Combining Texts

All the ideas for 'What is Cantor's Continuum Problem?st1=Kurt Gödel', 'Wittgenstein' and 'Letters to Samuel Masson'

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8 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 / d. Actual infinite

13190

I don't admit infinite numbers, and consider infinitesimals to be useful fictions [Leibniz]

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]

15. Nature of Minds / A. Nature of Mind / 4. Other Minds / d. Other minds by analogy

7091	The argument from analogy is not a strong inference, since the other being might be an actor or a robot [Grayling]