This is a really interesting question. John Locke, in his Essay Concerning Human Understanding, famously defined a person as "a thinking intelligent being, that has reason and reflection, and can consider itself as itself, the same thinking thing, in different times and places; which it does only by that consciousness which is inseparable from thinking, and as it seems to me, essential to it." He then goes on to talk about our personal identity over time: "For, since consicousness always accompanies thinking, and it is that that makes everyone to be what he calls self, and thereby distinguishes himself from all other thinking things, in this alone consists personal identity, i.e., the sameness of rational being; and as far back as this consciousness can be extended backwards to any past action or though, so far reaches the identity of that person." The notion of consciousness extending backward is often taken to signify memory, and so a Lockean theory of personal identity suggests...

The prospect of going under anesthesia is a scary one, for all sorts of reasons. But I don't think you should have much cause to worry about identity issues. I have two comments that might help alleviate your concerns. First, you might ask yourself: What would be the difference between its being you who wakes up from the anesthesia and its being a doppelganger with your memories? From the outside, you would seem exactly the same. And from the inside, it would seem the same too. Your doppelganger might be thinking something like this: "Yesterday I was worried about whether I would wake up from the anesthesia, and I'm glad that my worries were for naught -- here I am." In other words, the prospect that you're proposing is not really one that can be discerned -- either from the inside or from the outside -- as one that makes any difference to anything. But if that doesn't help (and I'm a bit worried that it won't), it might better reassure you if you think about anesthesia on the...

One point that's implicit in Professor Pogge's answer above, but that it might be useful to make explicit, is that philosophers often use the notion of "person" in such a way that it contrasts with the genetic notion of "human". Whether or not you are human is a matter of your DNA. But whether or not you are a person cannot be settled by genetic testing. Rather, as Professor Pogge notes, it is usually taken to be a matter of having certain capacities. Thus, there may well be humans who are non-persons (for example, some philosophers have suggested that humans in persistent vegetative states fall into this category -- another controversial example concerns fetuses) and there may be persons who are non-humans (some advanced mammals, for example -- or if you want to get into the realm of science fiction, Data or Spock from Star Trek). Specifying which capacities are necessary and/or sufficient for personhood turns out to be quite difficult. Some of the essays in Matters of Life and Death ...

There is a little book by John Perry called A Dialogue on Personal Identity and Immortality that contains a good introduction to many of the issues about personal identity over time that are raised by your question.

See also the discussion in response to this question .