The possibility of a systematic philosophy which is not first-philosophy in Badiou's 'Being and Event'

It is appropriate to read Badiou's Being and Event through three interconnected theses: (1) the non-being of the One, (2) the non-doctrinality of philosophy, and (3) that the mathematics is ontology. The decision on the non-being of the One can be understood as an expression of the break with the ontotheology. This is the initial decision of Being and Event. The decision of the non-doctrinality of philosophy means that the philosophical category of truth does not have a substantial oneness. Philosophical truth is not an object whose existence can be reached as a result of a derivation. Philosophy does not produce truth; in other words, philosophy is not a truth procedure. The truth procedures that Badiou calls the "conditions of philosophy" are science, art, politics and love, in which truths come into being as non-knowledge. Therefore, the philosophical category of truth and the truths that come into being in these four procedures are different. Philosophical truth functions as a void in which the truths in these four disciplines are recognised. Non- doctrinal philosophy, conceived in this way, has various appearances. The systematic non-doctrinal philosophy is a discourse that constructs a fiction of knowledge based on science, which is its condition, and shows the possibility of the existence of truth by recognising the irreducibility of truth to this fiction of knowledge. In this sense, Being and Event is a book of systematic philosophy. We can thus say that the establishment of non-doctrinality of philosophy is Badiou's primary goal in Being and Event. On the other hand, the decision that mathematics is ontology which is the third thesis is the first step in the route followed in Being and Event, which starts with the decision of the non-being of the One and aims at a philosophy thought without doctrine. This is precisely because mathematics is seen as the name of a thinking compatible with the non-being of the One in terms of its axiomatic nature on the one hand and its relation with set theory on the other. Mathematical ontology is the fiction of knowledge of Being and Event. The theory of subject of Being and Event, which is anticipated based on the mathematical ontology, is the place where the truth, which is thought to be irreducible to mathematical ontology, is recognised. Therefore, we can say that within this tripartite structure of Being and Event, a special type of relationship between philosophy and mathematics comes to the fore. One of our expectations from this relationship is that philosophy should not have a determining power on mathematics. In other words, this tripartite structure can only function properly if mathematical practice remains independent from philosophical discourse. Otherwise, we would have to say that philosophy has a doctrinal content and that this doctrinal content has a oneness, which would contradict the non-being of the One and the non-doctrinality of philosophy. Therefore, in the relationship between philosophy and mathematics conceived in Being and Event, the direction of determination should be from mathematics to philosophy. While recognising that this expectation can be tested based on different aspects of Being and Event, this study, after constructing a reading of Being and Event based on the aforomentioned tripartite structure, problematises this expectation -which it calls the non-first-philosophisation of metaontology- with reference to the use of the ̋The Axiom of Empty Set ̋ in Being and Event.