Combining Philosophers

All the ideas for Herodotus, James Pryor and John von Neumann

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


17 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
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
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
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
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
Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]
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
For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
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
All the axioms for mathematics presuppose set theory [Neumann]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
An experience's having propositional content doesn't make it a belief [Pryor]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / e. Pro-foundations
The best argument for immediate justification is not the Regress Argument, but considering examples [Pryor]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
Impure coherentists accept that perceptions can justify, unlike pure coherentists [Pryor]
Coherentism rests on the claim that justifications must be beliefs, with propositional content [Pryor]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
Reasons for beliefs can be cited to others, unlike a raw headache experience [Pryor]
13. Knowledge Criteria / C. External Justification / 5. Controlling Beliefs
Beliefs are not chosen, but you can seek ways to influence your belief [Pryor]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus]