Connexivity in Aristotle’s Logic

Abstract

At APr 2.4 57a36–13, Aristotle presents a notorious reductio argument in which he derives the claim ‘If B is not large, B is large’ and calls that result impossible. Aristotle is thus committed to some form of connexivity and this paper argues that his commitment is to a strong form of connexivity which excludes even cases in which ‘B is large’ is necessary. It is further argued that Aristotle’s view of connexivity is best understood as arising from his analysis of affirmation and negation in terms of combination and separation: a proposition that separates two terms cannot entail a proposition that combines the same two terms. In order to motivate this account of connexivity, this paper interprets Aristotle as emphasising the predicative structure, especially the copulae, of the argument’s component propositions. The arguments for this are based on a consideration of the larger context of APr 2.2–4. A reconstruction of the argument using propositional variables does not fully capture Aristotle’s intentions.