Combining Texts

All the ideas for 'Necessary Existents', 'On the Introduction of Transfinite Numbers' and 'Internalism and Externalism: a History'

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7 ideas

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]
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]
13. Knowledge Criteria / C. External Justification / 1. External Justification
4254 Externalist accounts of knowledge do not require the traditional sort of justification [Kornblith]
19. Language / D. Propositions / 3. Concrete Propositions
19216 Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]