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Ideas for 'Axiomatic Theories of Truth', 'Reference and Definite Descriptions' and 'New Essays on Human Understanding'

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7 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry

13008

Geometry, unlike sensation, lets us glimpse eternal truths and their necessity [Leibniz]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units

12956

Only whole numbers are multitudes of units [Leibniz]

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry

12937

We shouldn't just accept Euclid's axioms, but try to demonstrate them [Leibniz]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic

16321

The compactness theorem can prove nonstandard models of PA [Halbach]

16343

The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach]

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

16312

To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory

16308

Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach]