Abstract

David Hume's central distinction in the Treatise and Enquiry is between relations of ideas and matters of fact. Although most of the attention in the secondary literature is on the latter, I am directly concerned with analyzing Hume's characterization of relations of ideas. In particular, I analyze Hume's attempt to secure certainty and necessity within his empiricist system since these are the defining characteristics of Hume's perfect species of knowledge--arithmetic. The focus, then, is on how Hume justifies the special status of arithmetical knowledge. ;Two interpretations of Hume's philosophy of arithmetic have been offered in the secondary literature. But I argue that both are inadequate since, among other things, they fail to render arithmetic consistent with Hume's general theory of meaning nor do they connect the certainty of arithmetic with Hume's discussion of 1-1 correspondence. After critically analyzing these two positions, I argue for a new interpretation. I show that Hume's aversion to abstraction and infinite divisibility leads to a constructivist account of number--one which bears a strong resemblance to mathematical intuitionism. ;Not surprisingly, certainty and necessity are difficult to obtain in the Humean system. The subjective nature of psychological links of association precludes certainty. So Hume needs to connect arithmetic with something outside of his phenomenological experience. And I argue that this something else is the metaphysical makeup of space. In Book I, Part II of the Treatise, Hume adapts Zeno's metrical paradox to demonstrate that objective reality must consist of absolute simples, which Hume calls "units". Hume then uses these units as the building blocks for his constructivist theory of number. For only after establishing the existence of units, does Hume make his central distinction between relations of ideas and matters of fact and deploy his constructivism. ;Although problematic, Hume's philosophy of arithmetic provides us with a new perspective on his empiricism. Hume's frequently ignored discussion of space is found to impact directly his views on arithmetic. And his commitment to absolute simples provides direct evidence that Hume is a skeptical realist, having more in common with Locke than previously recognized