Combining Texts

Ideas for 'Actions', 'Realism in Mathematics' and 'On the Foundations of Logic and Arithmetic'

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5 ideas

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

10718

A natural number is a property of sets [Maddy, by Oliver]

6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics

8756	Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism

17733

We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

17697

The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

17698

Logic already contains some arithmetic, so the two must be developed together [Hilbert]