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Single Idea 10226

[from 'Philosophy of Mathematics' by Stewart Shapiro, in 7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete ]

Full Idea

Mathematicians use the 'abstract/concrete' label differently, with arithmetic being 'concrete' because it is a single structure (up to isomorphism), while group theory is considered more 'abstract'.

Gist of Idea

Mathematicians regard arithmetic as concrete, and group theory as abstract

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 4.1 n1)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.109


A Reaction

I would say that it is the normal distinction, but they have moved the significant boundary up several levels in the hierarchy of abstraction.