Combining Texts

All the ideas for 'fragments/reports', 'There is no a Priori' and 'On the Introduction of Transfinite Numbers'

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10 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]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
9354 Why should necessities only be knowable a priori? That Hesperus is Phosporus is known empirically [Devitt]
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
9353 We explain away a priori knowledge, not as directly empirical, but as indirectly holistically empirical [Devitt]
12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori
9356 The idea of the a priori is so obscure that it won't explain anything [Devitt]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]