[FOM] Why not this theory be the foundational theory of mathematics?

[Colin McLarty]

I am curious to know what this means:

On Wed, Mar 27, 2019 at 7:55 PM Thomas Klimpel <jacques.gentzen at gmail.com>
wrote

(The category of all sets is
> specified by a sort of "last word quantification", but this is
> troublesome for a foundational theory. A foundational theory should
> lay down the first words, not insist on having the last word.)
>

Colin
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