Combining Texts

All the ideas for 'Mathematics and Indispensibility', 'Mathematical Intuition' and 'works'

expand these ideas     |    start again     |     specify just one area for these texts

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5 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

3340	Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn]

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

3355	Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers

22716

Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

18201

General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C]

7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems

9558	All scientific tests will verify mathematics, so it is a background, not something being tested [Sober]