Combining Texts

All the ideas for 'Wiener Logik', 'On the Introduction of Transfinite Numbers' and 'Papers of 1913'

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9 ideas

2. Reason / D. Definition / 2. Aims of Definition
A simplification which is complete constitutes a definition [Kant]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic gives us the necessary rules which show us how we ought to think [Kant]
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 / B. Possibility / 1. Possibility
Only the actual exists, so possibilities always reduce to actuality after full analysis [Russell]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
If we knew what we know, we would be astonished [Kant]