6 Mai 2019

Colin McLarty (Case Western Reserve University)

Philosophy of mathematics is all ephemeral: The cases of Grothendieck and Voevodsky

I would specifically argue against Ian Hacking's view
that "perennial" philosophic questions
create the important parts of philosophy of mathematics.

Hacking says that "ephemeral" daily concerns of mathematicians
raise some issues, but are less important philosophically.

At the same time Hacking takes Grothendieck and Voevodsky
as paradigms of opposite kinds of mathematician.

Hacking says AG works with structure and Voevodsky works with computation.
(Hacking is not very specific but evidently had heard of COQ realizations of HoTT and such.)

First, I will point out that Voevodsky's math grew from Grothendieck's.

There is no opposition beetween those styles,
but an on-going challenge to combine them.

And I will argue that, the really important philosophy
(which will last in the long run) only shows when you actually look at their math itself.

And of course I will look at that math,
more seriously than philosophers usually do.