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
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12330
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In ontology, logic dominated language, until logic was mathematized
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1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
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9808
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Philosophy aims to reveal the grandeur of mathematics
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1. Philosophy / D. Nature of Philosophy / 8. Humour
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12318
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The female body, when taken in its entirety, is the Phallus itself
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1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
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12325
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Philosophy has been relieved of physics, cosmology, politics, and now must give up ontology
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2. Reason / A. Nature of Reason / 4. Aims of Reason
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12324
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Consensus is the enemy of thought
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4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
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12337
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There is 'transivity' iff membership ∈ also means inclusion ⊆
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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12321
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The axiom of choice must accept an indeterminate, indefinable, unconstructible set
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5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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12342
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Topos theory explains the plurality of possible logics
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5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
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12341
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Logic is a mathematical account of a universe of relations
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6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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9812
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In mathematics, if a problem can be formulated, it will eventually be solved
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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12334
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There is no single unified definition of number
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12335
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Numbers are for measuring and for calculating (and the two must be consistent)
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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12333
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Each type of number has its own characteristic procedure of introduction
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12322
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Must we accept numbers as existing when they no longer consist of units?
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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9813
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Mathematics shows that thinking is not confined to the finite
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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12327
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The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
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12329
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If mathematics is a logic of the possible, then questions of existence are not intrinsic to it
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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12328
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Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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12331
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Logic is definitional, but real mathematics is axiomatic
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7. Existence / A. Nature of Existence / 1. Nature of Existence
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12320
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Ontology is (and always has been) Cantorian mathematics
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7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
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12340
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There is no Being as a whole, because there is no set of all sets
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9809
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Mathematics inscribes being as such
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7. Existence / A. Nature of Existence / 3. Being / b. Being and existence
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12323
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Existence is Being itself, but only as our thought decides it
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7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
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12332
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The modern view of Being comes when we reject numbers as merely successions of One
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12326
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The primitive name of Being is the empty set; in a sense, only the empty set 'is'
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7. Existence / A. Nature of Existence / 6. Criterion for Existence
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9811
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It is of the essence of being to appear
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19. Language / F. Communication / 3. Denial
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12338
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We must either assert or deny any single predicate of any single subject
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21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
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9814
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All great poetry is engaged in rivalry with mathematics
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25. Social Practice / E. Policies / 2. Religion in Society
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12316
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For Enlightenment philosophers, God was no longer involved in politics
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29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
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12317
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The God of religion results from an encounter, not from a proof
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