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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]
| 9821 | A definition need not capture the sense of an expression - just get the reference right [Frege, by Dummett] |
| 17446 | Counting rests on one-one correspondence, of numerals to objects [Frege] |
| 9577 | The naïve view of number is that it is like a heap of things, or maybe a property of a heap [Frege] |
| 9578 | If objects are just presentation, we get increasing abstraction by ignoring their properties [Frege] |
| 9580 | Our concepts recognise existing relations, they don't change them [Frege] |
| 9579 | Disregarding properties of two cats still leaves different objects, but what is now the difference? [Frege] |
| 9581 | Many people have the same thought, which is the component, not the private presentation [Frege] |
| 9582 | Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves [Frege] |
| 9583 | Psychological logicians are concerned with sense of words, but mathematicians study the reference [Frege] |
| 9584 | Identity baffles psychologists, since A and B must be presented differently to identify them [Frege] |
| 9585 | Since every definition is an equation, one cannot define equality itself [Frege] |
| 9586 | In a number-statement, something is predicated of a concept [Frege] |
| 9587 | How do you find the right level of inattention; you eliminate too many or too few characteristics [Frege] |
| 9588 | Number-abstraction somehow makes things identical without changing them! [Frege] |
| 9589 | Numbers are not real like the sea, but (crucially) they are still objective [Frege] |