Abstract

In this essay, I argue that Hume’s theory of Quantitative and Numerical Philosophical Relations can be interpreted in a way which allows mathematical knowledge to be about a body of objective and necessary truths, while preserving Hume’s nominalism and the basic principles of his theory of ideas. Attempts are made to clear up a number of obscure points about Hume’s claims concerning the abstract sciences of Arithmetic and Algebra by means of re-examining what he says and what he could comfortably have said about relations of qualitative resemblance.