Immortal Beauty: Does Existence Confirm Reincarnation?

ABSTRACT

I argue that a popular view about self-locating evidence implies that there are cases in which agents have surprisingly strong evidence for their own reincarnation. The central case is an ‘Immortal Beauty' scenario, modelled after the well-known Sleeping Beauty puzzle. I argue that if the popular ‘thirder’ solution to the puzzle is correct, then Immortal Beauty should be confident that she's going to be reincarnated. The essay also examines another pro-reincarnation argument due to Michael Huemer (2021). I argue that his argument fails, and that my argument establishes an alternative way in which mere existence can be evidence for reincarnation. I then examine whether my result generalizes.

KEYWORDS:

• Sleeping Beauty
• immortality
• de se
• probability
• Bayesianism

Disclosure Statement

No potential conflict of interest was reported by the author.

Notes

1 See Almeder [1992] for an attempt to argue that we do have the requisite evidence. See Dilley [1995] and Hales [2001] for rebuttals.

2 See also Ayer [1956: 220].

3 To take an example from Huemer [2021], in eternally recurrent universes, theories that identify subjects based on certain qualitative similarities—e.g. personality profile and upbringing—imply reincarnation.

4 Given countable additivity, this would entail probability zero that you are ever born. Let us assume here, for Huemer’s sake, merely finite additivity. This permits non-zero probability that you are ever born, despite zero probability of being born at any given century. We could also choose to model the situation with a hyperreal-valued probability function. We would still forsake countable additivity, but we may recover regularity. The approach wouldn’t change any of the paper’s essential results. If our present existence has infinitesimal probability given H, positive real-valued probability given ¬H, and the prior probabilities of H and ¬H are positive and real-valued, then one should still become confident in H upon learning that one is presently alive (one’s posterior of H should be infinitesimally close to 1). For convenience, I’ll stay with real-valued probability functions.

5 This is echoed by popular formalizations of de se content. Consider a centred-worlds account, on which belief contents are sets of agent-time-world triples. A triple <x, t, w> represents that [I am x and t is present and w is actual]. Hence only triples <x, t, w> such that x is located at t in w represent epistemic possibilities. (For certainly I am not both x and currently at t in w if x isn’t at t in w!) But ‘I exist now’ plausibly expresses the set of triples <x, t, w> such that x is located at t in w. Hence, it exhausts all epistemic possibilities and is thus a priori knowable. Meanwhile, ‘I exist five centuries ago’ expresses the set of triples <x, t, w> such that x is located five centuries prior to t in w. This set does not exhaust all epistemic possibilities: it leaves out centres where the agent hasn’t existed five centuries prior. (It also includes epistemically impossible centres.)

6 Perhaps someone is tempted to object that ‘I exist now’ isn’t a priori knowable, on the basis that ‘I exist (sometime)’ isn’t a priori knowable. But I have two comments on that. (1) Even if ‘I exist (sometime)’ is only knowable a posteriori, the conditional ‘I exist (sometime) → I exist now’ might still be knowable a priori. In that case, Huemer’s argument is still blocked. For Huemer provides no reason for thinking that my existence at some time should make me confident of reincarnation. Learning ‘I exist (sometime) → I exist now’ is instead doing all of the work in his argument. (2) My main concern isn’t a priori knowability per se, but only that ‘I exist now’ (or the conditional) has more a priori plausibility than ‘I exist five centuries ago’ (or its corresponding conditional). And that much strikes me as hard to deny. (In further support of this, note that my learning a de se proposition that resists Huemer’s indifference reasoning is compatible with my also learning something further, to which Huemer’s reasoning does apply—namely, a de re proposition (see the main text). So, the view that I learn something that is on equal footing, epistemically, to similar propositions about the past can be accommodated.)

7 I’ve been equivocating somewhat, running together ‘I exist now’ and ‘I am alive now.’ This potentially invites the following further complaint: ‘I exist now’ might be a priori knowable, but ‘I am alive now’ is not; for it is not a priori knowable that I am a living thing rather than an inanimate object. For the purposes of our discussion, we may grant this complaint. For it won’t save Huemer. ‘I exist now’ and ‘I am alive now’ are epistemically equivalent, conditional on ‘I am alive at any time at which I exist’ (something that’s plausibly true of agents). And it’s hard to see why learning this latter proposition should shift my credences in infinite reincarnation or singular incarnation. (The proposition doesn’t play any role in Huemer’s own argument.) So, for the purpose of examining our posterior credences in reincarnation, the equivocation is harmless: we may conditionalize our probabilities on ‘I am alive at any time at which I exist’ without distorting the result. (Note that Huemer also freely switches between ‘alive’-talk and ‘existence’-talk throughout his paper.)

8 One might think, however, that Huemer’s disregard of qualitative evidence is premature. Qualitative evidence would still allow for a strong update in favour of immortality, if the evidence excluded all but a finite number of centuries. (For ‘I am alive in such-and-such a century’, where ‘such-and-such a century”s extension is finite, is infinitely more likely on infinite reincarnation than on singular incarnation.) Huemer doesn’t consider this case, probably due to the kinds of cosmological assumptions that he adopts. For example, if the universe is infinitely recurrent, no purely qualitative evidence about the present time picks out a merely finite set of centuries. Note, though, that my response to Huemer in section 3 also responds to a qualitative version of his argument.

9 I understand ‘de re’ as follows: on a possible worlds account of content, a set S of worlds ‘involves a time t de re’ iff each world in S has t (or a counterpart of t) as a part. On a Russellian account of content, a content ‘involves a time t de re’ iff t is one of the content’s constituents. (Not everyone uses ‘de re’ in this way. For example, Lewis [1979: 538–43] suggests a weaker notion, where belief de re about an object O is compatible with some worlds’ in one’s belief content not having O, or any of O’s counterparts, as a part.)

10 One might think that Huemer explicitly rejects a de re reading of his argument, given that he also stresses the importance of the ‘indexicality of evidence’ [2021: 133]. I have two comments on this. (1) Huemer draws the relevant contrast between ‘indexical expressions such as “I” and “now”’ and ‘purely qualitative terms’. This isn’t an exhaustive distinction, since it ignores proper names, like ‘t’. (2) Huemer’s examples don’t discriminate between indexicals and proper names. For example, ‘Flippy The Coin comes up heads ten times in a row’ is just as little evidence for many coins’ being flipped as ‘this specific coin comes up heads ten times in a row’ [ibid.].

11 SI is a slight strengthening of [(i) and (ii)], since clause (i) is compatible with not existing at all. But this is a harmless convenience: given that one is alive at t, SI is epistemically equivalent to [(i) and (ii)]. So, one’s posterior credence in SI, after learning that one is alive at t, should equal one’s posterior credence in [(i) and (ii)].

12 For any H with P(H) > 0, the conditional probability is given, as usual, by the ratio formula: P(E|H) = P(E & H) / P(H).

13 One possible formulation of the Principle of Indifference is this: if there is no reason to favour (epistemically) one possibility over another, then the two possibilities have the same probability.

14 Note that the truth of Premise (B) isn’t entirely obvious. Conditional on II, there is an uncountable set U of infinite candidate sets of centuries specifying when I’m alive. Premise (B) requires that the subset of U of sets whose members include t has non-zero measure. This needs to be supported with argument. One way might be to argue that, conditional on infinite reincarnation, there’s a non-zero probability that I’m alive in every century. This could be the implication of a multiverse theory, together with an account of personal identity according to which, upon my local death, I immediately continue existence in a counterpart of mine in another part of the multiverse. Other accounts might be feasible, too.

15 Given that ‘I am alive now’ is a priori knowable, there’s a question whether a framework of hypothetical priors would even in principle allow non-trivial updates on the proposition. I’ll return to this question in note 25.

16 Here I’m relying on the ‘total evidence requirement’: rational credences should reflect one’s total evidence, and not merely a proper part of it. Huemer himself accepts the requirement, for familiar reasons (cf. his [2021: 7]).

17 It’s also straightforward to rehash the previous calculations in the two frameworks. Take the centred-worlds account: in (Finite Universe), conditional on ‘I am alive at t’ and any specific ten-times reincarnation thesis (specifying who I am, when I live, and what world is actual) consistent with it, my probability distributes uniformly over ten centred worlds, exactly one of which has t for its time index. Hence the conditional probability of ‘t is now’ is 1/10. This yields Eq. 7; other equations are obtained similarly. The calculations for the Guise Russellian are exactly analogous, granted that there’s a distinct guise for each century, and a single ‘now’ guise. For any time s, let g(s) denote s’s ‘de re’ guise. Conditional on ‘I am alive at t’ and any specific ten-times reincarnation thesis consistent with it, my probability distributes uniformly over ten proposition-guise pairs, one of which is ((t, t, is identical to), ⌜g(t) is now⌝). This yields Eq. 7; similarly for other equations.

18 See note 8, though. The issue is arguably not about qualitativeness per se, but about whether one’s evidence is specific enough to pick out a finite number of centuries.

19 This wouldn’t, properly speaking, be de re evidence of time, but it would fulfil the same role in our calculations.

20 Additionally, some might question whether the birth of Jesus Christ even features de re in my thoughts, or whether it is instead picked out by description. See Lewis [1979: 538–43] for a defence of the latter view.

21 Cf. Lewis [1979: 522–4].

22 Prominent defenders of thirding include Elga [2000], Dorr [2002], Horgan [2004], and Titelbaum [2008].

23 Several concrete accounts of thirding concur. Among them is the Self-Indication Assumption (SIA) (cp. Bostrom [2010] and Manley [ms.]); Elga’s [2000, 143] argument for thirding based on long-run frequencies; and Horgan’s [2004; 2008] synchronic updating scheme for ‘preliminary’ probabilities.

24 Many thirders agree with this: see, e.g., Horgan [2008] and Manley [ms.]. One account that disagrees is Elga’s [2000].

25 We’ve noted that ‘I am alive now’ is plausibly a priori knowable. Hence, Eq. 13 requires that some hypothetical priors don’t assign probability 1 to all a priori knowable truths. This might seem surprising, since rational credences arguably don’t have this feature (cf. Gallow [ms.: 24]). But hypothetical priors needn’t perfectly align with rational credence functions. The purpose of hypothetical priors is to encode epistemic norms in the absence of any evidence at all, and this includes a priori knowable evidence. Prior to conditionalizing on such evidence, hypothetical priors may thus differ from rational credences. An alternative way to read Eq. 13 would be as a direct restriction on rational initial credences. The restriction would say, roughly, that, as m grows large, any rational initial credence function should favour Tails over Heads. This would permit equating hypothetical priors with credences. If we take this route, I’ll need to adjust my conclusion slightly: existence isn’t evidence for immortality; rather, prior belief in immortality is rationally required by an additional epistemic norm.

26 Since the argument is a conditional argument from thirding, people who are certain of halfing won’t be moved much. But I take it that most people, if not thirders, at least lend thirding considerable credence. Upon finding themselves in an Immortal Beauty setup, they should still update in favour of immortality, in proportion to their credence in thirding.

27 More concretely, the case for the analogy would go like this: start with a ‘Modified Many-Subjects SB’ (leaving unspecified the dates of the group’s Heads awakening); then ‘Created Many-Subjects SB’ (the group is created de novo intra-experiment, rather than already being alive on Sunday); ‘Reincarnated Many-Subjects SB’ (the group dies and is reincarnated, on Tails); and ‘Multiply Reincarnated Many-Subjects SB’ (the group is multiply reincarnated given Tails); and ‘Immortal Many-Subjects SB’ (the universe is temporally infinite in both directions, and the group is infinitely reincarnated given Tails).

28 Here is another consideration. What if we replace the infinite universe in Immortal Beauty with a finite universe? Beauty doesn’t outlive the universe, and so literal immortality is off the table. But she should still update in favour of finite multiple reincarnation. The update is weaker than in the infinite case: from Eq. 10 it follows that, if you start with a prior probability of reincarnation lower than 1/m, then your posterior probability still favours singular incarnation (Heads). For example, suppose that your priors are P(Tails) = 1/n and P(Heads) = 1-1/n for some natural number n > 1. Then your posterior probabilities are related as P’(Heads)= ${\displaystyle \frac{n}{n-1}{\displaystyle \frac{n}{m}\cdot P^{\mathrm{\prime }}\left(\mathrm{T}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{s}\right)}}$. For large n, this is approximately $P^{\mathrm{\prime }}\left(\mathrm{H}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{s}\right)\approx {\displaystyle \frac{n}{m}\cdot P^{\mathrm{\prime }}\left(\mathrm{T}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{s}\right)}$. So, for n > m, your posterior still favours Heads. In the finite case, the update isn’t strong enough to overcome priors heavily biased against reincarnation. (Thanks to an anonymous referee for pressing me to clarify this.)

29 For example, in the SB-Twin case below, synchronic accounts of thirding, like Horgan’s [2008] or SIA, and arguably also diachronic accounts like Titelbaum’s [2008], will treat Heads and Tails symmetrically, and as a result recommend halfing.

30 More concretely, the analogy from SB-Twin would proceed like this: start with a ‘Modified SB-Twin’ (leaving the dates of Beauty’s and Twin’s Heads awakenings unspecified); ‘Created SB-Twin’ (Beauty and Twin are both created intra-experiment); ‘Reincarnated SB-Twin’ (Beauty is killed and reincarnated); ‘Multiply Reincarnated SB-Twin’ (on Heads, many distinct twins of Beauty’s are created, each on separate days; the total number of twins equals the number of Beauty’s Tails-incarnations minus 1); ‘Immortal SB-Twin’ (as described).

31 There are obvious parallels here to Elga’s [2004] Dr. Evil case, where conservative views correspondingly say that Dr. Evil should maintain his belief that he is Dr. Evil even after the creation of his clone.

32 See Schwarz [ms.] for more on the distinction between ‘conservative’ and ‘evidentialist’ credence dynamics. Schwarz defends a particular conservative diachronic norm, which recommends halfing in Sleeping Beauty.

33 For, given any agent M living on Monday and any agent T who lives on Tuesday iff Heads comes up, conditional on [being M or being T], the epistemic situation is analogous to Beauty’s in SB-Twin. Further, the disjunction [being M or being T] doesn’t favour Heads over Tails.

34 To put what’s been said more formally, let Perm be the proposition that a ‘permissive’ theory of personal identity is true (i.e. a theory that allows for reincarnation), and let Restr (short for ‘restrictive theory’) be the negation of Perm. Suppose that there are n mutually exclusive and jointly exhaustive candidate theories—C₁, … ,C_n—about the number and distribution of conscious bodies in the universe. Then P(C₁ $\vee$ C₂ $\vee$ … $\vee$ C_n) = 1. If we assume that these theories are entirely independent of issues of personal identity, we get P(C_i |Perm) = P(C_i |Restr), for all i = 1, … ,n. Further, as we’ve learned, once the distribution of conscious bodies is fixed, thirders needn’t think that existence is evidence for immortality. That is, P(I am alive now|C_i $\vee$ Perm) = P(I am alive now|C_i $\vee$ Restr), for all i=1, … ,n. Putting this together, we have P(I am alive now|Perm) = P(I am alive now|Restr). Given the independence of each C_i from issues of personal identity, learning that you’re currently alive (de se) doesn’t favour permissive theories over restrictive theories.

35 A referee asks whether there could be a spatial analogue of the Immortal Beauty argument, perhaps concluding that there would be evidence that we’ll be simultaneously reincarnated in multiple bodies. Such an argument might start with a variant of Wolfgang Schwarz’s [ms.] ‘Broken Duplication Machine’: if the coin lands heads, Beauty is woken on Monday; if the coin lands tails, Beauty fissions into two copies, each of whom is woken on Monday (in separate rooms). The argument would conclude with ‘Universal Beauty’: Beauty is either incarnated once or incarnated in many bodies simultaneously. ‘Thirding’ in the variant of Schwarz’s case leads to assigning probability 1 to simultaneous incarnation in Universal Beauty. Perhaps there is a case here, but I note that (i) it’s arguably impossible for Beauty to be identical to its fission products (who are presumably not identical to each other); (ii) without personal identity, the case for thirding in the variant Schwarz’s case is arguably weaker than in Sleeping Beauty; and (iii) as with Immortal Beauty, our own situation is not analogous to that of Universal Beauty.

36 Thanks most of all to David Chalmers, for helpful comments and advice at every stage of the paper’s development. Many thanks also to Cian Dorr, for extensive written comments and discussion. I am also indebted to Mike Huemer, Marko Malink, Soren Schlassa, and Patrick Wu for helpful discussion. Finally, thanks to two anonymous referees of this journal.