Badious philosophy is predicated on Set Theory, in its incarnation as the materialist set theory ZFC. He calls mathematics the very site of ontology.

Nietszche famously declared the death of God (in Europe). Thus Deicide. And the loss of the transcendent, and the return of the material, as exhibited in Sartres Existentialism. Being faced with Nothing.

Derrida has remarked that the shadow of God haunts European philosophy. The escaped centre. The transcendent centre that is not there.

Badiou appears to want to anchor the centre on Platos Theory of Forms as interpreted by the science and art of form mathematics - Platonism - Whiteheads third Kingdom.

This is anchoring the centre transcendentally - not in the theological sense - but in the sense that it escapes the world.

Is it fair to say that Badiou is returning Philosophy to a transcendental centre?

  • I'm not an expert but I've heard he just uses mathematical terminology incorrectly to make philosophical points; and postmodernism being what it is, nobody is willing to call him a fraud. Did I hear wrong?
    – user4894
    Apr 10 '14 at 19:17
  • Well Badiou isn't keen on post-modernism as it is now, he considers it as destabilising the grand tradition of working towards truth by destabilising the notion of truth. I'm trying to get some coordinates on his work, but its proving a difficult task. I'm offering the above as a first approximation to his project, as far as I understand it in the context of Modern European Philosophy. This link offers some confirmation of what I've outlined: they describe the last century of Philosophical thought as various phases of anti-platonism. Apr 10 '14 at 20:26
  • This then clears the way for them to show that Badiou is returning to Plato. Zizek also names him as such. Is he a fraud - probably not; is he any good - I don't know enough. Apr 10 '14 at 20:33
  • He isn't using mathematics as mathematicians use it - but then mathematicians use boundaries, chains and spectra in a way most people don't understand but there is of course a family relationship. Apr 10 '14 at 20:36
  • He also says that he isn't using mathematics as metaphor. Note how I used 'coordinates on his work' and 'first approximation to his project' - the first approximation one has in a taylor series. Am I using mathematical language metaphorically? What is a metaphor anyway, and isn't all language at bottom a metaphor - a metaphor being two words yoked together and somehow synthesising a new sense. Apr 10 '14 at 22:35

Yes and no (stack exchange is pretty horrible for philosophy eh?)

  1. Badiou is affirming that mathematics = ontology. The status of ontology (being or beings) is hereby sutured to the procedure of mathematics. While we can debate whether or not this is possible or if we like it, in Badiou's philosophy, the transcendental is divorced from its Kantian signification of a supersensible noumena that we can't say anything about and becomes "thinkable" as the One via the language of mathematics. This preservation-destruction of the transcendental occurs in the moment of the "event" where the transcendental is deduced as the regulative "count-as-one" that iterates the event and comprises it within a sequence of events.
  2. In "the last instance" (I mean this in terms of what his project accomplishes), Badiou's Platonism is a hysterical conservatism that hides a betrayal-realization of the original Platonic notion of forms by lending them some sort of dialectical inertia that destabilizes and complicates the notion of the One = the True. In other words, what Badiou has done is more Hegelian than Platonic: he united being with logic via math so that the transcendental becomes either a mathematical constant or a function. Regardless, for Badiou, it is the "appearance" of the transcendental that authorizes philosophy. So here it is somewhat fair to say that Badiou is returning to the transcendental (this is Francois Laurelle's critique) or recentering philosophy around it.
  3. However, the transcendental actually does very little in Badiou's philosophy--math is the workhorse that explains the transcendental (by not reducing it to the virtual or subsuming it under the symbolic-real--here Badiou's enemy is obviously Deleuze and the "spontaneous philosophy of the Lacanians"). It would seem that the Platonic inheritance is weighted on the side of mathematics and not the transcendental as it is traditionally understood. The return, then, is to math which is reimagined as the "traditional" center of philosophy in a reversal of the philo-fiction which treats philosophy as anterior to math. The question is what this allows, i.e. what the mathematically preserved transcendental "smuggles" into his philosophy.
  • StackExchange is terrible for philosophy. SE is designed for questions that have answers. Philosophy is all about questions that don't have cut-and-dried answers. It's an impossible mismatch.
    – user4894
    Apr 11 '14 at 0:52
  • 1
    Except for the notion of accepting an answer it's (surprisingly) good. If you ignore this, what you have is a system where you get points for writing good things. One Phil.SE points is probably worth two on other SE sites in terms of effort, but the format works. It's not as discursive and open ended as a forum, but the result is collections of relatively well articulated, self-contained writings about a particular topic. It's much more direct and accessible than the meandering conversations of fora, and easier work than articles or books.
    – Lucas
    Apr 11 '14 at 1:04
  • The One, given Badious Ontology, presumably refers to the Universal Set - but via Russell - the One is (thus) not. So definitively ontology as practise (procedural) and not a traditional ontology of mathematics - Platonism? Apr 11 '14 at 1:27
  • 1
    It also looks as though Badiou is suturing ontology to not just any math, but the math of set theory, the foundational study of math, could one say the ontology of math conceived in mathematical terms, rather than philosophical terms. Apr 11 '14 at 1:30
  • Spontaneous philosophy - is this Badious term for the eventually corrosive effects of post-modern philosophy? Apr 16 '14 at 23:39

It's my understanding that Badiou uses ZFC explicitly to block the possibility of a transcendent center, or, in his words, the One. Whether ZFC then becomes the One or not is paradoxical, and points toward current debates among set theorists as to whether different models of set theory reduce to ZFC or rather to a multiverse of models.

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