This paper aims to explain the distinction between syllogisms and subsyllogisms in Stoic logic. Subsyllogisms replace at least one premise in a syllogism with a premise that is, according to Galen and Alexander, equipollent to the respective syllogistic premise. This equipollence is not synonymy of meaning between two linguistic expressions, but obtains between two propositions when they are true or false by the same standard. Subsyllogistic premises are simple propositions that are equipollent to the non-simple premises of the respective syllogisms. (...) For subsyllogistic premises that replace syllogistic premises consist of predicates combining with cases rather than of connectives or negations governing propositions. Because of this difference in their premises, subsyllogisms have a different logical form than syllogisms and are not formally valid. (shrink)

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. (shrink)

The theory of sign and proof is an essential component of Stoic epistemology. This book examines the fragmentary evidence from Sextus Empiricus and sheds light on the two aspects that characterise signs and proofs: the logical relation that holds between a sign and that which it signifies and an additional epistemic relation that is called revelation. All signs feature in conditionals that are true in virtue of the strong modal account of conditionals that the Stoics developed. This modal account is (...) one aspect that makes it possible to gain certain knowledge of that which is signified. But signs and proofs must also reveal that which they signify to produce knowledge. This requirement is fulfilled when an inference proceeds from premises that are justified through knowledge of the causal relation in virtue of which the premises are true. (shrink)