Combining Texts

All the ideas for 'Hilbert's Programme', 'Precepts for Advancing Science and Arts' and 'fragments/reports'

expand these ideas     |    start again     |     specify just one area for these texts

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5 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]

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

20769

Sphaerus he was not assenting to the presence of pomegranates, but that it was 'reasonable' [Sphaerus, by Diog. Laertius]

13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique

19392

I don't recommend universal doubt; we constantly seek reasons for things which are indubitable [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]