Combining Texts

All the ideas for 'fragments/reports', 'Five Milestones of Empiricism' and 'On the Introduction of Transfinite Numbers'

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11 ideas

2. Reason / D. Definition / 7. Contextual Definition
Contextual definition shifted the emphasis from words to whole sentences [Quine]
Bentham's contextual definitions preserved terms after their denotation became doubtful [Quine]
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
Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
In scientific theories sentences are too brief to be independent vehicles of empirical meaning [Quine]
Empiricism improvements: words for ideas, then sentences, then systems, then no analytic, then naturalism [Quine]
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
Holism in language blurs empirical synthetic and empty analytic sentences [Quine]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]