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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
|
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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9388
|
Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege]
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Full Idea:
Of any concept, we must require that it have a sharp boundary. Of any object it must hold either that it falls under the concept or it does not. We may not allow a third case in which it is somehow indeterminate whether an object falls under a concept.
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From:
Gottlob Frege (Logic in Mathematics [1914], p.229), quoted by Ian Rumfitt - The Logic of Boundaryless Concepts p.1 n1
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A reaction:
This is the voice of the classical logician, which has echoed by Russell. I'm with them, I think, in the sense that logic can only work with precise concepts. The jury is still out. Maybe we can 'precisify', without achieving total precision.
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12153
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Geach denies Frege's view, that 'being the same F' splits into being the same and being F [Perry on Frege]
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Full Idea:
Frege's position is that 'being the same F as' splits up into a general relation and an assertion about the referent ('being the same' and 'being an F'). This is what Geach denies, when he says there is no such thing as being 'just the same'.
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From:
comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by John Perry - The Same F I
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A reaction:
It looks as if you can take your pick - whether two things are perfectly identical, or whether they are identical in some respect. Get an unambiguous proposition before you begin the discussion. Identify referents, not kinds of identity, says Perry.
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9853
|
Identity between objects is not a consequence of identity, but part of what 'identity' means [Frege, by Dummett]
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Full Idea:
Part of Frege's profound new idea of identity is that the criteria for identity of objects of a given kind is not a consequence of the way that kind of object is characterised, but has to be expressly stipulated as part of that characterisation.
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From:
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.13
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A reaction:
This makes identity a relative concept, rather than an instrinsic concept. Does a unique object have an identity? Do properties have intrinsic identity conditions, making them usable to identify two objects. Deep waters. Has Frege muddied them?
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