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Single Idea 10603

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction ]

Full Idea

If the logic of arithmetic doesn't have second-order quantifiers to range over properties of numbers, how can it handle induction?

Gist of Idea

The logic of arithmetic must quantify over properties of numbers to handle induction

Source

Peter Smith (Intro to Gödel's Theorems [2007], 10.1)

Book Ref

Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.71