“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

Introduction
Being and Event (1988)

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Alain Badiou 29

French writer and philosopher 1937

Christian Heinrich von Dillmann (1829–1899) German educationist

Source: Die Mathematik die Fackelträgerin einer neuen Zeit (Stuttgart, 1889), p. 94.

“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 (1937) French writer and philosopher

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

“The subject must distinguish itself through opposition from the rational being, which it has assumed outside of itself. The subject has posited itself as one, which contains in itself the last ground of something that is in it, (for this is the condition of Egohood, or of Rationality generally;) but it has also posited a being outside of itself, as the last ground of this something in it. It is to have the power of distinguishing itself from this other being; and this is, under our presupposition, possible only, if the subject can distinguish in that given something how far the ground of this something lies in itself and how far it lies outside of itself.”

Johann Gottlieb Fichte (1762–1814) German philosopher

Source: The Science of Rights 1796, P. 63

“Dialectical thought understands the critical tension between “is” and “ought” first as an ontological condition, pertaining to the structure of Being itself. However, the recognition of this state of Being — its theory — intends from the beginning a concrete practice. Seen in the light of a truth which appears in them falsified or denied, the given facts themselves appear false and negative.”

Herbert Marcuse book One-Dimensional Man

Source: One-Dimensional Man (1964), p. 133

“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

Introduction
Being and Event (1988)

“What renders a problem definite, and what leaves it indefinite, may best be understood from mathematics. The very important idea of solving a problem within limits of error is an element of rational culture, coming from the same source. The art of totalizing fluctuations by curves is capable of being carried, in conception, far beyond the mathematical domain, 65 where it is first learned. The distinction between laws and coefficients applies in every department of causation. The theory of Probable Evidence is the mathematical contribution to Logic, and is of paramount importance.”

Alexander Bain (1818–1903) Scottish philosopher and educationalist

Source: Education as a Science, 1898, pp. 151-152.

“Necessary truth is merely the subject-matter of mathematics, not the reward we get for doing mathematics. The object of mathematics is not, and cannot be, mathematical certainty. It is not even mathematical truth, certain or otherwise. It is, and must be, mathematical explanation.”

David Deutsch book The Fabric of Reality

The Fabric of Reality (1997)

“The arithmetization of mathematics… which began with Weierstrass… had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics.
These latter, in the opinion of the formalists, are so firmly entrenched in mathematical thought that in spite of the most careful circumspection in the choice of words, the meaning concealed behind these words, may influence our reasoning. For the trouble with human words is that they possess content, whereas the purpose of mathematics is to construct pure thought.”

Tobias Dantzig (1884–1956) American mathematician

p, 125
Number: The Language of Science (1930)

“There is no denying existence itself. Something must exist and anyone who says nothing exists at all makes a mockery of sense and necessity. The proposition that there is no denying being itself, then, is a necessary premise. Now this Being which has been admitted in principle is either necessary or contingent… What this means is that a being must be self-sufficient or dependent… From here we argue: If the being the existence of which is conceded be necessary, then the existence of a necessary Being is established. If, on the other hand, its existence is contingent, every contingent being depends on a necessary Being; for the meaning of its contingency is that its existence and non-existence are equally possible. Whatever has such a characteristic cannot have its existence selected for without a determining or selecting agent. This too is necessary. So from these necessary premises the existence of a necessary Being is established.”

Abu Hamid al-Ghazali (1058–1111) Persian Muslim theologian, jurist, philosopher, and mystic

(1964) Fada’ih al-Batiniyya. Edited by Abdurahman Badawi. Kuwait: Muasassa Dar al-Kutub al-Thiqafa, p. 82.

“1. We are the contemporaries of a third epoch of science after the Greek and Galilean. The caesura which opens this third epoch is not (a with the Greek) an invention - that of demonstrative mathematics - nor is it (like the Galilean) a break - that which mathematized the discourse of physics. It is a split, through, which the very nature of the base of mathematical rationality reveals itself, as does the character of hte dision of thought which establishes it.”

Alain Badiou (1937) French writer and philosopher

Introduction
Being and Event (1988)

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