more on this theme | more from this thinker
Full Idea
One need not conceive of the numerals as objects in their own right in order to count. The numerals are not mentioned in counting (as objects to be correlated with baseball players), but are used.
Gist of Idea
In counting, numerals are used, not mentioned (as objects that have to correlated)
Source
Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 3)
Book Ref
-: 'Notre Dame Journal of Formal Logic' [-], p.194
A Reaction
He observes that when you name the team, you aren't correlating a list of names with the players. I could correlate any old tags with some objects, and you could tell me the cardinality denoted by the last tag. I do ordinals, you do cardinals.
| 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] |