Alain Badiou

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Logics of Worlds (Being and Event, 2)

…insofar as being, qua being, is nothing other than pure multiplicity, it is legitimate to say that ontology,

the science of being qua being, is nothing other than mathematics itself.

-Alain Badiou

(Author’s preface, «Being and Event», p. xiii)

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«Obviously, since we show that there is no universe, it belongs to the essence of the world that there are several worlds, since if there were only one it would be the universe.
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As a situation of being, a world is not an empty place—akin to Newton’s space—which multiple beings would come to inhabit. For a world is nothing but a logic of being-there, and it is identified with the singularity of this logic. A world articulates the cohesion of multiples around a structured operator (the transcendental).
At the core of transcendental questions lies the evaluation of the degrees of identity or difference between a multiple and itself, or between a being there and other beings. The transcendental must therefore make possible the ‘more’ and the ‘less’. There must exist values of identity which indicate, for a given world, to what extent a multiple-being is identical to itself or to some other being of the same world. This clearly requires that the transcendental possess an order-structure.
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…our operational phenomenology identifies the condition of possibility for the worldliness of a world, or the logic of the localization for the being-there of any being whatever.

It is very striking that this phenomenology is absolutely complete with only three operations, bound together by a simple axiomatic:

• a.A minimum of appearance is given.
• b.The possibility of conjoining the values of appearance of two multiples (and therefore of any finite number of multiples).
• c.The possibility of globally synthesizing the values of appearance of any number of multiples, even if there is an infinity of them.

When we say that the description of these operations makes up a complete phenomenology, we mean that the transcendental determination of the minimum, the conjunction and the envelope (or synthesis) provides everything that is needed for being-there to consist as a world.

– «Logics of Worlds (Being and Event II)», pp. 102-103

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