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Single Idea 10227
[filed under theme 7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
]
Full Idea
The epistemic proposals of ontological realists in mathematics (such as Maddy and Resnik) has resulted in the blurring of the abstract/concrete boundary. ...Perhaps the burden is now on defenders of the boundary.
Gist of Idea
The abstract/concrete boundary now seems blurred, and would need a defence
Source
Stewart Shapiro (Philosophy of Mathematics [1997], 4.1)
Book Ref
Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.111
A Reaction
As Shapiro says, 'a vague boundary is still a boundary', so we need not be mesmerised by borderline cases. I would defend the boundary, with the concrete just being physical. A chair is physical, but our concept of a chair may already be abstract.
The
26 ideas
with the same theme
[general ideas about the abstract/concrete border]:
12966
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Objects of ideas can be divided into abstract and concrete, and then further subdivided
[Leibniz]
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10539
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Frege refers to 'concrete' objects, but they are no different in principle from abstract ones
[Frege, by Dummett]
|
11093
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We don't say 'red' is abstract, unlike a river, just because it has discontinuous shape
[Quine]
|
1630
|
We can only see an alien language in terms of our own thought structures (e.g. physical/abstract)
[Quine]
|
10515
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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]
|
10540
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We can't say that light is concrete but radio waves abstract
[Dummett]
|
9884
|
The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy
[Dummett]
|
10577
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Concrete objects have few essential properties, but properties of abstractions are mostly essential
[Yablo]
|
10578
|
We are thought to know concreta a posteriori, and many abstracta a priori
[Yablo]
|
9210
|
Possible objects are abstract; actual concrete objects are possible; so abstract/concrete are compatible
[Fine,K]
|
10227
|
The abstract/concrete boundary now seems blurred, and would need a defence
[Shapiro]
|
10226
|
Mathematicians regard arithmetic as concrete, and group theory as abstract
[Shapiro]
|
9918
|
Abstract/concrete is a distinction of kind, not degree
[Burgess/Rosen]
|
9929
|
Much of what science says about concrete entities is 'abstraction-laden'
[Burgess/Rosen]
|
9619
|
David's 'Napoleon' is about something concrete and something abstract
[Brown,JR]
|
10512
|
The abstract/concrete distinction is based on what is perceivable, causal and located
[Hale]
|
10517
|
Colours and points seem to be both concrete and abstract
[Hale]
|
10519
|
The abstract/concrete distinction is in the relations in the identity-criteria of object-names
[Hale]
|
10520
|
Token-letters and token-words are concrete objects, type-letters and type-words abstract
[Hale]
|
8953
|
Abstract entities don't depend on their concrete entities ...but maybe on the totality of concrete things
[Szabó]
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22287
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If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete
[Potter]
|
13744
|
The cosmos is the only fundamental entity, from which all else exists by abstraction
[Schaffer,J]
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10493
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If concrete is spatio-temporal and causal, and abstract isn't, the distinction doesn't suit physics
[Ladyman/Ross]
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14934
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Concrete and abstract are too crude for modern physics
[Ladyman/Ross]
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