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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 Objects of ideas can be divided into abstract and concrete, and then further subdivided [Leibniz]
10539 Frege refers to 'concrete' objects, but they are no different in principle from abstract ones [Frege, by Dummett]
11093 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]
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]
9884 The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett]
10577 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]
22287 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]
10493 If concrete is spatio-temporal and causal, and abstract isn't, the distinction doesn't suit physics [Ladyman/Ross]
14934 Concrete and abstract are too crude for modern physics [Ladyman/Ross]