FOM: Godel and infinitesimals

David Ross ross at
Wed Nov 12 11:48:30 EST 1997

Bill Tait wrote:

> There really does not seem to have been that much support for the 
> existence of infinitesimals---prior, that is, to Robinson's work. Leibniz 
> seems not to have believed in them---or better, in mathematics he 
> regarded them as a dispensable computational convenience, to be 
> understood as `syncategorematic infinites' (i.e. epsilon-delta more or 
> less).

I think your term "dispensible" here is unfortunate; it implies
less support for the *role* (if not existence) of infinitesimals
than seems to be the case. Robinson describes their use as "strongly 
advocated by Leibnitz and unhesitatingly accepted by Euler" in his 1961 paper.
I don't know what grounds he had for this assertion, however.

- David Ross (ross at

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