Full Idea
What is fundamental to possession of any notion of natural number at all is not the knowledge that the numbers may be arrayed in a progression but the knowledge that they are identified and distinguished by reference to 1-1 correlation among concepts.
Gist of Idea
It is 1-1 correlation of concepts, and not progression, which distinguishes natural number
Source
Crispin Wright (Frege's Concept of Numbers as Objects [1983], 3.xv)
Book Reference
Wright,Crispin: 'Frege's Conception of Numbers' [Scots Philosophical Monographs 1983], p.120
A Reaction
My question is 'what is the essence of number?', and my inclination to disagree with Wright on this point suggests that the essence of number is indeed caught in the Dedekind-Peano axioms. But what of infinite numbers?
Related Ideas
Idea 13892 One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C]
Idea 13894 Sameness of number is fundamental, not counting, despite children learning that first [Wright,C]