By Gabriel Riera
An creation to Badiou's philosophical notion and its implications for different humanistic disciplines and the social sciences.
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Extra resources for Alain Badiou: Philosophy and Its Conditions
In Ba diou's view set theory, with its intrinsic ontology, axiomatic approach and rooting in ontology, stems from Platonism. However, in the argumentative virtuosity Ba diou displays, this coordination between Aristotle and Plato comes close to philo sophical self-interest at best, or, at worst, to Sophistry. Badiou needs Plato. The work of the Academy's founder most clearly exhibits the emergence and process of philosophy. Aristotle and Kant, on the other hand, appear in Badiou's reading to deter philosophy from its greater potential, notwithstanding the vast and innova tive range of the sciences created by Aristotle and Kant, especially in their rela tivizing mathematics and the matheme to logic.
Peano's smart formalization led to an attempt in the sciences to reduce mathematics to logic. " This is largely owing to two key domains that interact in his system: math· ematics and, uncharacteristically for set theory, ontology. Badiou identified ontology's paradigm in set theory. However, he has also had to confront category theory, which has vied for foundational status within the field of mathematics. Albeit in schematic form, in what follows we will attempt a philosophical reconstruction of this ontology to confront it with the notion of cat· egory.
In Badiou's perspective, Platonism better describes philosophy as being under condition of an event in thought. Platonism attests to the surfacing of the infinite through the finite world, as it were. "Plato's fundamental concern is to de· clare the immanent identity and co· membership of the known and the knowing mind, their essential ontological commensurability. Were there one point on which he is Parmenides' son asserting 'the Same is both Thought and Being,' it is on that point" (CTOT 96).