Combining Philosophers

Ideas for Hermarchus, Charles Chihara and Carrie Jenkins

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9 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
17730 Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins]
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 / 4. Mathematical Empiricism / a. Mathematical empiricism
17719 Arithmetic concepts are indispensable because they accurately map the world [Jenkins]
17717 Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins]
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 / 6. Logicism / d. Logicism critique
17724 It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins]
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]