Badiou links the various anti-philosophical themes of chance, risk, freedom, and change to the notion of negation: “one can say that I am pursuing from one end of my philosophical enterprise to the other … a meditation on negation. I am simply trying to explain the possibility of change, the possibility of passing from a certain regime of laws of that which is to another regime, by the mediation of a protocol of a truth and of its subject. I am thus in dialectical thought, and in a dialectical theory of happiness, which is the paraconsistent negation of finitude by a complete infinite” (82).
So Badiou can say that his thought embodies a dialectics without determinism: “as my dialectical thought includes a figure of hasard, it is non determinist” (82).
Hegel’s Absolute is deterministic. Badiou argues that as he incorporates an element of chance in his system, his Absolute is non-deterministic. He tells us that in the futue book THE IMMANENCE OF TRUTHS he will discuss Hegel’s concept of the Absolute, as he agrees with Hegel and Plato that “all real happiness is a sort of provisional access to the Absolute” (82).
Describing the forthcoming book: “with the presence of an aleatory element, I introduce the principle of a cut which is not exactly homogeneous to the classical principles of negation. That is why, finally, I will be using three different and interwoven logics: classical logic, intuitionist logic, and paraconsistent logic” (83).
“At the same time, I will raise to the absolute the ontological system of reference – the thought of the pure multiple – by means of the truly sensational theory of “very big infinities” Threefold logic and infinity of infinities will be the key of a general theory of happiness” (83).