Combining Philosophers

All the ideas for Pittacus, Luke Westaway and John von Neumann

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14 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 / 5. Conceptions of Set / f. Limitation of Size
15943 Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]
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 / c. Priority of numbers
13489 Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
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]
12336 A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
18179 For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
18180 Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
15925 Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13672 All the axioms for mathematics presuppose set theory [Neumann]
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
6900 A prior understanding of beauty is needed to assert that the Form of the Beautiful is beautiful [Westaway]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
6956 At what point does an object become 'whole'? [Westaway]
10. Modality / A. Necessity / 8. Transcendental Necessity
3016 Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius]
17. Mind and Body / C. Functionalism / 7. Chinese Room
7335 The Chinese Room should be able to ask itself questions in Mandarin [Westaway]