Symbolic Cramps

Although I 've been very interested in Badiou's concept of the Event for some time, the mathematical theory that grounds Badiou's work is something I'm utterly unfamiliar with. So, I've recently made some very tentative forays into this stuff, dabbling in the odd equation, entertaining cursory thoughts on set theory etc.

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? It is the Real which cramps our symbolic codes and structures into paradox. But this needs refining. There are two positions here: 1. these 'kinks' in the Symbolic indicate the presence of the Real, which is not directly visible but only in the ruffles and distortions its leaves on the surface of our language(s); or, 2. that 'the real' is just the name we give to this outer limit of the symbolic. Where our symbolic languages reach an impass, these impasses indicates their boundary, and the Real is the name for what's 'beyond the boundary'.

I also thought here of one of Borges' parables, which articulates a related notion. It notes the curious points of paradox and contradiction, the 'knots' in our basic categories - the paradoxes of Zeno and so on - and concludes that these constitute a series of loose ends, or unravelled signs that this universe we inhabit is 'unreal', that the inter-subjective fiction we nominate 'reality' doesn't in fact 'add up'. Here -

We (the indivisible divinity that works in us) have dreamed the world. We have dreamed it resistant, mysterious, visible, ubiquitous in space and firm in time, but we have allowed slight, and eternal, bits of the irrational to form part of its architecture so as to know that it is false.

Or, if you prefer:

We... have dreamed the world. We have dreamed it as enduring, mysterious, visible, omnipresent in space and stable in time; but we have consented to tenuous and eternal intervals of illogicalness in its architecture that we might know it as false.'

With a bit of tweaking, we can translate this as: the architecture of our symbolic systems runs into insoluble difficulties at the edges. These insolubles are the index of what we cannot directly know, are indeed 'caused' by this unknowable and unnameable X, which bends our symbolic systems of knowledge into puzzle and paradox.

Needless to say, all this is rather, or vaguely, Lacanian. See, for example, Bruce Fink:

".. a symbolic system brings with it a syntax - a set of rules or laws - that is not inherent in the "pre-existing" reality. The resulting possibilities and impossibilities can thus be seen to derive from the way in which the symbolic matrix is constructed..." (Please note I have quoted slightly out of context to suite my own purposes.)