Preliminary Notes Towards A Badiousian Dialectics

For a while the idea of doing what Reinhold or Fichte tried to do to Kant, but to Badiou, has appealed to me: that is, a more "systematic" and unified rendering of the most key philosophical developments of Badiou's system. It is not necessarily that I wish to subscribe to such a system, and whatever system I would create would not be able to "cover" the diversity and transformations of a thinker's oeuvre. The project would unavoidably produce its own philosophy, and even then not something I would necessarily wish to take up. But I believe this kind of formalization has its own kind of intrinsic interest, especially when it comes to discerning key philosophical problematics and logics. I also thus leave the text in acknowledgment of the full possibility of internal errors.

The Two is the thinking and inteligibility of the separation between the one and the void.
The Two as movement, retroactively constructs this separation.
The separation that The Two performs is the sole relation between the one and the void, thus their connection.
This separation-connection is not constituted by the Two, for its condition of possibility is the material point of the Event
The Event is the aleatory encounter of the one and the void, where what is encountered is their impossible combination.
This impossible combination is nothing but the connection of their separation at the point of the un-thought.
After the Two has come into movement, it dialectizes the situation. The Two dialectizes the one by splitting it from within. This is the consequence of the appearance of separation in a one, that is, in a local situation.
We can call this dialectization the split-one. It has two moments: the one-as-one (also named “the State”) and the becoming-one-of-infinity that is the split-one’s essence. These two moments are in conflict.
This conflict is the dialectical unity of the situation. It is nothing else but connection-separation as it appears in the one.
In the split-one and in its dialectical unity, only one side - the becoming-one of infinity - represents this unity. The split-one has a certain asymmetry.
The split-one is only truly a split-one when the one-as-one is thwarted by the positivity of the becoming-one of infinity. This is because the split-one is nothing but the fact that the one is not as one. The Two determines the one solely as separated-connected from the void.
Though separation occurs as split-one, or in-a-one, it is global separation (or: truth is universal). This is because the one limits through the one-as-one, but the one-as-one has become the inessential.
Although the Two is an equalizing unity-of-difference - the connection-separation of the Two - there is ontological asymmetry. The globality of the split-one requires that the void be said to be, while the one be said to not be.
This requires that the distinction of Being and non-being as asymmetrical does not exactly coincide with the connection-seperation of the Two. Otherwise Being and non-being would be the opening moment of a unity-of-difference indistinguishable from the Hegelian dialectic, and consequently non-aleatory and non-materialist.
How then is the distinction between Being and non-Being thinkable, when thought is the Two as connection-separation? We will see that there is asymmetry through a self-mediation of The Two.
In order for ontology to be thought, it must be a unique form of the Two. This difference in the Two is a Two-of-the-Two.
The Two-of-the-Two is the separation-connection of separation-connection. Seperation-connection is generic unity of absolute difference, or a unity which is nothing but the absoluteness of this difference. What would it mean to say that absolute difference was absolutely different from itself? It would mean it was absolute identity.
The Two-of-the-Two is the identity of the void and the one, the void-of-the-one (it is also the one-of-the-void, or appearance). And the sublation of difference in this identity is ontological assymetry. The Two-of-the-Two performs the non-being of the one. Or: the non-being of the one is the-void-of-the-one.
The affirmation of the Being of multiplicity cannot be dialectically inferred from the Two. It is specific to ontology’s real forms of practice. The concept of the Two-of-the-Two is only the elaboration of the possibility of ontology.
Ontology’s existence is necessary for thought, but its coming into being is aleatory (like any Two).
Ontology as Two-of-the-Two cannot itself think the Two. Though thinking is The Two, this does not mean that a Two-of-the-Two would be a self-thinking.
The Two-of-the-Two annihilates the one in the void-of-the-one. Without a one there can be no split-one, and so the Two cannot act as thought. While remaining thought, its thought is eliminated for it. It is unconscious thought.
How then is the Two itself thinkable? There is only the void and the one, and the Two which thinks their separation. The Two cannot think itself, so that which thinks the Two is either the one or the void. But only the Two is thought, so the only solution is that the Two be deployed as one or void.
If the Two were deployed as void, it would mean the Two was no-where, for the one is localization. We have as yet of yet no evidence that the human being can be no-where.
if the Two is going to come to our knowledge and be thought, it must then be deployed as one. We will call the one-of-the-Two philosophy.
Philosophy would not be the Two "in-itself." It is the one of the Two, or Two as one. Nor is it the Two of-the-Two as for-itself self-thinking, for the Two-of-the-Two is unconscious thought.
Nor is philosophy the one-as-one (the state). The one-as-one is a moment of the Two as split-one, not as one. Or put differently, it is one-as-one not the-Two-as-one. If philosophy exists, it is not ideology.
However, if philosophy is a one (the one-of-the-Two) philosophy finds itself “caught between” the two one-moments in the split-one, the one-as-one and the becoming-one of infinity. In order to think the Two it must “ally” itself with that which represents it, the becoming-one of infinity in the split-one.
The next installment will broach the operations of this “allying” through establishing a concept of subjectivity.