Now, the conditions of valid inference when the terms are all singular, apply also to the cases in which the terms are general, and for the same reasons. The latter cases, we have just seen, call for special precautions. As a matter of fact, however, these special precautions relating to the distribution of terms are actu ally satisfied (though without any special care on our part) in the case of mediate inference with singular terms. The following more comprehensive rules of mediate inference with general terms may accordingly be formulated as the general rules of all mediate inferences:— I. There are three propositions, namely two premises and a conclusion.
2. There are three distinct terms, one of which (called the middle term) occurs in both premises, and the others occur one in each premise, while one of them (the minor term) is the subject of the conclusion, and the other (the major term) is the predicate of the conclusion.
3. The middle term must be distributed at least once.
4. No term may be distributed in the conclusion unless it is distributed in its premise—that is to say, the conclusion must not be general unless the minor term is distributed in the minor premise, and the conclusion must not be negative unless the major term is distributed in the major premise.
5. One premise, at least, must be affirmative; that is to say, no inference can be drawn from two irreducibly negative prem ises.
6. If both premises be affirmative, the conclusion (if any) can only be affirmative.
7. If one premise is negative, the conclusion (if any) can only be negative ; and conversely, if there is to be a negative conclu sion, one premise must be negative.
These rules are only an application of the law of contradiction and of the general rule about the distribution of terms to mediate inference, and a statement of the essential character of such in ference. They can be abridged by applying directly the principles just mentioned; they can also be expanded by added corollaries deducible from them—namely, (i.) that no conclusion can be in ferred from two particular premises, (ii.) that if one premise is particular, the conclusion can only be particular, and (iii.) that no conclusion can be inferred when the major premise is particu lar and the minor premise is negative. But in the form given above rules 3-7 are convenient and serviceable for testing the validity of most mediate inferences.
ated with the term mediate inference has already been explained. The term "deductive inference" may, more or less in accordance with tradition, be defined as inference from general propositions. Syllogism is commonly conceived as inference which is at once mediate and deductive, and confined to propositions involving only the relation of substances and attributes. Yet deductive inference is somehow indentified with syllogism. The result is inconsistency and confusion. There is no good reason why the inference of a singular or a particular proposition from a general proposition should not be described as deductive inference, although it is immediate inference. On the other hand, there is no reason why mediate inferences involving singular propositions only, should not be called syllogisms, although they are not deductive ; in fact, the text-books do include them among syllogisms in spite of their inconsistent definitions of syllogism. Here it is pro posed to use the term syllogism as synonymous with mediate inference, for that is just what syllogism literally suggests; "putting two and two together" is no far-fetched translation of the term. So understood, a syllogism need not be deductive, though it can be and often is. On the other hand, deduction need not be mediate, though it can be, and frequently is. "Syllogism" and "mediate inference" will, therefore, be used as synonymous here. As compared with "mediate inference," the term "syllo gism" has the advantage of greater brevity, even if it suffers from misleading associations. In the light of what has just been said, there is no harm in calling the above-mentioned "general rules of mediate inference" also, "general rules of the syllogism." In what follows the term "syllogism" will be used in place of the term "mediate inference." Figures and Moods of Syllogisms.—A syllogism, we have seen, has two premises—a major premise containing the middle and major terms (M and P), and a minor premise containing the middle and minor terms (M and S). Each premise might have either of its terms as subject and the other for its predi cate—the major premise, that is to say, might be M-P or P-M, and the minor premise might be M-S or S-M. There are thus four possible arrangements of the terms in a syllogism :— Major premise : Minor premise : S-31, S-M, M-S, M-S.