Against Personal Numerical Identity over Time

By | February 8, 2024

The topic of identity over time has long been a topic in philosophy. Frequently, these discussions take it for granted that, for understanding the persistence of persons at least, we need to have numerical identity over time. One motivating idea is that we commonly say, in reference to photos or memories of our younger selves, things like “That’s me when I was seven,” which may be taken to mean that younger-me is (=) numerically identical to me-now. And, if we believe in an afterlife of any sort, we want to be able to explain why I-now should be concerned about the status of future-me. If I-now just is (=) numerically identical to future-me, then we have a straightforward answer to that question.

On the other hand, we also commonly say things in reference to our earlier selves that seemingly deny numerical identity over time. For example, a recovering alcoholic may say, “I’m not the man I used to be.” At face value, this says that I-now is not (≠) numerically identical to past-me. Furthermore, we all naturally think of ourselves as changing over time as we acquire and lose different intrinsic properties or “temporary intrinsics,” as they are called. This poses a conceptual problem for the idea of personal numerical identity over time. The principle of the indiscernability of identicals, famously articulated by Leibniz, says that if A = B, then A and B have the same intrinsic properties. So if I’m intrinsically changing throughout my life, then it seems that I-at-time-T1 cannot be numerically identical to myself-at-time-T2 (where T1 ≠ T2).

To handle the problem of temporary intrinsics, defenders of the idea that we have personal numerical identity over time have to develop a concept of the self or “I” that is intrinsically invariant over time. There are, so far as I can see, only three ways to do this:

  1. Perdurantism or “Four-dimensionalism” (4D): The self or “I” is a complete space–time worm. When I refer to my younger or older self, I’m not referring to me (the complete space–time worm that is me) but to different slices of that worm. Strictly speaking, I (= the complete worm) do not change over time. I only change in slice-relative ways (e.g., my T1 slice is standing up whereas my T2 slice is sitting down).
  2. Endurantism + temporally indexed properties (E+TI): The self or “I” exists wholly at each temporal moment, but the self that exists at each moment has a complete set of temporally indexed properties that together completely describe the self intrinsically at all moments of its past, present, and future existence. So, if at T1 I am standing and T2 I am sitting, then at T1 I have the intrinsic property of going to be sitting at T2 and at T2 I have the intrinsic property of having been standing at T1.
  3. Bare particularism (BP): Instead of incorporating temporary intrinsics into the self, this approach strips them out completely. The core self, on this view, is defined by a haecceity or “individual essence” that is temporally invariant and that has no accidental intrinsic properties at all. I-at-T1 am numerically identical to myself-at-T2 because the numerically same individual essence exists at both times. That I’m standing at T1 and sitting at T2 is irrelevant.

Each of these views faces serious problems:

  • The first (4D) only works on a B-theory of time. This is controversial and counterintuitive, at the very least. The more natural and commonsense view is that time is fundamentally dynamic. This is called the A-theory of time.
  • The first two (4D and E+TI) are both fatalistic. The reason has to do with the necessity of identity – if A = B, then necessarily, A = B. By building all temporary intrinsics throughout a person’s whole life into the self, these views make those intrinsics necessary to the essence or identity of that person. Change any of those details and that person, that token individual, no longer exists and is replaced by a numerically different individual. But if every intrinsic detail of my life is specified in my individual essence, including which choices I make throughout my life, then I cannot be free to do otherwise at any point on pain of ceasing to exist as the individual that I am.
  • The last view (BP) defines the “self” in a way that is so incredibly “thin” that it’s not clear why anyone should care about it. If none of my experiences, memories, or anticipations matters to who I am, or whether I exist, then how can I be an object of self-concern? What could an afterlife even mean to a mere individual essence, one to whom even the direct experience of God’s presence in heaven is essentially irrelevant?

I reject each of these views. As a committed A-theorist, I reject 4D. As a committed open-futurist and anti-fatalist, I reject 4D and E+TI. And as someone who believes that the contingent future, including my particular future experiences and choices, matters, I reject BP.

If not numerical identity, then what?

Some readers may be uneasy at this point. If we deny our personal numerical identity over time, then how do we account for things like (a) our responsibility for the past, (b) our concern for the future, and (c) present continuity of thought? How can we say that I-at-T1 am not identical to myself-at-T2 and yet we don’t simply have two completely different individuals who happen to resemble each other to some degree?

What we need, I say, is not a numerical identity relation, but a transitive continuity relation. Regarding transitivity, my future self should be related to my past self in such a way that (a) moral responsibility carries forward and (b) present anticipations carry forward to future fulfillment or disappointment. Regarding continuity, our conscious (and subconscious) states from moment-to-moment should smoothly transition so that we can, for example, follow an argument or carry a conversation.

One way to establish transitivity is by affirming the essentiality of origins. This is the idea that I am constituted by my past history, including my genetic endowment and my past experiences and memories. This seems plausible to me. I would not literally be (=) the man I am now if had had different biological parents, had different experiences growing up, or made different choices. For better or worse, these things have made me who I now am. But I don’t have to stay like I now am. Essentiality of origins does not entail, like 4D and E+TI do, its future-oriented flip-side–let’s call it the essentiality of destiny, which holds that my future experiences and choices are essential to me as well. That, I have argued, leads to fatalism.

To establish continuity, I believe we need a richer conception of time, or more specifically of the present moment, one that allows it to be, not merely a discrete “point” that divides the past from a future, but a two-sided boundary that also unites the past with the future, joining as it divides. I have an unpublished paper in which I develop this idea in some depth by drawing on the work of both Peirce and Brentano. Perhaps I’ll try to blog through it in the near future. The idea can also be developed with reference to the mathematics of smooth infinitesimal analysis. The general idea is that the present moment carries a “memory” of the immediate past along with it and simultaneously “anticipates” the immediate future. The succession of present moments is a succession of memory/anticipation pairs.

So, even in the absence of strict numerical identity over time, I retain responsibility for my past decisions because (due to essentiality of origins) those decisions have constituted my present self as someone who did those things then. Likewise, I should be concerned about my future experiences because, however my life unfolds, each possible future-me is a continuous extension of me-now that carries my intrinsic memory along with it. Even if (due to amnesia, say) I have forgotten my past, I am still constituted by that past, and because God perfectly remembers my past, those memories can be restored to me in the afterlife. (I think this is part of what the resurrection entails). Retrospectively, future-me will be able to look back at me-now and own that history. Prospectively, present-me contemplates a variety of possible future-mes, each of which is a continuous extension of me-now.

In conclusion, it is my view that we don’t have, don’t need, and shouldn’t want to have strict personal numerical identity over time. I am not the same (identical) man I used to be, and that (for the most part, I hope) is a good thing! I am an overall better person now than I used to be. And, by God’s grace, I am not now what I someday shall be. That too is a good thing (1 John 3:2)!

3 thoughts on “Against Personal Numerical Identity over Time

  1. Charles Bakker

    I love this, though I wonder why you did not explore the idea that William James raised in his Principles – that we are actually collections of different selves, each of which is brought forth in different contexts. For instance, the person I am around my children overlaps with, but is not the same as, the person I am around my work peers, or again, my in-laws, etc. Thus there is almost a sense in which I am comparable to the intersection in a venn diagram.

    1. Alan Rhoda Post author

      Hi Charles,
      Thanks for the comment! To answer your question honestly, I didn’t explore James’s idea because it wasn’t on my radar and because, even if it had been, I probably still would have left it out as tangential to the main concerns of this post. I appreciate your bringing James up, though. I shall have to give some thought to that. Offhand, based on your description, I take James to be saying that the “self” is multi-faceted and that different facets come to the fore in different contexts. This could be developed in one of two different ways. In one way it could be used to support a “bundle” theory of the self, which denies any stable unity of the self. In another way, which I am more sympathetic too, it could be used to say that the self is unified, but not fully accessible to introspection. This would have more the view of James’s lifelong friend Charles Peirce. Peirce believed that there are many layers of “depth” to consciousness, that we only really aware of the “surface” layers, and that shifting experiences bring different layers nearer to the surface (for a time), with the result being that manifest self—the self that manifests to others and to ourselves in self-consciousness—is always in flux.

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