Hence the formulæ are Induction. SS" S", &c. are taken at random as M's, S'S S", &c. are P; .. Any Mis probably P. directing observation. But I have shown above that certain premises will render an hypothesis probable, so that there is such a thing as legitimate hypothetic inference. It may be replied that such conclusions are not hypotheses, but inductions. That the sense in which I have used "hypothesis" is supported by good usage, I could prove by a hundred authorities. The following is from Kant: "An hypothesis is the holding for true of the judgment of the truth of a reason on account of the sufficiency of its consequents." Mill's definition (Logic, Book III. Ch. XIV. § 4) also nearly coincides with mine. Moreover, an hypothesis in every sense is an inference, because it is adopted for some reason, good or bad, and that reason, in being regarded as such, is regarded as lending the hypothesis some plausibility. The arguments which I term hypothetic are certainly not inductions, for induction is reasoning from particulars to generals, and this does not take place in these cases. The positivist canon for hypotheses is neither sufficient nor necessary. If it is granted that bypotheses are inferred, it will hardly be questioned that the observed facts must follow apodictically from the hypothesis without the aid of subsidiary hypotheses, and that the characters of that which is predicated in the hypothesis, and from which the inference is drawn, must be taken as they occur, and not be picked out in order to make a plausible argument. That the maxim of the positivists is superfluous or worse, is shown, first, by the fact that it is not implied in the proof that hypothetic inference is valid; and next, by the absurdities to which it gives rise when strictly applied to history, which is entirely hypothetical, and is absolutely incapable of verification by direct observation. To this last argument I know of but two answers: first, that this pushes the rule further than was intended, it being considered that history has already been so verified; and second, that the positivist does not pretend to know the world as it absolutely exists, but only the world which appears to him. To the first answer, the rejoinder is that a rule must be pushed to its logical consequences in all cases, until it can be shown that some of these cases differ in some material respect from the others. To the second answer, the rejoinder is double: first, that I mean no more by "is" than the positivist by appears" in the sense in which he uses it in saying that only what "appears" is known, so that the answer is irrelevant; second, that positivists, like the rest of the world, reject historic testimony sometimes, and in doing so distinguish hy. pothetically between what is and what in some other sense appears, and yet have no means of verifying the distinction by direct observation. Another error in reference to hypothesis is, that the antecedent probability of what is testified to cannot affect the probability of the testimony of a good witness. This is as much as to say that probable arguments can neither support nor weaken one another. Mr. Venn goes so far as to maintain the impossibility of a conflict of probabilities. The difficulty is instantly removed by admitting indeterminate probabilities. Hypothesis. Any Mis, for instance, P P" P, &c., .. S is probably M. § 2. Moods and Figures of Probable Inference. It is obvious that the explaining syllogism of an induction or hypothesis may be of any mood or figure. It would also seem that the conclusion of an induction or hypothesis may be contraposed with one of the premises. § 3. Analogy. The formula of analogy is as follows: S', S", and S"" are taken at random from such a class that their characters at random are such as P', P", P'"'. Such an argument is double. It combines the two following: 1. S', S", S" are taken as being P', P", P'". S', S", S"" are q. .. (By induction,) P', P", P is q. t is P, P", P. .. (Deductively,) t is q. 2. S', S", S are, for instance, P', P", P'". t is P', P", P'"'. .. (By hypothesis,) t has the common characters of S', S", S', S", S'" are q. .. (Deductively,) t is q. Owing to its double character, analogy is very strong with only a moderate number of instances. § 4. Formal Relations of the above Forms of Argument. If we take an identical proposition as the fact to be explained by induction and hypothesis, we obtain the following formulæ. By Induction. S, S', S" are taken at random as being M, S, S', S" have the characters common to S, S', S". By Hypothesis. Mis, for instance, P, P', P". Whatever is at once P, P', and P" is P, P', P. By means of the substitution thus justified, Induction and Hypothesis can be reduced to the general type of syllogism, thus: Induction. S, S', S" are taken as M, S, S', S' are P; .. Any M is P. Reduction. S, S', S" are P; Almost any M has the common characters of S, S', S'. Induction may, therefore, be defined as argument which assumes that a whole collection, from which a number of instances have been taken at random, has all the common characters of those instances; hypothesis, as an argument which assumes that a term which necessarily involves a certain number of characters, which have been lighted upon as they occurred, and have not been picked out, may be predicated of any object which has all these characters. There is a resemblance between the transposition of propositions by which the forms of probable inference are derived and the contraposition by which the indirect figures are derived; in the latter case there is a denial or change of modal quality; while in the former there is reduction from certainty to probability, and from the sum of all results to some only, or a change in modal quantity. Thus probable inference is related to apagogical proof, somewhat as the third figure is to the second. Among probable inferences, it is obvious that hypothesis corresponds to the second figure, induction to the third, and analogy to the second-third. Five hundred and eighty-second Meeting. The PRESIDENT in the chair. The Corresponding Secretary read letters relative to exchanges. The President read a letter from Dr. J. Mason Warren, presenting to the Academy a copy of his work on "Surgical Operations." The following paper was presented: On a New List of Categories. By C. S. PEIRCE. § 1. THIS paper is based upon the theory already established, that the function of conceptions is to reduce the manifold of sensuous impressions to unity, and that the validity of a conception consists in the impossibility of reducing the content of consciousness to unity without the introduction of it. § 2. This theory gives rise to a conception of gradation among those conceptions which are universal. For one such conception may unite the manifold of sense and yet another may be required to unite the conception and the manifold to which it is applied; and so on. § 3. That universal conception which is nearest to sense is that of the present, in general. This is a conception, because it is universal. But as the act of attention has no connotation at all, but is the pure denotative power of the mind, that is to say, the power which directs the mind to an object, in contradistinction to the power of thinking any predicate of that object, so the conception of what is present in general, which is nothing but the general recognition of what is contained in attention, has no connotation, and therefore no proper unity. This conception of the present in general, or IT in general, is rendered in philosophical language by the word "substance" in one of its meanings. Before any comparison or discrimination can be made between what is present, what is present must have been recognized as such, as it, and subsequently the metaphysical parts which are recognized by abstraction are attributed to this it, but the it cannot itself be made a predicate. This it is thus neither predicated of a subject, nor in a subject, and accordingly is identical with the conception of substance. § 4. The unity to which the understanding reduces impressions is the unity of a proposition. This unity consists in the connection of the predicate with the subject; and, therefore, that which is implied in the copula, or the conception of being, is that which completes the work of conceptions of reducing the manifold to unity. The copula (or rather the verb which is copula in one of its senses) means either actually is or would be, as in the two propositions, "There is no griffin," and "A griffin is a winged quadruped." The conception of being contains only that junction of predicate to subject wherein these two verbs agree. The conception of being, therefore, plainly has no con tent. 66 If we say "The stove is black," the stove is the substance, from which its blackness has not been differentiated, and the is, while it leaves the substance just as it was seen, explains its confusedness, by the application to it of blackness as a predicate. Though being does not affect the subject, it implies an indefinite determinability of the predicate. For if one could know the copula and predicate of any proposition, as ". . . . is a tailed-man," he would know the predicate to be applicable to something supposable, at least. Accordingly, we have propositions whose subjects are entirely indefinite, as "There is a beautiful ellipse," where the subject is merely something actual or potential; but we have no propositions whose predicate is entirely indeterminate, for it would be quite senseless to |