Combining Texts

All the ideas for 'Review of Bob Hale's 'Abstract Objects'', 'Cosmic Apprentice' and 'On the Introduction of Transfinite Numbers'

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8 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
9184 We can't presume that all interesting concepts can be analysed [Williamson]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
16567 Scientists know everything about nothing, philosophers nothing about everything [Sagan,D]
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]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
9183 Platonism claims that some true assertions have singular terms denoting abstractions, so abstractions exist [Williamson]