just to throw in the mix, clifford is also pretty interesting (eg clifford numbers, even popular now in quantum theory) and hao wang (who hung out with godel---he has a big book on this which is quite interesting---penrose discusses his work on tilings, which translate undecidability results into spatial terms regarding 'tiling' 2-dimensional space; also emile post is pretty good (his essay in martin davis' collection on the undecidable (turing, goedel, etc.) may be closest to badiou you get in the strict logic community.
--- On Tue, 7/28/09, Chuck Grimes <cgrimes at rawbw.com> wrote:
> From: Chuck Grimes <cgrimes at rawbw.com>
> Subject: Re: [lbo-talk] Being and Event: the Deep, Penetrating Massage Review, Coming Soon!
> To: lbo-talk at lbo-talk.org
> Date: Tuesday, July 28, 2009, 9:49 PM
> ``Considering the "mathematics is
> ontology" bit and some of the material
> in Number and Numbers, I am at a loss for any short-term
> strategy to
> *evaluate* Badiou. I am at a point where with some effort I
> might be
> able to remember and rework the relevant mathematical
> developments
> from about 1870 to 1960 (Dedekind to Cohen). But even if
> this
> strenuous task can be completed, I am not sure I can then
> move up a
> level to address and understand the implications of the
> mathematical
> results...'' ravi
>
> -----------
>
> The day after...sorry I swamped the list with all that wild
> ride math
> talk... I never get to talk or write like that anywhere
> except here.
> guess that's what they mean by loosing your inhibitions
> and
> judgement... Wish we were all in a bar in NYC about 1950...
> time warp.
>
> There is a way to approach understanding the impact and
> development
> of set theory. Hilbert was a teacher, and Gottingen was
> something like
> a math giant professor production line.
> There were twin developments in German mathematics that
> vastly
> condensed and systemized mathematical education proper. One
> theme of
> those developments followed the Geometry line. The other
> followed the
> Number line. In the former we have starting with Riemann,
> followed
> Felix Klein and his use and development of group theory and
> the
> re-axiomization of geometry which superceeded the
> controversy over the
> parallel postulate. The other or number line starts again
> with
> Riemann, then follows, Cantor, et al and sets. This line
> sort of has
> multiple branches that creat the `morass' of analysis.
> (There is also
> Riemann himself to look at, study, think about and how he
> generated
> such numerous and giant spawn: Cantor, Klein, Hilbert,
> Einstein in the
> next generation. Mostly his contributions go to what I
> think of as the
> join of number and space into analysis and physics, while
> the
> number-space line goes the re-organization of algebra, via
> the same
> core concepts used in sets and groups.
>
> Together these two topics Set Theory and Group Theory, went
> through
> the entire spectrum of maths and re-codified, compacted,
> and
> `simplified' this entire branch of thought. They
> essentially created
> `modern' mathematics including many of its new branches
> like
> topology. Both Klein and Hilbert were also philosophers in
> their own
> way by doing what amounted to mathematical ontology. Both
> men and
> lines of thought --number, space-- have theoretical and
> concrete
> applications that were discovered along the way and that in
> turn
> re-fed back into these developments.Well like nuclear war
> and cyber
> space.
>
> So when I read/study mathematics and/or about mathematics,
> I look for
> theme content in applications within mathematics and
> applications
> within the sciences, sometimes the arts.
>
> I just ordered Number and Numbers to start. So we'll see
> maybe if I can get
> enough through it to figure out what's going on... In the
> meanwhile,
> I know I will use something like the above pov to think
> about
> Badiou. Will the math crew get anything out of these works.
> Will the
> sciences get something they don't know? Will I get insights
> I didn't
> have? Do I like the style, the method of approach, etc.?
> The thing is,
> I am into raw ideas, good, bad, true, false, great, small,
> and the
> lowest of the low, totally middle brow, whatever...
>
> CG
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