In my previous post on Personal Identity, I suggested that the idea of a 'pure ego', independent of all physical and psychological facts, is just senseless. I presented Parfit's reductionist view as an alternative. According to Parfit, identity merely consists in physical and psychological continuity. It is not some 'further fact' to be discovered on top of these more mundane facts.
(I personally think psychological continuity is all that matters. You can test your own intuitions with this fun game at The Philosophers' Magazine.)
In this post and the next, I want to discuss some of the interesting thought-experiments Parfit presents in Reasons and Persons. The first shows that personal identity is a vague concept, so (remarkably!) questions like "am I about to die?" do not always have a determinate answer. The second shows that personal identity does not explain our unity of consciousness, because it is possible for one person to have two independent streams of consciousness simultaneously. The third shows that identity is not what matters. It doesn't matter if you die, so long as another person connected to you in the right way lives on.
Once we understand identity in terms of physical or psychological continuity, it should come as no surprise that we can have indeterminate results. After all, such continuities can vary widely, and it would be arbitrary to impose some particular threshold to specify what counts as 'identity' or not. This idea is illustrated by the following thought experiment.
Imagine a mad scientist could replace parts of your brain with someone else's. Now consider the spectrum of cases where he replaces none, 1%, 2%, ..., 99%, or 100% of your brain. It's clear in the leftmost cases, where the procedure has minimal effect, that the resulting person would still be you. It's equally clear in the rightmost cases that the resulting person is not you, for your entire brain has been destroyed and replaced by someone else's. But what about the middle cases in the spectrum? Where do you draw the line? Any decision would be arbitrary. Personal identity is supposed to be deeply significant, so it is implausible to claim that it could be affected by something so trivial as a couple of cells either way.
So to hold that personal identity is determinate, as non-reductionists must, is both arbitrary and trivializing. We should instead recognize that the concept is vague. There are some cases where there is no determinate answer as to whether a person's identity will persist. This is not because of ignorance - we can know all the facts about their physical and psychological continuity. Personal identity is not some 'further fact' on top of this. (See the Parfit quote in my earlier post.) It may simply be unclear whether 'identity' is the best description to give of these facts.