Single Idea 8761

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism]

Full Idea

A 'system' is a collection of objects with certain relations among them; a 'pattern' or 'structure' is the abstract form of a system, highlighting the interrelationships and ignoring any features they do not affect how they relate to other objects.

Gist of Idea

A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them


Stewart Shapiro (Thinking About Mathematics [2000], 10.1)

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.259

A Reaction

Note that 'ignoring' features is a psychological account of abstraction, which (thanks to Frege and Geach) is supposed to be taboo - but which I suspect is actually indispensable in any proper account of thought and concepts.