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Single Idea 10309
[filed under theme 9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
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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.
Gist of Idea
Frege says singular terms denote objects, numerals are singular terms, so numbers exist
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Bob Hale - Abstract Objects Ch.1
Book Ref
Hale,Bob: 'Abstract Objects' [Blackwell 1987], p.11
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.
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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