Single Idea 18097

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

Full Idea

The Peano Axioms are categorical, meaning that they describe a unique structure.

Gist of Idea

The Peano Axioms describe a unique structure

Source

David Bostock (Philosophy of Mathematics [2009], 4.4 n20)

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.103


A Reaction

So if you think there is nothing more to the natural numbers than their structure, then the Peano Axioms give the essence of arithmetic. If you think that 'objects' must exist to generate a structure, there must be more to the numbers.