Combining Texts

All the ideas for 'works', 'Reals by Abstraction' and 'On the Introduction of Transfinite Numbers'

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7 ideas

5. Theory of Logic / G. Quantification / 2. Domain of Quantification

17743

De Morgan introduced a 'universe of discourse', to replace Boole's universe of 'all things' [De Morgan, by Walicki]

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 / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

10632

The real numbers may be introduced by abstraction as ratios of quantities [Hale, by Hale/Wright]

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]