Saturday, February 25, 2006
(10:15 AM) | Anonymous:
Being and Event Reading Group: Week 2 (pp. 60-120)
Just some notes and comments on the reading:Meditation 5 To pick up a theme from last week: notice that the axioms do not make a claim about the existence or not of being. They are "completely compatible with the non-existence of anything whatsoever," (62) such that even those storied ultra-Humeans may have a place at the table. But if there is being, if there is presentation, the axioms of ZF are meant to be the rule by which it is presented. Interesting that Badiou does not appeal to the doxa that "of course there is being," but affirms the presentation of being indirectly, by affirming, first, "the unpresentable alone as existent; on its basis the Ideas will subsequently cause all admissible forms of presentation to proceed." (67)
Meditation 6 This section follows Aristotle almost all the way through - identifying void not with the atomist universal milieu (and hence not with the modern Cartesian sense of space), but with the question of natural situation (rocks fall because the ground is their natural place, remember). There's the rather shocking discussion whereby Aristotle allows that void might be "the matter of the heavy and the light as such," and then that matter is "in some manner a quasi-substance." Void thence as almost-being. Any Scholastic readers are hereby invited to get all philological on us at will. Badiou gives Heidegger credit (70) for making this kind of examination of Aristotle possible; for at the very least some decent cites, see my paper from last fall on Heidegger and maths.
Meditation 7 The discussion at pp. 86-89 - a defense of the two claims that the void is a subset of any set and itself possesses a subset - is of particular interest because it defends the introduction of the void into the notation with more attention than even the textbooks provide. Typically, we learn that the power set of A (where A = {1, 2, 3}) is just {{ }, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}, or A, { } (the null set or void), and all the combinations of A. The null set satisfies the axiom, so it's included. Badiou gives a nice demonstration of this deduction, and this is a wise move since he derives so much (everything hereafter, you might say) from the excess of inclusion over belonging.
Meditations 8-9 Nine is a demonstration in politics of the principles of eight, is interesting, and if anything needs de-emphasizing. It's just an example: the claim that Badiou's is a "philosophy for activists" only holds if we ignore his fairly strenuous effort to dissociate philosophy from its four conditions. So where the notion of the state of the situation is introduced, we read that this notion has [only, I say] "a metaphorical affinity with politics" (95). Eight is crucial for the introduction of the difference between presentation (belonging) - where elements of the situation are counted as one - and representation (inclusion) - where presentation itself is counted. Also, we meet the normal, excrescent, and singular multiples which, provocatively enough for any phenomenologist, are "the most primitive concepts of any experience whatsoever." (100)
This week is technically supposed to take us through 10 as well, on Spinoza. But who has the time?
I've added a section on Spinoza. -APS
Meditation 10 Badiou's Spinoza, represented through the language of set theory, is the creator of a philosophy that "forecloses the void" by assuring each count-as-one through the metastructure of what he calls God or Substance (113). For Spinoza the finite of causality always refers back to the finite and not to the infinite origin of causality. It is here that Badiou makes a potentially helpful statement on the void, "The rift between the between the finite and the infinite, in which the danger of the void resides, dos not traverse the presentation of the finite (117)." Or, in other words, a supreme count-as-one (God or Nature) may suture both the state of a situation and the situation itself, it will still not annul the excess of inclusion over belonging (which is the errancy of the void) (120). Badiou says that Spinoza's "infinite mode" is this naming of the void, thus showing that Spinoza has failed to foreclose the void.
