Combining Texts

All the ideas for 'fragments/reports', 'The Architecture of Mathematics' and 'On the Foundations of Logic and Arithmetic'

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7 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
10190 From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17697 The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
17698 Logic already contains some arithmetic, so the two must be developed together [Hilbert]
19. Language / F. Communication / 3. Denial
1554 Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind]
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
1555 People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus]
28. God / C. Attitudes to God / 5. Atheism
535 The gods are just personified human benefits [Prodicus]
1543 He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus]