Reason, Habit, and Applied Mathematics

Hume is aware that reason is useful for drawing conclusions about matters of fact: "Mathematics, indeed, are useful in all mechanical operations, and arithmetic in almost every art and profession" (T 2.3.3.2; SBN 413-14). But he offers no account of how relations of ideas direct our judgment concerning matters of fact. This is a pity, because the application of mathematics offers an excellent opportunity to observe the interplay between reason and experience, and thus it provides an interesting perspective on Hume's philosophy. This article aims to turn a handful of Hume's remarks into a Humean account of applied mathematics (§§1-3). The account is interesting on its own, but it reveals also an odd consequence for Hume's philosophy, viz., the existence of a species of probability, in which reason lends force and vivacity to inferences involving matters of fact (§4).