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Ideas for 'reports', 'works' and 'Intro to 'The Reason's Proper Study''

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5 ideas

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 / 5. Definitions of Number / e. Caesar problem

10232

Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro]

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

18176

Pure mathematics is pure set theory [Cantor]

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]