Combining Texts

All the ideas for 'On Plural Reference and Set Theory', 'On the Nature of Mathematical Reasoning' and 'Models and Reality'

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

6 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
13655 The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro]
9915 V = L just says all sets are constructible [Putnam]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
10670 A 'singulariser' converts a plural like 'number of' to a syntactically neutral form [Cartwright,H, by Hossack]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
9913 The Löwenheim-Skolem Theorem is close to an antinomy in philosophy of language [Putnam]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
15923 Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Poincaré, by Lavine]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
9914 It is unfashionable, but most mathematical intuitions come from nature [Putnam]