Single Idea 13862

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

Full Idea

Informally, Peano's axioms are: 0 is a number, numbers have a successor, different numbers have different successors, 0 isn't a successor, properties of 0 which carry over to successors are properties of all numbers.

Gist of Idea

There are five Peano axioms, which can be expressed informally

Source

Crispin Wright (Frege's Concept of Numbers as Objects [1983], Intro)

Book Reference

Wright,Crispin: 'Frege's Conception of Numbers' [Scots Philosophical Monographs 1983], p.-9


A Reaction

Each statement of the famous axioms is slightly different from the others, and I have reworded Wright to fit him in. Since the last one (the 'induction axiom') is about properties, it invites formalization in second-order logic.