EXISTENCE IS NOT EVIDENCE FOR IMMORTALITY Abstract. Michael Huemer argues, on statistical grounds, that \existence is evidence for immortality". On reasoning derived from the anthropic principle, however, mere existence cannot be evidence against any non-indexical, \eternal" hypothesis that predicts observers. This note attempts to advertise the muchouted anthropic principle's virtues and workings in a new way, namely by calling attention to the fact that it is the primary intension of one's indexically-described evidence that best characterizes one's epistemic position. Theories of persons and the Bayesian conception of evidence Michael Huemer (2019) notes that if the universe is innite, then under certain natural hypotheses every conguration of \stu" (physical matter, energy, psychons, ectoplasm, whatever) that occurs in a bounded region of it will recur, up to an arbitrarily ne degree of approximation, innitely many times.1 Since you occur, presumably, in a nite region of the universe, the conguration of stu that constitutes you would on these hypotheses recur, to arbitrarily ne approximation, innitely many times. Call such recurrences your \Poincare clones". If your Poincare clones are you, you are immortal. So: are your Poincare clones you? Huemer thinks that this is a question between two substantive theories (and not, I take it, just a distinction between two ways of talking). Call a theory of persons on which your Poincare clones are you Permissive. Call a theory of persons on which your Poincare clones are not you Restrictive. Huemer thinks that statistical reasoning can decide which theory is correct. I shall argue, however, that Huemer has neglected something important in his calculations{the anthropic principle. Huemer begins his discussion by introducing the following seeming truism: Bayesian Conception of Evidence: E supports H if P (EjH) > P (Ej  H). He illustrates with an example running (very loosely) as follows. Imagine two competing hypotheses about an experiment in which participants toss fair coins. H is the hypothesis that there are 1000 participants and 1000 coins, with each participant tossing their coin ten times.  H is the hypothesis that (for some suitable numbering) only participants 1-10 toss their coins. After the experiment you know that you will be handed a coin, chosen uniformly at random from those coins that were tossed, and told how that coin landed during the experiment. Suppose that you are told that the coin landed heads ten consecutive times. 1Huemer alludes to the Poincare recurrence theorem here, although he does neglect to mention the crucial hypothesis that one is dealing with a volume (measure) preserving transformation. To tweak an example he discusses where the theorem fails due to unbounded phase space, consider a system where two particles move apart monotonically, with distance approaching a nite limit L. This system is bounded in the relevant sense, but states don't recur. 1 EXISTENCE IS NOT EVIDENCE FOR IMMORTALITY 2 Huemer considers two candidate expressions that might be taken to capture your total relevant evidence proposition in an utterance. The rst is indexical: E = \this specic coin lands heads ten consecutive times". We believe that Huemer would say here that P (EjH) = P (Ej  H) = 2 10, so that there is no conrmation of H by E. The second is E = \some coin in the experiment lands heads ten consecutive times". (I'll mostly ignore the second, less tempting expression.) Now we return to the main argument. Let H be the expression \a Permissive theory of persons is true", and let  H be the expression \a Restrictive theory of persons is true". By analogy with the coins case your relevant evidence is captured by the expression E = \this specic person exists in this century".2 (By \this specic person" you ostend yourself.) Since according to a Restrictive theory you get to exist at most once, then assuming the universe is innite, Huemer claims that P (Ej  H) = 0. But, he goes on to say, Poincare clones of you exist with positive probability in any given century. So on a Permissive theory you exist with positive probability in any given century. This implies that P (EjH) > 0, so by the Bayesian conception of evidence E conrms H. In fact, it refutes  H a.s. Proponents of anthropic reasoning will see a problem with this argument. For example, it seems that Huemer translates indexical expressions such as \this specic person exists in this century" into propositions by their so-called secondary intension. As is well known, however, it is the expression's primary intension that most closely tracks the epistemic position of the speaker.3 To wit, if I compose a specic enough indexical expression, e.g. something like (but far more specic than) \I am sitting at my desk, there are two computer screens, that I own, in front of me, several markers that I also own, a broken pencil, a deck of cards to my left, my cell phone lies to my right (it just buzzed at me), I can see my garage out my window, as well as my car, a black 2005 Sequoia, my dogs (Ramsey and Hobbes) are on the couch..." etc. then the primary intension of this expression should pick out (to some degree...employing the primary intension does not come to a \description" theory of reference) something like my \epistemic alternatives"...the set of contexts that I might occupy, for all I know. In particular, it should pick out a set of contexts containing those of my Poincare clones.4 Apart from apparently clear-cut intuitions that it is the primary intension that captures epistemic position (one doesn't, after all, always even know that the 2Or now, which is somewhat stronger, but makes little dierence to what we have to say. 3The terminology is from Chalmers (1996, p. 57): \The primary intension of a concept is a function from worlds to extensions re ecting the way that actual world reference is xed. In a given world, it picks out what the referent of the concept would be if that world turned out to be actual." And (p. 64), \Composing the primary intensions of the terms involved yields a primary proposition, which holds in precisely those contexts of utterance in which the statement would turn out to express a truth." The secondary intension, meanwhile, treats referring terms as rigid: \reference is xed in the actual world, depending on how the world turns out...". 4Note that \a context of utterance...is an ordered pair consisting of a world and a center representing the viewpoint within that world of an agent" (Chalmers 1996) using the expression in question. This implies, in particular, that the primary intension of an expression picks out not a classical proposition, but a so-called \centered proposition", i.e. a set of such pairs. EXISTENCE IS NOT EVIDENCE FOR IMMORTALITY 3 propositions picked out by the secondary intensions of our asserted indexicals are true), trying to adapt the secondary intension to this end breeds monsters. For example, if it's right to identify the secondary intension of \this specic person exists in this century" with one's evidence in the current case, then it isn't clear what could prevent one from using it to identify the secondary intension of \this specic coin lands heads ten consecutive times" with one's evidence in the coins case. But that leads to disaster, because if H is true and the coin is numbered above 10, one would thereby get P (Ej  H) = 0, since that specic coin, on its secondary intension, wouldn't be tossed at all conditional on  H. No such trouble arises for the primary intension, according to which P (EjH) = P (Ej  H) = 2 10, consistent with the intuition that neither H nor  H should be conrmed. Note that on this interpretation the probability of this specic coin is tossed by that specic participant is 1; you knew prior to being shown the coin/participant pair that you would arm that indexical.5 Back in the main argument, we can assume that your relevant evidence is captured by the indexical expession \this specic person exists in this specic century". The secondary intension of this expression has positive probability (again by analogy with the Poincare recurrence theorem, which says that in a nite measure preserving system almost every orbit originating in a positive measure set returns to that set with positive asymptotic density) conditional on H (the Permissive theory) but zero (or innitesimal) probability conditional on :H (the Restrictive theory). So Huemer's argument would succeed if it were the secondary intension that tracked epistemic position. Again, though, it is the primary intension that does this...and if E is the primary intension of the expression \this specic person exists in this specic century" then E cannot conrm anything, as P (EjH) = P (Ej  H) = 1. For the primary intension of an utterance is true in those contexts where it would express a truth...all contexts, in this case. The ring squad thought experiment But consider John Leslie's ring squad (cf. Leslie 1996, p. 141).6 If fty marksmen have just taken aim at you and missed then \I exist now" seems to be, in your context, evidence for the proposition that someone has conspired to keep you alive. So is it just wrong to say that \I exist now" cannot be evidence for anything? The primary intension of \I exist now" does not in fact support the conspiracy theory{though something like \I was recently convicted, set before a ring squad and red upon by fty marksmen, and yet I am still alive" does. Most observers at contexts where the latter is true are at contexts where \someone conspired to keep me alive" is also true. It is not however the case that most observers at contexts where \I exist now" is true are at contexts where \someone conspired 5One could decompose the primary intension formally as Ep =W j   j is observed and lands all heads  , where the disjunction runs over all tossed coins j. Note in particular that Ep 6= W j   j lands all heads  = some coin lands all heads. 6Thanks to Michael Huemer for calling my attention to this example, and for other helpful remarks on an earlier draft of this paper. EXISTENCE IS NOT EVIDENCE FOR IMMORTALITY 4 to keep me alive" is also true. So \I exist now" is not evidence for \someone conspired to keep me alive". If you still think that it is, imagine that you fainted just before the bullets were red and woke up an hour later with amnesia. You could then truthfully assert \I exist now", but you wouldn't have any evidence for \someone conspired to keep me alive". Such evidence requires greater specicity. Huemer responds to the objection that expressions such as \I exist now" cannot constitute evidence in Section 5.7 of his paper along similar lines: Some philosophers hold that one's own existence cannot serve as Bayesian evidence for any hypothesis. The reason is that the epistemic probability of one's own existence, in any epistemic position one might be in, is 100%. By a general theorem of probability, for any e; h, if P (e) = 1, then P (hje) = P (h). But on a Bayesian conception of evidential support, e supports h only if P (hje) > P (h). Thus, it appears that when P (e) = 1, e cannot support h. (...) This claim has perfectly mundane counterexamples. For instance, the fact that you exist is obviously evidence, for you, that your parents were not infertile. (...) Perhaps the critic of Bayesianism would argue that the preceding example is not genuinely one of Bayesian reasoning, that there is some account of the reasoning that does not involve application of Bayes' Theorem or anything like it. Such a move, however, would obviate the objection to the argument for Reincarnation. For whatever account is to be given of how your existence supports that your parents (were not infertile), that account may be deployed to explain how your existence supports Reincarnation. (It does not matter whether the account qualies as truly Bayesian.) Both pieces of reasoning involve the claim that if a certain hypothesis were true, one would be less likely to exist than otherwise; hence, one's existence supports the rejection of that hypothesis. The objection raised to the reincarnation inference, that you were never uncertain of your existence, applies just as well to the infertility inference. There is no reason to think that whatever would block the objection in the infertility case would somehow allow the objection to succeed in the reincarnation case. Huemer's \critic" might be correct to think that the infertility example is not genuinely one of \Bayesian" reasoning.7 Applications of Bayes' theorem require prior and posterior probability functions. But \my parents were infertile" is indexical, and the evaluation of an indexical's primary intension requires \situatedness". I may be able, ex post facto, to construct some prior probability in the expression's secondary intension (based on facts about the frequency of infertility in the population of adult persons8), but in order to have ex post facto access to a plausible prior in the expression's primary intension, I would need to entertain, as if from 7Though I wouldn't characterize the critic as a \critic of Bayesianism" for thinking this. 8Since Huemer views the current objection as a species of the \conrmation by old evidence" problem, I suspect that this may be precisely what he takes himself to be doing. EXISTENCE IS NOT EVIDENCE FOR IMMORTALITY 5 a vantage of non-existence, some distribution or other over possible contexts of utterance. That is, I would have to engage in self-selection (anthropic) reasoning. Carter's formulation of the anthropic principle The locus classicus on modern anthropic reasoning is Carter (1983). His formulation of what Huemer calls the Bayesian Conception of Evidence is as follows: pE(A) pE(B) = pS(EjA) pS(EjB) pS(A) pS(B) : We will interpret this equation as follows. E is an indexical expression taken to capture your current evidence, and pE() = pS(jE). Here pS is a \Selected" or \Subjective" probability function that Carter is careful to distinguish from \Original" or \Objective" probability pO. (It may be helpful to think of pO as objective chance.) Carter writes: \S denotes the totality of all the selection conditions that are implied by the hypothesis of application of the theory to a concrete experimental or observational situation, but which are not necessarily included in the abstract theory". Here a \theory" (or \abstract theory") is a collection of objective chances, population means or expected statistical frequencies. One may think of these as probabilities for classical propositions. pS in contrast is dened over centered propositions, and is sensitive to one's prior distribution over contexts. Suppose, for example, that you are asleep in a room and that a fair coin is being tossed in an adjoining room. The coin is tossed two minutes after each tails toss and one minute after each heads toss. Since the coin is fair, the \abstract theory" has it that the probability of each toss landing tails is 1 2 , independent of the other tosses. Suppose now that you wake up and contemplate the indexical expression \the previous toss landed tails". You should assign this expression's secondary intension probability 1 2 (in agreement with theory), but the probability that you assign to its primary intension should, in the absence of further evidence, be 2 3 . (In the absence of further evidence, you should take yourself to have awakened at a uniformly random time.) So here we would say that pO(\previous toss lands tails") = 1 2 , but pS(\previous toss lands tails") = 2 3 . Similarly, in the case where B is \my parents were fertile" Carter would say that pO(B) might be .95 (some gure derived from a fertility baserate), but pS(B)  1. So it seems plausible to say that, when A is an indexical expression, Carter intends by pO(A) the probability of the expression's secondary intension, and intends by pS(A) the probability of the expression's primary intension. Since it is only after accounting for selection conditions (i.e. employing pS) that Bayes' theorem is applied, that the posterior pE(B) comes out to be greater than :95 isn't due to distinctively \Bayesian" reasoning. It's due rather to anthropic reasoning. The critic's work is not done, though, for as Huemer notes, it doesn't matter whether we view the infertility example as distinctively \Bayesian" in avor or not. Some feature of it blocks the critic's objection, so in order for the critic's objection to the reincarnation argument to be successful, the critic should say why such blocking does not occur in that particular application. Now the EXISTENCE IS NOT EVIDENCE FOR IMMORTALITY 6 feature blocking the critic's objection in the infertility example is plainly that pS(B) 6= pO(B). So what the critic must show is that in the reincarnation case, one has pS(H) = pO(H). This is right, I'll argue, for the following reason. In the reincarnation case the competing expressions H = \some Permissive theory of persons is true" and  H = \some Restrictive theory of persons is true" are nonindexical, and the primary intension of a non-indexical expression agrees with its secondary intension. So, since pS(H) is the probability of H's primary intension and pO(H) is the probability of H's secondary intension, we have pS(H) = pO(H). The event/theory distinction My proposal, then, is that (to some degree of approximation) it is the primary intension of the expressions to which one would assent that constitute one's evidence, and that, accordingly, hypotheses communicated by non-indexical expressions (call these theories) are not subject to the same selection pressures as hypotheses communicated by indexical expressions (call these events).9 Such an event/theory distinction is implicit in Carter (1983), in that he only dares apply his anthropic principle to the testing of rival hypotheses A and B of the \theory" type, and for these pairs always assumes that pS(A) pS(B) = pO(A) pO(B) . It is relatively more explicit in Lewis (2001), where one nds the following thought experiment involving three equally likely theories: A: God tosses coin, creates 10 persons if heads and 1000 persons if tails. B: God tosses coin, creates 10 persons if heads and 1010 100 persons if tails. C: God tosses coin, creates 1000 persons if heads and 1010 100 persons if tails. His presentation is cryptic, but it's clear (it helps to be antecedently aware of an event/theory distinction) that Lewis subjects the toss of the coin (an indexical matter) to selection eects, but does not subject the choice of theory (a nonindexical matter) to such eects. In particular, he advocates that observers put the probability of M = there are 1010 100 persons at approximately 2 3 .10 There are traces of an event/theory distinction in the writings of philosophers as well. John Leslie (1996, p. 248-250) suggested that selection pressures apply to Doomsday alternatives only if the process choosing which is actual is \radically indeterministic", and Nick Bostrom (2007) noted (the so-called \Presumptuous Philosopher gedanken") that it is less tempting to subject a \theory of everything" 9There are exceptions. Theories that predict no observers with certainty are obviously refuted by any observations whatsoever, and contingent propositions picked out by non-indexical expressions might (if there are such things) be exceptional as well. Lewis (2001) discusses theories that predict no observers with non-trivial probability, but oers only speculations as to how anthropic reasoning should treat such cases. These issues run orthogonal to our task here. 10Lewis would put pS(B) = pS(C) = pO(B) = pO(C) = 1=3 (no selection eect), and pS(M jB) = 10 10 100 =(1010 100 + 10), pS(M jC) = 10 10 100 =(1010 100 + 1000) (selection eect). Note: Lewis is explicit that his anthropic reasoning treats nite cases as if they were iterated (under the auspices of the same theory) ad innitum. So this case is relevant for us, despite its niticity. EXISTENCE IS NOT EVIDENCE FOR IMMORTALITY 7 to the selection pressures that rational agents (Sleeping Beauty thirders, more generally) subject indexicals such as \the coin in question landed heads" to.11 A symbolic dynamics example Here's a parting shot for those still on the fence. Suppose you know that you are the only conscious being in the universe, are immortal, and that all of your conscious observations are completely determined by a process that spits out characters a1; a2; : : : from the alphabet. Initially there are two equally likely candidate stationary theories describing the local statistical features of the output: Theory A: P (an = \C") = 1 103 ; P (an+1 = \E"jan = \C") = 1 3 . Theory B: P (an = \C") = 1 106 ; P (an+1 = \E"jan = \C") = 2 3 . You know that you spend most of your existence asleep, but that whenever a \C" is spat out, you are aroused and get to observe the next letter spat, after which your memory of the episode is erased and you are put back to sleep. Now...if you nd yourself awake and having an observation of an \E", which theory should that conrm? On the method of anthropic reasoning I have been advocating for in this paper, it conrms Theory B. (Your posterior probability that Theory B is true should be 2 3 .) That the rst process would give you more (per unit time) \E"-observations is irrelevant, because your unconscious moments don't count for anything. (Why would they?) In other words, it's the frequency of \E" observations in the stream of observations that matters, not the frequency of \E" observations in the stream of all moments (conscious or not). To put it another way, no selection eect favors the rst process. Conclusion If the arguments I've given are correct then Huemer left out something crucial in assuming, with no justication, that there was \no reason to think that whatever would block the objection in the infertility case would somehow allow the objection to succeed in the reincarnation case". There is a reason, because what blocks the objection in the infertility case, namely selection pressure induced by the context sensitivity or indexicality of the rival hypotheses considered there, is not present in the reincarnation case, since the rival hypotheses there are non-indexical. If that's right, it'll take some new argument to resurrect reincarnation. Until then, I'd advise against crossing anything o your bucket list you don't remember doing. 11Probably neither Leslie nor Bostrom would arm the event/theory distinction entirely, however, especially conditional on the universe being nite. In a passage remnicient of Huemer (2019), for example, Bostrom (2001) wrote: \...it is hard to see what the relevant dierence is between" a case in which the number of observers is a matter of theory and a case in which the number of observers is determined by coin tossing. However, given that Bostrom held that members of an observer's \reference class" ought to be actual, in an innite universe his anthropic reasoning agrees with that of Carter and Lewis. (In an innite universe, the asymptotic statistics converge to that of the underlying theory almost surely.) Huemer's position may be closest to the one that Bostrom attributes to his \Presumptuous Philosopher", in which observers belonging to nomologically impossible worlds (Permissive theory of persons worlds, perhaps) can gure into the calculations of probabilities in self-selection experiments. EXISTENCE IS NOT EVIDENCE FOR IMMORTALITY 8 References Bostrom, Nick. 2001. The Doomsday Argument, Adam & Eve, UN++, and Quantum Joe. Synthese 127(3):359-387. Bostrom, Nick. 2007. Sleeping Beauty and Self-Location: a Hybrid Model. Synthese 157(1):59-78. Carter, Brandon. 1983. The Anthropic Principle and its Implications for Biological Evolution. Philosophical Transactions of the Royal Society of London. Series A, Mathmatical and Physical Sciences. 310:347-363. Chalmers, David. 1996. The Conscious Mind: In Search of a Fundamental Theory. OUP, Oxford. Huemer, Michael. 2019. Existence is Evidence for Immortality. Nous. Forthcoming. Leslie, J. 1996. The End of the World: The Science and Ethics of Human Extinction. New York: Routledge. Lewis, Antony. 2001. Comparing cosmological theories. Online. Available at http://cosmologist.info/anthropic.html. rmcctchn@memphis.edu