Combining Texts

All the ideas for 'What is Cantor's Continuum Problem?st1=Kurt Gödel', 'On Recent German Literature. Fragments' and 'Aspects of the Theory of Syntax'

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8 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
20947 Thoughts are learnt through words, so language shows the limits and shape of our knowledge [Herder]
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]
19. Language / C. Assigning Meanings / 1. Syntax
18006 Chomsky's 'interpretative semantics' says syntax comes first, and is then interpreted [Chomsky, by Magidor]