Aristotle’s Prior Analytics identifies deductions simpliciter with inferential necessity, so that a deduced conclusion is necessarily inferred from some premises. Modern logical reconstructions claim that inferential necessity in Aristotle corresponds to logical validity. However, this logical reconstruction fails on two accounts. First, logical validity does not highlight Aristotle’s distinction between inferential necessity and predicative necessity, meaning that the inferential necessity of a deduction is not of the same kind as the predicative necessity of a non‑deductive argument. Second, logical validity does (...) not explain the relevance of Aristotle’s distinction between complete and incomplete deductions. Logicians speak of complete deduction by adding the term “obvious” or “transparent” to logical validity, and then criticize Aristotle’s view for being unclear. However, Aristotle’s position is not confronted with this difficulty. There is nothing to add to inferential necessity, which already means complete deducibility, as opposed to incomplete deducibility, deemed to be potentially complete. Accordingly, the Prior Analytics reduces the incomplete deductions to the complete deductions in order to prove the potential, inferential necessity of the incomplete deductions. Logical validity would have been faithful to Aristotle’s text, if it had been possible to coin a notion of potential validity, distinct from both validity and invalidity. (shrink)

This paper shows that Aristotle's De Interpretatione does not separate syntax from semantics. Linguistic sentences are not syntactic entities, and non-linguistic meanings are not semantic propositions expressed by linguistic sentences. In fact, Aristotle resorts to a mental conception of meaning, distinguishing linguistic meanings in a given language from non-linguistic mental contents in relation to actual things: while the former are not the same for all, the latter are shared by everyone. Aristotle is not a modern logician, like Boole, Frege, or (...) Russell, in so far as a mental conception of meaning does not reveal an abstract semantics for a syntactic language. (shrink)

Many logicians have tried to formalize a modal logic from the Prior Analytics, but the general view is that Aristotle has failed to offer a consistent modal logic there. This paper explains that Aristotle is not interested in modal logic as such. Modalities for him pertain to the relations of predication, without challenging the assertoric system of deductions simpliciter. Thus, demonstrations or dialectical deductions have modal predicates and yet are still deductions simpliciter. It is a matter of distinguishing inferential necessity (...) that applies to every deduction from the modal predicates in the two premises and conclusion. The modality of demonstrations can be either necessary or possible. The necessity is predicative, i.e., independent of inferential necessity. While the possible demonstration challenges the predicative necessity of the necessary demonstration, it preserves the inferential necessity of the deduction simpliciter. (shrink)