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Full Idea
To recognise that there is no objection in principle to abstract objects requires acknowledgement that some form of the context principle is correct, since abstract objects can neither be encountered nor presented.
Clarification
The 'context principle' says linguistic expressions are only meaningful in a context
Gist of Idea
Abstract objects need the context principle, since they can't be encountered directly
Source
Michael Dummett (Frege philosophy of mathematics [1991], Ch.16)
Book Ref
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.207
A Reaction
I take this to be an immensely important idea. I consider myself to be a philosopher of thought rather than a philosopher of language (Dummett's distinction, he being one of the latter). Thought connects to the world, but does it connect to abstracta?
10320 | If a genuine singular term needs a criterion of identity, we must exclude abstract nouns [Dummett, by Hale] |
10547 | Abstract objects can never be confronted, and need verbal phrases for reference [Dummett] |
9872 | Abstract objects need the context principle, since they can't be encountered directly [Dummett] |
18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
18498 | Abstract objects wouldn't be very popular without the implicit idea of truthmakers [Heil] |
10315 | We can't believe in a 'whereabouts' because we ask 'what kind of object is it?' [Hale] |
8915 | How we refer to abstractions is much less clear than how we refer to other things [Rosen] |