this is the review i mentioned in another post (to shag). i basically agree with this review---also, constructivism is fairly big in math now (some discussions are on the blog 'mathematics under the microscope' ).
i am not by any means an expert, but the paper is showed to paul cohen was actually called 'forces, forcing and information' . and the idea was to try to show what he was calling 'forcing' actually had an interperetation in terms of what physicists call forces. the idea is not completely new because people have been trying to figure out if 'cantor's paradise' of the transfinite numbers, and the godelian independence results, mean anything in terms of the real world. the only ones i give credence to are the undecidability results for fractal sets and ones discussed by Penrose in shadows of the mind on noncomputable solutions of dynamical equations like newton's laws, though i don;t really know. (the ramsey theorems and goodstein's theorems (on wikipedia) arent convincing to me despite the hype.
connecting logic to physics is actually pretty common nowadays. the 'information' i used in the title also usdes the common idea of viewing physical and math laws as information. (eg the second law of thermodynamics can be viwewed as a proposition about properties of a set used to model the universe.) this does or can lead to a semi-platonist view in that the universe of logically possible worlds actually exists----ie you can pretty much dedeuce the whole world if you start with a 0 and a 1 and make a few rules for combining them. (Max Tegmark's popular paper 'shut up and calculate' more or less contains the ideas; seth lyod and even wolfram have this sort of view while wheeler (feynman's prof) took the physical side ('it from bit'). the math paper i referred to actually is along this line----how to get everything starting with nothing.
but this may simply be an ideological projection onto math based on the pull yourself up by your bootstraps theory --- horatio alger. (but wasnt darwinism modeled on adam and eve smith?
--- On Mon, 7/27/09, ravi <ravi at platosbeard.org> wrote:
> From: ravi <ravi at platosbeard.org>
> Subject: [lbo-talk] Alain Badiou - Number and Numbers - Reviewed by John Kadvany
> To: "LBO List" <lbo-talk at lbo-talk.org>
> Date: Monday, July 27, 2009, 10:47 PM
>
> Another review of Number and Numbers:
>
> http://ndpr.nd.edu/review.cfm?id=14345
>
> Despite j.fisher's reassurance, I have been uneasy about
> this chap since he seems to be espousing a dressed up
> version of Quine's views (as the above review sort of
> suggests), the chief attraction of which (Quine's ideas) is
> their minimalism i.e., if you can get over the stuffy
> language.
>
> But the review reveals to me that Badiou was one of Sokal's
> targets. That alone casts him in a better light to my eyes!
>
> From the review:
>
> > It's not that being ismathematical, but that
> mathematical discourse "pronounces" what is expressible of
> "being qua being." Theories of anything, but mostly the
> natural and social world as described using numeric methods,
> are re-presentations of this ontology. Consistent with the
> primacy of natural science, numbers and numeric structure
> have to be "immanent" (76, 101, 177), and especially, not
> "constructed" via syntax, grammar or other inductive
> procedures, of which Badiou is completely disdainful: "if it
> is true that mathematics, the highest expression of pure
> thought, in the final analysis consists of nothing but
> syntactical apparatuses, grammars of signs, then a fortiori
> all thought falls under the constitutive rule of language".
>
>
> While I share his worship of mathematics, I find myself in
> no rush to claim that it *is* ontology to avoid reducing it
> to syntactical apparatuses, etc. Am I wrong?
>
> j, you write that we should gain our impressions by reading
> the original material, but Number and Numbers is really
> tough material -- I have read Wittgenstein, Heidegger,
> philosophers like that, and its equally tough going, but
> mathematics is a space that has always defined clarity, so
> it’s a mental block as well to read someone talking about
> mathematics, and using mathematical concepts, but in some
> hitherto unseen ways! ;-) Well not really... Wittgenstein
> does the same sort of thing in his Cambridge lectures and I
> find myself reluctantly nodding in puzzlement with Turing
> (but not Sokal, I hope!).
>
> Like take this part from the review that describe the first
> part of Badiou's book:
>
> > The set theoretic universe just doesn't look much like
> the ordinary real number line, and this Badiou dislikes. In
> particular, Cantor's transfinite ordinals are discrete,
> unlike the real numbers. The symbol "ω" is for the first
> transfinite ordinal, and in set theory it is defined as the
> set {0, 1, 2, . . .}. You can add 1 to ω to get ω + 1,
> which is just the set {0, 1, 2, . . . , ω}, i.e. ω + 1 =
> ω ∩ {ω}. But there's no ordinal a between ω and ω + 1,
> just as there is no counting number nbetween 2 and 3, or 100
> and 101, even though there are lots of such real numbers,
> like 2.002 or 100.101100111 . . . . There is some algebra
> for calculating with transfinite ordinals, but not like the
> algebra for rational and real numbers. For Badiou, Cantor's
> great insight, to generalize just the discrete counting
> numbers into the transfinite, is ultimately an ontological
> flaw.
>
> This is a strange way to describe the history of the
> mathematical developments of the time, and even Cantor's
> project. Transfinite numbers were a natural consequence,
> AFAIK, of issues raised by consideration of countability and
> so on. However, their discrete nature is very much a source
> of worry -- it’s the very same Cantor who authored the
> continuum hypothesis, which Hilbert gave prominence in his
> list of 23. And it was 60+ years later that Cohen
> demonstrated that the continuum hypothesis remains a tricky
> customer and is unprovable from ZFC. In fact, Badiou seems
> to be following the same Platonist road as Gödel in being
> dissatisfied with the continuum hypothesis.
>
> OTOH, it seems like Badiou is a big fan of forcing --
> perhaps Mart can comment on this? Especially w.r.t whether
> Cohen's results had anything to say that presage the
> implications drawn by Badiou.
>
> --ravi
>
> --
> Anyone who takes an effort to intellectually challenge the
> status quo and established habits is infinitely more
> venerable than hacks defending that status quo and
> established habits, regardless of the truth function of
> their propositions. -- W.Sokolowski
>
>
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