Parfit’s non-identity problem depends on what he refers to the Time-Dependence Claim (TDC). The TDC is a feature of certain theories of personal identity across possible histories. According to the TDC,
If any particular person had not been conceived when he was in fact conceived, it is in fact true that he would never have existed. (Reasons and Persons, p. 351)
Every human is grown from a particular egg cell and a particular spermatozoon. The timing of conception determines which egg will be fertilized by which spermatozoon. Different egg or spermatozoon, different human. So, different time, different human — at least, according to the TDC.
The non-identity problem needs only the TDC, not any particular account of personal identity, and there is no theory the follows uniquely from the TDC. Rather, Parfit thinks any credible theory of personal identity across possible histories must accept the TDC. Parfit supports this claim by negative argument, i.e. considering and rejecting a number of alternative theories of identity that are not dependent on the TDC. Without the TDC, all of these alternatives have unacceptable implications. He concludes that whatever the correct account of identity across possible histories turns out to be, it must include the TDC.
The views Parfit considers are as follows.
1. The Featureless Cartesian View. Identity is something like a featureless Cartesian ego or primitive thisness that does not depend on anything more fundamental. I am Stephen only in virtue of having this particular thisness. I could have had any parents, been born in any time or place, or had any number of other different characteristics. In principle, I could have been a rock!
Parfit rejects this view on the grounds that I could only be aware of my identity as a Cartesian ego if I am directly aware of this identity; because a Cartesian ego is a pure thisness, identity cannot be inferred from any other quality I might have. Because I could only be aware of my identity if I were directly aware, and I am not directly aware of my identity, I have no reason to believe the Featureless Cartesian View and thus I can reject it.
2. The Descriptive View. The identity of an individual depends on a list of necessary properties, but these properties do not include having been grown from a particular egg and spermatozoon.
3. The Descriptive Name View. The identity of an individual depends on a list of necessary properties that would be given to describe a particular named individual. Parfit gives Kant as an example. In this world, Kant wrote a number of books including Critique of Pure Reason. Authorship of Critique of Pure Reason is a candidate for the list of necessary properties that Kant’s identity depends on. In any other world where some individual wrote Critique of Pure Reason, etc., that individual is Kant.
Both Descriptive Views have counterintuitive consequences. If one of Kant’s necessary properties is that he wrote Critique of Pure Reason, Parfit points out, then it is logically impossible that Kant could have died at an early age before writing any books at all. (A further difficulty, I think, is that this raises the equally thorny question of how we are to determine the identity of books across possible histories!) The Descriptive Views may be weakened so that authorship of Critique of Pure Reason, etc. is not a necessary feature of Kant, but it is peculiar to Kant. In any possible world where Critique of Pure Reason was authored, that author will have been Kant. Parfit’s objects that this leads to an unacceptable picture of human history in which the identities of individuals (like Kant) are supplied by impersonal historical facts (like the fact that there is a Critique of Pure Reason). Rather than explaining historical facts by reference to persons, we are forced to explain persons solely by reference to historical facts.
4. The Origin View. The identity of an individual depends on them having grown from particular sperm and egg cells. I am Stephen in virtue of having grown from two particular cells. I would exist in any world where an organism was grown from those particular cells, and I would not exist in any world where no organism grew from those particular cells. This is Parfit’s view.
This fourth view is no less troubling than the first three. The Origin View makes my identity dependent on the identities of particular sperm and egg cells. So what are the identity conditions of particular sperm and egg cells?
There are, again, four possibilities. Individual cells may not be a candidate for having Cartesian egos, but they are candidates for having thisnesses. This answer has all the same problems as the Featureless Cartesian View, and in fact it seems to entail the Featureless Cartesian View. If the Featureless Cartesian View is true, I could have been a rock. If it is true only of sperm and egg cells, they could have been rocks. If we accept the Origin View of personal identity and the Featureless Cartesian View of sperm and egg identity, I could have been a rock garden!
The Descriptive Views are not as obviously problematic, and I’m not sure it runs into the same problem as the Descriptive Views as applied to people. After all, we do not expect sperm and egg cells to possess historical agency. But no description will be able to identify particular cells without reference to the origins of those cells or the identities of the people they come from.
This leaves the Origin View. As applied to cells, I suppose this would mean that the identity of a particular cell depends on it being constituted by particular molecules. Different molecules, different cells. Different cells, different person. And now we need to know the identity conditions for molecules. It seems that this cycle would continue all the way down to the level of fundamental particles. This implies that individuals could not exist in worlds that were even slightly physically different from one another. The Origin View is inadequate as a theory of identity across possible histories because it denies the very possibility of identity across possible histories.
Parfit claims that this list of possible views is exhaustive. If this claim is false, he has failed to establish the Time-Dependence Claim. In fact, all of the views Parfit considers are unacceptable. There must be other alternatives. Until these alternatives have been explored, we should not accept the Time-Dependence Claim.