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Full Idea
In a number-statement, something is predicated of a concept.
Gist of Idea
In a number-statement, something is predicated of a concept
Source
Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.328)
Book Ref
-: 'Mind July 1972' [-], p.328
A Reaction
A succinct statement of Frege's theory of numbers. By my lights that would make numbers at least second-order abstractions.
Related Idea
Idea 17460 A statement of number contains a predication about a concept [Frege]
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] |