Single Idea 13891

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers]

Full Idea

Benacerraf claims that the concept of a progression is in some way the fundamental arithmetical notion, essential to understanding the idea of a finite cardinal, with a grasp of progressions sufficing for grasping finite cardinals.

Gist of Idea

To understand finite cardinals, it is necessary and sufficient to understand progressions

Source

report of Paul Benacerraf (What Numbers Could Not Be [1965]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xv

Book Reference

Wright,Crispin: 'Frege's Conception of Numbers' [Scots Philosophical Monographs 1983], p.117


A Reaction

He cites Dedekind (and hence the Peano Axioms) as the source of this. The interest is that progression seems to be fundamental to ordianls, but this claims it is also fundamental to cardinals. Note that in the first instance they are finite.