Banalisation of the Real
Mark Kaplan writes somehing which expresses brilliantly part of the way I’ve been interpreting what I’ve read of Badiou:
>Think, for example of the predictable paradoxes produced by ‘the set of all that exists’.
> How can this set include itself? If we create another set to include it, the paradox simply
> recurs. My first and provisional thought is: is it not at moments like this, when the
> symbolic language buckles - is this not a _sign of the Real_?
Unfortunately, this is expressed so well it helps me realise I’m disatisfied with the position. Isn’t it translatable straightforwardly into Kantianism? The mathematical paradoxes are functioning like antinomies, allowing a transcendental deduction of the existence of the Real. And the Real itself is fundamentally unrepresentable; we can only become aware of “this outer limit of the symbolic.”
But I think Badiou interprets the mathematical paradoxes in almost exactly the opposite way, perhaps because he trusts the maths more. For him, they demonstrate not that what we thought was coherent is actually not, but that what we thought was incoherent is actually rigorously understandable. Unconstructible sets, unique unnameable objects and unprovable statements all _seem_ like they are impossible, but maths shows us that they’re actually perfectly acceptable objects we can talk about without incoherence.
Now, the infinite would be the central example of this use of maths in Badiou. In ‘Philosophy and mathematics: infinity and the end of romanticism’, Badiou criticises those philosophers who maintain a conception of the infinite as an unreachable horizon for ignoring mathematical developments; contemporary maths, he says, has _banalised the infinite_, allowed us to see that it is omnipresent and comprehensible. I wonder if we could extend this idea to cover Badiou’s philosophy more generally. This would make his mathematical ontology an attempt to banalise the Real.
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