more from Fraser MacBride

Single Idea 8923

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers]

Full Idea

The mathematically significant properties and relations of natural numbers arise from the successor function that orders them; the natural numbers are identified simply as the objects that answer to this basic function.

Gist of Idea

Numbers are identified by their main properties and relations, involving the successor function

Source

Fraser MacBride (Structuralism Reconsidered [2007], 1)

Book Reference

'Oxf Handbk of Philosophy of Maths and Logic', ed/tr. Shapiro,Stewart [OUP 2007], p.563


A Reaction

So Julius Caesar would be a number if he was the successor of Pompey the Great? I would have thought that counting should be mentioned - cardinality as well as ordinality. Presumably Peano's Axioms are being referred to.