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Full Idea
For intuitionists, it ceases to be true that abstract objects are not observable and cannot be involved in causal interaction, since such intuitive apprehension of them may be regarded as just such an interaction.
Gist of Idea
If we can intuitively apprehend abstract objects, this makes them observable and causally active
Source
Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
Book Ref
Dummett,Michael: 'Frege Philosophy of Language' [Duckworth 1981], p.511
A Reaction
I would say that since abstract objects can be involved in causal interactions, in the mind, and since the mind is entirely physical (oh yes), this makes abstract objects entirely physical, which may come as a shock to some people.
13387 | Our conceptual scheme becomes more powerful when we posit abstract objects [Quine] |
16980 | We need a logical use of 'object' as predicate-worthy, and an 'ontological' use [Strawson,P] |
18950 | Physics is full of non-physical entities, such as space-vectors [Putnam] |
10555 | If we can intuitively apprehend abstract objects, this makes them observable and causally active [Dummett] |
18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |