Combining Texts

Ideas for 'The Gettier Problem', 'Modern Philosophy:introduction and survey' and 'works'

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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 / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

3907	Could you be intellectually acquainted with numbers, but unable to count objects? [Scruton]

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

3908	If maths contains unprovable truths, then maths cannot be reduced to a set of proofs [Scruton]