Combining Texts

All the ideas for 'Realism in Mathematics', 'Hilbert's Programme' and 'On Copernicanism and Relativity of Motion'

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9 ideas

3. Truth / A. Truth Problems / 8. Subjective Truth
13157 Choose the true hypothesis, which is the most intelligible one [Leibniz]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
8755 Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
17809 Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
17810 The study of mathematical foundations needs new non-mathematical concepts [Kreisel]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10718 A natural number is a property of sets [Maddy, by Oliver]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
8756 Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17733 We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
13158 The Copernican theory is right because it is the only one offering a good explanation [Leibniz]
27. Natural Reality / C. Space / 3. Points in Space
17811 The natural conception of points ducks the problem of naming or constructing each point [Kreisel]