Combining Texts

All the ideas for 'Presidential Address of Am. Math. Soc', 'Does Conceivability Entail Possibility?' and 'Mathematics without Foundations'

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9 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 / A. Overview of Logic / 2. History of Logic
10247 We have no adequate logic at the moment, so mathematicians must create one [Veblen]
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]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
16473 Modal Rationalism: conceivability gives a priori access to modal truths [Chalmers, by Stalnaker]
19258 Evaluate primary possibility from some world, and secondary possibility from this world [Chalmers, by Vaidya]