Combining Philosophers

All the ideas for Hans-Georg Gadamer, Richard T.W. Arthur 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
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]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
22333 Only language is understandable Being [Gadamer]
10. Modality / B. Possibility / 1. Possibility
19378 Early modern possibility is what occurs sometime; for Leibniz, it is what is not contradictory [Arthur,R]
17. Mind and Body / A. Mind-Body Dualism / 4. Occasionalism
19380 Occasionalism contradicts the Eucharist, which needs genuine changes of substance [Arthur,R]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
20928 Facts don't oppose values; they are integrated into each person's aspirations [Gadamer, by Zimmermann,J]