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Single Idea 9869
[filed under theme 7. Existence / D. Theories of Reality / 2. Realism
]
Full Idea
Fully fledged realism depends on - indeed, may be identified with - an undiluted application to sentences of the relevant kind of straightforwards two-valued semantics.
Clarification
'Two-valued' semantics just recognises True or False
Gist of Idea
Realism is just the application of two-valued semantics to sentences
Source
Michael Dummett (Frege philosophy of mathematics [1991], Ch.15)
Book Ref
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.198
A Reaction
This is the sort of account you get from a whole-heartedly linguistic philosopher. Personally I would say that Dummett has got it precisely the wrong way round: I adopt a two-valued semantics because my metaphysics is realist.
The
27 ideas
from 'Frege philosophy of mathematics'
9848
|
Content is replaceable if identical, so replaceability can't define identity
[Dummett, by Dummett]
|
9993
|
There is no reason why abstraction by equivalence classes should be called 'logical'
[Dummett, by Tait]
|
18257
|
Why should the limit of measurement be points, not intervals?
[Dummett]
|
18255
|
Addition of quantities is prior to ordering, as shown in cyclic domains like angles
[Dummett]
|
9896
|
A prime number is one which is measured by a unit alone
[Dummett]
|
9895
|
A number is a multitude composed of units
[Dummett]
|
9820
|
In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical
[Dummett]
|
9829
|
The identity of a number may be fixed by something outside structure - by counting
[Dummett]
|
9828
|
Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1
[Dummett]
|
9833
|
To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too
[Dummett]
|
9836
|
Fregean semantics assumes a domain articulated into individual objects
[Dummett]
|
9842
|
Frege introduced criteria for identity, but thought defining identity was circular
[Dummett]
|
9847
|
A contextual definition permits the elimination of the expression by a substitution
[Dummett]
|
9852
|
We understand 'there are as many nuts as apples' as easily by pairing them as by counting them
[Dummett]
|
9849
|
Maybe a concept is 'prior' to another if it can be defined without the second concept
[Dummett]
|
9850
|
An argument for conceptual priority is greater simplicity in explanation
[Dummett]
|
9857
|
We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus'
[Dummett]
|
9869
|
Realism is just the application of two-valued semantics to sentences
[Dummett]
|
9858
|
Abstract objects nowadays are those which are objective but not actual
[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]
|
9872
|
Abstract objects need the context principle, since they can't be encountered directly
[Dummett]
|
9873
|
Abstract terms are acceptable as long as we know how they function linguistically
[Dummett]
|
9876
|
Set theory isn't part of logic, and why reduce to something more complex?
[Dummett]
|
9884
|
The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy
[Dummett]
|
9880
|
Nominalism assumes unmediated mental contact with objects
[Dummett]
|
9885
|
The existence of abstract objects is a pseudo-problem
[Dummett]
|