Single Idea 10273

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

Full Idea

Some structures are exemplified by both systems of abstracta and systems of concreta.

Gist of Idea

Some structures are exemplified by both abstract and concrete

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 8.2)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.248


A Reaction

It at least seems plausible that one might try to build a physical structure that modelled arithmetic (an abacus might be an instance), so the parallel is feasible. Then to say that the abstract arose from modelling the physical seems equally plausible.