Matematica e ontologia in Alain Badiou - Giorgio Rizzo (Kaiak)
Badiou’s philosophical project is to outline the Number as the resource of Being within the limits of a situation, the ontological or mathematical situation. In doing so, the French philosopher establishes the being of number as the form of the pure multiple, removing it from the operational and serial manipulations which dominate our society. A society in which what counts- in the sense of what is valued- is that which is counted. Conversely, everything that can be numbered must be valued. Establishing a correct distance between thought and countable manipulations, Badiou attempts at an ontologisation of the concept of number, more in particular of the universal series of the ordinals upon which he grounds his theory. Resorting to Cantor’s set theory, the French philosopher invites the readers not to count, but to think the count. And this invitation, once accepted, requires a decision, that is, the effort of overtaking any consistent presented multiplicity, governed by the regime of thecount-as-one, in order to grasp the ontological-mathematical void from which multiplicities arise. His philosophical project, however, is not entirely consistent to the extent that it shows some terminological ambiguities (as regard, e.g., the notions of presentation and infinite) and dilemmatic situations: if we admit that a situation is composed of multiplicities in which there is no trace of the One, how can we recognize those without resorting to the count-as-one?