Combining Texts

All the ideas for 'Reality and Representation', 'What is Cantor's Continuum Problem?' and 'Intro to 'Rationality in Greek Thought''

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8 ideas

2. Reason / A. Nature of Reason / 1. On Reason

23249

The early philosophers thought that reason has its own needs and desires [Frede,M]

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]

11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs

12583

Belief truth-conditions are normal circumstances where the belief is supposed to occur [Papineau]