[FOM] constructivism and physics

Timothy Y. Chow tchow at alum.mit.edu
Tue Feb 14 19:21:09 EST 2006

Alasdair Urquhart <urquhart at cs.toronto.edu> wrote:
> It follows from this that to look for a theorem that
> you can only prove by nonstandard methods, but not
> by standard methods, is to go on a wild-goose chase.
> The strength of infinitesimal methods lies in their heuristic
> power, as Leibniz said several centuries ago.

If I have been following this thread correctly, the claim that there are 
methods that can be justified by infinitesimals but not by rigorous 
calculus is about "infinitesimals" in the classical nonrigorous sense, not 
in the sense of the rigorous infinitesimals of nonstandard analysis.

I am also interested in examples, and I confess that I was unable to 
understand the ones given by Antonino Drago.  For example, I think there 
wsa some example about all Taylor series converging.  I'll grant that this 
is a "result" that has not been recovered in modern rigorous analysis, but 
is there really a *justification* of this claim via a nonrigorous argument 
using infinitesimals?  I had the impression that this was simply something 
that was assumed without too much scrutiny, but I don't know my history 
well enough.  Can someone clarify?

Tim Chow

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