Single Idea 17905

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers]

Full Idea

The condition on an explication of number can be put succinctly: any progression will do nicely. Russell once held that one must also be able to measure multiplicity, but this was a mistake; any progression can be fitted to that further condition.

Gist of Idea

Any progression will do nicely for numbers; they can all then be used to measure multiplicity

Source

Willard Quine (Word and Object [1960], §54)

Book Reference

Quine,Willard: 'Word and Object' [MIT 1969], p.262


A Reaction

[compressed] This is the strongest possible statement that the numbers are the ordinals, and the Peano Axioms will define them. The Fregean view that cardinality comes first is redundant.

Related Idea

Idea 17906 To explain numbers you must also explain cardinality, the counting of things [Benacerraf]