Combining Texts

All the ideas for 'What is Cantor's Continuum Problem?st1=Kurt Gödel', 'On the Individuation of Attributes' and 'Unity of Science as a Working Hypothesis'

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11 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 / B. Properties / 12. Denial of Properties
18439 Because things can share attributes, we cannot individuate attributes clearly [Quine]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
18442 You only know an attribute if you know what things have it [Quine]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
18441 No entity without identity (which requires a principle of individuation) [Quine]
9. Objects / F. Identity among Objects / 6. Identity between Objects
18440 Identity of physical objects is just being coextensive [Quine]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
20653 Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]