more from this thinker | more from this text
Full Idea
When Husserl says that sameness of number can be shown by one-one correlation, he forgets that this counting itself rests on a univocal one-one correlation, namely that between the numerals 1 to n and the objects of the set.
Clarification
'Univocal' means having only one meaning
Gist of Idea
Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves
Source
Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.326)
Book Ref
-: 'Mind July 1972' [-], p.326
A Reaction
This is the platonist talking. Neo-logicism is attempting to build numbers just from the one-one correlation of objects.
| 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] |