despite his theorems, godel actually was a kind of Platonist (which i guess could hold that number can be an ontology, or the reverse). godel also had a proof of the existence of god (using ultrafilters, as a kind of dictator, reminiscient i guess of the filters chomsky discusses---to filter the wheat from chaff, some decision theory or oracle must exist).
its kinduh nice to see political philosophers take on set theory (i remember i once met paul cohen, who finished up godel's results on undecidability, and discussed my own 'theory' which connected his stuff to physics---he told me he was only doing group theory then (also 'we dont do it that way'---so maybe its wrong?). i didn't have politics except to suggest rather than religious or ideological wars, we could have nations and wars based on axioms for a change. the strict finitists will win in real time.). it can be mentioned some right wing types also rely on set theory to justify their own political ideologies. Oswald Spengler also had a more materialistic approach to number (which may be closer to the constructivist approaches probably discussed by Kennealy, which apparently Badiou dislikes (being a platonist). i gather sokal went after badiou, but i guess this is since his platnoism is not the same flavor. )
i am skeptical of sets being distinct from space (remember from back in the day, rene descartes?) to me these are just different ways of representing the same idea, though likely these different percpetions each actually contribute things you otherwise might not notice.
--- On Sun, 7/26/09, Chuck Grimes <cgrimes at rawbw.com> wrote:
> From: Chuck Grimes <cgrimes at rawbw.com>
> Subject: Re: [lbo-talk] Review of Badiou's Number and Numbers
> To: lbo-talk at lbo-talk.org
> Date: Sunday, July 26, 2009, 9:05 PM
> ``..mathematics is ontology.''
> (Badiou, via ravi)
>
> -------
>
> Wow. Absolutely god dmaned right. But Badiou my dear, never
> get out of
> the boat, or you might get eaten by tigers...
>
> Here is the problem with the deep platonism of this idea.
> Crudely put
> it was destroyed by Goedel's dual theorems on consistancy
> and
> completeness. This in effect killed the most simple sort of
> ideal
> statements about number and being as the great castle of
> eternal and
> rational truth. Remember we have had a conceptual unity
> about number
> and being since at least Pythagorus.
>
> On a different level ignoring these details, understanding
> some
> of the conceptual forms within mathematics helps a great
> deal to
> understand the nature of our techno-scientific ontological
> premises,
> and the nature of the kinds of minds we inhabit.
>
> ``His major work, Being and Event, kicks off with this
> stark assertion,
> and proceeds to derive a series of bold conclusions – the
> wresting of
> ontology from Heidegger’s embrace, the construction of a
> rigorous and
> rationalist metaphysics..''
>
> I'll have to read it, but this conflict was part of the
> famous Davos
> dust-up between Cassirer, Heidegger, and Carnap. I'll have
> to go over
> that again too. Roughly to sum that up: a neo-Kantian
> analysis of
> symbolic forms v. existantial analysis of being in the
> world, a
> logio-mathematical analysis of thought and language.
>
> One of the more important spin-offs of these discussions is
> found in
> the strange problem of the mind-language seen in some of
> the current
> survey of work in biological-linguistic studies Kenneally
> does. I
> still haven't finished it either.
>
> Here's the basic problem. You have to have theory of mind
> in order to
> do empirical work on the nature of mind. And most of the
> researchers
> in biological sciences and linguistics do not have a theory
> of
> mind. The way I imagine this goes, is you have to find room
> for both
> mathematics and arts, science and animal behavior. Your
> concepts have
> to be foundationally comprehensive enough to not be
> exclusionary. That's a pretty tall order.
>
> Okay, I just read the article, which is a review of
> Badiou's two
> books. I am familiar with all these subjects in my own
> junior level.
>
> If you want to make the claim that mathematics is ontology,
> then the
> best place to start is not with number, but with
> mathematic's other
> representation as space. (This was Cassirer's brillant
> move.) This
> leads to point-set topology and its analog of combinatorial
> topology,
> downward into geometries and current physical theory. This
> in turn
> leads to all the most wild of current cosmological theory,
> where the
> unity between philosophy, mathematics, and the physical
> cosmos join up
> with pre-socratic concepts of the Cosmos, all that is.
> (BTW, I have
> another book I haven't gotten more than fifty pages, Roger
> Penrose,
> The Road to Reality. Penrose also starts off with space.)
>
> So then getting back to space. You can see that space is a
> concept
> that can be shared with a great variety of animals, since
> we all have
> to navigate our environmental spaces, and we have
> evolutionary
> adaptations of great variety of anatomical systems to do
> that. The
> consequence is that space-nagivation is part of the
> foundation of a
> theory of mind.
>
> If you want to develop an anti-capitalist theory of the
> political
> economy, then space comes in remarkably handy, since the
> very first
> act of a capitalist is to expropriate land through money
> lending, Land
> is the material embodiment of space, the space we all must
> live in to
> reproduce our society.
>
> CG
> ___________________________________
> http://mailman.lbo-talk.org/mailman/listinfo/lbo-talk
>