personal identity consists in memory; sameness of episodic memory is metaphysically necessary and sufficient for sameness of persons. In other words, on the Memory Theory, what makes a person identical with herself over time is her remembering or being able to remember the events to which she was witness or agent. If she cannot episodically remember an event, then she is not identical with any of the persons who was witness or agent to the event. In such a case, she would bear the same relation to that event as any other person for whom a memory of the event could rise at best to the level of a semantic memory. If she can episodically remember an event, then her recollection or ability to recall that event makes her identical with the person represented in that memory as agent or witness to the even.One problem with the Memory Theory, as Thomas Reid pointed out, is that there are periods of interrupted consciousness or memory, such as sleep.
Now, some researchers argue that sleep is required for forming long-term memories.
If it is true that one has to sleep in order to remember past events, and sleep is a period of interrupted consciousness, and hence interrupted personhood (as the Memory Theory entails), does it mean that one has to cease to exist as the same person in order to continue to exist as the same person? And if so, does that make sense? If it doesn't make sense, should the Memory Theory of personal identity be abandoned?