بنيادهاي رياضياتي فلسفه‌ي الن بديو، بر اساس كتاب هستي و رخداد

Mathematical Foundations of Alain Badiou’s Philosophy, Based on Being and Event

از ديدگاه الن بديو، فيلسوف معاصر فرانسوي، رياضيات هستي­ شناسي است و نظامي اصل موضوعي بر پايه­ي نظريه­ ي مجموعه­ ها يگانه شكل انديشيدنِ ممكن به هستي بما هو هستي است. بدين­ قرار، در فلسفه­ ي الن بديو علاوه بر به خدمت گرفته شدنِ اصول موضوع رياضي، مفاهيمي كه در سنت هستي ­شناسي فلسفي مي­ شناسيم دگرگون مي­ شوند و با مفاهيمي از نظريه­ ي مجموعه ­ها گره مي ­خورند يا تناظر مي­ يابند؛ گرچه بايد تأكيد كرد كه هستي در فلسفه­ ي او نه شكلي رياضياتي دارد نه ابژه ­اي رياضي است. مي ­توان گفت دشوارترين بخش فلسفه ­ي بديو همين مبحث هستي ­شناسي است، شايد تا حدي، به اين دليل كه براي احاطه بر آن ­بايد هم با سنت فلسفي غرب آشنا بود و هم با نظريه­ ي مجموعه ­ها. مضاف بر اين، بدون داشتن درك درستي از مباحث فنيِ او در هستي شناسي نمي­ توان درك كاملي از بدنه­ ي فلسفه­ ي او داشت. در اين مقاله، نخست نظام رياضياتي و اصل موضوعي مورد نظر بديو تا حد ممكن تشريح مي­ شود و سپس برخي از مفاهيم بنيادين فلسفه­ ي او بر پايه­ ي نسبت ­شان با مفاهيم متناظر در نظريه­ ي مجموعه­ ها بيان خواهد شد تا از رهگذر روشن شدنِ بنيادهاي رياضياتي فلسفه­ ي وي، معلوم گردد كه او چگونه از طريق رياضيات به هستي مي ­انديشد.

According to Alain Badiou mathematics is ontology. This is a meta-ontological thesis; that is, it is neither mathematical nor ontological. The crucial consequence of this thesis is that philosophy is separated from ontology. So it is not no longer the task of philosophy to think of being. Instead, Badiou regards an axiomatic system based on set theory as the sole form of thinking about being qua being. In his philosophy, the traditional concepts of philosophical ontology transform and link up with set theoretical concepts. It should be mentioned, however, that being in his thought neither has a mathematical form nor is a mathematical object. Not surprisingly the most difficult part of Badiou’s philosophy is ontology, partly for the reason that to fully grasp it one must know both the western tradition of philosophy and the set theory. Moreover, it is impossible to fully comprehend the body of his philosophy without having a deep understanding of his fundamental and technical discussions in ontology. In this essay, firstly we explain what Badiou means by the axiomatic system, and then we give an account of some basic concepts of his philosophy on the basis of their corresponding concepts in set theory, in order to show that how Badiou thinks of “being” by means of mathemathics.