Combining Philosophers
Ideas for H.Putnam/P.Oppenheim, Volker Halbach and Nicholas P. White
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5 ideas
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
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Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]
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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 / 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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