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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.
| 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] |