Combining Texts

All the ideas for 'Areopagiticus', 'Mathematics without Foundations' and 'Human Freedom and Divine choice'

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8 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 / 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]
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]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
13083 The essence is the necessary properties, and the concept includes what is contingent [Leibniz]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]