Editing Syllogism (section)

==Terms in syllogism==
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With Aristotle, we may distinguish [[singular term]]s, such as ''Socrates'', and general terms, such as ''Greeks''. Aristotle further distinguished types (a) and (b):

{{Ordered list|terms that could be the subject of predication; and|terms that could be predicated of others by the use of the copula ("is a").|type=lower-alpha}}

Such a predication is known as a [[Distributive (linguistics)|distributive]], as opposed to non-distributive as in ''Greeks are numerous''. It is clear that Aristotle's syllogism works only for distributive predication, since 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, for a term to be interchangeable—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 that employ only 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, is not a categorical syllogism. An example is ''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 would require that we 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.