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The concept of the subject is very important for the contemporary French philosopher, Alain Badiou, and it is discussed in works such as the Theory of the subject, Ethics, Being and Event, and the Logic of worlds. Paying attention to the changes and developments in Badiou's thought leads us to the conclusion that his perspective on the subject has also undergone changes. For the first time in his book Theory of the Subject, he examines the concept of the subject. A time still under the influence of Althusser and Mao, Therefore, the basis of the subject is social actions and purely political functions and the ontological foundations of the subject are not examined by him. While, later in the last course of his thought, He writes the book "Being and Occurrence" with an ontological subject as his focus, and his attention to subtractive ontology leads him to a mathematical subject. finally, in the Logic of Worlds, it continues its evolutionary path, one we believe transforms the subject from a purely human and political awe to a finite and abundant part of an infinite truth in subtractive situations. In this article, while examining the above path, we mentioned some criticisms in this regard because we believe that Badiou's explanation of the subject contains flaws that are in conflict with the logic of subtractive ontology.

Undoubtedly, Kant is one of the most effective figures in the history of western philosophy because he created a great evolution in this history by his so-called Copernican revolution and the interwoven relation of subject and object. As is acknowledged by many scholars, Critique of Pure Reason is one of the most important epistemological works in the new era that has set the boundaries of knowledge and has offered a new and unmatched description of how knowledge is gained by subject. Accordingly, most released commentaries of Kant’s philosophical outlook are epistemological. But Alain Badiou, contemporary French philosopher, contrary to common interpretation, presents an ontological one. He himself offers a kind of ontology named subtractive ontology, and believes that we can recognize it, due to how Kant formulates transcendental subject and object, forms of sensible intuition, and categories of understanding. As a result, he describes the features of Kantian ontology in his works Briefings on Existence and Theoretical Writings. The authors of this article see his claim notable and realizable. So, we will try to introduce the specifications of subtractive ontology and then check Badiou’s claim of Kant’s ontology. Finally, we will explain some reasons to criticize his belief.
Key Words: Badiou, Kant, Subtractive Ontology, Transcendental Subject, Transcendental Object The authors of this article try to read Badiou’s interpretation of Kant’s philosophy. In doing so, first we see two of his most famous books about Kant: Briefings on Existence and Theoretical Writings. In them, he claims that Kant should be read as an ontologist, because of some main notions as subject and object. Then, he tries to compare ontology in Kant with the one he names subtractive ontology and which is based on mathematics. So, we read his book, Being and Event, and review some of Badiou’s important ontological foundations as situation, set theory, void set, presentation, power set etc. in order to study his claim.
According to Badiou, the existence of transcendental subject and transcendental object, which he names proto-transcendental subject and proto- transcendental object, proves that we can consider Kant as an ontologist, and therefore an ontological interpretation of him is inevitable. In spite of this claim, Badiou also remember that, because of relational character of subject and object, we essentially describe them as epistemological entities.
Finally, we conclude that ontological and epistemological interpretation of Kant seems inseparable. For this reason, we have to pay attention to key role of void in Badiou's ontology, i.e. subtractive ontology, and show its differences with Heidegger's fundamental ontology. Ontology in Kant, according to Heidegger, is preceded by epistemology and, according to Badiou, they are implicit in Kant's thought; hence, according to Heidegger, Kant's ontology is complete and more important than epistemology. In contrast, Badiou says that Kant cannot never completely rid himself of epistemological strains. Heidegger even talks about Kant's ability to better understand. He believes that if we consider Kant to be an ontologist, we can understand him better than himself. Badiou believes that by relying more on a number of categories, instead of relying on the connection between the subject and the object, the Kantian can be seen deeper than conventional and epistemological believers. Kant is an ontologist.
However, Badiou's insistence on the existence of Kant's ontological dimensions is significant. On the one hand, he himself cannot ignore the great and inevitable role of epistemology in Kant, because the characteristics of the subject and object in his view, moreover, of the form of formation Recognizing the human being from the real world through the certainty and necessity of the past elements, and drawing the focus of past writing theorems. Therefore, the relationship between the whole and the whole subject with the object makes it impossible for each other to exist, because, in Kant's opinion, the subject creates the universe; therefore, the existence of the subject and object serves their epistemological function. Whereas the distinction Kant between Neumann and Phenomenon confines his ontological view to phenomena, while he does not directly associate the existence with such a distinction, he basically dismisses it. Counts On the other hand, the elements of Kant's philosophy, as the ontological foundations, cannot be fully coherent with the definition of a person from the ontology of introspection, because the recognition of concepts such as subject, object, sensory intuition, and categories Understanding their epistemological functions in Kant's view of one and the other, and the reasons for their explanation, namely, the need to respond to the circumstances of Kant's time on the other. Consequently, even if we want to accept the ontology of the discourse in Kant, we must rightly affirm that the ontology of discourse in Kant is on epistemology. - Badiou, A. (2006) a. Being and Event, translated by Oliver Feltham, London: Continuum.
- Badio, A. (2006) b. Briefings on Existence: A Short Treatise on Transitory Ontology, translated by Norman Madarasz, New York: SUNY Press.
- Badiou, A. (2009) Logics of Worlds, translated by Alberto Toscano, London: Continuum.
- Badiou, A. (1991) "On a Finally Objectless Subject", in Who Comes after the Subject, translated by B.Fink, 24-32, New York: Routledge.
- Badiou, A. (2004) Theoretical Writings, translated by Ray Brassier and Alberto Toscano, New York: Continuum.
- Forster, Michael N. (2008) Kant and skepticism, Prinston University Press.
- Heidegger, M. (1990) Kant and the Problem of Metaphysics, Forth edition enlarged, translated by Richard Taft, Bloomington: Indian University Press.
- Kant, I. (1998) Critique of Pure Reason, translated by Paul Guyer and Allen W. Wood, Cambridge: Cambridge University Press.
- Kullman, O. (2011) Some Remarks on the Philosophy of Alain Badiou: Mathematics, Ontology, Politics, available in http://cs.swan.ac.uk/~csoliver/ Sun Yat-sen University, Institute of Logic and Cognition.
- Wolf, R. P. (1963) Kant`s Theory of Mental Activity, A Commentary on the Transcendental Analytic of the Critique…, United States: Harvard University Press.

Alain Badiou, the French famous contemporary philosopher, considers ontology as identical with mathematics. He speaks about a kind of ontology entitled subtractive ontology which is based on pure multiplicity from which the one is subtracted. The fundamental claim of this ontology pertains to the mathematics of ontology. According to Badiou, this idea can be explained only by set theory. Within this ontological bed no reference is made to the meaning of being, nor sought to answer the question: “what is the nature of beings, as they are?” Instead, just like some great philosophers such as Leibnitz and Heidegger, in his philosophical struggle, he put the following question as his watchword: "why there are beings, instead of nonbeings?”. Undoubtedly, raising such question indicates the importance of nothingness in Badiou’s outlook. In this line, as void set plays a very important role in the set theory, nothingness is also important in subtractive ontology. In this paper, an attempt is made to study the notion of nothingness in Badiou’s ontology and highlight the importance of using mathematics to describe nothingness in this sort of ontology.