Combining Texts

All the ideas for 'Human Freedom and Divine choice', 'Statements about Universals' and 'On the Introduction of Transfinite Numbers'

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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]
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
Nominalists cannot translate 'red resembles pink more than blue' into particulars [Jackson]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
Colour resemblance isn't just resemblance between things; 'colour' must be mentioned [Jackson]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
The essence is the necessary properties, and the concept includes what is contingent [Leibniz]