Single Idea 9888

[catalogued under 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism]

Full Idea

Mill's mistake is taking particular applications as integral to the sense of arithmetical propositions. But what is integral to arithmetic is the general principle that explains its applicability, and determines the pattern of particular applications.

Gist of Idea

Mill mistakes particular applications as integral to arithmetic, instead of general patterns

Source

comment on John Stuart Mill (System of Logic [1843], 2.6) by Michael Dummett - Frege philosophy of mathematics Ch.20

Book Reference

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.258


A Reaction

[Dummett is summarising Frege's view] Sounds like a tidy objection, but you still have to connect the general principles and patterns to the physical world. 'Structure' could be the magic word to achieve this.