Consequences of the Idealist Interpretation for the Divisibility of Space

In this chapter, I discuss the third metaphysical implication of the Idealist reading, pertaining to the divisibility of space. Is space infinitely or merely finitely divisible? I rebut Hume’s argument for the latter possibility, showing that it is invalid on both readings – the Materialist and the Idealist. I then show that there is a better Idealist argument in support of the merely finite divisibility, drawing on other assumptions in Hume’s system, and (to the best of my knowledge) no Materialist counterpart. So whereas on the Idealist reading, the finite divisibility of space is defensible within the Treatise, on the Materialist interpretation, Hume must remain agnostic on this question (even if he can wield other assumptions he makes in the Treatise).