A question for all you Badiou scholars

I’m working my way through Being and Event and I’m confused by a seeming aporia concerning Badiou’s understanding of inclusion and belonging.  In Meditation Seven, he writes ‘inclusion can be defined on the basis of belonging alone’ (83)  Later, in his discussion of the void-set, he writes that while it is true that Ø is included in Ø, it is not true that Ø belongs to Ø (87).  I understand, more or less, the arguments that flow from this latter statement, but I don’t understand who it can be true given that inclusion can be defined on the basis of belonging alone.

I may be missing something really simple here, but if anyone has any insight, I would be grateful.

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2 comments

  1. Inclusion is defined on the basis of belonging as follows: S is included in P if everything that belongs to S, also belongs to P (alternatively: S is included in P if there isn’t anything that belongs to S that doesn’t also belong to P). “S is included in P” entails that for all possible x’s, “x belongs to S” entails that “x belongs to P”.

    Ø is included in Ø because everything that belongs to Ø (that is, nothing) belongs to Ø (to which nothing belongs). There isn’t anything that belongs to Ø that doesn’t belong to Ø. (Every set is included in itself; Ø is no exception. No set belongs to itself, Ø included).

    Ø does not belong to Ø, because nothing does. But it does belong to {Ø}. It’s also included in {Ø}, because there isn’t anything that belongs to Ø that does not also belong to {Ø}. However, {Ø} is not included in Ø, because there is something – Ø – that belongs to {Ø}, that does not belong to Ø.

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