Combining Texts

All the ideas for 'fragments/reports', 'Hilbert's Programme' and 'Il Saggiatore ('The Assayer')'

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8 ideas

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]

10. Modality / A. Necessity / 8. Transcendental Necessity

490	Everything happens by reason and necessity [Leucippus]

12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities

7401	Heat and colour don't exist, so cannot mislead about the external world [Galileo, by Tuck]

5454	Tastes, odours and colours only reside in consciousness, and would disappear with creatures [Galileo]

14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism

16560

Galileo introduced geometrico-mechanical explanation, based on Archimedes [Galileo, by Machamer/Darden/Craver]

26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature

3645	To understand the universe mathematics is essential [Galileo]

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]