Combining Texts

All the ideas for 'On the Natural Faculties', 'On the Introduction of Transfinite Numbers' and 'Certain Physical Essays'

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8 ideas

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
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]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
Explanation is generally to deduce it from something better known, which comes in degrees [Boyle]
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
The best explanations get down to primary basics, but others go less deep [Boyle]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
We just use the word 'faculty' when we don't know the psychological cause [Galen]