17/08/31 20:01:41.30 AnxaeSI4.net
>>563 つづき
Katz & Katz analyze Connes' criticisms of non-standard analysis, and challenge the specific claims (1) and (2).[7] With regard to (1),
Connes' own infinitesimals similarly rely on non-constructive foundational material, such as the existence of a Dixmier trace. With regard to (2), Connes presents the independence of the choice of infinitesimal as a feature of his own theory.
Kanovei et al. (2012) analyze Connes' contention that non-standard numbers are "chimerical". They note that the content of his criticism is that ultrafilters are "chimerical", and point out that Connes exploited ultrafilters in an essential manner in his e