Hume on Abstraction and Identity

Hume’s critique of traditional abstraction entails a result that undercuts his account of the idea of identity. To save his account of identity, Hume would have to accept abstraction as well. What links these two discussions is (1) Hume’s widely shared assumption that traditional abstraction is separating in the mind what are inseparable in reality, (2) his principle that what are different are mentally separable, and (3) his principle that we cannot conceive of the impossible. Given these, it will turn out that abstraction is mentally separating something from itself, which will entail that abstraction is conceiving of something as distinct from itself. But it is impossible for something to be distinct from itself, and so it is inconceivable. Therefore abstraction is impossible. Yet consider Hume’s account of the idea of identity. On that account, to conceive of an identity is to conceive of something as one single thing viewed one way and as two distinct things viewed another. How we can take these opposing views of the same thing is a problem that I’ve termed Hume’s Difficulty concerning Identity. It will turn out that we can take the opposing views only if we can conceive of the single thing viewed one way as somehow distinct from itself when viewed the other way. That is, we must be able to conceive of something as distinct from itself. However, if we cannot conceive of something as distinct from itself when abstracting, then we cannot do it when conceiving of an identity. So traditional abstraction and Hume’s account of the idea of identity stand or fall together.