Combining Philosophers

Ideas for Proclus, Charles Chihara and Thoralf Skolem

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7 ideas

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
17880 Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]
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 / 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 / 1. Mathematical Platonism / b. Against mathematical platonism
17881 Mathematician want performable operations, not propositions about objects [Skolem]
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]
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]