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. t is P', P", and P'". S', S", and S"" are q .. t is q 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", 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 formula. 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: Almost any M has the common characters of S, S', S'. .. Almost any M is P. Hypothesis. Mis, for instance, P, P, P, S is P', P", P"; .. S is M. Reduction. Whatever is, at once, P', P', P is like M, S is P, P", P; .. S is like M. 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. 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 say, "A has the common characters of all things," inasmuch as there are no such common characters. Thus substance and being are the beginning and end of all conception. Substance is inapplicable to a predicate, and being is equally so to a subject. § 5. The terms "precision" and "abstraction," which were formerly applied to every kind of separation, are now limited, not merely to mental separation, but to that which arises from attention to one element and neglect of the other. Exclusive attention consists in a definite conception or supposition of one part of an object, without any supposition of the other. Abstraction or precision ought to be carefully distinguished from two other modes of mental separation, which may be termed discrimination and dissociation. Discrimination has to do merely with the essences of terms, and only draws a distinction in meaning. Dissociation is that separation which, in the absence of a constant association, is permitted by the law of association of images. It is the consciousness of one thing, without the necessary simultaneous consciousness of the other. Abstraction or precision, therefore, supposes a greater separation than discrimination, but a less separation than dissociation. Thus I can discriminate red from blue, space from color, and color from space, but not red from color. I can prescind red from blue, and space from color (as is manifest from the fact that I actually believe there is an uncolored space between my face and the wall); but I cannot prescind color from space, nor red from color. I can dissociate red from blue, but not space from color, color from space, nor red from color. Precision is not a reciprocal process. It is frequently the case, that, while A cannot be prescinded from B, B can be prescinded from A. This circumstance is accounted for as follows. Elementary conceptions only arise upon the occasion of experience; that is, they are produced for the first time according to a general law, the condition of which is the existence of certain impressions. Now if a conception does not reduce the impressions upon which it follows to unity, it is a mere arbitrary addition to these latter; and elementary conceptions do not arise thus arbitrarily. But if the impressions could be definitely comprehended without the conception, this latter would not reduce them to unity. Hence, the impressions (or more immediate conceptions) cannot be definitely conceived or attended to, to the neglect of an elementary conception which reduces them to unity. On the other VOL. 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