more from John Stuart Mill

Single Idea 5201

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

Full Idea

Mill maintained that the truths of logic and mathematics are not necessary or certain, by saying these propositions are inductive generalisations based on an extremely large number of instances.

Gist of Idea

Mill says logic and maths is induction based on a very large number of instances


report of John Stuart Mill (System of Logic [1843]) by A.J. Ayer - Language,Truth and Logic Ch.4

Book Reference

Ayer,A.J.: 'Language, Truth and Logic' [Penguin 1974], p.99

A Reaction

Ayer asserts that they are necessary (but only because they are tautological). I like the idea that maths is the 'science of patterns', but that might lead from an empirical start to a rationalist belief in a priori synthetic truths.