Combining Texts

Ideas for 'teaching', 'Axiomatic Theories of Truth' and 'Paradoxes of the Infinite'

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6 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One

7485	For Pythagoreans 'one' is not a number, but the foundation of numbers [Pythagoras, by Watson]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite

10856

A truly infinite quantity does not need to be a variable [Bolzano]

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]