1 Masterclass on Alain Badiou’s ontology • The thesis ‘mathematics is ontology’ and its arguments • The argument that being is inconsistent multiplicity • The argument that set theory writes inconsistent multiplicity • Question 1: What is inconsistent multiplicity? • Question 2: What is consistent multiplicity? • Question 3: What does set‐theory ontology do? • Question 4: What is the status of the argument on being? • Question 5: Why not many ontologies rather than one? • Interpretation: The historicity of mathematics as action Introduction My approach today will be to pull apart the early steps in Alain Badiou’s set up of set theory ontology, specifically in Being and Event, with some references to essays in Brief Treatise of Transitory Ontology, and Theoretical Writings. The idea is to open up these steps and question them so as to give us the freedom to imagine and explore other ways of setting up ontologies. In the context of French philosophy in the 1980s, specifically those philosophers and thinkers that Badiou had recognized and named as allies or rivals – Lacan, Lyotard, Derrida, Nancy and Lacoue‐Labarthe, Althusser – ‘ontology’ was an unusual term to use. It had often provided an object of critique, assimilated with ‘metaphysics’, or an object of interpretation as in Heidegger’s ‘fundamental ontology’, but it was not embraced as the name of a positive project. Badiou’s use of this term represented a decisive step. As he said in the first Manifesto for Philosophy in response to Lacoue‐ Labarthe and Derrida’s declared end of metaphysics, and Blanchot’s ‘Step Not Beyond’ we need to take one step further. What is this step, how does he introduce and remake this ancient philosophical discipline of ‘ontology’? Through one simple but startling thesis: THE THESIS: “Mathematics is ontology‐ the science of being qua being.” (BE,4) “Mathematics writes that which‐ of being itself, is pronounceable in the field of a pure Theory of the multiple.” (BE,5) How does he explain this thesis? In the first Meditation of Being and Event he sets out requirements for ontology (BE,29) and then in Meditation Three he proceeds to identify a particular kind of mathematics that satisfies those requirements. The requirement for ontology is that being is thought as inconsistent multiplicity. 1) The One is not: The starting point, anchored in the history of philosophy, is the thesis that the One is not, explored by Plato in the last four hypotheses of the Parmenides. 2) Inconsistent multiplicity: Parmenides’ exploration of the hypothesis “If the One is not, nothing is” leads to the concept of plethora, of a multiple that disseminates itself internally without limit, never uncovering atomistic elements: this is the ‘inconsistent multiplicity’. 3) Count‐for‐one: Nevertheless there is some Oneness, an effect of unity thus there is an operation of unification that distributes inconsistent (before) and consistent multiplicity (after its effect).