Combining Philosophers

All the ideas for Hermarchus, John von Neumann and Scott Shalkowski

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

18 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
12336 A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
22716 Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]
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]
9. Objects / D. Essence of Objects / 1. Essences of Objects
14221 Serious essentialism says everything has essences, they're not things, and they ground necessities [Shalkowski]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
14222 Essences are what it is to be that (kind of) thing - in fact, they are the thing's identity [Shalkowski]
9. Objects / D. Essence of Objects / 13. Nominal Essence
14226 We distinguish objects by their attributes, not by their essences [Shalkowski]
9. Objects / D. Essence of Objects / 15. Against Essentialism
14225 Critics say that essences are too mysterious to be known [Shalkowski]
10. Modality / A. Necessity / 4. De re / De dicto modality
14223 De dicto necessity has linguistic entities as their source, so it is a type of de re necessity [Shalkowski]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
9220 Lewis must specify that all possibilities are in his worlds, making the whole thing circular [Shalkowski, by Sider]
19. Language / C. Assigning Meanings / 7. Extensional Semantics
14224 Equilateral and equiangular aren't the same, as we have to prove their connection [Shalkowski]
25. Social Practice / F. Life Issues / 6. Animal Rights
6005 Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley]