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Single Idea 10205

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic]

Full Idea

Originally, the focus of geometry was space - matter and extension - and the subject matter of arithmetic was quantity. Geometry concerned the continuous, whereas arithmetic concerned the discrete. Mathematics left these roots in the nineteenth century.

Gist of Idea

Mathematics originally concerned the continuous (geometry) and the discrete (arithmetic)


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

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.13

A Reaction

Mathematicians can do what they like, but I don't think philosophers of mathematics should lose sight of these two roots. It would be odd if the true nature of mathematics had nothing whatever to do with its origin.