MEDIATE INFERENCE We have to consider now what kind of conclusions can be inferred from two or more propositions jointly that could not be inferred from any of them singly. Now two or more propositions with entirely different terms cannot between them imply more than the bare sum of their several implications. When, however, two propositions have one term in common, then the common term may mediate between the two other terms, so as to establish a relationship that could not be inferred from either proposition alone. It is such mediation of a common term between two other terms that constitutes the essence of mediate inference. Given the relationship of each of two terms to the same third term, it is possible, under certain conditions, to infer their relation to one another. Symbolically, given the relation of S to M and of P to M, it may be possible to infer the relation of S to P. The corn mon or mediating term is called the middle term; the term which becomes the subject of the conclusion is called the minor term; the term which becomes the predicate of the conclusion is called the major term. The proposition which contains the minor term and middle term is called the minor premise; the other premise, containing the major term and the middle term, is called the major premise. The middle term does not occur in the con clusion, only in the premises. Thus in the following schematic mediate argument, M is P, S is M, therefore S is P, the symbols S,M,P, represent respectively the minor, middle and major terms, M is P represents the major premise, S is M represents the minor premise, and S is P represents the conclusion. Mediate inferences vary greatly in complexity. We propose to begin with the simplest type, and proceed by degrees to the more complex types. In the first instance we shall confine our account to mediate inferences consisting of categorical propositions only, leaving the others for subsequent treatment.
Mediate Inferences with Singular Terms.—Let us begin with an example of the simplest type of mediate inference. The
story of the following incident will serve our purpose. At an "At Home" given by a French countess, Cardinal X. was among the early callers, and in reply to a sympathetic reference made by his hostess, to his varied and anxious experiences, remarked that he had started his clerical career rather ominously, for the very first person who confessed to him had confessed a murder. Later in the afternoon, while the cardinal was at the far end of the drawing room, Count S. called, and the hostess expressed a wish to introduce him to Cardinal X. Thereupon the count said no introduction was necessary, as he had known his holiness many years already. "In fact," said the count, "I was the very first person to confess to him." The consternation of the hostess may be imagined. Here, the conclusion that Count S. had confessed a murder is obvious. It is not implied in either of the two statements separately. It could not possibly be inferred from the cardinal's statement by itself, nor from the count's statement by itself, else neither would have said what he did. But it can be inferred from the two statements when combined, for the simple reason that in the two separate statements the two terms "a person who confessed a murder" and "Count S." are each identified with the same third (or middle) term, "the very first person who confessed to Cardinal X." They must, there fore, be identical with each other, that is, they must refer to the same person, and so the inference is that "Count S. is a person who had confessed a murder." M is P, S is M, therefore S is P. S being identical with M, they are really different de scriptions of the same thing, and so if it was possible for S not to be P, then the same thing (called indifferently S or M) would be P according to the first premise, and would not be P if the suggested conclusion were rejected; but this would be against the law of contradiction. In the above case both premises were affirmative, and the conclusion was affirmative.