Categorical Foundation of Mathematics?

[Harvey Friedman]

https://cs.nyu.edu/pipermail/fom/2022-May/023293.html offers up

The PNAS article is free at
https://www.pnas.org/doi/pdf/10.1073/pnas.52.6.1506

as an axiomatic treatment of Category Theory.

This is totally unacceptable foundationally, in that it has no prima facie
philosophical coherence and is comparatively extremely complicated compared
to the foundations of set theory.

It has been known for some time that philosophical coherence is not a high
priority among many mathematicians. So given their track record it is best
to leave foundations to the f.o.m. community where it is being handled so
powerfully.

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.

Harvey Friedman


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