By Gabriel Riera
An advent to Badiou's philosophical suggestion and its implications for different humanistic disciplines and the social sciences.
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Additional resources for Alain Badiou: Philosophy and Its Conditions
Badiou's lectures at the College International de Philosophie have been published as Circonstances. This page intentionally left blank. P A RT O N E M A T H E M A T I C S = O N TO LO G Y This page intentionally left blank. O N E O n Alain B adiou ' s T reatment o f Categor y T h eor y I n V iew o f a T rans itor y O ntolog y Norman Madarasz Of the many philosophical ideas in vogue during the twentieth century, that of "reduction" has fallen into uncertain disuse. After all, does reduction not imply the eminently dubitable feature of transcendent and positivist philosophies that, save for phenomenology, aim to crush the singular through a tendency toward the general?
Needless to say, Aristotle himself fell short of the task, leaving the science of Being qua Being as an unfulfilled sugges· tion while refusing to allot mathematics its Pythagorean-Platonist extension as a universal science of eternity. Still, the pure and empty multiple, subtracted from the One, can be attrib uted as a property of Being. In a mode faithful to Platonism, this allows Badiou to assert that "ontology" is a science of Being-qua·Being, a science of the void of which multiples are woven in their infinite development.
What is the extension of the idea of relation in set theory and does it differ dra· matically from category theory? The very idea of an identity relation between on· tology and mathematics depends on a clear elaboration of this problem. TH E INFINIT E AND TH E AP P EARING The ontological decision at the origin of Bad iou's system strikes a blow at the an· cestral relationship between the infinite and the One. Set theory asserts that the infinite is the inscription of a letter. Furthermore, this letter declares a funda· mental subtraction of the multiple·infinite with respect to a totalization by the 32 NORMAN MADARASZ One because one cannot posit the existence of a class of all classes, a set of all sets, without entailing a series of contradictions liable to compromise the whole theory.
Alain Badiou: Philosophy and Its Conditions by Gabriel Riera