Combining Texts

All the ideas for 'The Philosophy of Logic', 'Mathematics without Foundations' and 'Identity in Substances and True Propositions'

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10 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
9944 We understand some statements about all sets [Putnam]
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
9937 I do not believe mathematics either has or needs 'foundations' [Putnam]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
9939 It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
9940 Maybe mathematics is empirical in that we could try to change it [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
9941 Science requires more than consistency of mathematics [Putnam]
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]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
19405 Substances are in harmony, because they each express the one reality in themselves [Leibniz]
7. Existence / D. Theories of Reality / 4. Anti-realism
9943 You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam]