Abstract

The article argues that the case of a syllogism in Plato's Theaetetus, where two apparent negative premisses draw a conclusion, is simply a confirmation of the rule that there are no syllogisms with negative premisses and not, as Boethius suggests, a proof that a universal negation like 'Every man is not just' is equivalent to another one like 'Every man is not-just'. I have discussed this equivalence and similar ones arising from singular, particular and unquantified propositions, but the result is that if the equivalence in question does work, it cannot be a characteristic of every categorical proposition.