Russell, in “Introduction to Mathematical Philosophy,” says:
“It has been thought ever since the time of Leibniz that the differential and integral calculus required infinitesimal quantities. Mathematicians (especially Weierstrass) proved that this is an error; but errors incorporated, e.g. in what Hegel has to say about mathematics, die hard, and philosophers have tended to ignore the work of such men as Weierstrass.”
The philosophy of math class I’m taking now will probably show me what the work of a mathematician like Weierstrass has to offer philosophers. (I don’t really know.) However, this quote made me wonder what errors Russell had in mind. What errors were incorporated into what Hegel said about mathematics? Did Hegel talk about infinitesimals? Russell doesn’t specify what the errors are, which is too bad. I hope he doesn’t mean the alleged quip about the necessity of the number of planets being 9. Whether or not Hegel actually said that, it is a stretch to call that an error in mathematics.

Advertisements