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Full Idea
'Just as many' is independent of the ability to count, and we shouldn't characterise equinumerosity through counting. It is also independent of the concept of number. Enough cookies to go round doesn't need how many cookies.
Gist of Idea
We can know 'just as many' without the concepts of equinumerosity or numbers
Source
Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 4)
Book Ref
-: 'Notre Dame Journal of Formal Logic' [-], p.199
A Reaction
[compressed] He talks of children having an 'operational' ability which is independent of these more sophisticated concepts. Interesting. You see how early man could relate 'how many' prior to the development of numbers.
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] |