Combining Texts

All the ideas for 'The Languages of Art', 'What is Cantor's Continuum Problem?' and 'Relations'

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10 ideas

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]
8. Modes of Existence / A. Relations / 1. Nature of Relations
21354 It may be that internal relations like proportion exist, because we directly perceive it [MacBride]
8. Modes of Existence / A. Relations / 2. Internal Relations
21353 Internal relations are fixed by existences, or characters, or supervenience on characters [MacBride]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
21352 'Multigrade' relations are those lacking a fixed number of relata [MacBride]
21. Aesthetics / B. Nature of Art / 5. Art as Language
8113 Art is like understanding a natural language, and needs a grasp of a symbol system [Goodman, by Gardner]