Milford, Pa., 1902, July 15 To the Executive Committee of the Carnegie Institution, Gentlemen: I have the honor respectfully to submit to you herein an application for aid from the Carnegie Institution in accomplishing certain scientific work. The contents of the letter are as follows: #1. Explanation of what work is proposed. Appendix containing a fuller statement. #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 Carnegie Institution, in money and in efficiency. #9. Statement of my apprehension of the Basis of my claim for aid.

Explanation of What the Proposed Work is Some personal narrative is here necessary. I imbibed from my boyhood the spirit of positive science, and especially of exact science; and early became intensely curious concerning the theory of the methods of science; so that, shortly after my graduation from college, in 1859, I determined to devote my life to that study; although indeed it was less a resolve than an overmastering passion, which I had been for some years unable to hold in check. It has never abated. In 1866, and more in 1867, I ventured upon my first original contributions to the Science of logic, and have continued my studies of this science ever since, with rare interruptions of a few months only each. Owing to my treating logic as a science, like the physical sciences in which I had been trained, and making my studies special, minute, exact, and checked by experience, and owing 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 few fragments of outlying parts of

my work, or slight sketches of more important parts. For logic differs from the natural sciences and, in some measure, even from mathematics, in being more essentially systematic. Consequently, if new discoveries were made in the course of writing a paper, they would be apt to call for a remodelling of it, a work for mature reconsideration. Still, as far as I remember, no definitive conclusion of importance to which I have ever been led has required retraction, such were the advantages of the scientific method of study. Modification in details and changes (very sparse) of the relative importance of principles are the greatest alterations I have ever been led to make. Even those have been due, not to the fault of the scientific method, but chiefly to my adherence to early teachings. But what has, more than that cause, prevented my publishing has been, first, that my desire to teach has not been so strong as my desire to learn, and secondly, that far from there having been any demand for papers by me, I have always found no little difficulty in getting what I wrote printed; and

when the favor was accorded, it was usually represented to me that funds were sacrificed in doing so. My first papers, which have since been pronounced good work, were sent to almost every logician in the world, accompanied in many cases with letters; but for ten years thereafter I never could learn that a single individual had looked into them. Since then, I have had little ardor about printing anything. Now, however, being upon the threshold of old age, I could not feel that I had done my best to do that which I was put into the world to do, if I did not spend all my available forces in putting upon record as many of my logical results as I could. Therefore, what I hereby solicit the aid of the Carnegie Institution to enable me to do is to draw up some three dozen memoirs, each complete in itself, yet the whole forming a unitary system of logic in all its parts, which memoirs shall present in a form quite convincing to a candid mind the results to which I have found that the scientific

method unequivocally leads, adding in each case, rational explanations of how opposing opinions have come about; the whole putting logic, as far as my studies of it have gone, upon the undeniable footing of a science. (The text of the letter is resumed, page 50.) I here insert an Appendix to this section of my letter. I give it that title to signify that I do not ask that members of the Executive Committee should read more of it than they may think it concerns them to read. It is a list of the proposed memoirs, their titles, and in most cases, brief indications of the nature of their contents. The brevity of the explanations precludes any hint of the scientific procedure, except where it is of such a nature that some notion of it can readily be conveyed in general terms. Fuller sketches can be furnished, if desired. No important changes in this scheme will be made. Lines of division between memoirs may be slightly shifted; and some of the introductory memoirs may be transposed.

List of Proposed Memoirs on Logic No. 1. On the Classification of the Theoretic Sciences of Research. This will be a natural classification, not of possible sciences, but of sciences as they exist today; not of sciences in the sense of "systematized knowledge," but of branches of endeavor to ascertain truth. I shall not undertake to prove that there is no other natural classification of the sciences than that which I give; and this, being merely an introductory memoir, cannot have the same convincing character as the others. Every unitary classification has a leading idea or purpose, and is a natural classification in so far as that same purpose is determinative in the production of the objects classified. The purpose of this classification is nearly the same as that of Comte, namely, so to arrange a catalogue of the sciences, as to exhibit the most important of

the relations of logical dependence among them. In fact, my classification is simply an attempt to improve upon that of Comte; first, by looking less at what has been the course of scientific history, and more at what it would have been if the theoretically best methods had been pursued; secondly, by supplying the shocking omissions which Comte's rage against nonsense led him to commit; and thirdly, by carrying down the subdivision as far as my knowledge enables me to do. It was necessary for me to determine what I should call one science. For this purpose I have united under one science studies such as the same man, in the present state of science, might very well pursue. I have been guided in determining this by noting how scientists associate themselves into societies, and what contributions are commonly admitted into one journal, being on my guard against the

survival of traditions from bygone states of science. A study to which men devote their lives, but not, in the present stage of development of science, so numerously as to justify exclusive societies and journals for it, I call a variety of science. That which forms the subject of the narrowest societies and journals, so that any student of any part of it ought to be pretty thoroughly informed about every part, I call a species of science. That branch, of which the student of any part is well qualified to take up any other part, except that he may not be sufficiently acquainted with the facts in detail, I call a genus of science. If the only new training necessary to pass from one part to another is a mere matter of skill, the general conceptions remaining the same, I call the department a family of science. If different sorts of conceptions are dealt with in the different families of a depart-

ment, but the general type of inquiry is the same, I call it an order of science. If the types of inquiry of the different orders of a department are different, yet these orders are connected together so that students feel that they are studying the same great subject, I call the department a class of science. If there are different classes, so that different students seem to live in different worlds, but yet there is one general animating motive, I call the department a branch of science. Of course, there will be sub-branches, sub-classes, etc., down to sub-varieties; and even sometimes sub-sub-divisions. To illustrate, I call Pure Science and Applied science different branches; I call Mathematics and the Special Sciences, different classes, I say that general physics, biology, and geology belong to different orders of science. Astronomy and geognosy are different families. Thermotics and electrics are different families. Optics and electrics

are now different genera. Entomology and Ichthyology are different species of one genus. The study of Kant and the study of Spinoza are different varieties 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 that seemed economically recommended, be but a sketch. It will have fully attained all I hope for, if it is respectable enough to merit serious 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 that their errors should be exposed, so long as they lead to further scientific study of the subjects to which they relate. The relation of this present memoir to those which follow it in the series is that it gives, from a general survey of science, an idea of the place of logic among the sciences. I will here set down the larger divisions of the scheme as well as I remember it (not having the notes in my possession). But it will be the discussion which will form the chief value of the memoir, not the

scheme itself. Nearly a hundred schemes given hitherto will be criticized. A. Theoretical Science. I. Science of Research. i. Mathematics. ii. Philosophy, or Cenoscopy. 1. Categorics. 2. Normative Science. a. Esthetics. b. Ethics. c. Logic. 3. Metaphysics. iii. Idioscopy, or Special Science. 1. Psychognosy. a. Nomological, or General Psychology. b. Classificatory. . Linguistics. . Critics. . Ethnology.

c. Descriptive. . Biography. . History. . Archeology. 2. Physiognosy. a. Nomological, or General Physics. . Dynamics. . Of Particles. . Of Aggregations. . Elaterics and Thermotics. . Optics and Electrics. b. Classificatory . Crystallography. . Chemistry. . Biology. c. Descriptive. . Astronomy.

. Geognosy. II. Science of Review, or Synthetic Philosophy (Humboldt's Cosmos; Comte's Phil. Positive<title>.) B. Practical Science, or the Arts. <emph ren=und>No. 2. On the Simplest Mathematics</emph>. This is that mathematics which distinguishes only two different values, and is of great importance for logic. <emph ren=und>No. 3. Analysis of the Conceptions of Mathematics</emph>. Such are Number, Multitude, Limit, Infinity, Infinitesimals, Continuity, Dimension, Imaginaries, Multiple Algebra, Measurement, etc. My former contributions, though very fragmentary, have attracted attention in Europe, although in respect to priority justice has not been done them. I bring the whole together into one system, defend the method of infinitesimals conclusively, and give many new truths established by a new and striking method. <emph ren=und>No. 4. Analysis of the Methods of Mathematical Demonstration</emph>. I shall be glad to place early in the series so unquestionable an illustration of the great value of minute analysis as this Memoir will afford. The subjects of Corollarial and Theorematic Reasoning, of the Method of Abstraction, of Substantive Possibility, </p> <p ISP=358 CSP=13 RO=358> and of the method of Topical Geometry, of which I have hitherto published mere hints, will here be fully elaborated. <emph ren=und>No. 5. On the Qualities of the Three Categories of Experience</emph>. An analysis and description of three irreducibly different kinds of elements found in experience and even in the abstract world of pure mathematics. This memoir rests upon Observation of the experience of every day and hour, this observation being systematized by thought. It is proved, beyond doubt, that there are no more than the three categories. The list was first published by me in May, <date>1867</date>; but has since been repeatedly subjected to the severest criticism I could bring to bear upon it, with the result of making it far more evidently correct. The categories were originally called Quality, Relation, and Representation. The question of names and other terminology for them still somewhat perplexes me. I am inclined to call them Flavor, Reaction, and Mediation. <emph ren=und>No. 6. On the Categories in their Reactional Aspects</emph>. </p> <p ISP=359 CSP=14 RO=359> <emph ren=und>No. 7. On the Categories in their Mediate Aspects</emph>. These two memoirs develope and render clear a considerable number of conceptions of which I shall make constant use in the remaining memoirs, and which are of constant use in all parts of philosophy and even in mathematics. <emph ren=und>No. 8. Examinations of Historical Lists of Categories</emph>. My list differs from those of <propname>Aristotle</propname>, <propname>Kant</propname>, and <propname>Hegel</propname>, in that they never really went back to examining the Phenomenon to see what was to be observed there; and I do not except <propname>Hegel</propname>'s <title>Phnomenologie from this criticism. They simply took current conceptions and arranged them. Mine has been a more fundamental and more laborious undertaking; since I have worked up from the percepts to the highest notions. I examine those systems as well as some others. No. 9. On the Bearing of Esthetics and Ethics upon Logic. I begin by explaining the nature of the normative sciences. They have often been mistaken for Practical

Sciences, or Arts. I show that they are at the opposite pole of the sphere of science, and are so closely allied to mathematics, that it would be a much smaller error to say that like Mathematics they were simply occupied in deducing the consequences of initial hypotheses. Their peculiar dualism, which appears in the distinctions of the Beautiful and the Ugly, Right and wrong, Truth and Falsity, and which is one cause of their being mistaken for Arts, is really due to their being on the border between mathematics and positive science; and to this, together with their great abstractness, is due their applicability to so many subjects, which also helps to cause their being taken for arts. Having analyzed the nature of the precise problems of the three, and given some considerations generally overlooked, I show that Ethics depends essentially upon Esthetics and Logic upon Ethics. The latter dependence I had shown less fully in 1869. (Journal of Speculative Philosophy, Vol. II, pp. 297 et seq.) But the methods of reasoning by which the truths of logic are established must be mathematical, such reasoning alone

being evident independently of any logical doctrine. No. 10. On the Presuppositions of Logic. I here show that much that is generally set down as presupposed in logic is neither needed nor warranted. The true presuppositions of logic are merely hopes; and as such, when we consider their consequences collectively, we cannot condemn scepticism as to how far they may be borne out by facts. But when we come down to specific cases, these hopes are so completely justified that the smallest conflict with them suffices to condemn the doctrine that involves that conflict. This is one of the places where logic comes in contact with ethics. I examine the matter of these hopes, showing that they are, among other things which I enumerate, that any given question is susceptible of a true answer, and that this answer is discoverable, that being and being represented are different, that there is a reality, and that the real world is governed by ideas. Doubt and everyday belief

are analyzed; and the difference between the latter and scientific acceptance is shown. Other doctrines are examined. No. 11. On the Logical Conception of Mind. This memoir is here placed, or perhaps better before No. 9, for the sake of perspicuity of exposition. The matter of it will have to be somewhat transformed at a later stage. If the logician is to talk of the operations of the mind at all, as it is desirable that he should do, though it is not scientifically indispensible, then he must mean by "mind" something quite different from the object of study of the psychologist; and this logical conception of mind is developed in this memoir and rendered clear.* (See footnote.) No. 12. On the Definition of Logic. Logic will here be defined as formal semiotic. A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place

Foot-Note * My order of arrangement of the first eleven memoirs is subject to reconsideration. The Categories are applicable to the logical analysis of Mathematics. It is even a question whether this fact does not derange my classification, although I have carefully considered it, and have provisionally concluded that it does not. It further seems to me better to let the Categories first emerge in the mathematical memoirs before explicitly considering them. This is a question of methodeutic, which is not so exact in its conclusions as is critical logic. I think the arrangement I here propose is favorable to the reception of the Categories. But if I were to decide to postpone the mathematical memoirs until after the categories, they might better be placed last among the first eleven memoirs. In that case, also, and indeed in any case, it might [be] well to place the memoir on the logical conception of mind before that upon Esthetics and Ethics. The present arrangement has been pretty carefully considered; and the last transposition is the only one that I think there is much likelihood of my deciding upon. After No. 12, the only changes possible in the list are shifts of boundaries in order to equalize the lengths of memoirs.

which a particle occupies, part by part, during a lapse of time. Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C. It is from this definition, together with a definition of "formal", that I deduce mathematically the principles of logic. I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non-psychological conception of logic has virtually been quite generally held, though not generally recognized. No. 13. On the Division of Logic. By an application of Categoric, I show that the primary division of logic should be into Stechiology, Critic, and Methodeutic. There is a cross-division into the doctrines of Terms, Propositions, and Arguments, to which three kinds of signs, however, stechiology, critic, and methodeutic,

are quite differently related. The various historical divisions of logic are considered. No. 14. On the Methods of Discovering and of Establishing the Truths of Logic. I shall here show that no less than thirteen different methods of establishing logical truth are in current use today and mostly without any principle of choice and in a deplorably uncritical manner. I shall show that the majority of these methods are quite inadmissible, and that of the remainder all but one should be restricted to one department of logic. The one universally valid method is that of mathematical demonstration; and this is the only one which is commonly avoided by logicians as fallacious. I shall show in the clearest manner that this notion is due to a confusion of thought, which I shall endeavor to trace through all its metamorphoses. I hope to give this its quietus. The methods of discovering logical truth can naturally

not be numerous when discovery is pretty nearly at a standstill. I explain my own method. No. 15. Of the Nature of Stechiologic. This will contain especially a discussion of Erkenntnisslehre, what it must be, if it is an indispensable preparatory doctrine to critical logic. No. 16. A General Outline of Stechiologic. No. 17. On Terms. This memoir will be based on my paper of November 1867. Practice has shown that that paper needs extension in several directions. Besides, account has to be taken of important classes of terms there barely mentioned. The historical part, too, needs great amplification. My very conception of what a term is has been much improved by studies subsequent to that paper, and altogether original. The study of "agglutinative" languages has been an aid to me.

No. 18. On Propositions. The question of the nature of the judgment is today more actively debated than any other. It is here that the German logicians are best worthy of attention; and I propose to take occasion to give here an account of modern German logic. Although this seems rather the subject for a book than for a single paper, yet I think, by stretching this memoir, I can bring into it all that it is necessary to say about these treatises, which belong to near a dozen distinct schools. I shall then show how my own theory follows from attention to the three categories; and shall pass to an elaborate analysis, classification, symbolization, and doctrine of the relations of propositions. This will probably be the longest of all the memoirs, and will balance No. 16, which will be short. I think I shall treat No. 16 as a supplement to No. 15 and divide No. 21 into two parts to be handed in separately.

No. 19. On Arguments. I first examine the essential nature of an argument, showing that it is a sign which separately signifies its interpretant. It will be scrutinized under all aspects. I shall then come to the important question of the classification of arguments. My paper of April, 1867, on this subject divides arguments into Deductions, Inductions, Abductions (my present name, which will be defended), and Mixed Arguments. I consider this to be the key of logic. In the following month, May, 1867, I correctly defined the three kinds of simple arguments in terms of the categories. But in my paper on Probable Inference in the Johns Hopkins Studies in Logic, owing to the excessive weight I at that time placed on formalistic considerations, I fell into the error of attaching a name, the synonym I then used for abduction, to a probable inference which I correctly described, forgetting that according to my own earlier and correct account of it, abduction is not of the number of probable inferences. It is singular that I should have done that, when in the very same

paper I mention the existence of the mode of inference which is true abduction. Thus, the only error that paper contains is the designation as Abduction of a mode of induction somewhat resembling abduction, which may properly be called abductive induction. It was this resemblance which deceived me, and subsequently led me into a further error contrary to my own previous correct statement. Namely, continuing to confound Abduction and Abductive Induction, in subsequent reflections upon the rationale of Abduction, I was led to see that this rationale was not that which I had in my Johns Hopkins paper given of Induction; and in a statement I published in the Monist, I was led to give the correct rationale of Abduction as applying to Abductive Induction and so, in fact, to all Induction. All the difficulties with which I labored are now completely disposed of by recognizing that Abductive Induction is quite a different thing from Abduction. It is a very instructive illustration both of the dangers and of

the strength of my heuretic method. Similar errors may remain in my system. I shall be very thankful to whomever can detect them. But if its errors are confined to that class, the general fabric of the doctrine is true. I at first saw that there must be three kinds of arguments severally related to the three categories; and I correctly described them. Subsequently, studying one of these kinds, I found that besides the typical form, there was another, distinguished from the typical form by being related to that category relation to which distinguishes abduction. I hastily identified it with abduction, not being clear-headed enough to see that, while related to that category, it is not related to it in the precise way in which one of the primary divisions of arguments ought to be, according to the theory of the categories. This is the form of error to which my method of discovery is peculiarly liable. One sees that a form has a relation to a certain category, and one

is unable, for the time being, to attain sufficient clearness of thought to make quite sure that the relation is of the precise nature required. If only one point were obscure, it would soon be cleared up; but the difficulty is at first that one is sailing in a dense fog, through an unknown sea, without a single landmark. I can only say that if others, after me, can find some way of making as important discoveries in logic as I have done while falling into less error, nobody will be more intensely delighted than I shall be. My gratitude to the man who will show me where I am wrong in logic will have no bounds. Thus far, I have had to find out for myself as well as I could. Meantime, be it observed that the kind of error which I have been considering can never amount to anything worse than a faulty classification. All that I asserted about probable inference in my Johns Hopkins paper and in my Monist paper was perfectly true.

In this paper, besides very important improvements in the subdivision of the three kinds of simple arguments, with several hitherto unrecognized types, and far greater clearness of exposition, I shall have much that is new to say about mixed arguments, which present many points of importance and of interest that have never been remarked. I shall give a new classification of them based, not upon the nature of their elements, but upon their modes of combination. Besides setting forth my own doctrine of the stechiology of argument, I shall examine the most important of those which are opposed to it. No. 20. Of Critical Logic, in general. A thorough discussion of the nature, division, and method of critical logic. No. 21. On First Premisses. My position on this subject comes under the general head of sensationalism; but I contend that criticism

There is a page 27 1/2is inapplicable to what is not subject to control. Consequently, not sensation nor even percepts, but only perceptual judgments. I subject what goes under the title of the test of inconceivability to an elaborate examination, bringing out various useful truths. I also examine the tests of universality and necessity, first adding certain other characters which as much prove apriority as do those. These tests have been taken in two senses, and there is a third more advantageous than either. No. 22. The Logic of Chance. I here discuss the origin and nature of probability, by my usual method; also the connection between objective probability and doubt; the nature of a "long run"; in what sense there can be any probability in the mathematical world; the application of probability to the theory of numbers. I show that it is not necessary that there should be any definite probability that a given generic event should have a given specific determination. It is easy to specify cases where there would be none. There appears to

be no definite probability of a witness's telling the truth. I also show that it is quite a mistake to suppose that, for the purposes of the doctrine of chances, it suffices to suppose that the events in question are subject to unknown laws. On the contrary, the calculus of probability has no sense at all unless it in the long run secures the person who trusts to it. Now this it will do only if there is no law, known or unknown, of a certain description. The person who is to trust to the calculus ought to assure himself of this, especially when events are assumed to be independent. The doctrine of chances is easily seen to be applicable in the course of science. Its applicability to insurance companies and the like is not in any case to be assumed off-hand. When it comes to the case of individual interests, there are grave difficulties. The rules of probability are stated in a new way, with the application of high numbers and method of least squares according to several different theories. Pearson's developments examined. Inverse probabilities are shown to be fallacious.

There are many matters here under dispute; more than I here set down. In all these cases, I take pains to state opposing arguments in all their force, and to refute them clearly. This memoir is intended to form a complete vade mecum of the doctrine of chances, and to be plentifully supplied with references. It will be somewhat long, but I hope not of double length. No. 23. On The Validity of Induction. This restates the substance of the Johns Hopkins paper, relegating formalistic matters to separate sections, taking account of types of induction with which I was not acquainted twenty years ago, and rendering the whole more luminous. Other views will be considered more at large. No. 24. On the Justification of Abduction. The categories furnish the definition of abduction, from which follows its mode of justification, and from this again its rules. The various maxims

which are found in different books are passed in review and, for the most part, are found to sin only in vagueness. One question not very commonly studied is what is the character of a phenomenon which makes it call for explanation. The theory of Dr. Carus that it is irregularity, and that of Mr. Venn that it is isolation, though the latter is defended with some power, are positively refuted. This refutation does not apply to the theory that the character sought is that of being surprising. This, however, is open to another kind of objection. The true doctrine is nearly thus, however. No. 25. Of Mixed Arguments. This is a highly important memoir upon a subject of singular difficulty, although at first blush one would not anticipate any difficulty or interest in it.

No. 26. On Fallacies. There would be no advantage in devoting a special memoir to a strictly scientific treatment of fallacies in general. It would be like a chapter in a treatise on trigonometry which should treat of possible errors in trigonometry. But since my purpose is that these memoirs should not only be scientific but that they should also be useful, I propose to devote this to Fallacies, because I think, though it is not an attractive subject for a logician, that I can make the discussion very useful. I shall not attempt a strict theoretical development, but shall discuss fallacies under five heads, according to their causes, showing under each head how they come about, how we can avoid them in original reasoning and in controversy, how to detect them and reply to others who fall into them. The five heads are: 1st, slips; 2nd, misunderstandings; 3rd, fallacies due to bad logical notions; 4th, fallacies due to moral causes; and 5th, sophisms invented to test logical rules, etc. This will thus be of an entirely exceptional character among the memoirs, more so even than the first.

No. 27. Of Methodeutic. The first business of this memoir is to show the precise nature of methodeutic; how it differs from critic; how, although it considers, not what is admissible, but what is advantageous, it is nevertheless a purely theoretical study, and not an art; how it is, from the most strictly theoretical point of view, an absolutely essential and distinct department of logical inquiry; and how upon the other hand, it is readily made useful to a researcher into any science, even mathematics itself. It strongly resembles the purely mathematical part of political economy, which is also a theoretical study of advantages. Of the different classes of arguments, abductions are the only ones in which after they have been admitted to be just, it still remains to inquire whether they are advantageous. But since the whole business of heuretic, so far as its theory goes, falls under methodeutic, there is no kind of argumentation that methodeutic can pass over without notice.

* An abduction is an argument from mere similarity. We meet with a surprising fact and seek a possible explanation of it, and having found one, we conclude that perhaps the hypothetical explanation is true. This is the only form of argument which introduces new matter. An induction, properly speaking, is an argument in which a proposition is tested by means of a prediction which is then tested by observation. It is either what may be called a genuine, or extensive, induction, which samples a collection, and reasons, in reference to a predicted or predesignate character, that the whole collection will possess that character in approximately the same measure as this sample; or it is an abductive, or comprehensive induction (which in my paper on probable inference of 1882 I confounded with an abduction) which tests a hypothesis by drawing sample consequences as predictions, finding how far they are verified, and concluding that the results measure the degree of truth of the hypothesis. It differs from abduction in not starting a new hypothesis and in making and testing predictions. Deduction is necessary inference. Abduction is iconic argument, Induction is indicative argument, deduction is symbolic argument. This, of course, will be accurately stated and fully explained in the memoir.

Nor is methodeutic confined to the consideration of arguments. On the contrary, its special subjects have always been understood to be the definition and division of terms. The formation of systems of propositions, although it has been neglected, should also evidently be included in methodeutic. In its method, methodeutic is less strict than critic. No. 28. On the Economics of Research. In all economics the laws are ideal formulae from which there are large deviations, even statistically. In the economics of research the "laws" are mere general tendencies to which exceptions are frequent. The laws being so indefinite, at best, there is little advantage in very accurate definitions of such terms as "amount of knowledge". It is, however, possible to attach a definite conception to one increment of knowledge being greater than another. To work this out will be the first business of the memoir. I also establish a definite meaning for the

amount of an increment in diffusion of knowledge. I then consider the relation of each of these to the expenditure of energy and value required to produce them in varying conditions of the advancement or diffusion of knowledge already attained. Comparing knowledge with a material commodity, we know that in the latter case a given small increment in the supply is very expensive, in most cases, when the supply is very small, that as the supply increases it sinks to a minimum, from which it increases to a very large but finite value of the supply where no further increment would be possible at any finite cost. Putting instead of supply, the amount of knowledge attained, we find that there is a "law," or general tendency, subject to similar large irregularities as in the case of the supply of a material commodity, but here even greater. The final increase of cost of an increment with the increase of attainment already achieved is marked, on

the whole, in almost all cases, while in many cases, at least, there is a point of attainment where the cost of an increment is at a minimum. The same general tendency appears in reference to the diffusion of knowledge; but there is this striking difference, that attainments in advance of sciences are very commonly actually on the upward slope where increments are costing more and more, while there are few branches of knowledge whose diffusion is already so great that a given increment of the diffusion will cost more and more, as the diffusion is increased. I shall next pass to a study of the variation of the utility (meaning, generally, the scientific utility) of given small increments of scientific knowledge and of the diffusion of knowledge in varying states of attainment. This is to be compared with the variation of the total amount that will be paid for a commodity for a fixed small increment of the

demand, or amount thrown upon the market to fetch what it will, with varying amounts of that demand. Here, the additional total amount that will be paid for the small increment of amount sold will correspond to the utility of the small fixed increase of scientific knowledge or of the diffusion of knowledge; while the demand being equal to the supply, this demand, or total amount that is sold, will correspond as before to the amount of attainment in scientific knowledge or in the diffusion of knowledge. For a material commodity we know that if it is given away people will only carry home a finite amount. One would have to pay them to carry away more. On the other hand, there is probably some maximum price for most things, above which none at all would be sold. It necessarily follows that beyond a certain amount thrown upon the market, a small increment in that amount would actually diminish the total

receipts from the sale of it, while for any smaller amount the increment of receipts for a given small increment of amount sent to market would be less and less. With regard to the scientific utility of a small fixed advance of knowledge, the "law" is certainly very different from that. In the first place, there is no degree of knowledge of which a small increase would be worse than useless, and while the general tendency is that the utility of such fixed increase becomes less and less, yet the curve is rather saw-shaped, since like Rayleigh's small addition to our knowledge of the density of nitrogen, now and then a small increment will be of great utility and will then immediately sink to its former level. The scientific advantage of the diffusion of knowledge is difficult to determine. It cannot be believed that any increment of diffusion is positively unfavorable to science. It is favorable in two ways; first, by preparing more men to be eminent researchers;

and secondly, by increasing general wealth, and therefore the money bestowed on science. I am inclined to think that the general tendency is that a given increment of diffusion is less and less advantageous to science the greater the attained diffusion. But I am not confident that this is so, at any rate without very important deflexions. The general effect, however, is nearly the same for the advancement as for the diffusion of knowledge. Namely, beginning with dense ignorance, the first increments cost more than they come to. That is, knowledge is increased but scientific energy is spent and not at once recovered. But we very soon reach a state of knowledge which is profitable to science, that is, not only is knowledge increased, but the facility of increasing knowledge gives us a return of more available means for research than we had before the necessary scientific energy was spent. This increases to a maximum, diminishes, and finally, there is no further gain. Yet still, in the case of energy expended upon research, if it is persisted in, a

fortunate discovery may result in a new means of research. I shall analyze as far as I can the relative advantages, for pure science exclusively, of expending energy (which is of such a kind as to be equally capable of being directed either way) to the direct advancement of knowledge and to the diffusion of knowledge. I find the latter so overwhelmingly more important (although all my personal sympathies are the other way) that it appears to me that, for the present, to give to research, in money, one or two per cent of what is spent upon education is enough. Research must contrive to do business at a profit; by which I mean that it must produce more effective scientific energy than it expends. No doubt it already does so. But it would do well to become conscious of its economical position and contrive ways of living upon it. Many years ago I published a little paper on the economy of research, in which I considered this problem. Somebody furnishes a fund to be expended upon research without re-

strictions. What sort of researches should it be expended upon? My answer, to which I still adhere, was this. Researches for which men have been trained, instruments procured, and a plant established, should be continued while those conditions subsist. But the new money should mainly go to opening up new fields, because new fields will probably be more profitable, and, at any rate, will be profitable longer. I shall remark in the course of the memoir that economical science is particularly profitable to science; and that of all the branches of economy, the economy of research is perhaps the most profitable; that logical methodeutic and logic in general are specially valuable for science, costing little beyond the energies of the researcher, and helping the economy of every other science. It was in the middle of the 13th century that a man distinguished enough to become pope opened his work on logic with the words, "Dialectica est ars artium et scientia scientiarum, ad

omnium methodorum principia viam habens." This memorable sentence, whose gothic ornamentation proves upon scrutiny to involve no meaningless expression nor redundant clause, began a work wherein the idea of this sentence was executed satisfactorily enough for the dominant science of the middle ages. Jevons adopted the sentence as the motto of his most scientific contribution to logic; and it would express the purpose of my memoirs, which is, upon the ground well prepared by Jevons and his teacher DeMorgan, and by the other great English researchers, especially Boole, Whewell, Berkeley, Glanvill, Ockham, and Duns Scotus, to lay a solid foundation upon which may be erected a new logic fit for the life of twentieth century science.

No. 29. On the Course of Research. Comparing the two wings of the special sciences, i.e., Psychognosy and Physiognosy, and taking the history of their development as a basis, but correcting the history, as well as we can, in order to make it conform to what good logic and good economy would have made it, we get the idea of rational courses of development which these branches might have followed. Between these two there is a striking parallel; so that we can formulate a general rational course of inquiry. Now passing to the study of the history of special sciences, also modified by the same process, we find some traces of the same law; or to express it more clearly, it is as if in the special science showed us one part of the general scheme under a microscope. By successively examining all the sciences in this way (or all I am sufficiently

able to comprehend), we can fill in details, and make the general formula more definite. We find here a succession of conceptions which we can generalize in some measure, but which we find it difficult to generalize very much without losing their peculiar "flavors." These I call the Categories of the course of research. They have not the fundamental character of the Categories of Appearance; but appear, nevertheless, to be of importance. No. 30. On Systems of Doctrine. Singularly enough, it seems to have been left to me to make a first attempt to formulate in detail what a system of doctrine ought to be. I follow the same general heuretic method as in the memoir, No. 29, taking some of the most perfect systems extant, and imagining how they might be more rational.

In this way I work out a series of conceptions which I term the Categories of Systems. No. 31. On Classification. I study classification, after some general considerations, by actually drawing up a number of classifications of the only sort of objects which we can sufficiently comprehend; that is to say, different classes of objects of human creation; such as, contrivances for keeping the skin warm, languages, words, alphabets, sciences, etc. From these I endeavor to elicit a general series of Categories of Classification. No. 32. On Definition and the Clearness of Ideas. In January, 1878, I published a brief sketch of this subject wherein I enunciated a certain maxim of `Pragmatism,' which has of late attracted some

attention, as indeed, it had when it appeared in the Journal Philosophique. I still adhere to that doctrine; but it needs more accurate definition in order to meet certain objections and to avoid certain misapplication. Moreover, my paper of 1878 was imperfect in tacitly leaving it to appear that the maxim of pragmatism led to the last stage of clearness. I wish now to show that this is not the case and to find a series of Categories of clearness. No. 33. On Objective Logic. The term "objective logic" is Hegel's; but since I reject Absolute Idealism as false "objective logic" necessarily means more for me than it did for him. Let me explain. In saying that to be and to be represented were the same, Hegel ignored the category of reaction (that is, he imagined he reduced it to a mode of being

represented), thus failing to do justice to being, and at the same time he was obliged to strain the nature of thought, and fail in justice to that side also. Having thus distorted both sides of the truth, it was a small thing for him to say that Begriffe were concrete and had their part in the activity of the world; since that activity, for him, was merely represented activity. But when I, with my scientific appreciation of objectivity and of the brute nature of reaction, maintain, nevertheless, that ideas really influence the physical world, and in doing so carry their logic with them, I give to objective logic a waking like which was absent from Hegel's dream-land. I undertake in this memoir to show that so far from its being a metaphorical expression to say that Truth and Right are the greatest powers in this world, its meaning is just as literal as it is to say that when I open the

window in my study, I am really exercising an agency. For the mode of causation in the one case and in the other is precisely the same. In fact, there are two modes of causation corresponding to Aristotle's efficient and final causation, which I analyze and make clear, showing that both must concur to produce any effect whatever. The mind is nothing but an organism of ideas; and to say that I can open my window is to say than an idea can be an agent in the production of a physical effect. This naturally looks toward a special metaphysics of the soul; but I pass this by, as not germane to my present subject, and go on to examine the logic of ideas in their physical agency. Herein I find the key to the different series of categories which the studies of memoirs Nos. 29, 30, 31, 32 developed. The remaining three memoirs are of the nature

of elucidations of sound methodeutic by applying it in practice to the solution of certain questions, which, although they do not belong to logic, are of special interest in the discussion of logic. No. 34. On the Uniformity of Nature. The vagueness of the language with which men commonly talk of the uniformity of nature at once masks the diversity of a number of distinct questions which are wrapped up together in that phrase, and at the same time masks the great diversity of opinions that are very commonly held upon these questions. I have discussed these different questions in half a dozen different papers; but there is none of them whose statement of my argumentation cannot be much amplified and improved, and to which new historical matter cannot bring considerable light. More-

over, I wish to bring all the different questions to one focus, and consider them together. This, I am sure, will cause thinkers to be more favorable to the views which I have at different times defended. Among the questions is that of nominalism and realism, in connection with which I shall show that all modern philosophy, by an accident of history, has been blind to considerations of the greatest evidence and moment. No. 35. On Metaphysics. The great distinction between Aristotelian philosophy and all modern philosophy is that the former recognized a germinal mode of being inferior to existence, which hardly Schelling does; certainly no other modern philosopher. This question is considered in the light of the methodeutic developed in previous memoirs. The result is applied to all the questions of

high metaphysics. No. 36. On the Reality and Nature of Time and Space. This applies my methodeutic to the discussion of a question which will have repeatedly emerged during the course of the memoirs. I may say briefly that I defend the well-known opinion of Newton. But other questions are considered. I do not think any theory satisfactory which does not offer some explanation (a mathematically exact and evident one) of why space should have three dimensions.

Estimate of the Utility of the Work To my apprehension, any man over sixty years of age, who is endowed with reason, is a better judge of his own powers and of the utility of his performances than other people can be expected to be. Particularly is this true when the man has accumulated a large fund of unpublished results. Yet as soon as such a man assumes the attitude of seeking recognition for the utility of his work, suspicions as to the candor of his appreciations may be suggested by those who, for any reason, are unfavorable to the action he desires. For that reason, I shall confine myself to asserting in a general way my profound conviction of the utility of publishing my results, as likely to influence some sciences, but still more as themselves stimulating a most important branch of science, that of logic, which is at present in a bad way. The latter kind of utility is

not much diminished if I have fallen into some errors. Beyond averring that conviction, I do not offer myself as a witness to the utility of the work. I should, indeed, not have gone so far as I have done, were I not persuaded that the Executive Committee ought to require, as one of the first conditions of extending aid to any work, that the person who was to do it should be saturated with faith in its utility and value. I will indicate certain lines of thought which, if pursued by the Executive Committee, may determine an opinion in regard to the utility of the work I propose. These lines of thought are two. The one bears upon the value of my researches considered as contributions to pure science; the other relates to their probable influence, direct or indirect, upon the progress of other sciences. I will first venture upon a few suggestions along the latter line. What would be the degree of utility of a really good and

sound methodeutic, supposing that it existed, for the other sciences? I am not of opinion that a science of logic is altogether indispensable to any other science, because every man has his instinctive logica utenens, which he gradually corrects under the influence of experience. Indeed, instinct, within its proper domain, is generally less liable to err and is capable of greater subtlety than is any human theory. Perhaps it may sound like a contradiction to talk of "instinctive logic." It may possibly be thought that instinct is precisely that which is not logic or reason. But think of a man whose business it is to lend out money. The accuracy of his cool reason is what he relies upon; and yet he is not guided by a theory of reasoning, but much rather upon an intense love of money which stimulates his faculties of reasoning. That is what I call his logica utens. There are many fields in which few will maintain that any theoretical way of reaching conclusions

can ever be so sure as the natural instinctive reasoning of an experienced man. Yet let instinct tread beyond its proper borders but by ever so little, and it becomes the most helpless thing in the world, a veritable fish out of water. Sciences do often go wrong: that cannot be denied. Their history contains many a record of wasted time and energy that a good methodeutic might have spared. Think of the Hegelian generation in Germany! Is reasoning the sole business whose method ought not to be scientifically and minutely analyzed? To me, it is strange to see a man like Poincar (whom I mention only as a most marked case among many) who, in his own science, would hold it downright madness to trust to anything but the minutest and most thorough study, nevertheless discussing questions of the logic of science in a style of thought that seems to imply a deliberate disapproval of minute analysis in that field, and a trust to a sort

of "On to Richmond" cry,--I mean a cry that those who have not closely studied are better judges than those who have. Many will say that all that may be true, but that, as a matter of fact, we are already in possession of a scientific system of logic, that of Mill. Now it is displeasing to me to be forced to decry Mill's Logic; because, looking at it in certain very broad outlines, I approve of it. The book has unquestionably done much good, especially in Germany, which needed it most. But I must declare that quite no deep student of logic entertains a very high respect for it. If, however, that book, though written by a literary and not a scientific man, by a mere advocate of a shallow metaphysics, has had so beneficial an influence as unquestionably it has, would it not seem to be desirable that the same subject should be pursued, I do not say by me, but by scientific students of it? Surely, enough has been done to make it manifest that there is such a thing as strictly

scientific logic. For instance, the doctrine of chances is nothing else. The doctrine of chances has been called the logic of the exact sciences; and as far as it goes, so precisely it is. Its immense service to science will not be disputed by any astronomer, by any geodesist, nor probably by any physicist. Pearson and Galton have shown how useful it many be in biological and psychognostic researches. The utility of truly scientific logic, then, is indisputable. But that general logic is today in a bad way would seem to be sufficiently shown by the fact that it is pursued by thirteen different methods, and mostly by a confused jumble of those methods, of which I, a very fallible person of course but still a scientific man who has carefully weighed them, pronounce but one,--and that one in bad odor,--to be alone of general validity. Is it, then, not desirable that an interest in pursuing logical inquiries in a true scientific spirit and by acknowledged scientific methods should be aroused? If it be so, is not the

publication of my researches, even if they contain some errors, as likely to stimulate such studies as anything that could be suggested? Slight and fragmentary as my publications have been, dealing with the less important of my results, have they not in some appreciable degree stimulated the production of such work? I point to the third volume of Schrder's Logik. Look at it, or ask him, and I think you will say that I have exercised some stimulating agency. Everybody admires (nobody more than I) the beautiful presentation by Dedekind of the logic of number; and Dedekind, by the way, pronounces all pure mathematics to be a branch of logic. Read his Was sind und was sollen die Zahlen, and then read my paper on the Logic of Number, published six years earlier, and sent to Dedekind, and ask yourselves whether there is anything in the former of which there is not a plain indication in the latter. Let me not be misunderstood. I am simply arguing that my papers have stimulated the science of logic. I wish with all my heart that

the Executive Committee could have in view some other student of logic of vastly greater powers than mine. But even if they had, considering how much energy has been spent in obtaining my results, would it not be a pity not to have them presented to the world? It is my belief that science is approaching a critical point in which the influence of a truly scientific logic will be exceptionally desirable. Science, as the outlook seems to me, is coming to something not unlike the age of puberty. Its old and purely materialistic conceptions will no longer suffice; while yet the great danger involved in the admission of any others, ineluctable as such admission is, is manifest enough. The influence of the conceptions of methodeutic will at that moment be decisive. Vast, however, as the utility of logic will be in that direction, provided that logic shall at the critical

moment have developed into that true science which it is surely destined some day to become, yet the pure theoretical value of it is greater yet. No doubt, it is possible, while acknowledging, as one must, that logic produces useful truths, to take the ground that it is a composite of odds and ends, a crazy-quilt of shreds and patches, of no scientific value in itself. But seeing that pure mathematics is so close to logic, that eminent mathematicians class it as a branch of logic, it is hard to see how one can deny pure scientific worth to logic and yet accord such worth to pure mathematics. Probably there are naturalists of culture so narrow that they would deny absolute scientific value to pure mathematics. I do not believe the Committee will embrace such views. And then, there in Metaphysics to be considered. Everybody must have his Weltanschauung. It certainly influences science in no small measure. But metaphysics depends on logic, not merely as any science may occa-

sionally need to appeal to a logical doctrine, but, according to the greatest metaphysicians, the very conceptions of metaphysics are borrowed from the analyses of logic. Now if there is any such thing as pure scientific value, as distinguished from the admiration one might have for a newly discovered dye, in what can it consist if not in intellectual relations between truths? If so it be, then, in view of the relation of logic to metaphysics, and that of metaphysics to all science, how can it be said that logic is devoid of scientific value, if there be any such thing as scientific value? If logic is the science which my memoirs go to show that it is, it is the very keystone in the arch of scientific truth. Little known as my papers have been, I believe that there are some men, whose judgments must command respect in the world of science, who will testify to the utility of the work that I have done, and to the probable

utility of that which I am about to do. Estimate of the Labor required for the Work My results in each of the three dozen topics have to be carefully revised, though for the most part that has often been done already, have to be set into logical order, and have to be presented in the fully convincing forms which they merit. It is also most desirable that the presentation of each should be as brief and as closely confined to what is pertinent as is consistent with completeness and with perspicuity. A certain amount of labor must be bestowed upon their literary polish; for my purpose requires that they should be read by persons who are not professional logicians. Indeed, for persons who are disposed to think, I believe that as far as in me lies I should make them even attractive; although I am painfully conscious of my small literary ability.

Taking all these things into consideration, my experience of what I can do suffices to enable me to say that six memoirs a year is all I ought to promise, although I should confidently hope to finish the three dozen in five years. I should be loath to inflict as many as a million words upon a student: it would so narrow my field of influence. I am sure that my results could not be presented as they merit, in all their convincingness in half a million. The majority of the memoirs could be compressed into about 20,000 words each; but only by laborious and clever condensation. A very few which might be much shorter are overbalanced by quite as many or more that must inevitably mount to 50,000 words each, dividing themselves advantageously into two parts. To bring the total within the million, seeing that they so increase in matter as the series advances that every one of the last quarter of the series is excessively dense in matter, is going to be a task calling for all my vigor but most needful.

Persons whose business it is to write, and who are not troubled with having too much to say, may argue that 200,000 words a year is only 700 words a day for six days in every week, and that such a limit can only be set by indolence. To this I can only reply that it would be much easier to make the memoirs three times as long as I propose. At that rate they would be better, taken singly. But the whole would be too much. If anybody suspects me of indolence, I shall only have to turn in all the papers; and it will be seen that I have in each case written from three to five times as much as I include in the final copy. Estimate of Other Expenses involved These other expenses are mainly books, although the person who examines and reports upon the memoirs should be remunerated for his labor. Historical statements and critical examinations form an

essential part of the plan. Books must be hand. My entire library contains only about 2000 books. I shall require 500 more, costing say $2000. Need of the Aid asked for I am bound to confess that should the Carnegie Institution refuse all cooperation, I should continue to be animated by a robust faith that somehow my results would be given to the world; and I am fully satisfied that that faith is logically justified. It might prove mistaken; and if it did, my concern would be limited to knowing that I had performed my part. But while I fully believe that I shall succeed in any case, I have no definite idea of how I could do so in default of the aid which I ask from the Carnegie Institution; and in that sense I can truly say that such aid seems to be indispensible. I believe the Executive Committee will help me.

Suggested Plan for the requisite Aid I should suggest that each memoir, as finished, should be sent by me, in MS. or type written, to the office of the Carnegie Institution and should be at once placed in the hands of a man of my own rank as a thinker, or higher, whose duty it should be, not to go into any criticism of it but to look it over,--say in an hour or two,--and report upon whether or not it seems to be such a solid piece of work as is worthy of acceptance. Upon his favorable report, say within a week, the Carnegie Institution should cause a sum of money to be remitted to me and should become the owner of the copyright in the memoir sent in. I should suggest that if the length of the memoir was from 15000 to 30000 words it should count as a unit; if more as two units, and that the remittance should be so much per unit. This is a mere suggestion as, indeed, is the whole plan.

The Committee might see fit to put a limit upon the number of units that would be receivable in one year. I do not think that under any circumstances it could exceed nine, and that number could only be reached some year owing to special circumstances. The memoirs should be handed in in their regular serial order. Since the books needed would be needed at the outset, if the Carnegie Institution would supply me with 500 books of my choice to be kept for a term of years, I would agree that my whole library should go at my death to the free school of logic I desire to found or to any other party whom the Carnegie Institution might designate. If this plan is not agreeable, I should ask in some form to receive extra help the first year. By making selections of subjects, I could write nine memoirs in the first year; but it would be a bad plan. The memoirs ought to be written in their order of consecution.

Probability of the Completion of the Work Each memoir is complete in itself. The science of logic will be completed not earlier than the sciences of biology and of history are complete. But it is eminently desirable that the series of three dozen memoirs should be completed. Having all my life long sacrificed every interest to logic, it might seem that I was insulting the executive committee if I were to suppose that their knowledge of human nature was such that they could doubt my finishing this series if death, total incapacity, or the necessities of daily life did not intervene. It has been represented to me, however, by persons of the highest credit, that the Committee would insist on some assurance that the whole would be finished. Without permitting myself either to believe or to disbelieve this, I think I am justified in offering such assurance as lies in my power, in case the Committee should

require something of the sort. I am in excellent health and capital trim for this work. I do not think there will be much danger of my breaking down in five years. However, if the Committee thinks there is, I would suggest that in the first six months, instead of writing the first three memoirs, I write, in six equal monthly parts, each of not less than 15,000 words, abstracts of the memoirs, six memoirs in regular order being treated in each part. Then in case the work of writing the memoirs (which under this arrangement would only begin at the end of six months), were broken off, otherwise than by the action of the Carnegie Institution, the copyright of this abstract should pass to the institution; but the Carnegie Institution during those first six months should contribute liberally to aid the production of these abstracts. I say "liberally," because books

There is a page 68 1/2would have to be procured. If, on the other hand, the series of memoirs were completed, then, but not before, I should be at liberty to do what I pleased with the abstracts. What I should please to attempt would be to make out of them a logic for the people, a charming classic for the twentieth century, thus, as a secondary object, sparing my old age the mortifications of extreme poverty, although I am not capable of making such an object a leading one.* *In this I am not peculiar. For my observation is that the men are rare who are able to pursue steadily a purely egoistic purpose; a fact of psychology which those who are capable of it, are apt to overlook. If the memoirs were, say, half of them published, then this abstract (which I should have been continually polishing) could be used to complete the publication. But a better plan, I think, would be to devote the first three months to writing abstracts of the last nine memoirs, omitting altogether the historical and critical parts. This would be a very great loss; because, though the plan might result in a tolerably complete presentation of the main argument, its convincingness would be unfelt by the mass of readers. Still, it would leave the matter in such shape that a writer of ability coming after me

would be able to rewrite this part of the series, the most practically useful part, so as to bring out the whole force of the argument. But I should always object to the publication of any such abstracts as long as there was any hope of my producing the full memoirs. As an additional or alternative security, I should suggest, supposing that other security were desired by the Executive Committee, that a contract be executed between the Carnegie Institution and me by which I should be bound to send in the memoirs with no interval between any successive two exceeding three months, unless some visitation of providence (say, a five month's illness, a conflagration, or a domestic calamity) should intervene, and even then not exceeding five months. Otherwise, I failing in this, should be bound to repay to the Carnegie Institution all money up to that time paid to me, while losing the

copyrights of the printed memoirs. I would yearly furnish bonds that such money should be refunded, if failure should occur within one year. I should secure my bondsman by putting into his hands first draughts of the memoirs for the ensuing year, which though they would not be satisfactory to me, would, nevertheless, la rigueur conform to the agreement. Of course, this would be but partial security. I beg to say, lest the Executive Committee should deem this proposition ridiculous, that I express no opinion about it. I stand ready to carry it out, if desired. I am most anxious to meet what highly credible people believe to be the wish of members of the Committee; and no better plan occurs to me. Of course, in case any contract were made, the Carnegie Institution would by its terms become bound to persist in the arrangement to the end, and to publish

each memoir within, say, one year of the date of its approval. I have a reputation of not finishing things. I suppose there is some basis of truth beneath it. But it has been, like every evil reputation, exaggerated out of all semblance of truth by calumny. It should be remembered that I was connected for a long time with the Coast Survey; and it will be easy for members of the Committee to ascertain that that office has been, at times, a veritable hotbed of intrigue, and that I, in particular, have sometimes suffered great injustice there. Voluminous memoirs were prepared by me for publication which I never could get printed; and then I was accused, vaguely and in intangible forms, of not getting my work ready for publication. For the truth of this (except that the accusations were made)

I stand responsible. I have often made this statement. If it is not true, why am I not called upon to go ahead with the printing? Excepting in the case of one early paper on the logic of mathematics, which I concluded I did not know enough about to continue, I have never had a disinclination to go on with any series of publications which I had begun. On the contrary, the disinclination has always been on the side of those who were to pay for the printing. When such disinclination was manifested, of course I ceased to press the matter. Probable Net Cost Mill's Logic went through nine editions before the copyright expired. I should not expect anything like that. But still, the utility of these

memoirs will require me to make them as agreeable reading and as little tedious as their scientific character will allow. Great pains will be bestowed upon this; and it will be perfectly proper that they be handed over to a publisher and sold like any books. In time there will be some sale for them. It would certainly make up in considerable part for the remittances made to me. For five or six years' support of me and my wife, the Carnegie Institution would receive the fruit of over forty years' meditation and labor. For the price of 500 books, it would, after a term of years, have 2500 books to dispose of. I think its objects would profit by the transaction.

Basis of my Claim A man has put nearly fifty years of single-minded endeavor into a work of benefit to science. He has a sort of claim,-- vague only in being addressed to no particular party,--that he should be rewarded for what he has done. But the only reward which would be a reward would be that of being enabled to complete his life-work. At this juncture one of the most extraordinary figures of all humanity puts down an enormous sum of money and expresses the wish that it be used, as the second of six emphasized aims, "to discover the exceptional man in every department of study whenever and wherever found, inside or outside of schools, and enable him to make the work for which he seems specially designed his life work."

Composed as your body is, reason alone will determine your decision. Logic is a "department of study." Whether or not, in this narrow field, I am an "exceptional man,"--and to be such is anything but a good fortune, in such a direction nothing but a burden,--you will determine; looking probably into the third volume of Schroeder's Logik where my work is mentioned in some two hundred places. On page 1, I am called the "Hauptfrderer" of "eine grossartige Disziplin," the "Logik der Beziehungen." Although my explanations attached to the above list of proposed memoirs are of such a nature as to preclude their showing how greatly the logic of relatives really determines all my conclusions upon every topic of logic, nevertheless the impression which a reading of those explanations would create, that the subject of relations does not constitute any overwhelming part of the subjects of my researches, is quite correct. Should it

seem to you to be true that the duties of an "exceptional man" in the department of logic have to be borne by me, then it will become one of your duties to aid me in the performance of mine to make the work for which this man "seems specially designed his life work." I am frank to say that the idea that phrase embodies has long impressed me; namely, that men seem to be specially designed for various kinds of work, and that, if it be so, the work for which I seem to have been designed is that of working out the truths of logic. If you should be led to this opinion, then my claim to the reward for the life I have so far put into this work, the reward of being enabled to complete it, in the sense in which it is susceptible of completion, is no longer so vague; but I shall then find in you a definite party upon whom I have that claim; since in satisfying it, you will only be carrying out one of

the responsibilities which you have accepted. Whatever action you may take, it is my duty to believe, and I do believe, that the work will get done. At any rate, all that I feel much concern about is that I should do my very utmost to carry out my part effectively. I have no disposition to even ask myself what specifically your duty is, of which you are the sole judges, except so far as we shall all have to render account hereafter. Submitting, then, my application to your kindly wisdom, I remain, Gentlemen, With profound respect, etc., etc., C. S. Peirce

Milford, Pa., 1902 July 15 To the Executive Committee of the Carnegie Institution Gentlemen: I have the honor to submit to you herein an application for aid from the Carnegie Institution in accomplishing certain scientific work. The contents of this letter are as follows: 1. Explanation of what the proposed work is 2. Estimate of its utility 3. Estimate of thelabor it will require 4. Estimate of Other Expenses involved 5. Statement of the Need of aid from the Carnegie Institution 6. Suggestion of a Plan by which the requisite aid might be extended 7. Estimate of the Probability of Completion of the work 8. Estimate of the Probable net Cost to the Carnegie Institution 9. Statement of the Ground of my claim for aid

method unequivocally leads, adding in each case rational explanations of how it is that those who have opined differently have been let into error, the whole putting logic, so far as my studies of it have gone, upon the undeniable footing of a science. I proceed to give a list of the titles of the proposed memoirs, attaching brief explanations to most of them. These explanations can only give some approximate, general ideas of the contents of the different memoirs; since their brevity will commonly exclude any hint of the scientific procedure. Should the committee desire further information a further sketch of everyh memoir could be furnished. In some cases I may ultimately decide to draw the dividing lines between memoirs diferently, for some few under the present enumeration would be too short; while several ought to be divided into two each, and there are even one or two whose serial positions may be changed. [The following pages, to p. 49 inclusive, are of the nature of an appendix, to be examined so far as deemed necessary by the members of the committee.]

logical dependence among them

these journals and associations being affected by traditions which ought, in the present state of ideas, to be obsolete. A study to which a man may very well devote his life, but to which not enough men now do devote their lives to justify societies and journals devoted exclusively to it, I term a variety of science. A study to which societies and journals are, or very well might be, exclusively devoted, I call a species of science. Thus, I call the study of Kant, or Spinoza, or cephalopods, of differential equations, of the aromatic bodies, varieties of science. Entomology, Bacteriology, Folk-lore, Numismatics, Physical Chemistry, are species. But I cannot allow too much weight to such considerations; since,

the survival of old traditions. A study to which men do, or may very well, devote their lives, but to which in the present state of development would not justify special journals and societies, in my judgment (often, no doubt, mistaken; but the whole must be revised by specialists,) I set down as a variety of science. That which will form the subject of the narrowest societies and journals, I call a species of science. That branch, the student of one part of which is perfectly qualified to pursue any other, except for want or acquaintance with facts, will be a genus. If the only new training necessary for the man who wishes to pass from one part to another is mere skill in doing something, but not any new kind of thinking, I call that a family of science. If different intellectual operations are called for in different

is inapplicable to what is not subject to control. Consequently, not sensation, nor even the percepts, but perceptual judgments are the first premisses. I subject the test of inconceivability to an elaborate examination, in which many points are made pertinent to various doctrines. Finally, I show that a person may remain for a long time unable to doubt a proposition not a perceptual judgment; and as long as he cannot doubt it, his belief is not open to criticism. But in most cases an indisposition to doubt, due to breeding, is reinforced by certain real arguments.

No. 26. On Fallacies. Few logicians of theoretical strength have manifested any taste for the general doctrine of fallacies. It is no part of pure logic, but is an application of logic in attacking which one comes into direct competition with Aristotle in one of the directions in which he was the most incomparable. Most of the best modern treatises altogether ignore this subject. Mill attempted to say something fresh about it with little success. But though disagreeable, the topic is a useful one to treat, and I feel it my duty not to shirk it, but to treat it, not from a strict logical point of view but in a human, mundane manner, as well as my poor talent in that direction will. In that quite non-logical way, it seems to me useful to divide fallacies into five classes, according to their causes. Class I consists of fallacies due to mere slips, such errors as one may commit in footing up a long column of figures. It is useful to point out, first, in what sort of ope-

rations [they] are most likely to occur, and secondly, what can best be done to avoid them. Every slip by which one inadvertently substitutes one thing for another is essentially of the same kind as a slip in logic, even if it be not strictly such. There is no use in drawing any sharp boundary. We may as well consider putting salt in one's coffee and sugar on one's potatoes as fallacies of this description. All such inadvertencies are confined to intellectual operations of such extreme simplicity as to be almost relegated to the government of physiological habit, but yet not quite so. In algebraical calculations errors in regard to + and - are more frequent than all others put together. This is because the reversal of a sign is so simple a matter that one performs it mentally without setting down anything; and thus one is tempted to perform half-a-dozen such reversals before setting down a result. But to do this one has to carry five signs of one kind and six of the other in

one's head, with great risk of confusion. One may even acquire a habit of making a particular kind of error. It is found that a computer in going over his own work is more liable to repeat the same errors than to commit others. I have an annoying habit of writing perhaps in one case out of every fifty the word `than' in place of `that'. Perhaps this may be due to my often thinking in French and writing in English. We may also commit slips owing to our heedlessly extending a habit from its proper occasions to others that have some resemblance to them, as in the sugar-salt inadvertency. When we find we have a habit of committing a particular kind of slip, so that we do so in a certain proportion of cases, we shall carefully form a contrary habit, a business which will often involve no small expenditure of energy. It is bad economy to employ the brain in doing what can be accomplished mechanically, just as it would have been bad economy for Napolon

to write his own dispatches. But where it must be done, it will be best to work out each result in two different ways. Class II consists of misunderstandings, particularly the petitio principii and ignoratio elenchi. We have to consider, first, how to avoid these ourselves, and second, how to treat them when made by opponents. If a man follows the directions of my methodeutic, a petitio principii, in his original reasoning, will be impossible. But in attempting to refute the reasoning of others, one has to take pains to understand just how they have reached their opinions. The common mistake is that one thinks of a line of thought by which an opponent might have reached his opinion, and then hastily assumes that it is that process that he has followed, when in reality it may be a different and far more profound course of reasoning that he has pursued. Many men tire one to death with

their continual misapprehensions of this sort. Some writers take so much pains to write an easy, agreeable style that they lead, not only superficial persons, but even men of immense mental power, to suppose that their thought is equally of an easy, obvious kind, when in reality it may be quite the reverse. It is certainly the very worst style that one can use in philosophical discussions. Hume and J. S. Mill are great sinners in this resect. Thus, Prof. Langley, though I need not say how good a thinker he is, seems to have the idea that the kernel of Hume's opinion about miracles is that a miracle is a violation of a law of nature, though that remark was merely a concession by Hume to a mode of definition in vogue at his time, and his real argument is only strengthened if this be denied; and Kant, whose first business it was to understand Hume, equally mistakes his position about causality. Of course, the very thing which

makes these writers atrociously hard reading for careful readers, causes them to be applauded for their perspicuity by those who skim their pages. On the other hand, the writers who are really the easiest to read, if by reading we mean getting at their thought, are popularly considered dreadfully abstruse. Such, in the first line, are the mathematicians; and next Ricardo, Duns Scotus, Kant, etc. In order to understand a book, it is necessary to learn the whole history of the author's thought. A good "reading-book", in the sense of a book to exercise one's power of penetrating an author's real thought, is the first book of Euclid's Elements. To be sure, it is a very badly written book, an enigmatical book. That was Greek taste. A student has not really read it until he can answer these questions, and many others: Why, in the definition of a circle, does Euclid introduce the clause tn entos tou schmatos keimenon? Why does Euclid make it a postulate rather than

an axiom that all right angles are equal, and an axiom rather than a postulate that ? Why did he attain his purpose in this particular way? How could he assert such a monstrous proposition as that to holon tou merous meizon, when he well knew that a line unlimited at one end became no shorter by having a piece cut off from it? Why did he give the fifth postulate its extraordinary form? Why does he ignore projective and topical geometry? When a student has once read the first book of the Elements, he will have an idea of how philosophy has to be read. Coming to the consideration of cases in which one is disposed to accuse an opponent of committing a petitio principii or an ignoratio elenchi, one must not forget that such a plea involves the admission that the argument objected to logically deduces its conclusion from its premisses. Hence, those who say that a syllogism is a petitio principii

themselves, at best, commit an ignoratio elenchi; for their plea admits that the conclusion of a syllogism follows from its premisses; and this is all that the logics affirm. This remark applies more forcibly to the petitio principii than it dos to the ignoratio elenchi. For if you accuse an opponent of making an assumption which he had no right to make, you have not only to show that he had no right to make the assumption, but you have further to show that this was not a mere side remark, but that it is essential to his argument. Now if the argument is logically bad, one cannot say that anything is essential to it as a good argument. In the case of the ignoratio elenchi, you have to show that what he proves does not really conflict with what you maintain. Then your duty is not to quibble about the possibly inaccurate way in which he may have expressed his conclusion, but must examine what it really is that his argument does prove. If it

does not prove anything at all, you may still say `If this proves anything it is nothing that I have denied,' and may loosely call it an ignoratio elenchi with no particular inconvenience, although a true ignoratio elenchi does prove something. Class III consists of fallacies shaving their origin in a loose logica utens or in a faulty logica docens. This is a large class of very common fallacies, perhaps the commonest of all. A large part of the memoir must be devoted to them. One common fallacy consists in urging that the "burden of proof" lies upon the opponent to a purely theoretical proposition in order to establish it without any knowledge of the matter at all. The burden of proof is strictly an affair of legal procedure, where, owing to the necessity of deciding each case one way or the other, certain rules of presumption are adopted by courts. There is something analogous in other cases in which questions must be decided, and in which there are some recognized rules for

deciding them in the absence of data. But a purely theoretical question need not be decided at all, and therefore, in such a case, there is no "burden of proof." The person who talks of it may mean to say that there is some vague improbability in the proposition he opposes, which may be true. But then he should state his argument just as it really is, so that its true force or weakness may appear. For example, a non- euclidean geometer might say that the burden of proof is upon whoever says that the sum of the angles of a triangle is that of two right angles; to which his opponent will answer that it is certainly extremely near that, and that the burden of proof is upon whoever says it is not exactly so.

26. On Fallacies. This is a subject in which few logicians of great theoretical force have manifested much interest. Mill turned some attention to it; but more cannot be said. I conceive that it is a useful topic, however little it accords with my taste; and shall do my best to produce a useful account of fallacies. It belongs to critical logic, if to any department; but it is best not treated as belonging to pure logic. All sorts of considerations should be allowed to enter the treatment of it. Looking upon it then, as a practical matter, I distinguish five classes of fallacies.

the whole, in almost all cases, and in many cases, at least, there is a point of attainment where the cost of an increment is at a minimum. The same tendency appears in reference to diffusion of knowledge; but there is this difference, that for advance of knowledge the minimum is at a low attainment, while for the diffusion of knowledge it is at a very high attainment. I next study the variation of the utility of a given small increment of knowledge and of diffusion of knowledge with varying attainments. This is to be compared with the variation of the demand for a material commodity with the price. We know that if a thing costs nothing at all there will be a certain finite demand for it, that in order to diminish this demand by a small fixed amount, an extremely small addition to the price will usually be necessary when the demand is great, but that as the demand becomes less and less owing to successive rises in the

price, the increase of price necessary to reduce the demand by a given amount will usually be greater and greater.

fortunate discovery may result in new means of research. the difference between expending energy in research and in the diffusion of knowledge, as a general rule, seems to be this. We cannot perhaps discriminate between this part and that part of what is spent for diffusion. At least I do not attempt it; but taking it as a whole, it brings a profit to scientific energy, and a profit which would be increased in rate were the diffusion greater. But as for what is expended in the advancement of science, and which, being nearer to me, I can somewhat separate into more and less profitable parts, granting, of course, that all brings increase of knowledge, whether all brings more strength to science than it expends is not so certain. At any rate, the effect of increments of most of the sciences is that the profit will diminish with the increment. Of course, but a minute fraction of the money, and but a fraction, though a larger one of the total scientific energy goes at present, to research. All my warmest heart's desires are

for the advancement of science. I do not care, one straw, to see the human race advanced so far as that means no more than giving a general civilization and "culture"; still less do I care for giving a lot of young men "advantages," as far as any love for them personally is concerned. I know I ought to, but as a matter of fact, to be honest, all I care for is the embodiment of God's truth in ever so small a leaven. Yet looking at the matter with these eyes, I am far from thinking that research is getting too small a share of the dollars as compared with what education is getting. Let research find a way to make a business profit; by which I mean that the scientific energy expended must produce an augmentation of scientific energy,--aggregating under that term all the exhaustible factors of scientific advancement. Diffuse among our people the economic truths they ought to know, by which I do not mean the science of economics, but the deep appreciation that there is such a science which only special students can

understand, and teach them what kind of a man such a student is, so that they may not mistake their neighbor the livery-stable man for that student, and what would one not have added to the means of science, quite aside from money. As for science having a need of money, although I personally feel it keenly, I cannot but have a certain contempt for that need.

omnium methodorum principia viam habens." No. 32. On the Course of Research. An attempt to describe, in as much detail as possible, what the general course of procedure of any branch of inquiry must be. The categories of its stages elicited. No.33. On Systems of Doctrine. Strangely enough, it seems to be left to me first to attempt an general account of what any system of doctrine should be with the categories of its divisions. No. 34. On Classification. The nature of classification, of which some preliminary idea was given in the first memoir, is now studied more particularly. Classifications of various departments of human creations are studied (since in these fields we can comprehend

what the ideas are which have determined the production of the objects classified) in order from them to elicit the general categories of natural classification. No. 35. On Definition and Clearness of Ideas. In January, 1878, I published a very brief sketch of this subject wherein I enunciated a certain maxim of `Pragmatism' which has, of late years, attracted some attention. To that I fully adhere; but it must be more accurately defined so as to guard against certain interpretations which do not follow from the grounds of pragmatism. Moreover it allowed it to appear, by my silence in 1878, that pragmatism represents the highest grade of clearness of ideas. This is not true; and the matter will in this memoir be shown to be a fragment of a more extended doctrine.

omnium methodorum principia viam habens." The true edifice of logic, here so extraordinarily defined, without one meaningless word or needless clause, which, as Petrus Hispanus erected it, answered well enough to the poor science that flourished in This memorable sentence whose gothic ornamentation proves upon careful examination to involve no meaningless expression or redundant clause begins a work which the idea here expressed satisfactorily enough for the principal science of the middle ages. Jevons adopted it as the motto of his most scientific contribution to logic. The purpose of my memoirs is upon the ground so well prepared by him and his teacher DeMorgan and the other great English researchers, especially Boole, Whewell, Berkeley, Glanvill, Ockham, and Duns Scotus to lay solid foundations upon which may be erected a new logic to serve the purpose which will animate the science of the Twentieth Century

omnium methodorum principia viam habens." This, the true position of logic, wonderfully defined, it is the object of these memoirs, to begin to rebuild. No. 29. On the Course of Research. The object of this memoir is to formulate in as much detail as possible the general

moment have developed into a true science, such as it is surely destined some day to become, yet the theoretical value of it, as filling a gap in our final knowledge, is greater yet. I know that few can appreciate this; but I feel bound to declare that it is so, whether I am credited or not. Of course, I do not wish anybody to believe it because I say so; but I feel bound to testify to this truth.

moment have developed into that true science which it is surely destined some day to become, yet the pure theoretical value of it as science is greater yet. No doubt, it is possible to acknowledge, as one must, that logic produces useful truths and yet to maintain that it is a composite of odds and ends, a crazy-quilt of shreds and patches, of no scientific value it itself. Yet seeing that pure mathematics is so near to logic that eminent mathematicians pronounce it to be a branch of logic, one does not see how one can well deny pure scientific value to logic and yet accord such value to pure mathematics. I do not doubt that there are naturalists so narrow in their views that they would deny absolute scientific value to pure mathematics. But how about metaphysics? Everybody must have a Weltanschauung. It certainly influences science in no inconsiderable measure. Now metaphysics depends upon logic, not merely as other sciences may occa-

Taking all these things into consideration, my experience of what I can do is sufficient to enable me to say that six memoirs a year is all I could promise, although I should hope confidently to finish the whole three dozen in five years. I do not want to inflict as many as a million words upon a student; but I am sure that the whole list of subjects could not be covered as it should be, in half a million. The considerable majority of the memoirs can be brought down t the length of about 20,000 words each only by laborious and clever condensation. A very few can e much shorter. Not a few must positively be much longer, up to 50,000 words. To bring the total within the million, especially seeing that they increase in matter toward the end of the series, so that the last quarter of the number are all very dense, will be a difficult but necessary task.

would have to be procured. If, on the other hand, the series of memoirs were completed, then, but not before, I should be at liberty to do what I pleased with the abstracts. If the series of memoirs were, say, half published, then this abstract (which I should have been continually polishing) could be used to complete the publication. As an additional security, I should propose, if The Executive Committee desires additional security, that a contract be executed between the Carnegie Institution and me, by which I should be bound to send in the memoirs with no interval exceeding three months between two, unless a visitation of providence should intervene (say, severe illness, conflagration, death of a member of my family, etc.) and then of not over four months. Otherwise, I, failing in this, should

have to repay to the Carnegie Institution all the money paid to me so far, while the Institution should retain the copyrights. And I would yearly furnish bonds that such money should be refunded if such failure should occur within one year. I beg to say that if the Executive Committee deems this proposition ridiculous, I do not say that I do not share that opinion. But I stand ready to carry it out; and only mention it because I am anxious to meet what I am informed by the most credible persons is the wish of members of the Committee. It is the most reasonable plan that occurs to me. Of course, in case the contract were made, the Executive Committee, or the Carnegie Institution, would become bound by its terms to persist in the arrangement to the end, and to publish each

If I were to believe what I have been told, I should be obliged to admit that it was possible for a member of your responsible body to determine his will to oppose all aid to a certain individual, and to find reasons for doing so wherever he could. But I have never detected such a spirit in any committee of scientific men, and I do not believe, for one instant, that it would appear in yours. Logic is a "department of study." As to whether I am an "exceptional man" in this department, look to the third volume of Schrder's Logik, where I am named upwards of two hundred times, beginning with page 1, where I am called the "Hauptfrderer" of "eine grossartige Disziplin," the "Logik der Beziehungen berhaupt." Yet, important as that branch of logic is, my account of the proposed contents of my memoirs shows that it does not form any overwhelming proportion of my whole work.* *Its influence upon the work is, however, much greater than a reading of the above explanations of the list of memoirs would naturally suggest, the scientific methods not being there set forth. Still, my remark is strictly correct. So, then,

the Carnegie Institution having accepted the trust and its purposes, it is one of your first duties to enable the exceptional man in any department of study to make the work for which he seems "specially designed" his life work. In this phrase, is accepted precisely the view I have always taken of myself, that I "seemed specially designed" for certain work; and certainly, after more than forty years of labor upon it, I am more "specially designed" to complete it, by far, than I was when I first devoted my life to it. So then, it seems to me, that my claim to the reward for my work, that of being enabled to complete it, which had been before addressed to nobody in particular, now finds in you a definite party upon which I have such claim, since in satisfying it you will be simply carrying out one of the

chief responsibilities which you have accepted. Whatever action you may take, I, for my part, have a quiet faith that I am specially designed for the work for which I certainly seem specially designed, and that it will, therefore, get done in some way. My own duty in the matter will be performed in any case; and you are the sole judges of your own duty, except so far as we shall have to render account hereafter. Submitting, therefore, my application to your wisdom, I remain, Most respectfully, C. S. Peirce

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