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 mid-period
In ontology, logic dominated language, until logic was mathematized
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Philosophy aims to reveal the grandeur of mathematics
1. Philosophy / D. Nature of Philosophy / 8. Humour
The female body, when taken in its entirety, is the Phallus itself
1. Philosophy / E. Nature of Metaphysics / 7. 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 / 1. Mathematics
In mathematics, if a problem can be formulated, it will eventually be solved
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
There is no single unified definition of number
Numbers are for measuring and for calculating (and the two must be consistent)
6. Mathematics / A. Nature of Mathematics / 3. Nature of 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 / 5. The Infinite / a. The Infinite
Mathematics shows that thinking is not confined to the finite
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory
6. Mathematics / B. Foundations for Mathematics / 7. 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 / 6. Logicism / d. Logicism critique
Logic is definitional, but real mathematics is axiomatic
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
Mathematics inscribes being as such
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 modern view of Being comes when we reject numbers as merely successions of One
The primitive name of Being is the empty set; in a sense, only the empty set 'is'
7. Existence / A. Nature of Existence / 6. Criterion for Existence
It is of the essence of being to appear
7. Existence / D. Theories of Reality / 1. Ontologies
Ontology is (and always has been) Cantorian mathematics
19. Language / F. Communication / 3. Denial
We must either assert or deny any single predicate of any single subject
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
All great poetry is engaged in rivalry with mathematics
25. Social Practice / E. Policies / 2. Religion in Society
For Enlightenment philosophers, God was no longer involved in politics
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
The God of religion results from an encounter, not from a proof