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Full Idea
Counting rests itself on a one-one correlation, namely of numerals 1 to n and the objects.
Gist of Idea
Counting rests on one-one correspondence, of numerals to objects
Source
Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894]), quoted by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
Book Ref
-: 'Notre Dame Journal of Formal Logic' [-], p.193
A Reaction
Parsons observes that counting will establish a one-one correspondence, but that doesn't make it the aim of counting, and so Frege hasn't answered Husserl properly. Which of the two is conceptually prior? How do you decide.
Related Idea
Idea 17444 Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck]
| 15916 | Frege's one-to-one correspondence replaces well-ordering, because infinities can't be counted [Frege, by Lavine] |
| 17446 | Counting rests on one-one correspondence, of numerals to objects [Frege] |
| 9582 | Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves [Frege] |
| 17444 | Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck] |
| 14118 | We can define one-to-one without mentioning unity [Russell] |
| 9852 | We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett] |
| 17450 | Understanding 'just as many' needn't involve grasping one-one correspondence [Heck] |
| 17451 | We can know 'just as many' without the concepts of equinumerosity or numbers [Heck] |