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8647
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Not all objects are spatial; 4 can still be an object, despite lacking spatial co-ordinates [Frege]
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Full Idea:
To give spatial co-ordinates for the number four makes no sense; but the only conclusion to be drawn from that is, that 4 is not a spatial object, not that it is not an object at all. Not every object has a place.
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From:
Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §61)
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A reaction:
This is the modern philosophical concept of an 'object', though I find such talk very peculiar. It sounds like extreme Platonism, though this is usually denied. This is how logicians seem to see the world.
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10309
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Frege says singular terms denote objects, numerals are singular terms, so numbers exist [Frege, by Hale]
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Full Idea:
Frege's argument for abstract objects is: 1) singular terms in true expressions must denote objects, 2) numerals function as singular terms, 3) there must exist numbers denoted by those expressions.
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From:
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Bob Hale - Abstract Objects Ch.1
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A reaction:
[compressed] Given that most of the singular term usages can be rephrased adjectively, this strikes me as a weak argument, though Hale pins his whole book on it.
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10550
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Frege establishes abstract objects independently from concrete ones, by falling under a concept [Frege, by Dummett]
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Full Idea:
For Frege it is legitimate, in order to establish the existence of a certain number, to cite a concept under which only abstract objects fall, and in such a way guarantee the existence of the number quite independently of what concrete objects there are.
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From:
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14
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A reaction:
This approach of Frege's got into trouble with Russell's Paradox, which gave a concept under which nothing could fall. It strikes me as misguided even without that problem. I say abstracta are rooted in the concrete.
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8785
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For Frege, objects just are what singular terms refer to [Frege, by Hale/Wright]
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Full Idea:
In Frege's 'Grundlagen' objects, as distinct from entities of other types (properties, relations, or various functions), just are what (actual or possible) singular terms refer to.
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From:
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by B Hale / C Wright - Logicism in the 21st Century 2
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A reaction:
This seems to be the key claim that results in twentieth century metaphysics being done through analysis of language. The culmination is, of course, a denial of metaphysics, and then an eventual realisation that Frege was wrong.
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