Combining Philosophers

Ideas for Rescher,N/Oppenheim,P, Volker Halbach and Adam Swift

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4 ideas

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

16321

The compactness theorem can prove nonstandard models of PA [Halbach]

16343

The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach]

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

16312

To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory

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Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach]