excerpt: ----- While the equation of ontology and mathematics allowed him to mount a radical challenge to more familiar conceptions of being (such as those of Heidegger or Deleuze), its literal foundation on the void seemed to eliminate any significant link between the ontological and the ontic domains, between being-qua-*being* and being-qua-*beings*. It provided clarity and distinction in a realm where many other thinkers had preferred to draw on religion or art, but did so at the cost of rendering the discourse of being utterly abstract. It served to reduce the scope of ontology from the study of what and how something is to a manipulation of the consequences stemming from the assertion *that* it is. Conceiving the being or presenting of a person (or a particle, a planet, an organism) as a mathematical set can by definition tell us nothing about the empirical or material—let alone historical or social—existence of such beings. The definition of situation adapted from the mathematical model of a set reduced it to an elementary presentation or collection of units or terms, and such a definition pays no attention to the relations that might structure the configuration or development of those terms, for instance relations of struggle or solidarity. [ . . . ]
As its title suggests, the new book aims to provide an account of a ‘world’ understood not simply as a set or collection of elements but as a variable domain of logical and even ‘phenomenological’ coherence, a domain whose elements normally seem to ‘hold together’ in a relatively stable way. It supplements a set-theoretical account of being-qua-being with a topological account of ‘being-*there*’—an account of how a being comes to appear in a particular world as more or less discernible or ‘at home’ in that world. [ . . . ] ----
sorry -- i think i have answered you rather orthogonally (if you'll forgive my putting it that way ;-), ravi. but i think i am in the ballpark of your worries? as well as chuck's. i do have a sub to NLR, btw. you know, in case you don't.
j
On Mon, Jul 27, 2009 at 9:47 PM, ravi <ravi at platosbeard.org> wrote:
>
> 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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