Combining Philosophers

All the ideas for Alan McMichael, Keith DeRose and John von Neumann

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21 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 / 3. Individual Essences
14637 Only individuals have essences, so numbers (as a higher type based on classes) lack them [McMichael]
9. Objects / D. Essence of Objects / 9. Essence and Properties
14636 Essences are the interesting necessary properties resulting from a thing's own peculiar nature [McMichael]
14640 Maybe essential properties have to be intrinsic, as well as necessary? [McMichael]
9. Objects / D. Essence of Objects / 15. Against Essentialism
14638 Essentialism is false, because it implies the existence of necessary singular propositions [McMichael]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
19513 A contextualist coherentist will say that how strongly a justification must cohere depends on context [DeRose]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
19514 Classical invariantism combines fixed truth-conditions with variable assertability standards [DeRose]
19515 We can make contextualism more precise, by specifying the discrimination needed each time [DeRose]
19510 In some contexts there is little more to knowledge than true belief. [DeRose]
19516 Contextualists worry about scepticism, but they should focus on the use of 'know' in ordinary speech [DeRose]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / b. Invariantism
19511 If contextualism is about knowledge attribution, rather than knowledge, then it is philosophy of language [DeRose]
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
14639 Individuals enter into laws only through their general qualities and relations [McMichael]