Combining Philosophers

Ideas for Stilpo, Charles Chihara and Volker Halbach

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9 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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10265 Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro]
8759 We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro]
16308 Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
10264 Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]