In his introduction to Badiou’s Polemics, Steve Corcoran makes a couple of statements that strike me as very nicely capturing the spirit of Badiou’s political thought. First, Corcoran remarks,

In order to maintain this structure in dominance, certain elements must remain uncounted or excluded, elements that inhabit what Badiou calls the edge of the situations void. The void cannot, of course, be localed or presented in the sitaution, it is scattered throughout it (the capitalist situation, for example, is structurally incapable of recognizing the capcity for proletarian innovation which inhabits everyone). But those on the edge of the void, those with ‘nothing to lose but their chains’, are situated in it, but as a sort of negative magnitude, the living lack of positive qualities that define the way the situation is re-presented. In Badiou’s terms, then, they are presented in it, and hence belong to, the situation, but are not re-presented in it. So long as the elements of a situation do not radically deviate from their assigned places, or lack therof, this gap will normally not show. To the always total structure of knowledge, which knows neither void nor excess, this element will simply appear as a non-essential or contingent disturbance to the situation, not as a symptom of the structural ‘lie’ of the situation itself. From the standpoint of the state of the situation, this inconsistent multiplicity simply appears as nothing, as non-being.

Then, every so often, in a completely unpredictable fashion, a Truth-Event comes to peirce a hole in the totalizing, static structure of knowledge. An Event for Badiou is a properly contingent and unaccountable occurance, exceeding everything that can be known in the situation– its identity conflicts, ideological struggles, fluxes of people and money, etc. An event cannot, Badiou argues, be generated nor deduced from the situation; but that it exceeds the terms of the situation does not mean that it arrives from some beyond or outside. There is no transcendence here; the Event attaches itself precisely to the void of the situation, revealing its inherent inconsistency… But what can come to be counted, and what links each specific situation to this inconsistency, are those that inhabit the edge of the void. Politics, in so far as it is universal and democratic, is for Badiou a process that comes to count those who are uncounted. Stigmatizing the uncounted as backward, dangerous, etc., then, is the best way to ward off a more profound ‘evil’: the emergence of a popular subjective force that would be capable of opposing the sterility of comfortable self-perpetuation, capable of developing the latent possibilities for democratic action that are immanent to the situation; a subjective force that, as subtracted from all sociological categories and classifications (‘illegal immigrants’, ‘citizens’), is grounded in the simple norm of belonging to the situation. (xii-xiv

Badiou’s conception of politics as “counting those who are uncounted” is perfectly analogous to analysis (as opposed to therapy) and the shift from early consultations to “putting one on the couch”. Analysis counts what is uncounted, which is to say the desire embodied in the symptom and parapraxes, that embodies the fundamental lie of the analysand’s life (the betrayal of their desire). By contrast, therapy seeks to maintain the normality of the ego by treating the symptom as an “illness” from which the subject must be separated so as to return to normal family, marital, and work relations. I will refer to “politics” as that praxis that engages with the constitutive exception to social organizations, while I will refer to “governance” as that activity concerned with counting, power, how social institutions should be organized, identities, and so on. “Governance” is a wide term that denotes sociological phenomena such as social systems, power-structures, epistemes, apparati of state capture, the logic of the signifier, and any explicit systems of governance such as bureaucracies. However, governance need not be presided over by legislators or conscious intentions to count as governance.

Corcoran goes on to remark that,

In terms of Being and Event, what the Paris Commune succeeded in doing was making pure presentation, i.e. pure and simple belonging to a situation irrespective of all cultural predicates, the principle of its politics. It succeeded in rupturing with all relation and creating a new set that was subtracted from the existing classifications and nominations structuring the preceding situation. Badiou’s more recent work does not go back over this point, but sets out to grasp the way that an event comes to transform the logic of the situation, that is, the way that its elements appear in it or the intensity with which they are endowed. For not having any objective foothold in the situation, a truth will succeed in imposing itself on the situation only in so far as it manages to transvaluate the intensity of its elements– or come to impose a different regime for their appearing. So, a truth proceeds as a subtraction from the classifications and distributions of the state, but it does so by altering the appearing, or the intensity, of the elements composing the situation. As Peter Hallward says, ‘the key point of reference remains the anarchic disorder of inconsistent multiplicity’; but because the being of the situation must be made to be there (i.e. experienced as connected, related) it must be made subject to the logical constraints of a particular situation. As Badiou figures it, these logical constraints mean that there will always be, in any situation, elements that exist maximally (politically speaking, those whose voices are sanctioned, whose speech leads to action), elements that are less intense, and elements that, like those on the edge of the void, are effectively invisible (whose speech registers as pure noise, and who as such constitute the ‘non-existent’ element of this situation). (xvii-xviii)

By way of example, it could be said adjunct or part time professors (I’m not one) are a potential site of the political in the situation characterizing American universities. Adjuncts clearly belong to this situation, but are not re-presented within that situation. Rather, those who have the greatest degree of intensity in this situation would be professors and administrators, whereas adjuncts are almost non-existent in this situation, having little or no voice. Badiou’s point isn’t that we should find a way to include the voice of adjuncts, but rather that those elements of the situation that are on the edge of the void have the potential to transform all the elements of the situation by revealing the constitutive arbitrariness of the system of governance or organization of the particular question. The question of the political is that of how to shift something that has a very low degree of intensity with respect to appearing to having a high degree of intensity that transforms all elements of the situation (i.e., it’s not a question of identity politics).