Combining Texts

All the ideas for 'works', 'Consciousness, Philosophy and Mathematics' and 'Sources of Knowledge of Mathematics'

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6 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
8717 Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
9545 Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical [Frege, by Chihara]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
10113 The grounding of mathematics is 'in the beginning was the sign' [Hilbert]
10115 Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
10116 Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
8728 Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer]