Single Idea 17882

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic]

Full Idea

It is a remarkable fact that all the arithmetical properties of the natural numbers can be derived from such a small number of assumptions (as the Peano Axioms).

Gist of Idea

It is remarkable that all natural number arithmetic derives from just the Peano Axioms


Michael Potter (Set Theory and Its Philosophy [2004], 05.2)

Book Reference

Potter,Michael: 'Set Theory and Its Philosophy' [OUP 2004], p.92

A Reaction

If one were to defend essentialism about arithmetic, this would be grist to their mill. I'm just saying.