Combining Philosophers
Ideas for Thrasymachus, Alfred Tarski and Volker Halbach
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6 ideas
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
10157
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Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
16321
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The compactness theorem can prove nonstandard models of PA [Halbach]
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16343
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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
16312
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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
16308
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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 / 7. Formalism
10154
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Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman on Tarski]
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