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Single Idea 10549
[filed under theme 18. Thought / E. Abstraction / 7. Abstracta by Equivalence
]
Full Idea
Since we cannot pick an abstract object out from its surrounding, all that we need to master is the use of statements of identity between objects of a certain kind.
Gist of Idea
Since abstract objects cannot be picked out, we must rely on identity statements
Source
Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
Book Ref
Dummett,Michael: 'Frege Philosophy of Language' [Duckworth 1981], p.498
A Reaction
This is the necessary Fregean preliminary to using a principle of abstraction to identify two objects which are abstract (when the two objects are in an equivalence relation). Presumably circular squares and square circles are identical?
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
|
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
|
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]
|
10552
|
Intuitionism says that totality of numbers is only potential, but is still determinate
[Dummett]
|
10540
|
We can't say that light is concrete but radio waves abstract
[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]
|
10541
|
Concrete objects such as sounds and smells may not be possible objects of ostension
[Dummett]
|
10545
|
Abstract objects may not cause changes, but they can be the subject of change
[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]
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