Lawvere and Leibniz
Hi all, here is an philosophy article perhaps of interest to some on the list http://www.newappsblog.com/2011/11/the-truth-about-infinitesimals.html discussing the contrast between the 'old' solution (Weierstrass et al) to non-rigorous calculus a la Leibniz and the new solutions, nonstandard analysis and SDG, but mostly the latter. Not all ideas are credited, so only Lawvere is mentioned, and not Grothendieck, A. Kock, or others who contributed to the development of the philosophy of 'infinitesimals' in geometry. I think it is a nice advertisement for category theory, even mentioning the phrase 'The world or category of smooth spaces and smooth maps...'. David [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Very interesting. Curiously, nowhere in the post is its author identified. Some of the comments refer to a Dennis, but that is no one I can identify. Russell's view strikes me as especially inane. Had Weirstrass not produced his concept of limit, would Russell have simply discarded calculus as nonsense? An awful lot of problems were solved correctly, even before Weierstrass--would Russell have discarded them. Another point that bothered me was the tossing aside, without explanation, of dx^2 because it was infinitesimal vis-a-vis dx. Better to do what Robinson did, divide by dx and then take the ordinary part as the answer. Perhaps he could have introduced a different "equality" symbol. Still, it was a nice mention of categories. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (2)
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David Roberts -
Michael Barr