Single Idea 9804

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

Full Idea

Every statement of the result of an arithmetical operation is a statement of one of the modes of formation of a given number.

Gist of Idea

Arithmetical results give a mode of formation of a given number

Source

John Stuart Mill (System of Logic [1843], 3.24.5)

Book Reference

Mill,John Stuart: 'System of Logic (9th ed, 2 vols)' [Longmans, Green etc 1875], p.151


A Reaction

Although Mill sticks cautiously to very simple arithmetic, inviting empirical accounts of much higher mathematics, I think the phrase 'modes of formation' of numbers is very helpful. It could take us either into structuralism, or into constructivism.