Combining Texts

All the ideas for 'Logicism, Some Considerations (PhD)', 'works' and 'On the Introduction of Transfinite Numbers'

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10 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
13412 Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
13413 We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
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]
13411 If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
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 / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
13415 An adequate account of a number must relate it to its series [Benacerraf]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
4366 We can't accept Aristotle's naturalism about persons, because it is normative and unscientific [Williams,B, by Hursthouse]