Ideas from 'Intro to 'The Reason's Proper Study'' by B Hale / C Wright [2001], by Theme Structure
[found in 'The Reason's Proper Study' by Hale,B/Wright,C [OUP 2003,9780199266326]].
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox
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If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
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The incompletability of formal arithmetic reveals that logic also cannot be completely characterized

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
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The structural view of numbers doesn't fit their usage outside arithmetical contexts

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If structures are relative, this undermines truthvalue and objectivity

6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neologicism
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The neoFregean is more optimistic than Frege about contextual definitions of numbers

9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
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Objects just are what singular terms refer to

18. Thought / E. Abstraction / 7. Abstracta by Equivalence
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Abstracted objects are not mental creations, but depend on equivalence between given entities

19. Language / E. Analyticity / 2. Analytic Truths
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Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions
