Combining Philosophers

Ideas for Hermarchus, Charles Chihara and Carrie Jenkins

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6 ideas

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]