Ideas of Alain Badiou, by Theme
[French, b.1937, Born in Morocco. Chair of Philosophy at the École Normale Supérieure.]
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1. Philosophy / C. History of Philosophy / 5. Modern Philosophy / c. Modern philosophy midperiod
12330

In ontology, logic dominated language, until logic was mathematized

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
9808

Philosophy aims to reveal the grandeur of mathematics

1. Philosophy / D. Nature of Philosophy / 8. Humour
12318

The female body, when taken in its entirety, is the Phallus itself

1. Philosophy / E. Nature of Metaphysics / 6. Against Metaphysics
12325

Philosophy has been relieved of physics, cosmology, politics, and now must give up ontology

2. Reason / A. Nature of Reason / 4. Aims of Reason
12324

Consensus is the enemy of thought

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
12337

There is 'transivity' iff membership ∈ also means inclusion ⊆

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
12321

The axiom of choice must accept an indeterminate, indefinable, unconstructible set

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
12342

Topos theory explains the plurality of possible logics

5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
12341

Logic is a mathematical account of a universe of relations

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
9812

In mathematics, if a problem can be formulated, it will eventually be solved

6. Mathematics / A. Nature of Mathematics / 3. Numbers / a. Numbers
12334

There is no single unified definition of number

12335

Numbers are for measuring and for calculating (and the two must be consistent)

6. Mathematics / A. Nature of Mathematics / 3. Numbers / b. Types of number
12322

Must we accept numbers as existing when they no longer consist of units?

12333

Each type of number has its own characteristic procedure of introduction

6. Mathematics / A. Nature of Mathematics / 3. Numbers / e. Ordinal numbers
12336

A von Neumann ordinal is a transitive set with transitive elements

6. Mathematics / A. Nature of Mathematics / 4. The Infinite / a. The Infinite
9813

Mathematics shows that thinking is not confined to the finite

6. Mathematics / A. Nature of Mathematics / 4. The Infinite / g. Continuum Hypothesis
12327

The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory

6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / c. Nominalist structuralism
12329

If mathematics is a logic of the possible, then questions of existence are not intrinsic to it

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
12328

Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
12339

Aristotle removes ontology from mathematics, and replaces the true with the beautiful

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
12331

Logic is definitional, but real mathematics is axiomatic

7. Existence / A. Nature of Existence / 1. Nature of Existence
12320

Ontology is (and always has been) Cantorian mathematics

7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
12340

There is no Being as a whole, because there is no set of all sets

9809

Mathematics inscribes being as such

7. Existence / A. Nature of Existence / 3. Being / b. Being and existence
12323

Existence is Being itself, but only as our thought decides it

7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
12326

The primitive name of Being is the empty set; in a sense, only the empty set 'is'

12332

The modern view of Being comes when we reject numbers as merely successions of One

7. Existence / A. Nature of Existence / 7. Criterion for Existence
9811

It is of the essence of being to appear

19. Language / F. Communication / 3. Denial
12338

We must either assert or deny any single predicate of any single subject

21. Aesthetics / B. Nature of Art / 8. The Arts / b. Poetry
9814

All great poetry is engaged in rivalry with mathematics

25. Society / B. The State / 8. Religion in Society
12316

For Enlightenment philosophers, God was no longer involved in politics

29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
12317

The God of religion results from an encounter, not from a proof
