The substance theory's core intuition is that a person is not, at bottom, a bundle or chain of psychological states linked by memory, but a single persisting thing, a soul or self, which those states belong to and which continues to exist across gaps, whether the dreamless gap of deep sleep, the discontinuity of amnesia, or, on many religious versions, the far larger gap of bodily death; on this view, a person who wakes with no memory of yesterday has not become a new person, because the substance underlying both days' experiences is one and the same, whatever has happened to the memories attached to it.
Thomas Reid's classic objection to Locke's rival memory theory, sometimes called the brave officer paradox, presses exactly this point: imagine an old general who remembers, as a middle-aged officer, a brave act he performed as a young soldier, but who has, by old age, entirely forgotten that youthful act itself, even though the middle-aged officer still remembered it; Locke's criterion, applied strictly, seems to yield the contradictory result that the general both is and is not the same person as the young soldier, identical to the middle-aged officer, who was identical to the young soldier, and yet not identical to the young soldier directly, since identity, unlike memory-connection, should be transitive and admit of no such contradiction. Substance theorists take this as decisive evidence that some further fact, a persisting substance underlying and unifying the changing memories, must be doing the real work of identity that memory alone cannot do on its own.