[FOM] Voevodsky's views

[Frode Bjørdal]

It would be useful if the questions here were specified more
precisely. There are not just two of them below.

-- 
Frode Bjørdal
Professor i filosofi
IFIKK, Universitetet i Oslo
www.hf.uio.no/ifikk/personer/vit/fbjordal/index.html

2011/5/20 Walt Read <walt.read at gmail.com>:
> This discussion has been enlightening in many ways and I thank
> Friedman for initiating it, especially for his willingness to take
> bold positions that have stimulated strong responses. At this point it
> seems to be running in two parallel threads. On the one hand we have
> much technical discussion of FOM issues from what I take to be the
> view of most people on this list, elaborating on the major
> developments of the last 100 or so years. As often happens most of
> these developments are inward-looking, foundations of FOM more than
> foundations of math, to the point where Friedman, e.g., argues for
> their value in illuminating mathematical practice rather than as
> foundational. This may be a valuable contribution of FOM, and one I'm
> personally sympathetic to, but it's certainly not the original intent.
> Math makes a peculiar epistemological claim that requires a different
> kind of foundation than, say, physics. If FOM is really about
> foundations of math, then the mathematicians have to be the judges of
> its success. As is frequently noted here, mathematicians seem at best
> unimpressed by the technical developments. And so here on the other
> hand we have substantial and serious mathematicians, personified by
> Voevodsky, who apparently feel that FOM has failed to accomplish even
> something as basic as foundations of elementary arithmetic. For me
> this raises a couple questions.
>
> 1) Is the foundational goal defunct? Do we feel that FOM has
> found/created, or soon will, a foundation for math adequate to address
> mathematicians concerns? Or is FOM now just a branch of math
> comprising roughly logic and set theory, of interest mostly to
> specialists?
>
> 2) Is the lack of confidence from mathematicians due to poor
> communication or perhaps to simple ignorance or arrogance on their
> part or are their concerns legitimate? If mathematicians reasonably
> feel that they need foundations and FOM as it exists isn't working for
> them, where would they go?
>
> -Walt
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