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 2006,0-7914-6804-6]].

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1. Philosophy / C. History of Philosophy / 5. Modern Philosophy / c. Modern philosophy mid-period
In ontology, logic dominated language, until logic was mathematized
1. Philosophy / D. Nature of Philosophy / 7. Humour
The female body, when taken in its entirety, is the Phallus itself
1. Philosophy / E. Nature of Metaphysics / 6. Against Metaphysics
Philosophy has been relieved of physics, cosmology, politics, and now must give up ontology
2. Reason / A. Nature of Reason / 4. Aims of Reason
Consensus is the enemy of thought
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
There is 'transivity' iff membership ∈ also means inclusion ⊆
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The axiom of choice must accept an indeterminate, indefinable, unconstructible set
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Topos theory explains the plurality of possible logics
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
Logic is a mathematical account of a universe of relations
6. Mathematics / A. Nature of Mathematics / 3. Numbers / a. Numbers
Numbers are for measuring and for calculating (and the two must be consistent)
There is no single unified definition of number
6. Mathematics / A. Nature of Mathematics / 3. Numbers / b. Types of number
Each type of number has its own characteristic procedure of introduction
Must we accept numbers as existing when they no longer consist of units?
6. Mathematics / A. Nature of Mathematics / 3. Numbers / e. Ordinal numbers
A von Neumann ordinal is a transitive set with transitive elements
6. Mathematics / A. Nature of Mathematics / 4. The Infinite / g. Continuum Hypothesis
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
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
Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Aristotle removes ontology from mathematics, and replaces the true with the beautiful
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logic is definitional, but real mathematics is axiomatic
7. Existence / A. Nature of Existence / 1. Nature of Existence
Ontology is (and always has been) Cantorian mathematics
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
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
Existence is Being itself, but only as our thought decides it
7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
The primitive name of Being is the empty set; in a sense, only the empty set 'is'
The modern view of Being comes when we reject numbers as merely successions of One
19. Language / H. Pragmatics / 2. Denial
We must either assert or deny any single predicate of any single subject
25. Society / C. Political Doctrines / 1. Political Theory
For Enlightenment philosophers, God was no longer involved in politics
29. Religion / A. Religious Thought / 1. Religious Belief
The God of religion results from an encounter, not from a proof