# Section I: Of Knowledge explained — A Treatise of Human Nature > Chapter companion for A Treatise of Human Nature by David Hume. ## What happens Hume categorizes seven philosophical relations into two classes: those dependent solely on ideas (resemblance, contrariety, degrees in quality, proportions in quantity or number) and those that can change without altering the ideas (identity, relations of time and place, causation). He argues that only the former four can be objects of knowledge and certainty. Among these, three are known by intuition, while proportions in quantity or number require demonstration. Geometry, though useful, lacks perfect precision because its principles derive from appearances, whereas algebra and arithmetic achieve certainty through a precise standard. Hume also critiques the notion of abstract ideas, asserting that all ideas are copied from impressions and thus cannot be inherently obscure. ## Themes in this chapter ### Empiricism and the Primacy of Impressions Hume asserts that all ideas are copied from impressions, thereby rejecting the notion of abstract or obscure ideas and grounding knowledge in sensory experience. ### Skepticism About the External World Hume's critique of geometry and the limits of certainty in knowledge reflects a skeptical stance toward claims that go beyond what is given in impressions. ## Character check-ins ### David Hume Author of the Treatise, presenting his classification of philosophical relations and the limits of knowledge. ## Key lines > It appears, therefore, that of these seven philosophical relations, there remain only four, which depending solely upon ideas, can be the objects of knowledge and certainty. Thus, only four of the seven relations are based purely on ideas and can be known with certainty. _Hume identifies the relations that yield knowledge._ > There remain, therefore, algebra and arithmetic as the only sciences, in which we can carry on a chain of reasoning to any degree of intricacy, and yet preserve a perfect exactness and certainty. Algebra and arithmetic are the only sciences that allow complex reasoning with complete precision and certainty. _Hume elevates arithmetic and algebra above geometry in terms of certainty._ > But to destroy this artifice, we need but reflect on that principle so oft insisted on, that all our ideas are copied from our impressions. To refute this trick, we only need to recall that all ideas derive from impressions. _Hume uses his empiricist principle to undermine the notion of abstract ideas._ ## Links - HTML: https://www.betterreads.online/discover/a_treatise_of_human_nature_se/chapters/section-i-of-knowledge - Book: https://www.betterreads.online/discover/a_treatise_of_human_nature_se - All chapters: https://www.betterreads.online/discover/a_treatise_of_human_nature_se/chapters