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Single Idea 18269
[filed under theme 9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
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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?
Gist of Idea
Logical objects are extensions of concepts, or ranges of values of functions
Source
Gottlob Frege (Letters to Russell [1902], 1902.07.28), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 7 epigr
Book Ref
Coffa,J.Alberto: 'The Semantic Tradition from Kant to Carnap' [CUP 1993], p.113
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.
The
17 ideas
with the same theme
[examples amd principles of modern abstracta]:
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12939
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Wholly uniform things like space and numbers are mere abstractions
[Leibniz]
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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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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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18269
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Logical objects are extensions of concepts, or ranges of values of functions
[Frege]
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8719
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There can be impossible and contradictory objects, if they can have properties
[Meinong, by Friend]
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10543
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Abstract objects must have names that fall within the range of some functional expression
[Dummett]
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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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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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9858
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Abstract objects nowadays are those which are objective but not actual
[Dummett]
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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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10415
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Properties make round squares and round triangles distinct, unlike exemplification
[Zalta, by Swoyer]
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9878
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Contextually defined abstract terms genuinely refer to objects
[Wright,C, by Dummett]
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9969
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The empty set is the purest abstract object
[Jubien]
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10626
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Objects just are what singular terms refer to
[Hale/Wright]
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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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7783
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Bodies, properties, relations, events, numbers, sets and propositions are 'things' if they exist
[Lowe]
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10307
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The modern Fregean use of the term 'object' is much broader than the ordinary usage
[Hale]
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