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12939
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Wholly uniform things like space and numbers are mere abstractions
[Leibniz]
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Full Idea:
Things which are uniform, containing no variety, are always mere abstractions: for instance, time, space, and the other entities of pure mathematics.
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From:
Gottfried Leibniz (New Essays on Human Understanding [1704], 2.01)
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A reaction:
I presume that being 'mere abstractions' denies them ontological status, and makes them creations of thought. If so, I like this idea a lot.
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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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9859
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It is absurd to deny the Equator, on the grounds that it lacks causal powers
[Dummett]
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Full Idea:
If someone argued that assuming the existence of the Equator explains nothing, and it has no causal powers, so everything would be the same if it didn't exist, so we needn't accept its existence, we should gape at the crudity of the misunderstanding.
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From:
Michael Dummett (Frege philosophy of mathematics [1991], Ch.15)
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A reaction:
Not me. I would gape if someone argued that latitude 55° 14' (and an infinity of other lines) exists for the same reasons (whatever they may be) that the Equator exists. A mode of description can't create an object.
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9860
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'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object
[Dummett]
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Full Idea:
'We've crossed the Equator' is judged true if we are nearer the other Pole, so it not for philosophers to deny that the Earth has an equator, and we see that the Equator is not a concept or relation or function, so it must be classified as an object.
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From:
Michael Dummett (Frege philosophy of mathematics [1991], Ch.15)
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A reaction:
A lovely example of linguistic philosophy in action (and so much the worse for that, I would say). A useful label here, I suggest (unoriginally, I think), is that we should label such an item a 'semantic object', rather than a real object in our ontology.
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10489
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We deal with abstract objects all the time: software, poems, mistakes, triangles..
[Boolos]
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Full Idea:
We twentieth century city dwellers deal with abstract objects all the time, such as bank balances, radio programs, software, newspaper articles, poems, mistakes, triangles.
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From:
George Boolos (Must We Believe in Set Theory? [1997], p.129)
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A reaction:
I find this claim to be totally question-begging, and typical of a logician. The word 'object' gets horribly stretched in these discussions. We can create concepts which have all the logical properties of objects. Maybe they just 'subsist'?
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10415
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Properties make round squares and round triangles distinct, unlike exemplification
[Zalta, by Swoyer]
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Full Idea:
On Zalta's view, properties with the same encoding extensions are identical, but may be distinct with the same exemplification extension. So the properties of being a round square and a round triangle are distinct, but with the same exemplification.
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From:
report of Edward N. Zalta (Abstract Objects:intro to Axiomatic Metaphysics [1983]) by Chris Swoyer - Properties
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A reaction:
(For Zalta's view, see Idea 10414) I'm not sure about 'encoding' (cf. Hodes's use of the word), but the idea that an abstract object is just a bunch of possible properties (assuming properties have prior availability) seems promising.
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10626
|
Objects just are what singular terms refer to
[Hale/Wright]
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Full Idea:
Objects, as distinct from entities of other types (properties, relations or, more generally, functions of different types and levels), just are what (actual or possible) singular terms refer to.
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From:
B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.1)
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A reaction:
I find this view very bizarre and hard to cope with. It seems either to preposterously accept the implications of the way we speak into our ontology ('sakes'?), or preposterously bend the word 'object' away from its normal meaning.
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7699
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Numbers, sets and propositions are abstract particulars; properties, qualities and relations are universals
[Jacquette]
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Full Idea:
Roughly, numbers, sets and propositions are assumed to be abstract particulars, while properties, including qualities and relations, are usually thought to be universals.
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From:
Dale Jacquette (Ontology [2002], Ch. 9)
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A reaction:
There is an interesting nominalist project of reducing all of these to particulars. Numbers to patterns, sets to their members, propositions to sentences, properties to causal powers, relations to, er, something else.
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7783
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Bodies, properties, relations, events, numbers, sets and propositions are 'things' if they exist
[Lowe]
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Full Idea:
Not only material bodies but also properties, relations, events, numbers, sets, and propositions are—if they are acknowledged as existing—to be accounted ‘things’.
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From:
E.J. Lowe (Things [1995])
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A reaction:
There might be lots of borderline cases here. Is the sky a thing? Is air a thing? How is transparency a thing? Is minus-one a thing? Is an incomplete proposition a thing? Etc.
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