more from Stewart Shapiro

Single Idea 10203

[catalogued under 15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind]

Full Idea

The epistemological account of mathematical structures depends on the size and complexity of the structure, but small, finite structures are apprehended through abstraction via simple pattern recognition.

Gist of Idea

We apprehend small, finite mathematical structures by abstraction from patterns


Stewart Shapiro (Philosophy of Mathematics [1997], Intro)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.11

A Reaction

Yes! This I take to be the reason why John Stuart Mill was not a fool in his discussion of the pebbles. Successive abstractions (and fictions) will then get you to more complex structures.