Combining Philosophers
Ideas for Melvin Fitting, Carrie Jenkins and Volker Halbach
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8 ideas
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
17730
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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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The compactness theorem can prove nonstandard models of PA [Halbach]
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The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach]
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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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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 / b. Type theory
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Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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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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