Combining Philosophers

All the ideas for Anaxarchus, Charles Parsons and Alain Badiou

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39 ideas

1. Philosophy / C. History of Philosophy / 5. Modern Philosophy / c. Modern philosophy mid-period
12330 In ontology, logic dominated language, until logic was mathematized [Badiou]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
9808 Philosophy aims to reveal the grandeur of mathematics [Badiou]
1. Philosophy / D. Nature of Philosophy / 8. Humour
12318 The female body, when taken in its entirety, is the Phallus itself [Badiou]
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
12325 Philosophy has been relieved of physics, cosmology, politics, and now must give up ontology [Badiou]
2. Reason / A. Nature of Reason / 4. Aims of Reason
12324 Consensus is the enemy of thought [Badiou]
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
9470 Modal logic is not an extensional language [Parsons,C]
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 ⊆ [Badiou]
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 [Badiou]
13418 The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
12342 Topos theory explains the plurality of possible logics [Badiou]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
12341 Logic is a mathematical account of a universe of relations [Badiou]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
9469 Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C]
9468 On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
9812 In mathematics, if a problem can be formulated, it will eventually be solved [Badiou]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
12335 Numbers are for measuring and for calculating (and the two must be consistent) [Badiou]
12334 There is no single unified definition of number [Badiou]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
12333 Each type of number has its own characteristic procedure of introduction [Badiou]
12322 Must we accept numbers as existing when they no longer consist of units? [Badiou]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17447 Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
9813 Mathematics shows that thinking is not confined to the finite [Badiou]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
12327 The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory [Badiou]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
12329 If mathematics is a logic of the possible, then questions of existence are not intrinsic to it [Badiou]
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 [Badiou]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
18201 General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
12331 Logic is definitional, but real mathematics is axiomatic [Badiou]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
13419 If functions are transfinite objects, finitists can have no conception of them [Parsons,C]
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 [Badiou]
9809 Mathematics inscribes being as such [Badiou]
7. Existence / A. Nature of Existence / 3. Being / b. Being and existence
12323 Existence is Being itself, but only as our thought decides it [Badiou]
7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
12332 The modern view of Being comes when we reject numbers as merely successions of One [Badiou]
12326 The primitive name of Being is the empty set; in a sense, only the empty set 'is' [Badiou]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
9811 It is of the essence of being to appear [Badiou]
7. Existence / D. Theories of Reality / 1. Ontologies
12320 Ontology is (and always has been) Cantorian mathematics [Badiou]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
13417 If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
3061 Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
19. Language / F. Communication / 3. Denial
12338 We must either assert or deny any single predicate of any single subject [Badiou]
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
9814 All great poetry is engaged in rivalry with mathematics [Badiou]
25. Social Practice / E. Policies / 2. Religion in Society
12316 For Enlightenment philosophers, God was no longer involved in politics [Badiou]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
12317 The God of religion results from an encounter, not from a proof [Badiou]