Syllogism - Terms in Syllogism

Terms in Syllogism

We may, with Aristotle, distinguish singular terms such as Socrates and general terms such as Greeks. Aristotle further distinguished (a) terms that could be the subject of predication, and (b) terms that could be predicated of others by the use of the copula (is are). (Such a predication is known as a distributive as opposed to non-distributive as in Greeks are numerous. It is clear that Aristotle's syllogism works only for distributive predication for we cannot reason All Greeks are animals, animals are numerous, therefore All Greeks are numerous.) In Aristotle's view singular terms were of type (a) and general terms of type (b). Thus Men can be predicated of Socrates but Socrates cannot be predicated of anything. Therefore to enable a term to be interchangeable — that is to be either in the subject or predicate position of a proposition in a syllogism — the terms must be general terms, or categorical terms as they came to be called. Consequently the propositions of a syllogism should be categorical propositions (both terms general) and syllogisms employing just categorical terms came to be called categorical syllogisms.

It is clear that nothing would prevent a singular term occurring in a syllogism — so long as it was always in the subject position — however such a syllogism, even if valid, would not be a categorical syllogism. An example of such would be Socrates is a man, All men are mortal, therefore Socrates is mortal. Intuitively this is as valid as All Greeks are men, all men are mortal therefore all Greeks are mortals. To argue that its validity can be explained by the theory of syllogism it would be necessary to show that Socrates is a man is the equivalent of a categorical proposition. It can be argued Socrates is a man is equivalent to All that are identical to Socrates are men, so our non-categorical syllogism can be justified by use of the equivalence above and then citing BARBARA.