According to a common-sense platitude, identity is what matters in survival. To say that a relation is what matters in survival is to say that it is in virtue of that relation one has reasons for prudential concern for whether one’s survival will be good or bad.Footnote 1 The platitude can be given at least two readings. A first reading focuses on one’s relation to a particular future person:

The Strong Reading of the Platitude

Person \(P_1\) has at \(t_1\) reasons for prudential concern for the well-being of person \(P_2\) at \(t_2\) if and only if \(P_1\) is identical with \(P_2\).

A second, weaker reading focuses on one’s relation, more generally, to a future time:

The Weak Reading of the Platitude

Person \(P_1\) has at \(t_1\) reasons for prudential concern for some person’s well-being at \(t_2\) if and only if \(P_1\) is identical with some person who is alive at \(t_2\).

The most influential argument against the platitude is Derek Parfit’s division argument. It’s based around the following case, called My Division:

My body is fatally injured, as are the brains of my two brothers. My brain is divided, and each half is successfully transplanted into the body of one of my brothers. Each of the resulting people believes that he is me, seems to remember living my life, has my character, and is in every other way psychologically continuous with me. And he has a body that is very like mine.Footnote 2

To distinguish between the people resulting from the division, call the one with the left half of my brain Lefty and the one with the right half Righty.Footnote 3 Let \(t_1\) be a time when I am alive before the division and \(t_2\) be a time when Lefty and Righty are alive afterwards.

People have survived without half their brain; and one could plausibly, Parfit argues, survive a brain transplant.Footnote 4 Since this is so, we should accept that, if only one half of my brain had been successfully transplanted and the other half had been destroyed, I would have at \(t_1\) (before these events) reasons for prudential concern for the well-being of the unique resulting person at \(t_2\).Footnote 5 But, if a successful transplant of a single half would have been a success, then, in the case where both halves are successfully transplanted, we should have a double success rather than a failure.Footnote 6 Thus

  1. (1)

    I have at \(t_1\) reasons for prudential concern for the well-being of each one of Lefty and Righty at \(t_2\).Footnote 7

Since Lefty and Righty have both separate minds and different bodies at \(t_2\), it seems that

  1. (2)

    Lefty is not identical with Righty.Footnote 8

From (2), we have, by the transitivity of identity,

  1. (3)

    It is not the case that I am identical with both Lefty and Righty.

The upshot of the division argument is that the conjunction of (1) and (3) entails that the platitude is false, at least on the strong reading.

As Jens Johansson points out, however, the division argument does not refute the platitude on the weak reading.Footnote 9 On the weak reading, the platitude might still hold in conjunction with (1), (2), and (3) if I am identical with one of Lefty and Righty but it’s indeterminate which one of them I am identical with.Footnote 10 Yet Parfit’s stated target seems to be the platitude on the weak reading rather than the strong one.Footnote 11 Hence, if the division argument can’t be extended so that it also works on the weak reading, it would be less interesting.

In the following, I shall put forward an extension of the division argument which shows that, even on the weak reading, the platitude is not true. In this extension, Lefty survives longer than Righty.Footnote 12 Let \(t_3\) be a time after \(t_2\) such that there’s only one division product left alive at \(t_3\), and call him Old Lefty. And suppose that there’s been no further dramatic injuries or transplants and that the relation between Lefty at \(t_2\) and Old Lefty at \(t_3\) is just ordinary survival without division. Then, surely,

  1. (4)

    Lefty is identical with Old Lefty.

Since Righty is no longer alive at \(t_3\), the following seems to be true: apart from Old Lefty, there’s no one alive at t 3 with whom I am identical or for whom I have reasons to be prudentially concerned. Should this for some reason seem doubtful, we can make the case still more extreme by adding that Old Lefty happens to be the only person who is alive at \(t_3\). Hence

  1. (5)

    There is no person P alive at \(t_3\) who is not identical with Old Lefty such that either I am identical with P or I have at \(t_1\) reasons for prudential concern for the well-being of P at \(t_3\).

Now, consider my relation to Old Lefty. Do I have at \(t_1\) reasons for prudential concern for Old Lefty at \(t_3\)? This seems to follow from the same kind of double-success argument Parfit offered in support of (1): Suppose that only the left half of my brain had been successfully transplanted and the unique resulting person were still alive at \(t_3\). Since there would then be no division, it seems clear that I would have had at \(t_1\) reasons for prudential concern for the well-being of the resulting person at \(t_3\). And then, in the case where the right half is also successfully transplanted and the resulting person with that half survives until some time between \(t_2\) and \(t_3\), it seems again that we should have a double success rather than a failure. The added survival of Righty shouldn’t make it any less true that I have at \(t_1\) reasons for prudential concern for the well-being of the person with the left half of my brain at \(t_3\). Hence

  1. (6)

    I have at \(t_1\) reasons for prudential concern for the well-being of Old Lefty at \(t_3\).

From (5) and (6), we have, given the platitude on the weak reading,

  1. (7)

    I am identical with Old Lefty.

From (4) and (7), we have, by the transitivity of identity,

  1. (8)

    I am identical with Lefty.

Finally, from (3) and (8), we have

  1. (9)

    I am identical with Lefty but not with Righty.

But (9) is implausible. First, (1) and (9) in conjunction imply that I have at \(t_1\) reasons for prudential concern for the well-being of Righty at \(t_2\) even though I’m identical with someone else who’s alive at \(t_2\). Second, (9) seems especially implausible given a reductionist view about personal identity, that is, a view where personal identity over time holds in virtue of more basic physical, psychological, or phenomenal facts that can be described impersonally without asserting that any persons exist.Footnote 13 In terms of the impersonal facts that personal identity over time could plausibly consist in, there’s a symmetry between my relation to Lefty and my relation to Righty.Footnote 14 Hence it would be arbitrary if I were identical with Lefty but not with Righty, or vice versa.Footnote 15 Given this symmetry, it seems that either I am identical with neither of them or it’s indeterminate which one of them I am identical with. The claims from which we derived (9), however, do not seem indeterminate given the platitude on the weak reading. So, if the platitude on the weak reading is true, it seems that (9) is neither false nor indeterminate. Hence we can conclude that, even on the weak reading, the platitude is not true.

One way to get around these problems would be to take what matters in survival to be indeterminate identity rather than identity.Footnote 16 We could adopt one of the following readings:

The Strong Indeterminacy Reading of the Platitude

Person \(P_1\) has at \(t_1\) reasons for prudential concern for the well-being of person \(P_2\) at \(t_2\) if and only if it is not false that \(P_1\) is identical with \(P_2\).

The Weak Indeterminacy Reading of the Platitude

Person \(P_1\) has at \(t_1\) reasons for prudential concern for some person’s well-being at \(t_2\) if and only if it is not false that \(P_1\) is identical with some person who is alive at \(t_2\).

These readings are compatible with the conjunction of (1) and (3). So they are not open to Parfit’s division argument. And, on these readings, (7) doesn’t follow from (5) and (6). Hence the extended division argument is blocked too. The main problem with these readings, however, is that they don’t seem to fit the common-sense platitude that identity—rather than indeterminate identity—is what matters in survival.Footnote 17 The platitude is based on the prima facie compelling idea that prudential concern is concern for oneself, rather than concern for everyone of whom it’s not false that they are oneself.