Single Idea 17444

[catalogued under 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation]

Full Idea

Husserl famously argued that one should not explain number in terms of equinumerosity (or one-one correspondence), but should explain equinumerosity in terms of sameness of number, which should be characterised in terms of counting.

Gist of Idea

Husserl said counting is more basic than Frege's one-one correspondence


report of Edmund Husserl (Philosophy of Arithmetic [1894]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3

Book Reference

-: 'Notre Dame Journal of Formal Logic' [-], p.193

A Reaction

[Heck admits he hasn't read the Husserl] I'm very sympathetic to Husserl, though nearly all modern thinking favours Frege. Counting connects numbers to their roots in the world. Mathematicians seem oblivious of such things.

Related Ideas

Idea 17446 Counting rests on one-one correspondence, of numerals to objects [Frege]

Idea 17451 We can know 'just as many' without the concepts of equinumerosity or numbers [Heck]