three kinds ofelements. I might name them "qualities", "occurrences", and"meanings". In order to get an idea of what I mean by a "quality",imagine a being whose consciousness should be nothing but theperfume of a damask rose, without any sense of change, of duration,of self or anything else. Put yourself in that being's shoes, and whatof the universal phenomenon remains is what I call a "quality". Itmay be defined as that whose mode of |104| being consists simplyin its being what it is. It is selfessence. Suppose next that theconsciousness we have imagined should undergo the simplestpossible experience; that, for example, the roseodor shouldsuddenly change to violetodor. If it is to remain the sameconsciousness, there must be a moment in which it is conscious ofboth odors. It cannot in this moment be conscious of the flow oftime; but the former roseodor will appear as its ego, as itsconsciousness, while the new violetodor will at that moment be itsnonego, the object of its consciousness. We have this sort of

consciousness whenever we experience an event. The old, whichhas just come to an end, appears as an ego, with the new, which isjust about to begin, over against it as a nonego instantly passinginto the ego. The sense of actuality, of present fact, is thusessentially a consciousness of duplicity, of opposition. When wehave thus got the idea of an inner and an outer, we can |105|review our experience and place ourselves back to a moment whenboth the former and the latter states were nonegos, and thus weget the idea of a force acting between outward objects. I do notmean to say that historically we actually do so reflect; probably not.But I mean that that would be a logical reflection. Thus we mightlogically derive the notion of a thing, as something whose mode ofbeing consists in a reaction against something else. This is mysecond category. The occurrence is essentially present. When it isnot present its peculiar mode of being is gone. There is no timeconstituent in it; for the flow of time involves a very differentelement. There is always a certain resistance to the unexpected. Itis usually broken down so instantly that it can only be detected incases in which peculiar circumstances cause its continuance. Butthat the new experience always has to overcome a resistance on thepart of the old is proved by the |106| fact that we feel it to beirresistible. We feel its force. Now, there can be no force wherethere is no resistance. The two are but reverse aspects of the samephenomenon. This resistance is a counterforce. Hence the sense ofactual fact is a sense of reacting efforts.

So far, we have left out of account the staple element of theuniversal phenomenon. Since we have been considering things astemporal, we may as well continue to take the same point of view.The future grows into accomplished fact by a gradual unrolling; thenew becomes gradually old. Its effects remain, but they dwindle inimportance toward utter oblivion. According to legitimate physicalpresumption, the evidence certainly now is (although we may notthink it likely that it is quite true) that all physical forces are atbottom conservative. Now conservative forces necessarily producecyclical effects. It is true, that if two particles are attractedprecisely inversely as the cube of their |107| distance, or by anylaw equivalent to that, the one will move in a spiral nearer to theother forever. This is an interesting point; and I have never seen itstated with precision. Formulae given on p. 878 of my father'sAnalytic Mechanics show that if P is the rate of description of areaof the Boscovichian point moving round a fixed attracting center,then if we use a system of rectangular coordinates in which x shallbe equal to the square of the reciprocal of the radius vector, and yequal to the square of the velocity, then the straight line whoseequation is y = 4P2x will determine the condition of the movingparticle reaching an apse; that is, a maximum or minimum distance.Another curve, dependent on the law of the variation of theattraction with the distance, will determine how u2 will vary with 1/

2. If the attraction varies less rapidly than the inverse cube of thedistance, this second curve will be |108| concave downwards; if

more rapidly, concave upwards. But if itever crosses the straight line y = 4P2x thebody will have at that distance been at amaximum or minimum distance. If it istangent to that straight line, it maydescribe the circle at that distance. Whenit is below the straight line its velocity willbe insufficient and the distance willdiminish; so that x will increase.


Although I cannot in my present limited space make myselfclear, still less convincing, I will name the three elements which Ifind and give some rough notion of the significations of the names.They are called "qualities", "things", and "meanings". By a "quality" ismeant a selfessence, or something which is what it is by and initself alone. Such, for example, is any simple quality of sensation.Mind, I am not speaking of the occurrence of that sensation. What Imean can be understood by imagining a being whose consciousnessshould consist, we will say, in the sense of the perfume |135| of adamask rose, without any change, without any sense of time,without attributing the smell to any object, without any selfconsciousness. I do not say that one can realize that in theimagination; but one can perceive that such a state of consciousnessthere might be. One can even suppose, however groundlessly, thatthe attar of roses has a consciousness which is just that. Now takeaway the consciousness in which there is an element of fact, ofaction, and in which there is an element of representation, and thevery quality itself, which consists in its own peculiar selfbeing, andyou have what I mean by the elements of quality in the universalphenomena. The element that I call a "thing" is more familiar; butthe logical analysis of it which is given in the books is inaccurate,because it is colored by the peculiar ways of thinking of the IndoEuropean languages. It is true that there are proper |136| names inall languages; but common substantives, such as ours are, definitelynot verbs, are certainly not necessary in a language, and in myopinion they do not fully exist in the majority of languages. In theShemitic languages, for example, every common noun is regarded asa formation from a verb. Even if no such verb exists, it would seemthat the Shemites cannot think of a noun except as a part of a verb;for they give it a form as if it were of that nature. Indeed, there areIndoEuropean languages in which the idea of the common noun isnot completely hardened. For it is plain that with nouns, full nounsalone, one could not frame a sentence which should satisfy the mindas completely expressed. Now the majority of languages aredestitute of any substantive verb "is". In ancient Egyptian, a pronoun"that" usually takes its place. In Greek there is little or no feelingthat a sentence without a verb is elliptical. |137| It is, therefore,

impossible that in those languages the common noun should bethought as a mere name, as we think it. In Ancient Egyptian, itseems that the pictorial way of thinking, so prominent in thehieroglyphics, was more influential in their thought than it is withus. The word "man" would then be replaced by what we can nearestexpress as "something is a man", the word "animal" by "something isan animal". Hence to express the idea that "man is an animal", thepronoun "that" would naturally be more appropriate than "is". Theywould think "Something is a man that something is an animal". It isour idea of a common noun as a name which has caused thelogicians to regard a thing as something selfsubsistent. There is noroom for doubt that that is the way the idea arose. A proper name isalways the name of something more or less familiar to both theutterer of the sentence in which it occurs |138| and the personwhom he addresses. For otherwise the sentence would have nomeaning. If I inform you that the first king of England was Arthur,and you had never before heard of Arthur, still my description ofhim as the first king of England gives you some acquaintance withhim before I use the word "Arthur". If I say "Arthur was the first kingof England" I am using a faulty inversion. But a common noun doesnot suppose any such familiarity. The sentence "Flyingfishes arecommon in the gulf stream" is sufficiently intelligible to a personwho never heard of a flyingfish. That the idea of a thing or, as thelogicians say, a substantia, not only does not consist in selfsubsistence, which really describes a quality, but is downrightrepugnant to it, is seen by trying to imagine a universe in whichnothing should exist but a single atom. It has been shown above thatit is quite possible to conceive of a universe in which there |139|should be absolutely nothing but a roseodor, without time, space,or anything else. But to suppose that nothing existed but a singleatom would be absurd. Suppose it should exist and not exist everyother day: what difference would there be between the odd andeven days? The difference between an actually existing magnet anda phantasm of a magnet is that one actually pulls and the other doesnot. Actuality, or existence, consists in reaction. When I call aphenomenon a thing, I mean that it is an object, a something actingob, or over against me.


I will name these elements here, although I cannot stop toexplain what the names mean. They are simple qualities, subjectsof force, and mind. Mind, in particular, is a very differentconception from that which is current. It is nearly the HegelianBegriff. There are three points of view from which these elementshave to be studied before they can be clearly apprehended. Theseare the points of view of qualities, of subjects, and of minds. Fromthe point of view of quality, they appear respectively as quality,|141| reaction, and mediation. From the point of view of subjectsthey appear as quales, relates, and representations. This is [the]

point of view most familiar to ordinary thought, and will appear theclearest to a beginner in the subject. Remembering that by "theuniversal phenomenon" I mean everything which has got into themind in any way whatever, including every fiction and false notion,anyone can without difficulty see that there is an idea of a thing asit is in itself with certain qualities, however occult, which do notconsist in its actual relation to anything else. In the next place,things are related to one another in pairs. That is, they are atdistances from one another, attract or repel one another, etc. In thethird place, finally, there are things which represent other things tosome purposing mind; that is, they act as substitutes for those otherthings for some purpose; that is, again, they render the objectrepresented available for the |142| purpose. Thus, to take anexample where, at first sight, one does not perceive any element ofrepresentation, A gives B a present, C. As a consequence of that act,B comes into direct relation with C, and A has no more to do withthe matter. But as long as A's act of gift is in process ofperformance, this act consists in giving B a consciousness of having apower over C. It is a particular kind of representation to B of theobject C. In [the] third place, from the point of view of mind, thethree categories appear as feeling or immediate consciousness, asthe sense of fact, and as conception or mind strictly.

These three categories are compounded in a multitude of wayswhich can only be apprehended through experience. They cannot bebuilt up by an act of pure thought. Some of these forms ofcomposition have to be carefully examined in order to obtaindistinct conceptions with which to build a theory of logic.

EDITORIAL NOTE: Here is a tabulation of the nomenclature forthe three categories which Peirce uses in the different versionsof this memoir above:

quality relation representation

flavor reaction mediation

qualities of feeling reaction mediation

qualities occurrences meanings

qualities things meanings

simple qualities subjects offorce mind

quality reaction mediation

quales relates representation

feeling or immediateconsciousness

sense offact

conception or mindstrictly


MEMOIR 6

ON THE CATEGORIES IN THEIR REACTIONAL ASPECTS

[Peirce said nothing under this heading in any extant version of MSL75.]


MEMOIR 7

OF THE CATEGORIES IN THEIR MEDIATE ASPECTS

These two memoirs [i.e. Memoirs 6 and 7] develop and renderclear a considerable number of conceptions of which I shall makeconstant use in the remaining memoirs, and which are of constantuse in all parts of philosophy and even in mathematics.


MEMOIR 8

EXAMINATIONS OF HISTORICAL LISTS OF CATEGORIES

My list differs from those of Aristotle, Kant, and Hegel in thatthey never really went back to examining the phenomenon to seewhat was to be observed there; and I do not except Hegel'sPhnomenologie from this criticism. They simply took currentconceptions and arranged them. Mine has been a more fundamentaland more laborious undertaking since I have worked up from thepercepts to the highest notions. I examine those systems as well assome others.


MEMOIR 9

ON THE BEARING OF ESTHETICS AND ETHICS UPON LOGIC

I begin by explaining the nature of the normative sciences. Theyhave often been mistaken for practical |360| sciences, or arts. Ishow that they are at the opposite pole of the sphere of science,and are so closely allied to mathematics that it would be a muchsmaller error to say that, like mathematics, they were simplyoccupied in deducing the consequences of initial hypotheses. Theirpeculiar dualism, which appears in the distinctions of the beautifuland the ugly, right and wrong, truth and falsity, and which is onecause of their being mistaken for arts, is really due to their being onthe border between mathematics and positive science; and to this,together with their great abstractness, is due their applicability toso many subjects, which also helps to cause their being taken forarts. Having analyzed the nature of the precise problems of thethree, and given some considerations generally overlooked, I showthat ethics depends essentially upon esthetics and logic upon ethics.The latter dependence I had shown less fully in 1869. (Journal ofSpeculative Philosophy, Vol. II, pp. 297 et seq.) But the methods ofreasoning by which the truths of logic are established must bemathematical, such reasoning alone |361| being evidentindependently of any logical doctrine.


[This memoir] will explain the nature of a normative science andshow that, so far from such science approximating to practicalscience, or art, it is, on the contrary, its extreme abstractness,closely approaching the nature of pure mathematics, surpassing inabstractness all other positive science, or science of fact (whichpure mathematics is not), which imparts to it its peculiar dualism(fine and ugly, good and bad, true and false), and at the same timemakes it more nearly applicable to every subject than any othersuch science except mathematics and categorics. The preciseproblems of the three normative sciences are made clear in fourstages or degrees of clearness. In what manner the truths ofesthetics are to be discovered [is its] main proposition. Ethicsdepends upon esthetics; we cannot know how we are deliberatelyprepared to aim to behave until we know what we deliberatelyadmire. The two leading doctrines of ethics. Logic in its turnessentially depends upon ethics (as I showed, in a general andvaguer way in 1869, |162| Journal of Speculative Philosophy, II,207208), but its methods of reasoning must be mathematical, suchreasoning being evident and therefore not requiring the support ofany logical doctrine. Preliminary sketch of the three great doctrinesof logic.

From Draft D MS L75.231233

I here show the peculiar character of a normative science;namely, that while it is a purely theoretical science, and notessentially practical, it nevertheless pronounces some things to begood and others bad. Esthetics does so within the realm of thecategory of feeling, ethics in the realm of action, and logic in therealm of thought. As far back as 1869, I proved clearly that it isimpossible for a man to be logical unless he adopts certain highmoral aims. The argument is extremely |232| simple: All positivereasoning depends upon probability. All probability depends uponthe supposition that there is a "long run." But a long run is anendless course of experience. Now even if there be a future life,every man's course of experience with which his reasoning has to docomes to a speedy end. Therefore, if his purposes are purely selfishhe cannot be logical. That argument is open to some apparentobjection; but the subsequent careful analysis of it has only shownthat the argument has even more force than was supposed. Otherconsiderations have also appeared which make the dependence ofwhat we ought to think upon what we aim at still more close. Logicis, therefore, more or less dependent upon ethics. Ethics, in itsturn, or the question what we are deliberately prepared to aim at,depends in a similar way upon esthetics, or what it is that we woulddeliberately pronounce to be kalon k'agathon. Indirectly, therefore,logic even depends upon esthetics. For |233|this reason, with thehelp of the categories, I commence with an attempt at outline

analyses of the problems of esthetics and of ethics.

EDITORIAL NOTE: The Greek phrase "kalon k'agathon", theconventional but uninformative translation of which is"beautiful and good", combines the idea of that which excitesor calls forth admiration and fascination and that towardwhich something is directed in its movement or change.

End of PART 3 of 10 of MS L75

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MEMOIR 10

ON THE PRESUPPOSITIONS OF LOGIC

I here show that much that is generally set down as presupposedin logic is neither needed nor warranted. The true presuppositionsof logic are merely hopes and as such, when we consider theirconsequences collectively, we cannot condemn scepticism as to howfar they may be borne out by facts. But when we come down tospecific cases, these hopes are so completely justified that thesmallest conflict with them suffices to condemn the doctrine thatinvolves that conflict. This is one of the places where logic comes incontact with ethics. I examine the matter of these hopes, showingthat they are, among other things which I enumerate, that any givenquestion is susceptible of a true answer, and that this answer isdiscoverable, that being and being represented are different, thatthere is a reality, and that the real world is governed by ideas.Doubt and everyday belief are analyzed; and the differencebetween the latter and scientific acceptance is shown. Otherdoctrines are examined.


[This discussion concerns] what it is that the sincere student oflogic must certainly already believe beyond all doubt. He mustbelieve, or at least hope, that there is such a thing as The Truth, atleast with reference to some questions. He must therefore thinkthat there is some reality which is independently of its beingrepresented to be. He must therefore think that there is an externalworld, however intimately it may be connected with himself, or hewith it. He must agree that things happen, and that there is somesuch thing as compulsion, or at least as force. He must agree thatthere is such a thing as the influence of abstract ideas, such as TheTruth, upon hard facts. That it is really true, and no meremetaphor, that The Truth is a great power. All these things it will be

shown that the student of logic, if he is sincerely such, does believe.

From Draft D MS L75.230231

Most logicians, if not all, hold that there are certain"presuppositions," or postulates, which logic must assume to betrue; but they differ much as to what these presuppositions are, andeven as to their forming a definite list or code. I find that mostlogicians have outrageously exaggerated these presuppositions, butthat there nevertheless are certain beliefs which a man must holdfirmly or at least hope are true; otherwise there would be no sensein his studying logic. These I endeavor to catalogue and define. It isobvious that precision in this matter is quite indispensable. Myposition here seems to be secured by the fact that all thedifferences between me and other logicians consist in my holdingpropositions not to be presupposed which they hold are so. Now ifthey say that these things are presupposed by everybody, I opposeto that the fact that I do not presuppose them. If they say theyought to be presupposed, in the first place, they cannot saydefinitely how, and in the second place, I offer a proof which, if notdemonstrative, is very strong, that there can be no argumentestablishing such an ought.


Logicians generally, and especially the Germans, hold that themere fact of reasoning, or endeavoring to reason, commits us to thecategorical assertion of a considerable body of doctrine. But Iundertake to show that in this instance, as in innumerable others,those philosophical minds who have had no training in a progressiveand living science exaggerate enormously, if not infinitely, theconclusions which they are really entitled to draw. In this number, Ipropose to examine with care, first, in what sense anything is"presupposed" in merely entering upon an inquiry, and just what itis; and secondly, whether there is anything additional which aperson is committed to by the act of inquiring into logic, and if so,what it is, and how he is committed to it. I undertake to show beyond the possibility of any attentivereader's doubt, that the bulk of the propositions which the logicianssay we are bound to affirm, we are really, at most, only bound inconsistency to hope for or expect, and that instead of our beingbound to assert universal propositions, we merely hope that certainquite narrowly personal propositions may be true. At the same time,among the propositions that are said to be "presupposed," there aresome which, though the reasoner may not be bound to adhere to

them, it is quite clear that he does hold them to be evident orundoubted facts. I further undertake to show that operations ofwhich we are unconscious are beyond our direct control, and that itis idle to ask whether an operation over which we have no controlhas been properly performed or not. For example, I open my eyesand look; and I thereupon say "There seems to be a bay horse". Thisis a proposition. A percept is not a proposition. But the propositionis supposed truly to represent the seeming of the percept. It is, as Ihold, quite idle to inquire whether this is correct or not. It isconceivable that it should not be correct; but the operation offorming that perceptual judgment from the percept being utterlybeyond our control, at present, it must go unquestioned. It is out ofour power to doubt it. It appears evidently. Propositions which wecannot doubt have to be accepted without criticism. Genuinecriticism of them is impossible. It is true that we believe that amongthe propositions which seem evident to us there are some that arefalse and that we shall ultimately discover to be false. That is a goodreason for not hastily pronouncing that a proposition is indubitableby us today. Still, until we can contrive to doubt a proposition noreal inquiry into its truth can take place.

Having put these principles into a clear light, and examined allother possible objections to them, it will behoove me to admit thatthey are not free from the defect common to almost all propositionsin philosophy, that of being more or less vague and open tounwarrantable exaggeration. To be able to doubt a proposition, if itmeans to doubt it this instant, can include only actual doubt. If thetime be extended changes of mind may take place. Doubt may alsobe so slight that it is not decidedly recognizable. It is easy to findpropositions of which we cannot positively say whether they can bedoubted or not. Nevertheless, I undertake to show that theprinciples are sufficiently definite for the purposes of logic.

I next undertake something like an enumeration of theindubitable propositions. I shall not affirm that my enumeration iscomplete, but shall only mention those which must be taken accountof in logic. Nor shall I name all the individual propositions; for theywill be different for different persons and even for the same personat different times. But I shall enumerate categories of them. Thesewill be enumerated in the form of propositions which are notthemselves indubitable in advance of the proofs of them which Ishall adduce. Nor can these proofs be apodictic. They will leaveroom for hypothetical doubts; but I do not think they will leave anyreally possible doubt in the reader's mind.

I have not decided upon the order of my enumeration; nor will Ibe positive that upon reconsideration I may not slightly alter mypresent statement. But the propositions which I shall show to bebeyond criticism will be pretty nearly as follows.

I will first mention judgments descriptive of one's own state of

thought. These will include perceptual judgments, that is,judgments as to the character of present percepts, such as "The skyis blue". They will also include judgments as to the meanings whichthe person making the judgment himself attaches to words andother signs. Thus, if I say to myself "There seems to be a horse",then, that being true in the sense I attach to the word "horse", I amquite sure that there is an animal. For I am quite sure that by ahorse I mean a kind of animal. It is true that I am sometimes indoubt exactly what I do mean. Precisely where shall I draw the linebetween "many persons" and "not many persons"? Moreover, I mayblunder about my meaning. I may declare that in saying the sky isblue I therein imply that it is not orangecolored, although, in fact,when I said the sky was blue I was not referring at all to thepossibility of its being orange colored. But I shall show thatnevertheless all judgments concerning one's own thought are in theonly reasonable sense of the words beyond criticism.

The proposition here laid down, that all judgments concerningthe contents of our own thought are beyond criticism, is not itselfbeyond criticism. It is a matter to be argued out; and some logiciansvirtually deny it. Their doctrine is that it is only the first impressionsof sense or other immediate consciousness that are to be acceptedwithout criticism. But I deny both branches of this opinion, and holdthat the first impressions of sense and all immediate consciousnessare of the most dubious character, while certain propositions whosepsychological genesis may be traced are nevertheless quiteindubitable. I will undertake to put this beyond all real doubt.

Another class of propositions beyond criticism results from theapplication of one indubitable judgment to another. For example, ifI say that a judgment is false, I am referring to something out ofthought. For what I mean is that the proposition refers to a subjectand misrepresents it, which it could not do if it referred only to thecontents of thought. Consequently, the following proposition is notconfined to the thought of the person who judges it: "There is such athing as a false proposition." Now two things are indubitable; first,that to say that that proposition, if it were enunciated, would befalse would imply that that proposition was not enunciated, andsecond, the perceptual judgment that one hears that propositionenunciated. Consequently, the proposition is beyond criticism; andthis is an important result. It will be observed that I do not deny thatits being beyond criticism is itself a proposition requiring carefulexamination. Various objections might be made to it. For example,it may be said that Hegel does not admit it, so that it cannot be soincapable of doubt. I reply that it might be doubted if we overlookedwhat we actually perceive, as Hegel does. But if he would open hiseyes to the fact that his own opinion is denied, it would at oncebecome impossible for him to retain that opinion.

Another class of judgments exempt from criticism refers toobjects of the mind's own creations.


{65} German logicians generally maintain that the mereincipiescence of reasonin

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