FOM: Re: constructive analysis; topos confusion; set theory alienation

[Michael Thayer]

In an insightful summary of topos foundationism, Steve Simpson writes:
>I would remark that (i) the extra assumptions that Butz proposes are
>very specialized from the viewpoint of topos theory, (ii) these extra
>assumptions seem very difficult to motivate from the viewpoint of pure
>topos theory, outside the context of set theory.  So I don't think
>there is much left of "topos-theoretic foundations", at least as
>regards real analysis
I would like to ask Steve why the topos-foundationalist could not reasonably
respond to this as follows:
"Well the very lack of motivation of the extra assumptions suggests that the
simpler set theory picture may be glossing over some severe problems."
This approach might not be defensible after examination, but why is it not
prima facia plausible?
Michael Thayer