Being and Truth
The next three chapters outline the central components of Badiou's mature philosophical system. Chapter 4 goes over the details of Badiou's ontology, his general theory of “situation.” It includes a summary of the basic concepts of set theory, and an explanation of the crucial distinctions between belonging and inclusion, consistent and inconsistent notions of multiplicity, presentation and re-presentation, and the structure and state of a situation. Chapter 5 is concerned with the intervention, in a situation, of a subject and the truth she or he sustains. This chapter provides a comprehensive analysis of each stage of a truth procedure, from its inaugural decision (the naming of an indiscernible event) to its eventual restraint (with respect to an unnameable). Chapter 6 then more closely considers the precise axiomatic status of truth, before moving on to evaluate Badiou's response to his major philosophical rivals: Kant, Spinoza, Hegel, and Deleuze.