Combining Texts

Ideas for 'Causation', 'Philosophies of Mathematics' and 'works'

expand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

---

5 ideas

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order

17899

Second-order induction is stronger as it covers all concepts, not just first-order definable ones [George/Velleman]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic

10128

The Incompleteness proofs use arithmetic to talk about formal arithmetic [George/Velleman]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers

17902

A successor is the union of a set with its singleton [George/Velleman]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle

10133

Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle [George/Velleman]

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

10130

Set theory can prove the Peano Postulates [George/Velleman]