Combining Texts

Ideas for 'On the Question of Absolute Undecidability', 'In a Different Voice' and 'Intro to 'The Reason's Proper Study''

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7 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

17890

There are at least eleven types of large cardinal, of increasing logical strength [Koellner]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic

17887

PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]

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]

17891

Arithmetical undecidability is always settled at the next stage up [Koellner]

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]