Note 386 — Chapter V

This argument is Hamilton’s. He remarks that, in hypothetical syllogisms, “the same proposition is reciprocally medium or conclusion” (Logic, ii. p. 379). Dr Ray (Deductive Logic, Note C) holds that Hamilton is here wrongly interpreted; and that he meant no more than that with a hypothetical premiss If A is B, C is D, a relation between A and B may be either the other premiss (as in the modus ponens) or the conclusion (as in the modus tollens). Dr Ray is possibly right. But if so, Hamilton does not express himself clearly. For A is B (the premiss of the modus ponens) is certainly not the same proposition as A is not B (the conclusion of the modus tollens). It may be added that the argument in its new form is irrelevant. In the categorical syllogism we have something precisely analogous. For given a major premiss All M is P, a relation between M and S may be the minor premiss (in which case M will be the middle term), or it may be the conclusion (in which case M will be the major term). Compare the syllogisms: All M is P, All S is M, therefore, All S is P ; All M is P, No S is P, therefore, No S is M.