Categorical Foundation of Mathematics?
Timothy Y. Chow
tchow at math.princeton.edu
Wed May 18 23:10:29 EDT 2022
Harvey Friedman wrote:
> Generally speaking, philosophical coherence is required in order for a
> foundational scheme to have any traction in the wider intellectual and
> scientific community. Set theory has this, when presented using modern
> f.o.m. tools, but anything like that PNAS article certainly does not.
Let's be honest here. In the "wider intellectual and scientific
community" today, nobody cares about the foundations of mathematics. In
the arts and humanities (except for philosophy), nobody cares about
mathematics, period. In the sciences and engineering (except for
theoretical computer science, which is more or less mathematics), people
care about mathematics only insofar as it is a useful tool. In
philosophy, only specialists in the philosophy of mathematics care about
the foundations of mathematics.
The last time there was a development in the foundations of mathematics
that carried "general intellectual interest" was when Goedel proved his
incompleteness theorems. (Well, maybe a bit later, if the foundations of
computer science count as the foundations of mathematics.) The only
audience for this topic is a small subset of mathematicians and
philosophers. And within that subset, an even tinier fraction care a lot
about "philosophical coherence" in the sense you mean it.
Tim
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