Combining Texts

All the ideas for 'fragments/reports', 'The Theory of Transfinite Numbers' and 'Intro to 'The Reason's Proper Study''

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11 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
9616 A set is a collection into a whole of distinct objects of our intuition or thought [Cantor]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox
10631 If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
15896 Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10624 The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10629 If structures are relative, this undermines truth-value and objectivity [Hale/Wright]
10628 The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
10622 The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
10626 Objects just are what singular terms refer to [Hale/Wright]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10630 Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright]
19. Language / E. Analyticity / 2. Analytic Truths
10627 Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]