ABSTRACT
One of Aristotle’s major innovations had been to formalise the analysis of language and reasoning, by establishing assertoric syllogistic (Prior Analytics A.4-6), the rst system of formal logic. This work, he says, is about ‘demonstrative understanding’ (24a10), which aims at constructing valid arguments and rejecting invalid ones. The main argumentative form was the ‘syllogism’ (sullogismos), a formal argument which in its purest form consisted of a major (universal) premise, a minor (particular) premise, and a necessary conclusion that they entail.1 The famous example (‘All humans are mortal; Socrates is a human: therefore Socrates is mortal’) is intuitively valid and easy to understand (but note it is not Aristotle’s own). The syllogism in this basic form can be expressed in dierent forms, in which the use of negation (no, none) and various qualiers (all, some) produces variations (‘No man is a bird’, ‘Socrates is a man’, therefore ‘Socrates is no bird’ etc.).
