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Single Idea 10550
[filed under theme 9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
]
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.
Gist of Idea
Frege establishes abstract objects independently from concrete ones, by falling under a concept
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14
Book Ref
Dummett,Michael: 'Frege Philosophy of Language' [Duckworth 1981], p.504
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.
The
17 ideas
with the same theme
[examples amd principles of modern abstracta]:
12939
|
Wholly uniform things like space and numbers are mere abstractions
[Leibniz]
|
10309
|
Frege says singular terms denote objects, numerals are singular terms, so numbers exist
[Frege, by Hale]
|
10550
|
Frege establishes abstract objects independently from concrete ones, by falling under a concept
[Frege, by Dummett]
|
18269
|
Logical objects are extensions of concepts, or ranges of values of functions
[Frege]
|
8719
|
There can be impossible and contradictory objects, if they can have properties
[Meinong, by Friend]
|
10543
|
Abstract objects must have names that fall within the range of some functional expression
[Dummett]
|
9859
|
It is absurd to deny the Equator, on the grounds that it lacks causal powers
[Dummett]
|
9860
|
'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object
[Dummett]
|
9858
|
Abstract objects nowadays are those which are objective but not actual
[Dummett]
|
10489
|
We deal with abstract objects all the time: software, poems, mistakes, triangles..
[Boolos]
|
10415
|
Properties make round squares and round triangles distinct, unlike exemplification
[Zalta, by Swoyer]
|
9878
|
Contextually defined abstract terms genuinely refer to objects
[Wright,C, by Dummett]
|
9969
|
The empty set is the purest abstract object
[Jubien]
|
10626
|
Objects just are what singular terms refer to
[Hale/Wright]
|
7699
|
Numbers, sets and propositions are abstract particulars; properties, qualities and relations are universals
[Jacquette]
|
7783
|
Bodies, properties, relations, events, numbers, sets and propositions are 'things' if they exist
[Lowe]
|
10307
|
The modern Fregean use of the term 'object' is much broader than the ordinary usage
[Hale]
|