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By Fabio Gironi
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Extra resources for Naturalizing Badiou: Mathematical Ontology and Structural Realism
Example text
Badiou explains: the name of the void is a pure proper name, which indicates itself, which does not bestow any index of difference within what it refers to, and which auto-declares itself in the form of the multiple, despite there being nothing which is numbered by it. (2006a: 59) This void, ubiquitously found in any situation as the ‘suture to its being’ (2006a: 55) will allow Badiou to delineate the possibility of radical, extra-situational (and extra-ontological) novelty in his theory of evental truth, which I examine in Chapter 5.
He claimed paternity of a ‘Mengenlehre [doctrine of sets]’ and specified that ‘[b]y a ‘manifold’ or ‘set’ [Menge] I understand in general any many [Viele] which can be thought of as one [Eines], that is, every totality of definite elements which can be united to a whole through a law’ (Quoted in Hallett 1984: 33) and again that ‘[b]y ’aggregate‘ [Menge] we are to understand any collection into a whole [Zusammenfassung su einem Ganzen] M of definite and separate objects m of our intuition or our thought.
It is presented but never present, Badiou’s Mathematical Ontology 29 eluding recapture by the One. To this extent, Badiou’s is a subtractive ontology, where ‘the rigour of the subtractive’ is opposed to ‘the temptation of presence’ (2006a: 27). 5 Secularising infinity Given the Void, an infinity of infinities follows. This is Badiou’s vision of the ontological situation, regulated by ZFC set theory. But this insight into the nature of infinity was a hard-won historical achievement. 46 The classical, Greco-Roman pre-Christian sequence has a purely negative assessment of infinity as the a-peiron or absence of limit.