Here is a quick review of personal identity so far.
John Locke thinks that personal identity requires that there be continuity of memory. In other words, in order for you to be the same person now as you were when you were a child, you must have autobiographical memory of your childhood. Reid objects to this by providing us with the brave officer example, which is a case where Locke’s theory of personal identity violates the transitivity of identity. Sven thinks that what the takeaway from this case is that direct memory connections are not necessary for personal identity. There can be other kinds of psychological continuity such as indirect memory connections.
However, a problem with using other kinds of psychological continuity as a requirement, or criterion, for personal identity is that in cases of fission, where one person is split into two identical versions of himself of herself, we end up with two distinct people who also satisfy conditions of identity. In other words, they are both the same and distinct, which also violates the transitivity of identity.
Parfit tries to defend the use of psychological criteria for personal identity. Parfit claims that the above problem is only the case if when we say personal identity that we mean survival. Parfit notes that we only worry about violating the transitivity of identity when we use “identity” as a technical term. Parfit thinks that survival, not identity, is really the important concern.
Nozick steps in to the debate to say that he can improve on Parfit’s view, which he calls a no-rival theory. Nozick calls Parfit’s view a no-rival theory because Parfit does not allow for multiple rival candidates for identity. Nozick accounts for rival candidates by saying that the candidate with the strongest connection is the one who “survives” as the original individual.