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Single Idea 9580
[filed under theme 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
]
Full Idea
The bringing of an object under a concept is merely the recognition of a relation which previously already obtained, [but in the abstractionist view] objects are essentially changed by the process, so that objects brought under a concept become similar.
Gist of Idea
Our concepts recognise existing relations, they don't change them
Source
Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.324)
Book Ref
-: 'Mind July 1972' [-], p.324
A Reaction
Frege's view would have to account for occasional misapplications of concepts, like taking a dolphin to be a fish, or falsely thinking there is someone in the cellar.
The
15 ideas
from 'Review of Husserl's 'Phil of Arithmetic''
9821
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A definition need not capture the sense of an expression - just get the reference right
[Frege, by Dummett]
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17446
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Counting rests on one-one correspondence, of numerals to objects
[Frege]
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9577
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The naïve view of number is that it is like a heap of things, or maybe a property of a heap
[Frege]
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9578
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If objects are just presentation, we get increasing abstraction by ignoring their properties
[Frege]
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9580
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Our concepts recognise existing relations, they don't change them
[Frege]
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9579
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Disregarding properties of two cats still leaves different objects, but what is now the difference?
[Frege]
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9581
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Many people have the same thought, which is the component, not the private presentation
[Frege]
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9582
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Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves
[Frege]
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9583
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Psychological logicians are concerned with sense of words, but mathematicians study the reference
[Frege]
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9584
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Identity baffles psychologists, since A and B must be presented differently to identify them
[Frege]
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9585
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Since every definition is an equation, one cannot define equality itself
[Frege]
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9586
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In a number-statement, something is predicated of a concept
[Frege]
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9587
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How do you find the right level of inattention; you eliminate too many or too few characteristics
[Frege]
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9588
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Number-abstraction somehow makes things identical without changing them!
[Frege]
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9589
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Numbers are not real like the sea, but (crucially) they are still objective
[Frege]
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