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Ideas for 'works', 'Foundations without Foundationalism' and 'Logic in Mathematics'

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3 ideas

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers

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If principles are provable, they are theorems; if not, they are axioms [Frege]

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

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First-order arithmetic can't even represent basic number theory [Shapiro]

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

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Some sets of natural numbers are definable in set-theory but not in arithmetic [Shapiro]