Combining Philosophers

Ideas for Stilpo, Charles Chihara and Volker Halbach

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5 ideas

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry

9553	Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara]

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 / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism

10192

We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride]