Combining Texts

All the ideas for 'Subjectivist's Guide to Objective Chance', 'On the Introduction of Transfinite Numbers' and 'Two Kinds of Possibility'

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10 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]
10. Modality / A. Necessity / 1. Types of Modality
There are two families of modal notions, metaphysical and epistemic, of equal strength [Edgington]
10. Modality / A. Necessity / 5. Metaphysical Necessity
Metaphysical possibility is discovered empirically, and is contrained by nature [Edgington]
10. Modality / A. Necessity / 6. Logical Necessity
Broadly logical necessity (i.e. not necessarily formal logical necessity) is an epistemic notion [Edgington]
An argument is only valid if it is epistemically (a priori) necessary [Edgington]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
Lewis later proposed the axioms at the intersection of the best theories (which may be few) [Mumford on Lewis]