Badiou
Badiou starts with Cantor's set-theory, and introduces idea of something that does not belong to a given set:
‘I will term evental site an entirely abnormal multiple; that is, a multiple such that none of its elements are presented in the situation. The site, itself, is presented, but ‘beneath’ it nothing from which it is composed is presented. As such, the site is not part of the situation. I will also say of such a multiple that it is on the edge of the void, or foundational (these designations will be explained).’
So, evental sites are negative
‘negative aspect’ of evental sites (i.e. to not be represented) ‘One can only maintain that there are site-points, inside a situation, in which certain multiples (but not others) are on the edge of the void.’ – so there are evental sites in situations, but there is no evental situation – ‘Every radical transformational action originates in a point, which, inside a situation, is an evental site.’
So: ‘the existence of a multiple on the edge of the void merely opens up the possibility of an event’ – it doesn’t guarantee it – site has to be ‘abnormal multiple, on the edge of the void’ – so ‘there is no event save relative to a historical situation, even if a historical situation does not necessarily produce events.’
But event’s belonging to situation of site ‘is undecidable from the standpoint of the situation itself’ – i.e. ‘signifier of the event… is necessarily supernumerary to the site’ – ‘an event is not (does not coincide with) an evental-site. It ‘mobilizes’ the elements of its site, but it adds its own presentation to the mix.’
‘To declare that an event belongs to the situation comes down to saying that it is conceptually distinguished from its site by the interposition of itself between the void and itself. This interposition, tied to self-belonging, is the ultra-one, because it counts the same thing as one twice: once as a presented multiple, and once as a multiple presented in its own presentation.’
But the he says that event might not belong to situation – in which case… (da da da) ‘nothing has taken place except the place.’
‘Therefore: either the event is in the situation, and it ruptures the site’s being ‘on-the-edge-of-the-void’ by interposing itself between itself and the void; or, it is not in the situation, and its power of nomination is solely addressed, if it is addressed to ‘something’, to the void itself.’
He calls this undecidability a ‘double function’: ‘On the one hand, the event would evoke the void, on the other hand, it would interpose itself between the void and itself. It would be both a name of the void, and the ultra-one of the presentative structure.’ He calls this an ‘ultra-one-naming-the-void’: ‘It is this ultra-one-naming-the-void which would deploy, in the interior-exterior of a historical situation, in a torsion of its order, the being of non-being, namely, existing.’ Fucking great.
Event can’t be formalized mathematically, i.e. ontologically: ‘There is no acceptable ontological matrix of the event.’ – so event ‘belongs to that-which-is-not-being-qua-being’ – and he talks of ‘the brilliance, in which being is abolished, of the mark-as-one’
‘Mallarmé is a thinker of the event-drama, in the double sense of the staging of its appearance-disappearance…’
B sees (Mallarméan) poetry as ‘an action of which one can only know whether it has taken place inasmuch as one bets upon its truth.’ – and see Un Coup as perfect staging of evental-site being on edge of void (storm etc)
‘The paradox of the evental-site is that it can only be recognized on the basis of what it does not present in the situation in which it is presented.’
So, shipwreck: ‘every event, apart from being localized by its site, initiates the latter’s ruin with regard to the situation, because it retroactively names its inner void. The ‘shipwreck’ alone gives us the allusive debris from which (in the one of the site) the undecidable multiple of the event is composed.’
Then casting dice: ‘A cast of dice joins the emblem of chance to that of necessity, the erratic multiple of the event to the legible retroaction of the count. The event in question in A Cast of Dice… is therefore that of the production of an absolute symbol of the event. The stakes of casting dice ‘from the bottom of a shipwreck’ are those of making an event out of the thought of the event.’
But then B homes in on the HESITATION! This passage is super-important:
‘However, given that the essence of the event is to be undecidable with regard to its belonging to the situation, an event whose content is the eventness of the event (and this is clearly the cast of dice thrown ‘in eternal circumstances’) cannot, in turn, have any other form than that of indecision. Since the master must produce the absolute event (the one, Mallarmé says, which will abolish chance, being the active, effective, concept of the ‘there is’), he must suspend this production from a HESITATION which is itself absolute, and which indicates that the event is that multiple in respect to which we can neither know nor observe whether it belongs to the situation or its site. We shall never see the master throw the dice because our sole access, in the scene of action, is to a hesitation as eternal as the circumstances.’
‘Between the cancellation of the event by the reality of its visible belonging to the situation and the cancellation of the event by its total invisibility, the only representable figure of the concept of the event is the staging of its undecidability.’
And, of course, Hamlet emerges at this point – the feather etc – figure of undecidability
And then event disappears back into void – ‘Must we then conclude, in a nihilistic manner, that the ‘there is’ is forever un-founded, and that thought, devoting itself to structures and essences, leaves the interruptive vitality of the event outside its domain?’
‘That ‘nothing’ has taken place … means solely that nothing decidable within the situation could figure the event as such. By causing the place to prevail over the idea that an event could be calculated therein, the poem realizes the essence of the event itself, which is precisely that of being, from this point of view, incalculable. The pure ‘there is’ is simultaneously chance and number, excess-of-one and multiple, such that the scenic presentation of its being delivers non-being alone, since every existent, for itself, lays claim to the structured necessity of the one. As an un-founded multiple, as self-belonging, undivided signature of itself, the event can only be indicated beyond the situation, despite it being necessary to wager that it has manifested itself therein.’
So constellation compensates for this neutralizing equivalence of gesture and non-gesture by fixing ‘in the sky of Ideas the event’s excess-of-one.’
But Badiou ends by turning to the bet. And this ties in with ethics, for which Badiou has previously given imperative ‘Decide from the standpoint of the undecidable.’
‘Mallarmé writes: ‘Every thought emits a cast of dice.’ On the basis that ‘a cast of dice never will abolish chance,’ one must not conclude in nihilism, in the uselessness of action, even less in the management-cult of reality and its swarm of fictive relationships. For if the event is erratic, and if, from the standpoint of situations, one cannot decide whether it exists or not, it is given to us to bet; that is, to legislate without law in respect to this existence. Given that undecidability is a rational tribute of the event, and the salvatory guarantee of its non-being, there is no other vigilance than that of becoming, as much through the anxiety of HESITATION as through the courage of the outside-place, both the feather, which ‘hovers above the gulf’, and the star, ‘up high perhaps.’ – nb feather is also pen.
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