What Does Hume Say About Knowledge?

The following will pay close attention to Book 1 Part 3 Section 1 (Of knowledge) of Hume’s Treatise of Human Nature, paying close attention to Hume’s discussion of mathematic and geometric certainty. Furthermore, the following will ask four substantive questions: What does Hume say about knowledge? How does he say it? Why is the section important to the Treatise? And, lastly, is Hume’s theory on knowledge persuasive, or do his arguments crumble under greater scrutiny? In the section at hand, Hume attempts to offer his standard for epistemological certainty, presumably in response to René Descartes’ epistemology—his fusion of clear and distinct perceptions with innate ideas. Hume, in 1.3.1 of the Treatise, asserts “there is no single phenomenon, even the most simple, which can be accounted for from the qualities of the objects, as they appear to us, for which we [could] foresee without the help of our memory and experience” (1.3.1.1). In other words, Hume argues
To Hume, arithmetic (e.g. 7+5=12) or algebra (e.g. X2=9) allow for logical reasoning that preserves truth, without requiring humans to synthesize any information or ideas. While future thinkers, particularly Immanuel Kant, will consider these judgements amplicative, Hume posits that mathematics simply consists of the demonstration of the relation of ideas. The statement 7+5=12, according to Hume, is not asserting a new truth or judgement, instead such equation is expressing the necessary correspondence and relation between seven, five and twelve. It should be noted, however, that arithmetic and algebra are NOT unique in Hume’s epistemology because numbers are different types of ideas; instead, algebra and arithmetic are unique in that they are the only methods that offer or demonstrate epistemological