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Single Idea 9588

[filed under theme 18. Thought / E. Abstraction / 8. Abstractionism Critique ]

Full Idea

Number-abstraction simply has the wonderful and very fruitful property of making things absolutely the same as one another without altering them. Something like this is possible only in the psychological wash-tub.

Gist of Idea

Number-abstraction somehow makes things identical without changing them!

Source

Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.332)

Book Ref

-: 'Mind July 1972' [-], p.332

A Reaction

Frege can be awfully sarcastic. I don't really see his difficulty. For mathematics we only need to know what is countable about an object - we don't need to know how many hairs there are on the cat, only that it has identity.

The 15 ideas from 'Review of Husserl's 'Phil of Arithmetic''

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]