Combining Texts

All the ideas for 'What is so bad about Contradictions?', 'What is Cantor's Continuum Problem?' and 'Realism, Mathematics and Modality'

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8 ideas

2. Reason / B. Laws of Thought / 3. Non-Contradiction
9123 Someone standing in a doorway seems to be both in and not-in the room [Priest,G, by Sorensen]
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]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
8714 Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true [Field,H]