Alexander of Aphrodisias on Aristotle’s theory of the Stoic indemonstrables

In her important 1979 paper “Aristoteles über Syllogismen ‘aufgrund einer Hypothese’”, 1 Gisela Striker provided an in-depth analysis of these vexing and perplexing Aristotelian arguments. She showed that they were Aristotle’s way of providing a logical vehicle for inferences based on other than term-logical relations; that the ‘hypothesis’ that gives them their name is best understood as a rule that is not based on a relation of terms, 2 rather than as a premise; and that in those arguments “the thing taken instead” (τò μεταλαμβανóμενον) is an assertion that is used instead of the demonstrandum. 3 It was upon reading this paper that I realized that the (then) prevalent interpretation of later ancient texts on hypothetical syllogisms as presenting the Stoic theory of indemonstrables needed a thorough revision. For it is possible to show that, starting from Aristotle’s “syllogisms based on a hypothesis”, a specifically Peripatetic, (and from the third century CE also partly Platonist) development can be traced through the centuries up to the late ancient passages on hypothetical syllogistic in Philoponus and Boethius. Although the Stoic indemonstrables undoubtedly played a role in this development, the various theories of hypothetical syllogisms over the centuries are all Peripatetic (and sometimes a little Platonist) in form, function and terminology. 4 The present paper looks at Alexander of Aphrodisias’ role in this development.