Single Idea 10227

[catalogued under 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 Reference

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.