Combining Texts

All the ideas for '04: Gospel of St John', 'Truth' and 'What is Cantor's Continuum Problem?'

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12 ideas

2. Reason / A. Nature of Reason / 2. Logos
6294 In the beginning was the Word, and the Word was with God, and the word was God [John]
3. Truth / A. Truth Problems / 2. Defining Truth
8821 Jesus said he bore witness to the truth. Pilate asked, What is truth? [John]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
14965 Truth rests on Elimination ('A' is true → A) and Introduction (A → 'A' is true) [Gupta]
3. Truth / F. Semantic Truth / 2. Semantic Truth
14968 A weakened classical language can contain its own truth predicate [Gupta]
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]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
14964 The Liar reappears, even if one insists on propositions instead of sentences [Gupta]
14969 Strengthened Liar: either this sentence is neither-true-nor-false, or it is not true [Gupta]
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]