Combining Texts

All the ideas for 'fragments/reports', 'fragments/reports' and 'Mathematics without Foundations'

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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]

13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism

604	Knowledge is mind and knowing 'cohabiting' [Lycophron, by Aristotle]

13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism

2667	A false object might give the same presentation as a true one [Arcesilaus, by Cicero]