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Single Idea 9858
[filed under theme 9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
]
Full Idea
Objects which are objective but not actual are precisely what are now called abstract objects.
Gist of Idea
Abstract objects nowadays are those which are objective but not actual
Source
Michael Dummett (Frege philosophy of mathematics [1991], Ch.15)
Book Ref
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.181
A Reaction
Why can there not be subjective abstract objects? 'My favourites are x, y and z'. 'I'll decide later what my favourites are'. 'I only buy my favourites - nothing else'.
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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