Bourbaki and foundations

[Monroe Eskew]

> On 09.05.2022, at 02:01, Michael Sheard <msheard at stlawu.edu> wrote:
> 
> Earlier, Aczel had already said that Bourbaki's "greatest error" was "letting Grothendieck go and disagreeing with his vision for the future of mathematics" -- specifically, its unwillingness to revise its earlier volumes in order to replace set theory, a "discipline full of theoretical holes," with category theory, which "does not suffer from the inherent limitations of set theory," as the foundation of mathematics.

It sounds like there is a belief that categorical foundations can avoid Gödelian incompleteness.  Is that a fair reading?

Best,
Monroe