Combining Philosophers
Ideas for H.Putnam/P.Oppenheim, Carrie Jenkins and Michael Potter
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8 ideas
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
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If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17719
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Arithmetic concepts are indispensable because they accurately map the world [Jenkins]
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17717
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Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
17724
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It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins]
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
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The formalist defence against Gödel is to reject his metalinguistic concept of truth [Potter]
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6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
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Why is fictional arithmetic applicable to the real world? [Potter]
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