What was Hume's problem with personal identity?

An appreciation of Hume's psychology of object allows us to recognize certain tensions in his discussion of the origin of our belief in personal identity-tensions which have gone largely unnoticed in the secondary literature. This will serve to provide a new solution to the problem of explaining why Hume finds that discussion of personal identity so problematic when he famously disavows it in the Appendix to the Treatise. It turns out that the two psychological mechanisms which respectively generate the ideas of object and of personal identity are mutually incompatible. It is this sort of conflict within Hume's introspective or subjectivist psychology which is the source of his worry.