Orna Harari

I argue that Aristotle’s late-antique commentators read into his theory of demonstration the notion of tekmeriodic proofs in attempt to integrate into the theory of demonstration the assumption that the principles of demonstration should be evident. In so doing, I trace the late antique commentators’ view to Alexander of Aphrodisias’ discussion of the principles of demonstration, showing how his assumption that the principles of demonstration should be evident underlies their notions of tekmeriodic proofs.

I examine the question why in Proclus' view genetic processes provide demonstrative explanations, in light of the interpretation of Aristotle's theory of demonstration in late antiquity. I show that in this interpretation mathematics is not an explanatory science in the strict sense because its objects, being immaterial, do not admit causal explanation. Placing Proclus' account of demonstrative explanation in this context, I argue that this account is aimed at answering the question whether mathematical proofs provide causal explanation as opposed to grounds. I show further that Proclus can answer this question in the affirmative due to his realist view of mathematical objects and the priority he ascribes to causal relations over logical relations.