Abstract
Personal time, as opposed to external time, has a certain role to play in the correct account of death and immortality. But saying exactly what that role is, and what role remains for external time, is not straightforward. I formulate and defend accounts of death and immortality that specify these roles precisely.
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Notes
And in my (2007a) I made the same points about my account of being dead at a time.
Typically, ‘time is a continuum of instants’ is taken to mean that (i) time is the set that includes all and only the instants, (ii) the earlier than relation is a linear order (a transitive, asymmetric, and total relation) on this set, (iii) any partition of this set into two non-empty subsets s1 and s2 such that each instant in s1 is earlier than each instant in s2 (any cut of the set) must be such that either s1 has last instant and s2 has no first instant or s1 has no last instant but s2 has a first instant. For the set to count as a linear continuum, two further conditions must be met, which I omit here. A binary relation R is transitive iff for any x, y, z, if Rxy and Ryz then Rxz; asymmetric iff for any x and y, if Rxy then not Ryx; and total iff for any x, y, either Rxy or Ryx or x = y.
Standardly, the further condition is that the set must include any instant that is between any instants that it includes, where ‘t is between t* and t**’ means ‘either t* is earlier than t and t is earlier than t** or t** is earlier than t and t is earlier than t*’. But if time is circular, then every instant is earlier than every instant, including itself, and so for any instants t, t*, and t**, t is between t* and t**. And in that case the only way for a set to meet the ‘further condition’ is for it to include every instant! So a better definition of ‘interval’ would be framed in terms of the ternary relation mentioned in the main text below.
If time is circular, then each instant is earlier than itself, in which case earlier than is not asymmetric on the set of instants, and as a result time does not count as a continuum, according to the standard definition.
For further discussion of the difficulties of characterizing the structure of circular time in terms of a binary relation, see van Fraassen (1970: 66–70) and Newton-Smith (1980: 57–78). Oddly, when discussing alternative characterizations that invoke temporal relations of adicity greater than two, neither van Fraassen nor Newton-Smith mentions the ternary relation ‘after a, b comes before c’. Instead, both jump to the four-place relation of pair separation. Unlike ‘after a, b comes before c’, pair separation makes no distinction of orientation—e.g., between the points on a circle ordered by clockwise arrows and those same points, in the same positions, ordered by counterclockwise arrows.
The analogues of transitivity and asymmetry are:
- Transitivity*:
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if R(a, b, c) and R(a, c, d) then R(a, b, d);
if R(a, b, c) and R(b, d, c) then R(a, d, c); and
if R(a, b, c) and R(d, b, a) then R(d, b, c)
- Asymmetry*:
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if R(a, b, c) then: not R(c, b, a) and not R(a, c, b) and not R(b, a, c)
The second and third clauses of Transitivity* and second two conjuncts of the consequent of Asymmetry* are redundant given a cyclicity principle (if R(a, b, c) then R(b, c, a)) and hence are almost always omitted. Since I do not presuppose cyclicity, I retain them. From Asymmetry* it follows that if R(a, b, c) then a, b, and c are three different things, hence that R is irreflexive in the relevant sense. The view that time is dense can be stated as
- Density*:
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if R(a, b, c) then: ∃xR(a, x, b) and ∃xR(b, x, c).
Finally, an interval can be defined as a set s of instants such that: (1) s has either exactly one or at least three members, (2) R is total* over s, i.e., for any members a, b, and c of s:
- Totality*:
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if [a ≠ b & b ≠ c & a ≠ c] then either: [R(a, b, c) or R(a, c, b) or R(b, a, c) or R(b, c, a) or
R(c, a, b,) or R(c, b, a)],
and (3) for any members a, b, and c of s such that R(a, b, c): (i) if R(c, a, b) then either
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for any x, if R(a, x, c) then x is in s, or
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for any x, if R(c, x, a) then x is in s,
and (ii) if not R(c, a, b) then for any x, if R(a, x, c) then x is in x. The definition of ‘continuous’ is straightforward against the background of a cyclicity assumption or a non-cyclicity assumption, but it becomes much trickier without either assumption, so I will not attempt it here. For more details on cyclic orders, see Huntington (1924), Novák (1984) and the Wikipedia entry on ‘Cyclic Order’: https://en.wikipedia.org/wiki/Cyclic_order.
To say that t is a starting point of s is to say: (i) s is an interval, (ii) for any member y of s, if y is not identical to t, then for some member x of s, R(t, x, y), (iii) for any x and for any member y of s, if R(t, x, y), then x is a member of s, and (iv) if t is a member of s, then for any member x of s and for any y, if R(x, y, t), then there is some z such that z is not a member of s and R(x, z, t). Clause (ii) ensures that all other members of the interval can be reached by ‘moving forward’ from t. Clause (iii) ensures that there is no gap between t and s. Clause (iv) blocks the result that if time is like a circle ordered clockwise, then each instant in s counts as a starting point of s. The definition of ‘endpoint’ contains clauses with parallel functions. To say that t is an endpoint of s is to say: (i) s is an interval, (ii) for any member x of s, if x is not identical to t, then there is some member y of s such that R(x, y, t), (iii) for any y and any member x of s, if R(x, y, t) then y is a member of s, and (iv) if t is a member of s, then for any x and any member y of s, if R(t, x, y), then there is some w such that w is not a member of s and R(t, w, y). Finally, to say that t is a boundary point of s is to say that t is either a starting point or an endpoint of s.
One might accept this possibility for at least three reasons. First, one might think that things are not alive when they are in a state of cryptobiosis (Gilmore 2013). (Whether or not they are dead while in cryptobiosis is a separate question.) Suppose that a tardigrade, o, is alive from t1 to t2, in cryptobiosis from t2 to t3, and alive again from t3 to t4, at which time it dies and never exists thereafter. Then, if o is not alive when it is in cryptobiosis, its lifespan excludes (t2, t3) and hence is gappy. Second, one might think that it is possible for there to be a thing that lives from t1 to t2, dies at t2, is dead from t2 to t3, returns to life at t3, then dies at t4 and never exists thereafter. Again, the lifespan of such a thing would exclude (t2, t3) and would be gappy. Third, a living thing might jump forward or backward in time in such a way that the thing is alive at any time at which it exists, though there are gaps in the set of instants at which it exists. Cases 2 and 3 in the main text below are of this kind.
What is the difference between the case of Francis, who is described earlier as dying, then returning to life, and then dying again, and the case of Tanya? Informally, the difference is that there are stages of Francis’s career that are ‘causally between’ the event that is her ceasing to be alive at t1 and the event that is her becoming alive again at t2, whereas there are no stages of Tanya’s career that are ‘casually between’ the event that is her disappearance (and ceasing to be alive) at t1 and the event that is her reappearance (and becoming alive again) at t2. This causal difference gives rise to a difference in their respective personal times. Where ‘A’ represents a moment of personal time at which the associated entity is alive and ‘N’ represents a moment of personal time at which the associated entity is not alive, Francis’s personal time is (considerations of density and continuity aside) like this: AAANNNAAA, whereas Tanya’s personal time is like this: AAAAAA. (Tanya jumps from t1 to t2 after her third ‘A’.) Francis dies after her third ‘A’ and again after her sixth ‘A’. Tanya dies only after her sixth ‘A’. For a slight variation of the question, see Sect. 9.
As far as I am aware, everything I say in this paper is consistent with the view that each personal time is a continuum of moments, and I find that view plausible. But the central arguments of the paper do not require the view or its necessitation. For example, one might follow Dainton (2008) and take it to be possible for there to be a person or other organism whose personal time is not a continuum but rather is the union of two separate, disconnected continua, each analogous to a line segment. Informally, such a person would lead two parallel lives. Nothing in this paper requires me to rule that out.
Lewis (1976) does not explicitly address the question of whether there are such entities as moments of personal time and if so, what their nature might be. I suspect that he would prefer not to postulate such entities. However, Dainton (2008: 364–408) develops a theory of personal time that is built on Lewis’s views but that does postulate moments of personal time. Horwich (1987: 115) postulates entities that he calls ‘proper times’ of a time traveler, in the context of a discussion of time travel and general relativity. It is clear that these so-called proper times are not instants of external time; they are not, for example, maximal space like hypersurfaces. Gilmore (2007b) postulates ‘moments of proper time’ in a similar context.
i.e., if m, m* and some x instantiate R in some order.
Why might one take it to be possible for an organism to have a gappy personal lifespan? In note 10, I gave three reasons one might have for accepting the possibility of gappy (external) lifespans. The first two apply equally to the case of gappy personal lifespans. (1) Consider a tardigrade, call it o, that is alive for a year, then in cryptobiosis for a year, then alive for another year and non-existent thereafter. Unless no personal time elapses for o while it is in cryptobiosis (a controversial claim, especially given that (i) spending time in cryptobiosis is biologically normal for tardigrades, and (ii) they do undergo some intrinsic changes while in that state), it follows that o has a gappy personal lifespan. The total personal time of o, let us suppose, is a continuum composed of three consecutive year-long stretches, as follows: (m1, m2], throughout which o is alive, (m2, m3], throughout which o is cryptobiotic and not alive, and (m3, m4], throughout which o is alive. In that case, o’s personal lifespan would be the union of the first and third stretches, which is a gappy set. (2) Suppose that we people just are our bodies and that our bodies typically continue to exist for a while after we die (Feldman 1992; Thomson 2008). Suppose further that it is possible for a human body to die, then exist for a while as a corpse (during which time intrinsic changes are occurring in the corpse and causal processes are all running in the usual direction), and then return to life. Like the tardigrade, such a person’s personal time would be made up of three stretches, such that the person is dead, not alive, throughout the middle stretch. The person would have a gappy personal lifespan; the given personal lifespan, though not the person’s personal time, would exclude the middle stretch.
Since a person’s personal lifespan is a possibly proper subset of that person’s personal time, it might turn out that her personal lifespan is gappy despite the fact that her personal time is a non-gappy continuum.
A more ambitious goal would be to formulate a real definition of the relation expressed by ‘x dies at y’, in the sense targeted by Rosen (2015). Only a real definition of this relation would justify talk of having specified what death is or what it is for a thing to die a time. As I point out later, I suspect that my accounts of death and immortality can be converted into true real definitions with slight modifications. I focus on the schema in question (and its analogue in the case of immortality) mainly for simplicity.
Some philosophers will deny that there could ever be a fact of the matter as to whether a given organism has a topologically open (as opposed to a half open or closed) external timespan. Likewise for lifespans, personal lifespans, and total personal times. Call their view topological skepticism. Another group of philosophers will concede that there are, or could be, topological facts of the relevant sort, but will insist that no two organisms that differ only in whether their timespans, lifespans, personal lifespans, etc., are open (partially open, closed) can ever differ as to whether, or when, they die, or as to whether they are immortal. As a slogan: a mere topological difference never makes a mortal difference. Call this view topological insignificance.
Given the view that space and time, or spacetime, are continua of unextended instants and/or points, topological skepticism is implausible on its face. So, in the absence of any argument for topological skepticism, I am content to set it aside and explore the consequences of its negation.
As to topological insignificance, I feel its pull, and I have taken pains to accommodate what is right about it. I have, e.g., formulated C1 in such a way that that if x has an external timespan of [t0, t1), and if y differs from x only in having, as its external timespan, [t0, t1], then x dies at t1 iff y dies at t1. Further, I regard Case 5, involving Harold, as a problem for C3 mainly because it shows that C3 generates gratuitous violations of topological insignificance.
However, it would be heavy-handed to insist at the outset that topological insignificance must turn out to be true without exception, and that this constraint must take priority over all other theoretical desiderata. At most, we should embrace a qualified principle: if theory T1 allows mere topological differences to make mortal differences in a wider range of cases than does T2, then that fact constitutes an advantage of T2 with respect to T1, an advantage that might be overridden by other factors. Moreover, it shouldn’t be surprising if topological differences made mortal differences in some exotic cases. If time or spacetime are continua, then presumably we should say that topological features are among the intrinsic features of a life; in which case it is not wildly implausible that some facts about death depend on them.
The notion I employ is modelled on, but not identical to, the notion of the limit of a function. First, I do not assume that the relation in question is a function: I leave open the possibility that for some object o and some moment m of its personal time, there are two different instants t and t* such that: o, at m, is present at t, and o, at m, is present at t*. Second, the relata of the relation are not numbers.
To convert C4 into a real definition of the relation expressed by ‘x dies at y’ [in the sense of real definition targeted by Rosen (2015)], one might wish to restate C4 so that it avoided talk of any specific units, such a minutes. One might also wish to replace talk of sets with talk of pluralities or mereological sums. Since these issues are orthogonal to the central issues of the paper, I will leave the restatement to the reader.
More formally: x is a final stretch of y if and only if (i) x and y are both stretches, (ii) x is a subset of y, (iii) for any m1, m2, and m3 in x, if R(m1, m2, m3) and R(m2, m3, m1), then for some m* not in x, R(m1, m*, m2) or R(m2, m*, m3) or R(m3, m*, m1), (iv) any endpoint of x is an endpoint of y and vice versa, and (v) any such endpoint is included in x if it is included in y. Clause (iii) ensures that final stretches never ‘contain circles’. Clause (iv) ensures that if x is a final stretch of y, then x ‘extends exactly as far into the future’ as does y. Clause (v) ensures that if x is a final stretch of y, then x never excludes an endpoint that is included in y.
Some philosophers (Feldman 1992; Thomson 2008) say that trees and even people often continue to exist for a while, as dead things, after they die. Likewise, some will say that a tree, or even a person, might die at a certain moment of personal time and yet have later moments of personal time at which it is present but dead.
This is loose talk and can be spelled out in terms of the predicate ‘at x, y is present at z’. Everything that I say in this paper is intended to be compatible with a static, tenseless, B-theory of time, together with an analogous theory of personal time.
I suspect that Tipler would agree. Although he does not explicitly frame the issue in terms of the concept of death, he does claim that ‘life continues forever’ (1994: 132) in cases like John’s. These cases form the centerpiece of his book, The Physics of Immortality. He writes that
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although a [spatially finite] closed universe exists for only a finite proper [external] time, it nevertheless could exist for an infinite subjective [personal] time, which is the measure of time that is significant for living beings (1994: 136).
As Tipler notes (1994: 108), similar ideas are defended by Milne (1952).
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Sorensen’s primary interest in these cases is axiological, not metaphysical, but he does make some metaphysical claims about them in passing. In his discussion of (his version of) case 7, he writes that ‘if the pseudo-immortal discovers his veiled mortality, then he knows he will be dead in two minutes’ (2005: 123, italics original). I take this to indicate that, according to Sorensen: (i) John is mortal, not immortal, (ii) John is dead at t2 and at all times thereafter, and (iii) John dies at t2.
One need not resort to time travel cases to find a counterexample to (i). Suppose that an amoeba divides into two new amoebas at t. The amoeba is alive throughout some interval that ends at t and does not exist at t or afterward. But, contrary to (i), it doesn’t die at t, and it isn’t dead then or afterward. It lived, then it divided and ceased to exist without dying, and thereafter it was neither alive nor dead. Why not say something similar about John?
Sorabji writes, “I believe that circular time is in principle possible…. In principle it would have been possible for there to be a universe with a forty-year time cycle. In such a universe, we might dwindle and regrow, rather than die…” (2006: 326). Sorabji interprets a passage from the pseudo-Aristotelian Problemata as alluding to this same scenario. The passage considers whether time could be circular, and it includes the sentence, “In fact, Alcmaeon says that people die simply because they are not able to join beginning to end” (2006: 329). The possibility of entities with circular personal times (in worlds in which external time is circular) is defended in Gilmore (2007b) and (2010). Circular personal time is also mentioned by Dainton (2008: 407–408).
I have made no effort to describe the physiological details underlying case 8. I don’t claim that the case is physically or biologically possible, but I am confident that if circular time is metaphysically possible, then so is some case relevantly like case 8 and that, with enough effort, the details could be filled in. The fact that Joan is a conscious human being – as opposed to, say, a bacterium – is irrelevant.
Assume that one does not go in circles by going eastward*.
Consider a variant of case 7, call it case 7*, in which there is a final moment m* of John’s lifestretch, where m* is also the final moment of John’s personal time as whole. Moment m* is infinitely many years later than any other moment of John’s personal time, and (let me stipulate) at m*, John is alive and present at t2. Otherwise case 7* is as similar as possible to case 7. According to C4, John dies at t2 in case 7*. So, since C4 tells us that John dies at t2 in case 7 but not in case 7*, despite the fact that these cases differ ‘only topologically’, C4 violates the principle I called topological insignificance in note 18. I find C4’s verdicts about these cases to be more plausible than topological insignificance, so I do not see this point as a problem for C4.
More specifically, Lewis endorses the possibility that each of the two epochs has an infinite past and an infinite future: “Time might have the metric structure not of the real line, but of two copies of the real line laid end to end… Each epoch would have infinite duration, no beginning, and no end” (1986: 72). Presumably he would also endorse the possibility of case 12 in the main text below.
If the notion of a limit at work in C4 and C6 had been defined in metrical terms (‘x gets and eventually stays arbitrarily close to y’) as opposed to topological terms (‘x gets and eventually stays within any neighborhood of y’), the symmetry between the cases of John and Luis would be broken. John does get and eventually stay arbitrarily close to the relevant instant in his case, but Luis does not: Luis’s location in external time is always infinitely many years earlier than t2. But Luis does get and eventually stay within every neighborhood of t2.
My view harmonizes with that of Smith (1989: 316), who holds that any object like Luis counts as permanent.
For a view of resurrection that would permit this aspect of the case, see Merricks (2009).
In more detail: for each moment in the first 95 years of her personal time, Lydia has, relative to that moment, a location in space and a location in external time, but for the next 1000 years of her personal time, Lydia is not alive and exists ‘outside space and outside external time’. For each moment m in that 1000-year stretch of her personal time, there is no instant of external time t such that: at m, Lydia is present at t. Further, we can suppose that (i) the endpoint of that 1000-year stretch of her personal time is the moment m2, that (ii) m2 is not included in that stretch, and that (iii) at m2, Lydia is present at t-2. (I take no stand on whether this case is metaphysically possible).
In virtue of what, one might wonder, are the two stretches of personal time temporally unrelated? Various answers could be given. Perhaps, e.g., it is because Lydia’s intrinsic condition at m2 at t2 is not immanently caused by her intrinsic condition in any of the instants leading up to the end of the other stretch.
Which it is not. It will emerge that, on my account of immortality, things that die can still be immortal. Despite my title, I have no account of mortality to offer.
In terms of R: x is alive at some instant t and at every instant t2 such that, for some instant t1, R(t, t1, t2).
A final segment is to external time what a final stretch is to personal time. The formal definition is parallel.
As with C4, to convert IM7 into a real definition of the property expressed by ‘x is immortal’, one might wish to restate IM7 so that it avoided talk of any specific units, such a minutes. One might also wish to replace talk of sets with talk of pluralities or mereological sums. I leave this restatement to the reader.
As applied to case 7*, from note 30, IM7 tells us that John is not immortal, which I take to be correct.
According to Lewis, “a continuant is a person if and only if it is a maximal R-interrelated aggregate of person- stages” (1983: 60). There are only two continuants in the case that have any prima facie claim to satisfy this condition. One of them has a spatiotemporal shape that is analogous to a ‘ρ’, the other to the same shape minus the stem, roughly, an ‘ο’. But since the latter is a mere proper part of the former, the latter is not a maximal R interrelated aggregate, hence not a person, according to Lewis.
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Acknowledgment
I am grateful to the Immortality Project, directed by John Martin Fischer and funded by the John Templeton Foundation, for supporting a year of research leave during which a draft of this paper was written. Thanks also to an audience at the Immortality Project Capstone Conference at UC Riverside in 2015, and especially to Ben Bradley, Philip Swenson, Eric Yang, and two referees for this journal for their very helpful comments.
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Gilmore, C. The metaphysics of mortals: death, immortality, and personal time. Philos Stud 173, 3271–3299 (2016). https://doi.org/10.1007/s11098-016-0663-x
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DOI: https://doi.org/10.1007/s11098-016-0663-x