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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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18269
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Logical objects are extensions of concepts, or ranges of values of functions [Frege]
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Full Idea:
How are we to conceive of logical objects? My only answer is, we conceive of them as extensions of concepts or, more generally, as ranges of values of functions ...what other way is there?
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From:
Gottlob Frege (Letters to Russell [1902], 1902.07.28), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 7 epigr
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A reaction:
This is the clearest statement I have found of what Frege means by an 'object'. But an extension is a collection of things, so an object is a group treated as a unity, which is generally how we understand a 'set'. Hence Quine's ontology.
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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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8489
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The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege]
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Full Idea:
I regard a regular definition of 'object' as impossible, since it is too simple to admit of logical analysis. Briefly: an object is anything that is not a function, so that an expression for it does not contain any empty place.
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From:
Gottlob Frege (Function and Concept [1891], p.32)
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A reaction:
Here is the core of the programme for deriving our ontology from our logic and language, followed through by Russell and Quine. Once we extend objects beyond the physical, it becomes incredibly hard to individuate them.
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