Single Idea 10220

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism]

Full Idea

Because the same structure can be exemplified by more than one system, a structure is a one-over-many.

Gist of Idea

Because one structure exemplifies several systems, a structure is a one-over-many

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 3.3)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.84


A Reaction

The phrase 'one-over-many' is a classic Greek hallmark of a universal. Cf. Idea 10217, where Shapiro talks of arriving at structures by abstraction, through focusing and ignoring. This sounds more like a creation than a platonic universal.

Related Idea

Idea 10217 We can apprehend structures by focusing on or ignoring features of patterns [Shapiro]