Combining Texts

All the ideas for 'Hilbert's Programme', 'Steps Towards a Constructive Nominalism' and 'The Philosophy of Logic'

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7 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 / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
18200 Very large sets should be studied in an 'if-then' spirit [Putnam]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
17810 The study of mathematical foundations needs new non-mathematical concepts [Kreisel]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
18199 Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam]
8857 We must quantify over numbers for science; but that commits us to their existence [Putnam]
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
17619 We renounce all abstract entities [Goodman/Quine]
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]