Bowin begins with an apparent paradox about Aristotelian infinity: Aristotle clearly says that infinity exists only potentially and not actually. However, Aristotle appears to say two different things about the nature of that potential existence. On the one hand, he seems to say that the potentiality is like that of a process that might occur but isn't right now. Aristotle uses the Olympics as an example: they might be occurring, but they aren't just now. On the other hand, Aristotle says (...) that infinity "exists in actuality as a process that is now occurring" (234). Bowin makes clear that Aristotle doesn't explicitly solve this problem, so we are left to work out the best reading we can. His proposed solution is that "infinity must be...a per se accident...of number and magnitude" (250). (Bryn Mawr Classical Review 2008.07.47). (shrink)

In Physics, Aristotle starts his positive account of the infinite by raising a problem: “[I]f one supposes it not to exist, many impossible things result, and equally if one supposes it to exist.” His views on time, extended magnitudes, and number imply that there must be some sense in which the infinite exists, for he holds that time has no beginning or end, magnitudes are infinitely divisible, and there is no highest number. In Aristotle's view, a plurality cannot escape having (...) bounds if all of its members exist at once. Two interesting, and contrasting, interpretations of Aristotle's account can be found in the work of Jaako Hintikka and of Jonathan Lear. Hintikka tries to explain the sense in which the infinite is actually, and the sense in which its being is like the being of a day or a contest. Lear focuses on the sense in which the infinite is only potential, and emphasizes that an infinite, unlike a day or a contest, is always incomplete. (shrink)

David Bostock; III*—Aristotle, Zeno, and the Potential Infinite, Proceedings of the Aristotelian Society, Volume 73, Issue 1, 1 June 1973, Pages 37–52, https://.

In De Partibus Animalium I Aristotle sets out his philosophy of biology, discussing cause, necessity, soul, genus, and species, definition by logical division, and general methodology. In De Generatione Animalium I he applies his hylomorphic philosophy to the problem of animal reproduction. The translation is close, and includes passages from De Generatione Animalium II which complete Aristotle's theory of reproduction. The notes interpret Aristotle's arguments and discuss his views on major issues such as natural teleology. The original edition was published (...) in 1972. (shrink)