Combining Texts

All the ideas for 'works', 'Mathematics without Foundations' and 'Letter to Pythocles'

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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]
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
10121 Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal]
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]
14. Science / D. Explanation / 3. Best Explanation / c. Against best explanation
21386 We should accept as explanations all the plausible ways in which something could come about [Epicurus]
27. Natural Reality / E. Cosmology / 1. Cosmology
14051 A cosmos is a collection of stars and an earth, with some sort of boundary, movement and shape [Epicurus]
28. God / C. Attitudes to God / 3. Deism
1828 God does not intervene in heavenly movements, but is beyond all action and perfectly happy [Epicurus]