“Since its Parmenidean organization, ontology has built the portico of its ruined temple out of the following experience: what presents itself is essentially multiple; what presents itself is essentially one. The reciprocity of the one and being is certainly the inaugural axiom of philosophy - Leibniz formulation is excellent; 'What is not a being is not a being - yet it is also its impasse; an impasse in which the revolving doors of Plato's Parmenides introduce us to the singular joy of never seeing the moment of conclusion arrive. For if being is one, then one must posit that what is not one, the multiple, is not. But this is unacceptable for thought because what is presented is multiple and one cannot see how there could be an access to being outside all presentation. If presentation is not, does it still make sense to designate what presents (itself) as being? On the other hand, if presentation is, then the multiple necessarily is.”

— Alain Badiou

Meditation One: The One and the Multiple: a priori conditions of any possible ontology
Being and Event (1988)

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Alain Badiou 29

French writer and philosopher 1937

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“The initial thesis of my enterprise - on the basis of which this entanglement of periodizations is organized by extracting the sense of each - is this following: the science of being qua being has existed since the Greeks - such is the sense and status of mathematics. However, it is only today that we have the means to know this. It follows from this thesis that philosophy is not centered on on ontology - which exists as a separate and exact discipline- rather it circulates between this ontology (this, mathematics), the modern theories of he subject and its own history. The contemporary complex of the conditions of philosophy includes everything referred to in my first three statements: the history of 'Western'thought, post-Cantorian mathematics, psychoanalysis, contemporary art and politics. Philosophy does not coincide with any of these conditions; nor does it map out the totality to which they belong. What philosophy must do is purpose a conceptual framework in which the contemporary compossibilty of these conditions can be grasped. Philosophy can only do this - and this is what frees it from any foundational ambition, in which it would lose itself- by designating amongst its own conditions, as a singular discursive situation, ontology itself in the form of pure mathematics. This is precisely what delivers philosophy and ordains it to the care of truths.”

Alain Badiou (1937) French writer and philosopher

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“All things that are in the world are linked together, one way or the other. Not a single thing comes into being without some relationship to every other thing. Scientific intellect thinks here in terms of natural laws of necessary causality; mythico-poetic imagination perceives an organic, living connection; philosophic reason contemplates an absolute One. But on a more essential level, a system of circuminsession has to be seen here, according to which, on the field of Śūnyatā, all things are in a process of becoming master and servant to one another. In this system, each thing is itself in not being itself, and is not itself in being itself. Its being is illusion in its truth and truth in its illusion. This may sound strange the first time one hears it, but in fact it enables us for the first time to conceive of a force by virtue of which all things are gathered together and brought into relationship with one another, a force which, since ancient times, has gone by the name of "nature"”

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“Truth is what we are. It is our essential nature and Being. It is the pure Self, the limitless one, the ultimate reality – it is awareness itself.”

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“The above interpretation has been introduced, not on account of its immediate value in the present system, but as an illustration of a significant fact in the philosophy of the intellectual powers, viz., that what has commonly been regarded as the fundamental axiom of metaphysics is but the consequence of a law of thought, mathematical in its form.”

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“The Doctrine of Knowledge, apart from all special and definite knowing, proceeds immediately upon Knowledge itself, in the essential unity in which it recognises Knowledge as existing; and it raises this question in the first place — How this Knowledge can come into being, and what it is in its inward and essential Nature?”

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Context: The Doctrine of Knowledge, apart from all special and definite knowing, proceeds immediately upon Knowledge itself, in the essential unity in which it recognises Knowledge as existing; and it raises this question in the first place — How this Knowledge can come into being, and what it is in its inward and essential Nature?
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“I then arrived at the certainty that it was necessary to posit that mathematics writes that which, of being itself, is pronounceable in the field of a pure theory of the Multiple. The entire history of rational thought appeared to me to be illuminated once one assumed the hypothesis that mathematics, far from being a game without object, draws the exceptional severity of its law from being bound to support the discourse of ontology.”

Alain Badiou (1937) French writer and philosopher

Introduction
Being and Event (1988)

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