Combining Texts
Ideas for
'Axiomatic Theories of Truth', 'The Logic of Decision' and 'Intro to 'The Reason's Proper Study''
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6 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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The compactness theorem can prove nonstandard models of PA [Halbach]
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The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach]
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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 [Hale/Wright]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
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If structures are relative, this undermines truth-value and objectivity [Hale/Wright]
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The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright]
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