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Full Idea
Objections to Frege's argument for abstract objects: that the objects would not have the right sort of independence; that we could have no knowledge of them; that the singular term statements can't be had; that thoughts of abstracta can't be identified.
Gist of Idea
Objections to Frege: abstracta are unknowable, non-independent, unstatable, unindividuated
Source
Bob Hale (Abstract Objects [1987], Ch.1)
Book Ref
Hale,Bob: 'Abstract Objects' [Blackwell 1987], p.13
A Reaction
[compressed] [See Idea 10309 for the original argument] It is helpful to have this list, even if Hale rejects them all. They are also created but then indestructible, and exist in unlimited profusion, and seem relative to a language. Etc!
Related Idea
Idea 10309 Frege says singular terms denote objects, numerals are singular terms, so numbers exist [Frege, by Hale]
| 17619 | We renounce all abstract entities [Goodman/Quine] |
| 8529 | Deniers of properties and relations rely on either predicates or on classes [Armstrong] |
| 8501 | Quineans take predication about objects as basic, not reference to properties they may have [Devitt] |
| 8858 | Philosophers keep finding unexpected objects, like models, worlds, functions, numbers, events, sets, properties [Yablo] |
| 4478 | Nominalism needs to account for abstract singular terms like 'circularity'. [Loux] |
| 10310 | Objections to Frege: abstracta are unknowable, non-independent, unstatable, unindividuated [Hale] |
| 7971 | Real Nominalism is only committed to concrete particulars, word-tokens, and (possibly) sets [Macdonald,C] |
| 14596 | Call 'nominalism' the denial of numbers, properties, relations and sets [Dorr] |
| 19122 | Nominalists can reduce theories of properties or sets to harmless axiomatic truth theories [Halbach/Leigh] |