Combining Texts

All the ideas for 'A World of Propensities', 'What is Cantor's Continuum Problem?' and 'On Carnap's Views on Ontology'

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11 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
22153 Quine rejects Carnap's view that science and philosophy are distinct [Quine, by Boulter]
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]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
19485 Names have no ontological commitment, because we can deny that they name anything [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
19486 We can use quantification for commitment to unnameable things like the real numbers [Quine]
8. Modes of Existence / C. Powers and Dispositions / 7. Against Powers
11946 Propensities are part of a situation, not part of the objects [Popper]
19. Language / E. Analyticity / 3. Analytic and Synthetic
19487 Without the analytic/synthetic distinction, Carnap's ontology/empirical distinction collapses [Quine]