Ideas from 'Briefings on Existence' by Alain Badiou [1998], by Theme Structure
[found in 'Briefings on Existence' by Badiou,Alain (ed/tr Madarsz,Norman) [SUNY 2006,0791468046]].
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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 / 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 / 3. Numbers / a. Numbers
12335

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

12334

There is no single unified definition of number

6. Mathematics / A. Nature of Mathematics / 3. Numbers / b. Types of number
12333

Each type of number has its own characteristic procedure of introduction

12322

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

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 / 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

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

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

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

25. Society / C. Political Doctrines / 1. Political Theory
12316

For Enlightenment philosophers, God was no longer involved in politics

29. Religion / A. Religious Thought / 1. Religious Belief
12317

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