Hume approaches topics in metaphysics and epistemology via his theory of ideas and the cognitive faculties. In metaphysics, his primary interest is in questions not of the form ‘What is X?’ but of the form ‘What can we conceive X to be?’ His best-known contribution is his argument that causation, as far as we can conceive it, is just regular succession among objects or events, plus our habit of inferring one object or event from another. He also made important contributions concerning space and time, existence, identity, substances, and free will. In epistemology, his primary interest is in questions of the form ‘Which of our cognitive faculties is responsible for our belief in X?’ His best-known contribution is his argument that habit, not reason, engages us to suppose that unobserved events will resemble observed ones (a view concerning what philosophers now call induction). He also made important contributions concerning the distinction between the a priori and the a posteriori, belief in the external world, and religious belief.
Books that discuss Hume's views about a range of topics in metaphysics and epistemology (construed broadly, so as to include philosophy of mind, action and language) include Stroud 1977, Garrett 1997 and Allison 2008. Fogelin 1985 and Loeb 2002 are devoted to his epistemology. For three different approaches to his theory of causation, see Blackburn 1990, Kail 2007 and Millican 2009. For two different approaches to his argument about induction, see Owen 1999 and Peter Millican's article 'Hume's Sceptical Doubts Concerning Induction,' in Millican 2001.
Three introductory books that take quite different approaches to Hume's metaphysics and epistemology are Ayer 1980, Blackburn 2008 and Wright 2009. Norton & Taylor 2008 contains helpful introductory articles on Hume's views about several topics in metaphysics and epistemology.
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