Combining Philosophers

All the ideas for David Fair, Melissus and John von Neumann

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16 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]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
12270 Being is one [Melissus, by Aristotle]
26. Natural Theory / C. Causation / 4. Naturalised causation
8326 Science has shown that causal relations are just transfers of energy or momentum [Fair, by Sosa/Tooley]
10379 Fair shifted his view to talk of counterfactuals about energy flow [Fair, by Schaffer,J]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
3059 There is no real motion, only the appearance of it [Melissus, by Diog. Laertius]
27. Natural Reality / C. Space / 1. Void
5100 The void is not required for change, because a plenum can alter in quality [Aristotle on Melissus]
27. Natural Reality / E. Cosmology / 2. Eternal Universe
456 Nothing could come out of nothing [Melissus]