Combining Texts

All the ideas for 'The Case for Closure', 'poems' and 'Hilbert's Programme'

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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]

11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty

19553

Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne]

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure

19551

How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne]

19552

We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne]

19554

Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne]

22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention

6017	Nomos is king [Pindar]

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]