MS 690. [Only the first half of the MS is printed here; it was published in CP 7.164-231 and in Carolyn Eisele's Historical Perspectives on Peirce's Logic of Science, 2:705-762. In the second half of the manuscript, Peirce discusses three examples drawn from Aristotle (CP 7.232-255), Plato, and Pythagoras (Historical Perspectives, 2:763-800).]

Origin of the Text

On 13 May 1901 Samuel P. Langely, Secretary of the Smithsonian Institution, received Peirce's second attempt at writing a paper on Humes's argument against Miracles, titled "The Proper Treatment of Hypotheses" (MS 692). Langley rejected it because of its complexity. A draft of it reveals the first title Peirce had in mind: "On the Principles which ought to Guide us in Accepting or Rejecting Historical Testimony." Peirce wanted to develop this into three chapters, the second of which would have shown "how the principles of minute logic are to be applied in dealing with historical documents." Since Langley would not allow it, Peirce turned a few months later to his friend Francis Lathrop, an artist, for whom he had just written a paper on "University." Lathrop agreed to help find sponsors for a Logic book Peirce proposed to write. By the end of September Peirce had submitted the first chapter, and on October 22 Lathrop wrote Peirce to express his hope that the arrangement could be carried through, at $150 a chapter, and asked for four more chapters, "the first of which could be the one which you spoke of having now in hand 'On the Logic of Inference from Ancient Documents.'" Soon thereafter, on November 1, Peirce wrote to the Secretary of the National Academy of Science, Ira Remsen, about his intention to attend the November meeting in Philadelphia "to present a long paper 'On the Logic of Research into Ancient History.'" He added that he already had 27,000 words written, which he hoped to have typewritten before the meeting, and that he wanted to present a 40-minute abstract—which he eventually did. A note dated December 3 from Lathrop's secretary, H. A. Hammond Smith, indicates that a long document Peirce had recently sent was being typed in Smith's office. Internal evidence shows that this was "The Logic of Drawing History," which is extant both as a manuscript and as a typescript corrected by Peirce. The text published in EP2 is a transcription of the manuscript emended from the typescript. Many draft pages survive in MS 691. A draft of Peirce's report of the N.A.S. meeting, with an account of his own paper, is found in MS 1443 (partly published in CP 7.162-163), and the report itself, perhaps not fully authored by him, was published in The Nation on 21 November 1901 (Contributions to The Nation 3:53-57).

Companion to EP2, Selection 8, Page 98, Line 17, Note 31

The long handwritten "Note on Collections" that Peirce inserted in the typescript and that could not be reproduced in EP2 for lack of space follows below. It was partially printed in HP 2:737-42 (partially because the second sheet was missing at the time; it has been recovered since then).

Note on Collections.

I have subjected my definition of a collection to a searching reexamination, without being able to discover that there is any serious mistake in it; although there is more that needs clearing up than I can go into here. What strikes one as wrong about it is that I talk of a collection as being in essence not in existence when, by the very definition of it, it is an individual. How can it be in essence merely without violating its very definition? I think I said in the Monist, Vol. VII, that an individual must be known to exist by the utterer and interpreter; and that it must be known to each that the other knows this. This needs some modification. The first requisite to understanding the matter is to appreciate Kant's remark in his discussion of the Ontological Proof (C.d.r.V. 1st Ed. p. 599) that to attribute existence to a thing is not to predicate anything of it universally. The truth of this follows at once from the definition of universal predication (which definition is the dictum de omni.) For, by this definition, to predicate P universally of S, is to say that P is applicable to whatever singular there may be in the universe to which S is applicable. If, then, there is no singular in the universe to which S is applicable, P is predicable of S, whatever S may be. Or the nonexistent we may truly predicate universally, for example, that it is the only thing in the universe. Therefore, since everything is predicable universally of the non-existent, the peculiarity of the existent does not consist in anything being universally predicable of it. On the other hand, since a particular proposition is the precise denial of a universal proposition, existence consists in the fact that of the existent some particular proposition is true. But it is not sufficient to consider this as saying that taking any existent thing whatever some particular proposition is true of it; for this would be true if there were no existing thing: it is necessary to understand the assertion to be that there is a particular proposition, Some X is either P or not P which is true whatever existing thing be substituted for X. This is not a definition of 'existent'; for to define 'existent' is to assume it to be a universal predicate. The three most important contributions to Logic since Boole, I take to be my own on 'A New List of Categories,' 1867, De Morgan's 'On the Logic of Relations,' 1860, and Mitchell's 'New Algebra of Logic,' 1882. The idea of existence involves my second category, that of the exertion of force. Existence has reference to some asserted act of perception,—whether past, or positively and assertorially future, or else to a mass of other perceptions which give a quasi and doubtful existence. This perception belonging to the category of twoness deprives the perceiver of all freedom as to what idea he will have, and forces upon him that particular idea at that time. A proposition which, in like manner, leaves its interpreter no freedom of choice as to what it is to be applied to, namely, a singular or a particular proposition, asserts existence,—i.e. not merely universally predicates existence, but represents that there is, will be, (or would be, but this amounts to nothing unless it leads to a 'will be') a perceptive act in which that which is indicated is forced upon said interpreter. If this is to be denied, that is, if the interpreter turns and denies it, then in case the first utterer had reserved to himself a freedom of choice as to what act of perception it is to which he will consider his affirmation as referring, (as he does in the particular proposition,) then the utterer of the denial must allow his interpreter, that is, the original utterer, the same freedom of choice in a universal proposition. But if the original affirmer had not allowed himself such freedom, it does not concern the denier to allow his interpreter any freedom; so that the denial of a singular proposition is singular. This is merely a statement of the relation of the universal proposition to the particular proposition. It is, by no means, an adequate account of the universal proposition. The second category essentially supposes the first category, and the third both second and first. A sign, as such, involves the third category, in its reference to an interpretant. Its reference to an object is an affair of the second category. Its reference to a meaning is specially a first category concern. The Argument perfects a symbol, or specially third category sign, by explicitly indicating an interpretant; namely, its conclusion. For an interpretant is an idea or other sign legitimately and purposely determined by a sign. The proposition allows its interpretant to be what it may, but specially designates an object. Such object is its subject. The singular proposition takes the natural objective, or second category, attitude of a proposition. In the particular proposition, it is reduced, as far as possible, to a first category status. Hence it is, that it has seemed to some logicians that the problematic judgment, which is a kind of particular proposition, referring to some possible state of things, is no proposition at all. This is not correct; but it contains an element of truth. The universal proposition, on the other hand, gives its subject a third category status, in consequence of which some logicians mistake its definition, the dictum de omni, for a law of arguments. It is this squint at a possible argument, or, to state it better, this reference to possible interpretations, which constitutes the veritable differentia of the universal proposition. De Morgan's conception of a logic of relations at once shows us that the grammatical objects of a sentence are logically to be regarded as subject-terms. Although, in all the families of speech, it is usual to give prominence to one of these, as we do by putting it in the nominative, yet in every family, languages are to be found in which it is usual to place them all on par. Among European languages, this is true of the Old Irish and modern Gaelic, where the most usual form of a sentence puts what we should call the subject in the genetive case. (The construction is given in the grammars; but the statement that it is most usual in ordinary talk I derived from a lady whose native tongue was Gaelic.) A proposition may, therefore, be universal, particular, or singular in respect to different subjects; and if one of these allows a freedom to the utterer and another to the interpreter, the order in which their choice is to be made is material. Mitchell introduced into logic two associated ideas; one, that every proposition is an assertion about the universe; the other, that the universe of discourse has more than one dimension, there being one for each subject-term, although two or more may happen to be identical. Every proposition would be rendered true or false by some perception or perceptions, which present singular objects. Now it is true that we can reason about continua, which are really intuitional generals not composed of singulars, and to which the principle of contradiction (which is restricted to definite subjects, i.e. universal or singular) and the principle of excluded middle (which is restricted to individual subjects, i.e. particular or singular) do not apply. But logical studies, so far as published, (at least, studies in formal logic,) are restricted to cases in which the universe is a collection of independent singulars. This indicates a crying need, both for critical logic, for universal grammar, and for methodology, which I shall in some measure supply in the treatise I am now writing. A dimension of a universe is (in our hitherto developed logic) that collection from which a proposition, J, permits a singular subject to be drawn to be substituted for as subject-term thereof, whether by the utterer so as to produce a proposition from whose truth the truth of J would follow (being all it means,) or by the interpreter to produce a proposition whose truth would follow that of J (being an interpretant of it.) But Mitchell made it clear that every proposition has other subject-terms than which are explicitly set forth as such, and with them corresponding dimensions of the universe. Such are often dates of time, states of things, possibilities, logical, metaphysical, physical, etc. Such dimensions of the universe are, for the most part, general. But in every case, whatsoever, there is a primary universe and subject which is the Truth. Every metaphysician will have his way of describing this. I should say that it is that ideal state of ultimately settled opinion about the matter in hand, which we hope will be realized. If so, it plainly allows no liberty of choice about it, either to utterer or interpreter; and every metaphysician who admits that the principles of contradiction and excluded middle apply to it, thereby agrees with me that it is singular. At any rate, there can be no dispute that our hitherto developed formal logic assumes virtually that it is so. With this preface, we may proceed to consider hypostatic abstraction; that is, abstraction in the sense in which we speak of abstract nouns, as contradistinguished from precisive abstraction, which consists in concentrating attention upon a particular feature of a supposed state of things. Any respect in which one sign differs from another may be made a universe of discourse. Existence, however, is nothing but occurrence as a singular in a universe of discourse. According to this definition, there will be as many kinds of existence as there are universes. In particular, real existence will consist in being the singular subject of a true proposition. A really existing subject will be, hypostatically speaking, concrete to anybody who regards its existence as not consisting in the existence of anything else; while a subject will be for him the sign of a hypostatical abstraction if its existence is regarded by him as consisting in the existence of something else. I suppose all metaphysicians would agree that the Truth is, hypostatically speaking, concrete; although the conception may be precisively highly abstract. We should not regard the Truth as ultimate if we did not take it to be hypostatically concrete. But as to other things, it appears to me rather arbitrary what we take to be concrete. If a person conceives that the data of sense-perception are to be regarded as primary, since the information of direct perception concerns the apparent surfaces of bodies, his superficial metaphysics, as we may designate it, will lead him to regard points, lines, and solid bodies, as hypostatical abstractions. Another man may, with equal truth, as far as I can see, take a different position. In geometry, for example, we may take solid bodies as concrete; and say that surfaces are mere names enabling us to express more conveniently those things which, given any solid, A, are true of every body which consists of two parts, one wholly within A and the other wholly without A, and which are true of no other bodies; going on to explain lines and points in the same way. Or, with equal truth, we may take particles as concrete; and say that a line is merely a word which enables us to express conveniently the fact that certain things are exclusively true about a particle moving in a certain way throughout the whole time of its motion; and then supposing the place where the particle is in the course of time to be altogether occupied at one instant by a fictitious abstraction called a filament, and that this thing moves so as always instantaneously to completely change its place (so that only isolated particles remaining in it could remain unmoved,) then the place it occupies in the course of time is a surface, etc. Most of our abstract nouns are proper names of abstractions whose existence consists in the fact that a general predicate is true of some concrete singular; and I apprehend that it is the circumstance that general predicates do not form a collection, not being singulars independent of one another, that embarrasses logic, and occasions disputes as to how abstract nouns are to be regarded. 'Animal locomotion,' for example, is an abstraction whose real existence is regarded as consisting in the occurrence in the universe of the true fact that 'Some animal moves about.' Ordinary logic seems to be driven to considering it on the one hand, as singular, inas much as there is nothing equivocal in the statement that all animals move about, and on the other hand, as general, in so far as some locomotion is walking, some flying, etc. The truth seems to be that ordinary logic is here out of its element. But when we say that animal locomotion, 'as such,' 'in itself,' etc. is an adaptive character, it seems to be clearly a singular. A collection is a hypostatic abstraction which keeps within the bounds of ordinary logic, because its existence, instead of depending upon the truth of a general predicate depends upon the existence of independent concrete objects. Alexander, Caesar, and Hannibal make a collection. Our thinking them together, the nominalist will say, makes the collection. The reason he says so is that, owing to his admitting but one mode of being,—which is the essence of nominalism,—he is forced to say that, or be drawn into absurdity. But we who admit esse in futuro, and all that that carries along with it, are not forced into that falsification, and can simply and truly say that the existence of the trio consists in the mere existence of Caesar, Alexander, and Hannibal. Take away Hannibal, whether Napoleon be substituted or not, or add Napoleon, and we have a different collection. A collection, like anything else, may be described in general terms. Just as we speak of whatever inhabitant of Mars there may be, so we can speak of whatever population of Mars there may be, although there may be none, and although for aught we know, it may be identical with the collection Alexander, Caesar, Hannibal, and Napoleon, should it turn out that, at the present writing, they are the only inhabitants of Mars. As an inhabitant of Mars is an individual in essence, whose individuality and identity are indeterminate, so the population of Mars is a collection in essence, which until it exists, is indeterminate. How often have I heard a porter say 'What is in this trunk is light.' He speaks of whatever separate articles it contains, taken collectively, to form one load. If he sees the trunk opened, and finds it empty, he will not say, 'I was mistaken,' but 'I thought so.' Thus, even a man whose mind dwells in the concrete conceives of nothing as a collection. Still, 'whatever is in this trunk' was a general, not an individual, collection; although it is perfectly described, so as to be distinguished from any other; as the 'sun' is usually in the text-books set down as a general term, though there is but one. Now, however, we come to a more difficult case. Mathematicians and logicians speak of O, as a collection. At first sight, this appears to be not only a non-existent collection, but one whose existence is not even logically possible; and I have made the mistake in the text of saying it is only a collection in essence, not in existence. But it is not so. A collection is a singular whose existence consists in the existence of its members; that is, it is sufficient for its existence that whatever are its members should exist. Consequently, the collection O exists, even if nothing in the concrete universe exists. Hence, there is but one individual O collection; and the collection of no dogs is identical §riumö with the collection of no trees. Another point: Caesar and the collection of which Caesar is the sole member are not identical. For the existence of Caesar does not properly depend upon, or consist in, the existence of anything. Caesar is not is not a hypostatic abstraction or singular whose existence consists in the existence of something else, in the same sense in which the collection consisting of Caesar alone is so, but the very definition of a collection. This is a hard saying. I am sorry I cannot make it clearer; but it seems to me certainly true. The obscurity of this point marks an inadequacy in my account of what a collection is; but still, I think that that account is far from being vague to the point of uselessness. On the contrary, very difficult propositions in the theory of multitude can be deduced from it quite evidently.