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Single Idea 10548
[filed under theme 7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
]
Full Idea
The dictum that a name has meaning only in the context of a sentence repudiates the conception of a special philosophical sense of 'existence', which claims that numbers do not exist while affirming existential statements about them.
Gist of Idea
The context principle for names rules out a special philosophical sense for 'existence'
Source
Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
Book Ref
Dummett,Michael: 'Frege Philosophy of Language' [Duckworth 1981], p.497
A Reaction
He refers to Frege's Context Principle. Personally I would say you could make plenty of 'affirmations' about arithmetic without them having to be 'existential'. I can say there 'is' a number between 6 and 8, without huge existential claims.
The
23 ideas
from 'Frege Philosophy of Language (2nd ed)'
10320
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If a genuine singular term needs a criterion of identity, we must exclude abstract nouns
[Dummett, by Hale]
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19168
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Concepts only have a 'functional character', because they map to truth values, not objects
[Dummett, by Davidson]
|
10549
|
Since abstract objects cannot be picked out, we must rely on identity statements
[Dummett]
|
10516
|
A realistic view of reference is possible for concrete objects, but not for abstract objects
[Dummett, by Hale]
|
10547
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Abstract objects can never be confronted, and need verbal phrases for reference
[Dummett]
|
10531
|
There is a modern philosophical notion of 'object', first introduced by Frege
[Dummett]
|
17621
|
What matters in mathematics is its objectivity, not the existence of the objects
[Dummett]
|
10537
|
The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}}
[Dummett]
|
10542
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To associate a cardinal with each set, we need the Axiom of Choice to find a representative
[Dummett]
|
10554
|
Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal
[Dummett]
|
10540
|
We can't say that light is concrete but radio waves abstract
[Dummett]
|
10552
|
Intuitionism says that totality of numbers is only potential, but is still determinate
[Dummett]
|
10515
|
Ostension is possible for concreta; abstracta can only be referred to via other objects
[Dummett, by Hale]
|
10544
|
The concrete/abstract distinction seems crude: in which category is the Mistral?
[Dummett]
|
10546
|
We don't need a sharp concrete/abstract distinction
[Dummett]
|
10548
|
The context principle for names rules out a special philosophical sense for 'existence'
[Dummett]
|
10281
|
The objects we recognise the world as containing depends on the structure of our language
[Dummett]
|
10532
|
We can understand universals by studying predication
[Dummett]
|
10534
|
'Nominalism' used to mean denial of universals, but now means denial of abstract objects
[Dummett]
|
10545
|
Abstract objects may not cause changes, but they can be the subject of change
[Dummett]
|
10541
|
Concrete objects such as sounds and smells may not be possible objects of ostension
[Dummett]
|
10555
|
If we can intuitively apprehend abstract objects, this makes them observable and causally active
[Dummett]
|
10543
|
Abstract objects must have names that fall within the range of some functional expression
[Dummett]
|