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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]
| 17448 | In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck] |
| 17449 | We can understand cardinality without the idea of one-one correspondence [Heck] |
| 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] |
| 17454 | Children can use numbers, without a concept of them as countable objects [Heck] |
| 17455 | Is counting basically mindless, and independent of the cardinality involved? [Heck] |
| 17456 | Counting is the assignment of successively larger cardinal numbers to collections [Heck] |
| 17453 | The meaning of a number isn't just the numerals leading up to it [Heck] |
| 17457 | A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck] |
| 17458 | Equinumerosity is not the same concept as one-one correspondence [Heck] |
| 17459 | Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck] |