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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]