LOGIC (ante). Regarding the science as concerned directly only with the form and not the substance of reasoning, logic finds its starting point in human iutuitions and thoughts, which, by the processes of conceiving, judging, and reasoning, produce, respectively, concepts, judgments, and arguments. These products, in turn, are ex pressed in language by terms, propositions, and syllogisms. It is with the division, definition, classification, and contradistinction of these, and more especially with the truth or fallacy of all conceivable syllogisms, that logic principally deals. Thus, concepts may be congruous or incongruous, may or may not be true, or valid, or distinct; judgments may be as to quantity, universal (all :II is P) or particular (some III is P); as to quality, they may be affirmative (all M is P) or nega tive (no III is P), they may be categorical or conditional, true or not, and so on. Each judgment contains two concepts, which stand in the relation of subject and predicate and are connected by some verb of being; and it may be noted that predicables, or terms affirmable of others, are grouped in five classes, as they denote genus, species, dif ference, property, and accident. Either of these concepts is said to be distributed when it is taken as a whole, and undistributed when but part is taken. From the various attributes and varieties of the judgments and their elementary concepts are evolved rules as to opposition and distribution, such as: "The truth of a universal implies the truth of a negative," and "All universals distribute the predicate." As concepts compose the judgments, so judgments or propositions cornpose the syllogism. For exaniple, in this simple but complete syllogism: " All III is P; all S is M; hence, all S is P," the first proposition is called the major premise, the second the minor premise, and the third the conclusion. Now, ir has already been seen that every proposition may be affirmative or negative and either universal or particular. We thus
have the four primary propositions: universal affirmative, all S is P (A); universal nega tive, no S is P (E); particular affirmative, some S is P (T); particular negative. some S is not P (0), which in all works of logic are designated by the capitals A E I 0, as above indicated. Combined in all possible ways to form syllogisms (three in each), we obtain 64 conceivable forms, of which only 11 are found to be sound when tested by the laws of distribution, and others which apply. These are called moods. Again, by changing the position of the middle term, each mood may be made to take four forms, which are termed figures. But of the 44 resulting syllogisms, only 19 can be proven true under the usual tests. To designate these, there has long been in use a set of otherwise mean ingless words, often arranged in mnemonic Latin verses, in which the vowels represent the propositions and their order. These are as follows: Fig. I. BArbArA, cE/ArEnt, dArI I, fErIOque, prioris: II. CEsArE, cAmEstrEs, fEstInO, bAr0k0, se,eundee: III. Tertia dArAptI, dIsAmIs, fElAptOn, BOkArd0, fErIsOn habet: quarts insuper addit, IV . .BrAmAntIp, cAmEnsEs, dImArIs, fEsAp0, frEsIsOn.
Ferio, for instance, stands for the syllogism E I 0, as: " No 111 is P; some S is 411; hence, some S is not P." The syllogisms of the last threes-figures may all be reduced to the form of the first for convenience in applying tests. One of the most interesting discus sions connected with the science of logic arose from the proposition of sir William Hamilton to substitute for these 19 universally accepted syllogisms, others arising front the fact that any affirmative proposition mav or may not have its subject, and any nega tive proposition its predicate, distributed. This would give eight propositions instead of four, and entirely overthrow the old method. Most modern treatises expound Hamilton's theory and notation, but the system descended from Aristotle is more easily understood and applied.