Combining Texts

All the ideas for 'Fragments of Democritus', 'What is Cantor's Continuum Problem?' and 'Truth'

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11 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
10838 To explain a concept, we need its purpose, not just its rules of usage [Dummett]
3. Truth / A. Truth Problems / 1. Truth
10837 It is part of the concept of truth that we aim at making true statements [Dummett]
3. Truth / A. Truth Problems / 2. Defining Truth
10840 We must be able to specify truths in a precise language, like winning moves in a game [Dummett]
3. Truth / F. Semantic Truth / 2. Semantic Truth
19171 Tarski's truth is like rules for winning games, without saying what 'winning' means [Dummett, by Davidson]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
8679 We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
9942 Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
18062 Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10868 The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
13517 If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
10271 Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
18. Thought / E. Abstraction / 1. Abstract Thought
10839 You can't infer a dog's abstract concepts from its behaviour [Dummett]