This topic was first put on a proper scholarly footing by the late Werner Jaeger and by Charles H. Kahn; earlier scholars tended either to refrain from speculating on the relation to Anaximander of Aristotle's Physics arguments on the infinite, or to deduce the Milesian provenance of one of them simply from its inclusion of a mention of Anaximander's name. It way my original intention in this paper to execute a tidying-up operation after the two well-planned attacks on Anaximander's argument (...) by Jaeger and Kahn. I said some time ago in a footnote that I hoped to strengthen Professor Kahn's case for the unity of the argument concerning the infinite at Physics 203b4-15. If the following remarks achieve anything, it will be the half-fulfilment of that half-promise: instead of strengthening Kahn's reasoning for the unity of Aristotle's argument, what follows will tend to weaken it. But without the materials and the example of Jaeger and Kahn this present operation could never have been mounted, and disagreement with their strategy or tactics indicates no ingratitude and no narrowly polemical intention. (shrink)