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  • 129 © 2006 The Author. Journal compilation © 2006 Blackwell Publishing Ltd., 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA Blackwell Publishing LtdOxford, UKPHIBPhilosophical Books0031-8051© Blackwell Publishers Ltd 2006472 RECENT WORK XXXX THE DOOMSDAY ARGUMENT   The University of Edinburgh 1. Introduction: Carter-Leslie Doomsday Despite humankind’s perennial fascination with its own extinction, the Doomsday Argument was only comparatively rarely discussed before c. 1990. Consequently, rather than cover the last few years’ work on Doomsday, this article tries to survey all of at least the major Doomsday discussions since the topic was first aired in 1983. The term ‘Doomsday Argument’ (‘DA’ henceforth) was first proposed by Frank J. Tipler. John Leslie subsequently adopted and popularised ‘DA’ as a handy shorthand name for a family of Bayesian arguments about our species’ likely survival prospects. 1 Besides frequently appearing in philosophical and scientific journals, DA has been expounded in popular science books 2 and even forms the basis of a science fiction novel. 3 Unlike other arguments about the future, DA does not issue in a prophecy or straightforward projection. DA aims to raise our personal probabilities for human extinction, usually conditional on our birth-rank in history. One may think DA sound yet believe 1. The locus classicus for DA is John Leslie’s The End of the World: The Science and Ethics of Human Extinction , (Routledge: 1996). Leslie’s other works that discuss or mention DA include: ‘Risking the World’s End’, Bulletin of the Canadian Nuclear Society , 10 (1989), pp. 10–15; Universes , (Routledge, 1989), p. 214, fn. 1; ‘Is the End of the World Nigh?’, The Philosophical Quarterly , 40 (1990), pp. 65–72; ‘Doomsday Revisited’, The Philosophical Quarterly , 42 (1992), pp. 85–9; ‘The Doomsday Argument’, Mathematical Intelligencer , 14 (1992), pp. 48–51; ‘Bayes, Urns and Doomsday’, Interchange , 23 (1992), pp. 289–95; ‘Time and the Anthropic Principle’, Mind , 101 (1992), pp. 521–540; ‘Doom and Probabilities’, Mind , 102 (1993), pp. 489–91; ‘More About Doom’, Mathematical Intelligencer , 15 (1993), pp. 5–7; ‘Testing the Doomsday Argument’, Journal of Applied Philosophy , 11 (1994), pp. 31–44; ‘Observer-Relative Chances and the Doomsday Argument’, Inquiry , 40 (1997), pp. 427–36; ‘Our Place in the Cosmos’, Philosophy , 75 (2000), pp. 10–12. 2. E.g. Paul Davies’ About Time , (Penguin, 1995, pp. 258–64) usefully summarises DA and some major objections to it, while situating DA in the context of physical debates about time. 3. A version of DA called ‘the Carter Catastrophe’ is the keystone of Stephen Baxter’s novel Time: Manifold 1 , (HarperCollins, 2000). Philosophical Books Vol. 47 No. 2 April 2006 pp. 129–142
  • 130 © 2006 The Author. Journal compilation © 2006 Blackwell Publishing Ltd. in a long human future. One may reject DA but think the human race has entered its last lap. Perhaps unsurprisingly, DA has been more criticized than endorsed. However, a consensus over where DA fails has been slow to emerge and several objections to DA are mutually incompatible. (It seemed for a time that almost any stick would do to beat a Doomsday.) DA sprang from the Anthropic Principle debate about observation-selection effects in science. Seeking a balance between excessive anthropocentrism and excessive insistence on our typicality, physicist and mathematician Brandon Carter coined the term ‘Anthropic Principle’ to denote the inter-relations between our existence as observers and the physical conditions we observe. 4 Besides familiar anthropic topics like cosmic fine-tuning and Dirac’s large- number coincidences, Carter also applied anthropic reasoning to our location in time. He first aired DA in a 1983 lecture on the likely number of crucial steps in our evolution and the striking similarity between the time it took life to evolve on Earth and the time remaining before the Sun burns out. 5 The published version of his lecture 6 does not invoke DA. However, in a discussion appendix to the published paper, he outlines some anthropic speculations on the likelihood of extinction and what explanatory roles a future ‘cut-off ’ might play. 7 Carter mainly uses DA as a way of rebutting charges that anthropic reasoning doesn’t yield testable predictions. However, he declines to discuss DA in print and insists that Leslie should share any credit for DA’s discovery. The Carter-Leslie DA can be encapsulated thus. Recent history has seen apparently unprecedented growth in human population. Our c. six billion contemporaries may be a significant percentage of all humans there have ever been. 8 If humanity survives and the all-time human total rises much higher, our birth-ranks will be unusually early in human history, i.e. many more people will have lived after us than lived before us. However, if human population drops irreversibly in the near future, we who live now will also be a significant fraction of the all-time human total. If Doom looms, our location seems relatively probable but if Doom is deferred, we are unusually early humans. Granted some ‘lottery’ assumptions, our birth-ranks receive higher posterior probabilities with ‘Doom Soon’ than they do with ‘Doom Deferred’. 9 4. See ‘Large Number Coincidences and the Anthropic Principle in Cosmology’, in M.S. Longair (ed.), Confrontation of Cosmological Theories With Observational Data , (Reidel, 1974), pp. 291–98. 5. For more on Carter’s ‘crucial steps’ formula, see John D. Barrow and Frank J. Tipler, The Anthropic Cosmological Principle , (Oxford University Press, 1986), pp. 562–4 6. ‘The Anthropic Principle and its Implications for Biological Evolution’, Philosophical Transactions of the Royal Society of London , Series A, 310, 1983, pp. 347–63. Carter (ibid., pp. 358 ff.) also offers anthropic explanations for why we observe neither advanced extra-terrestrials nor natural analogues of the wheel. 7. E.g. “a man-made ecological disaster . . . is an eventuality which might well be discussed with reference to the anthropic principle”, ‘The Anthropic Principle and Its Implications’, p. 363. 8. Leslie often suggests that perhaps as many as 10% of all humans who have ever been are alive now, giving contemporary humans birth-ranks of the order of sixty billion. 9. The usual DA ‘lottery’ assumptions are: (a) that all hypotheses about the total human population receive the same prior probability and (b) that the likelihood of your having a particular birth-rank i , conditional on the total population being j , is equal to 1/ j where i ≤ j , and otherwise equals zero.
  • 131 © 2006 The Author. Journal compilation © 2006 Blackwell Publishing Ltd. Assuming we should favour explanations that make our explanandum relatively probable, we seemingly must favour impending Doom as the better explanation of our location. DA is thus a probabilistic force-multiplier: whatever personal probability we now accord imminent extinction should be increased once we take anthropic explanations of our birth-rank into account. Carter-Leslie DA does not attempt to derive a precise probability for Doom. Leslie says only that DA should act to increase our probability for Doom—as in any subjectivist Bayesian argument, the precise priors to be fed in have to be derived from elsewhere. DA is not an alternative to empirical arguments about Doom but requires empirical input in order to work. Thus, DA can only yield a high ‘Doom’ posterior probability if your ‘Doom’ prior is non-negligible. Even if DA increases your probability for Doom a thousand-fold, this shouldn’t trouble you if your prior for human extinction was only around one in ten billion, say. Leslie often illustrates DA-reasoning with ‘Urn’ stories. Imagine your name is written on a slip of paper and dropped into an urn. Your prior probability for the urn holding 10 names is 0.02, while your prior probability for it holding 1000 names is 0.98. Slips of paper are withdrawn from the urn, without subsequently being replaced. Your name appears on the third draw. Should your name appearing so early in the draw affect your probabilities? If you assume the draw was random, it’s easy to demonstrate that you should change your probabilities. Indeed, Bayes’s Theorem suggests that your prior of 0.02 should yield to a posterior probability around 0.67. 10 Oddly enough, some DA variants started life as objections to DA. Thus began the ‘Shooting Room’ DA, which Leslie first proposed as a problem for DA. 11 Imagine you are placed in a room with several other people and told that 90% of those who enter the room will be shot. However, you are also told you will leave unharmed unless two fair dice, thrown simultaneously, both yield sixes. How are these claims reconciled? The answer is that, at each throw of the dice, ten times more people occupy the Shooting Room than did on the round before. Are your chances of leaving the room alive an alarming 1/10 or a more comfortable 35/36? Leslie says the answer hinges on the truth or falsity of determinism; if determinism is true, your survival-chances are 1/10 but if the world is significantly indeterministic, your chances are 35/ 36. Leslie maintains that the only really threatening criticism of DA hitherto has been that DA requires the truth of determinism. Few critics agree with Leslie that DA requires determinism. William Eckhardt objects that if DA did hinge on how deterministic the world is, we could effectively test determinism by seeing how far DA yields successful predictions. 12 10. Thus: P(H|e) = (P(e|H).P(H))/(P(e|H) P(H) + P(e| ¬ H) P(| ¬ H)). Here, P(H | e) = (0.02 × 0.3)/((0.02 × 0.3) + (0.98 × 0.003)) ≈ 0.67. (Cf. Leslie, ‘Time and the Anthropic Principle’, p. 526.) 11. Based on a query about DA from David Lewis. See Leslie, The End of the World , pp. 235–6. 12. ‘A Shooting-Room View of Doomsday’, Journal of Philosophy , 94 (1997), pp. 244–59. Eckhardt also accuses DA-reasoning (a) of conflating Bayes’s Theorem with Bayesianism, and (b) of always increasing any (non-extreme) probability for extinction.
  • 132 © 2006 The Author. Journal compilation © 2006 Blackwell Publishing Ltd. 2. Doomsday according to Nielsen, Franceschi and Gott In 1988, physicist Holger Bech Nielsen independently proposed another DA, 13 which somewhat resembles the Carter-Leslie version but also shows important differences from it. Nielsen’s investigation into random dynamics 14 led him to consider the notion of random location in time. In particular, he considered the pair as randomly selected from all the ‘human moments’ there will be. Assuming the total of humans will be finite 15 and that we should favour the most probable location for our present moment, we should conclude that we are at, or near, the maximum human population. If maximal population is still to come, or our population endures near its present level, our location is unlikely. Nielsen’s DA thus predicts probable Doom within a period commensurable with the time it takes our population to double. Therefore, humans should either be extinct or greatly reduced in numbers within a hundred years . 16 Nielsen also discusses some objections to his DA: (1) reference-classes of humans and times might be too subjective to yield concrete predictions, (2) our present location may be a statistical fluctuation; (3) if you have an unusual property, (for example, having a birthday today or being more than 95 years old), you can suspect your pairing is atypical. Paul Franceschi claims to have a third form of DA, whose method of population-sampling differs from both Carter-Leslie ‘Urn’ and Eckhardt/ Sowers ‘ball dispenser’ versions. 17 Rather than birth-ranks being generated as names drawn from an urn, Sowers imagines human births as unmarked balls which are dispensed from a machine and only then have numbers added to them. Franceschi’s diagnosis of DA is that neither scenario above strikes the right balance between temporal and atemporal population-sampling. Instead, he proposes that something like either sampling method could apply to our situation, so that a DA probability-shift might be possible. Thus, Franceschi’s ‘third route’: uncertainty as to how our birth-ranks are assigned means DA Bayesian shifts are permissible but non-obligatory. 13. ‘Random Dynamics and Relations between the Number of Fermion Generations and the Fine Structure Constant’, Acta Physica Polonica , Series B, 20 (1989), pp. 427–68 (SPIRES HEP reprint at: +j+APPOA,B20,427). 14. I.e. that nature’s fundamental laws are of such complexity that they can be treated as de facto random. 15. Nielsen makes this stipulation so we can take a Lebesque measure on our class of person- moments. 16. Such a numerical prediction is not a feature of Carter-Leslie DA, and neither is the sugges- tion that we should expect Doom in roughly the time it would take our population to double. 17. See Franceschi, ‘A Third Route to the Doomsday Argument’, original (2003) preprint at:; later (2005) preprint at See also William Eckhardt, ‘Probability Theory and the Doomsday Argument’, Mind , 102 (1993), pp. 483–88 and George F. Sowers Jr, ‘The Demise of the Doomsday Argument’, Mind , 111 (2002), pp. 37–45. NB: the latter do not accept DA and offer their alternative birth-rank mechanisms as objections to the Carter-Leslie DA. Eckhardt thinks DA errs by treating actual and non-existent humans the same way, while Sowers thinks birth-ranks must be indexed on our temporal position and so fail to be random.
  • 133 © 2006 The Author. Journal compilation © 2006 Blackwell Publishing Ltd. J. Richard Gott III has proposed a ‘delta t ’ DA, using the Copernican Principle of Mediocrity. 18 Gott says we should not expect to find ourselves located anywhere special in human history. Thus, if we assume that all loca- tions in history are a priori equiprobable, we can calculate from observations of the past duration of our species how long our future extent is likely to be. Using the usual 95% confidence interval deployed in scientific contexts, Gott argues there is a 95% chance we are not observing human history from within its first (or last) 2.5%. Thus, humanity’s future should be between 1/39 th and 39 times as long as its past. (Gott claims his method let him suc- cessfully estimate the longevity of the Berlin Wall and Stonehenge, both of which he observed in 1969.) If humanity’s past ≈ 200,000 years, Gott suggests we can be 95% confident humanity will last another 5,100 to (7.8 × 10 6 ) more years. Some critics find this too broad-brush a prediction and think Gott’s method has implausible empirical consequences if applied (as Gott suggests) more generally, to human lifespans, for instance. 19 Ken D. Olum 20 accuses Gott of (a) failing to justify any choice of prior probabilities for his argument and (b) ignoring a significant constraint on our prior probabilities for duration, i.e. that the longer a process lasts, the more likely we are to be observing it. Gott claims his method does not neglect the need for prior probabilities and that he is justified in setting a ‘vague prior’: P(N) = k/N, where N is the all-time total of humans and k is a normalizing constant. 21 Bradley Monton and Sherrilyn Roush 22 charge Gott’s argument with (amongst other failings) invalidly excluding an infinite human future and being self-refuting. An intriguing twist to Gott-criticism comes from P. T. Landsberg and J. N. Dewynne, who propose a meta-DA which threatens to make Gott’s method topple into self-contradiction. 23 In a (qualified) defence of Gott, Bradley Monton and Brian Kierland argue that his argument may fail in many contexts but that it can be defended against many previous criticisms and that its general methodology (for estimating future duration from past duration) is sound. 24 18. Gott’s DA was first presented in ‘Implications of the Copernican Principle for Our Future Prospects’, Nature , 363 (1993), pp. 315–9. He offered some replies to objections in ‘Future Prospects Discussed: Gott Replies’, Nature , 368 (1994), p. 108. A popular exposition of Gott’s DA appears in his book Time Travel in Einstein’s Universe , (Houghton Mifflin, 2001). 19. For this, and other, objections to Gott, see Carlton M. Caves’ ‘Predicting Future Duration from Present Age: A Critical Assessment’, Contemporary Physics , 41 (2000), pp. 143–153, archived by at: Caves’ paper ends with a challenge to Gott to test the ‘delta t ’ argument with a $1,000 bet on the longevity of a sample of dogs. 20. ‘The Doomsday Argument and the Number of Possible Observers’, The Philosophical Quarterly , 52 (2002), pp. 164–84, at pp. 174–79. 21. Leslie’s DA does not seek to justify a choice of priors; rather, Leslie says, the force of DA resides in the effect it has on any existing priors for extinction. Thus, were one’s prior probability for extinction sufficiently low, one’s probability for extinction might still be low even after using Leslie’s DA. 22. ‘Gott’s Doomsday Argument’, at: gott1f.pdf. 23. ‘A Probable Paradox’, Nature , 389 (1997), p. 779. 24. ‘How to Predict Future Duration from Present Age’, The Philosophical Quarterly , 56 (2006), pp. 16–38.
  • 134 © 2006 The Author. Journal compilation © 2006 Blackwell Publishing Ltd. 3. Objections to Carter-Leslie Doomsday DA has received many ripostes, some of them independently-discovered many times. Leslie sounds a cautionary note for DA sceptics: “Given twenty seconds, many people believe they have found crushing objections to Carter’s line of thought”. 25 Some can be dealt with quite quickly. Many people belie their own uniqueness by protesting ‘But I’m unique’ on first hearing DA. Doomsayers can reply: ‘You are unique, but it is not an explanatory desider- atum that you appear improbable.’ All humans are atypical in some ways but this does not prevent them being typical in others. (It seems a safe bet that most readers of these pages are carbon-based and oxygen-breathing.) DA is not an a priori ‘ontological proof ’ of human extinction, but requires empirical facts about population change. Neither does DA urge us to tailor our evid- ential basis purely to make our present location appear likely. All these man- oeuvres lack DA’s anthropic appeal to our location as observers. Likewise DA requires no commitment to ‘four-dimensionalism’ about time rather than presentism—DA is not meant to address the question ‘Why is it this moment now ?’ but rather ‘Why are we alive with this segment of humanity?’. Carter and Leslie are not pondering whether or not they lived c. 2000  —rather, DA invites us to consider where creatures like ourselves are likely to be. A sample of major objections follows. A hardy perennial is the ‘Neanderthal’ or ‘ancient Roman’ objection, i.e. earlier observers could have used DA to reach an erroneous result. Any earlier DA must have failed so it’s likely present-day DA will too. We might be unlucky enough to be the unique generation of correct Doomsayers but we shouldn’t think thus of ourselves. Leslie offers several replies to this objection, (of varying plausibility): (1) Any probabilistic reasoning will fail for someone who is improbably located—prior to the result being announced, the eventual winner of a million-ticket lottery should still rationally expect to lose. 26 (2) Perhaps the preponderance of moments in history where DA fails could be offset by the number of successful users of DA: “Reasoning which ‘failed’ for people at most points in human history by suggesting wrong predictions to them might still suggest a correct prediction to most humans who could use it if human numbers expanded rapidly soon before humankind became extinct”.27 (3) no cave man shared the Earth with six billion contemporaries plus H-bombs, ozone depletion and biological weapons. (4) Maybe not all earlier applications of DA were wrong after all.28 In a meta-inductive spin on ‘cave man’ objections, Kevin Korb and Jonathan J. Oliver invoke a targeting truth (TT) principle: “no good inductive method 25. ‘Time and the Anthropic Principle’, p. 528. 26. “It would not be a defect in probabilistic reasoning if it encouraged an erroneous conclusion in the mind of someone who happened to be improbably situated” (Torbjörn Tännsjö, ‘Doom Soon?’, Inquiry, 40 (1997), pp. 243–52), at p. 247). 27. Leslie, The End of the World, p. 23, original emphasis. 28. “Any Roman might well have been right in thinking that the human race would end fairly shortly. If it ended by the year 2150, this would be fairly soon after Roman times” (The End of the World, p. 205).
  • 135 © 2006 The Author. Journal compilation © 2006 Blackwell Publishing Ltd. should—in this world—provide no more guidance to the truth than does flipping a coin”.29 They argue that if “the total population is bounded by two times the sample value . . . , then 499 inferences using the Doomsday argument are wrong and 501 inferences are right”, hence “in a perfectly reasonable metainduction we should conclude that there is something very wrong with this form of inference”.30 Bostrom replies (a) odds of 501/499 are still better than 50/50 and (b) we can easily run DA with a bounded value three, or more, times the sample-size.31 Korb and Oliver retort: DA’s success-rate can be made arbitrarily small “simply by increasing the population size in the example”,32 and that DA-inferences tend asymptotically to a success-rate no better than random. Bostrom argues that it’s a mistake to read the conclusion of DA as neces- sarily implying human extinction.33 Instead, he maintains, even if DA succeeds, it is not strictly speaking a Doomsday argument and really issues in a disjunctive conclusion. Besides updating our probabilities for Doom, DA reasoning is compatible with the following alternative conclusions: (1) our having a ‘Doom Soon’ prior so low that our posterior probability for Doom is still negligible even after applying DA; (2) the all-time total of humans being infinite and so making DA’s conclusion ill-defined; (3) human population starting to dwindle soon but only very gradually; and (4) future humanity changing into some- thing in an altogether different reference class from ours. The ‘supernova’ objection alleges that DA seemingly grants us paranormal powers, such as non-local and retroactive causation.34 Imagine that a nearby star has a high probability of becoming a supernova and killing most of humanity. However, if this happened, the world government would immedi- ately initiate a crash programme to create a hugely expanded human bio- sphere in space. (If the supernova doesn’t occur then neither will the crash colonization programme.) Thus, if DA gives us reason to think we’re late humans, it also gives us reason to believe the supernova won’t occur or hasn’t occurred. We seemingly have some paranormal, non-local connection with events outside our direct causal control or events that have already occurred. However, Bostrom argues that any claims that DA licenses strange quasi- causal powers spring (in part) from confusing indications that an event is likely to happen with the causes of that event.35 29. Korb and Oliver, ‘A Refutation of the Doomsday Argument’, Mind, 107 (1998), pp. 403– 410, at p. 404. 30. ‘A Refutation of the Doomsday Argument’, p. 405. 31. See Bostrom’s ‘The Doomsday Argument is Alive and Kicking’, Mind, 108 (1999), pp. 539–550. Also, Nick Bostrom’s Ph.D. dissertation, Observational Selection Effects and Probability, (LSE, 2000), (Chapter 6), pp. 121–122), available at The TT objection is also discussed in the (substantially expanded) book-version of Bostrom’s Ph.D., Anthropic Bias: Observation Selection Effects in Science and Philosophy, (Routledge, 2002), pp. 109–110. 32. Korb and Oliver, ‘Comment on Nick Bostrom’s “The Doomsday Argument is Alive and Kicking”’, Mind, 108 (1999), pp. 551–553, at p. 551. 33. Anthropic Bias, pp. 107–08. 34. See Olum, ‘The Doomsday Argument and the Number of Possible Observers’, pp. 172–73. 35. ‘The Doomsday Argument, Adam and Eve, UN++ and Quantum Joe’, Synthese, 127 (2001), pp. 359–387.
  • 136 © 2006 The Author. Journal compilation © 2006 Blackwell Publishing Ltd. Surely the Urn model fallaciously reduces all possible human futures to two, artificial scenarios?36 This objection may mistake a pedagogical device for part of DA’s logical and probabilistic scaffolding. The Urn model can work with many urns, of widely differing sizes. We needn’t even confine ourselves to considering finite numbers of urns or human beings. Paul Bartha and Christopher Hitchcock discuss the use of nonstandard measures for infinite confirmation-theoretic DA cases.37 Carter and Leslie’s DA has had a life-expectancy parody. If your life is near its end, there will be few moments after this one and your present is not unusually early. However, if your death is distant, then this moment is unusu- ally near the beginning of your life. Hence, ‘Death Soon’ makes your present location more probable than ‘Death Later’ and you should not expect to complete this article.38 However, this ‘longevity’ DA faces at least two prob- lems: (a) it assumes the reference-class problem has been solved and we have a clear-cut way of defining appropriate reference-classes for the moments of our lives and (b) it falls foul of an important restriction on DA inferences Bostrom calls the ‘no outsider’ requirement, i.e. that in applying the sampling intuitions behind DA, “there must be no outsiders—beings who are ignored in the reasoning but who really belong in the reference class”.39 In the DA case, we have no relevant data about the longevity of human species but data about lifespans is in plentiful supply. Timothy Chambers argues DA faces a probabilistic mirror he calls the ‘Ussherian Corollary’, after Bishop Ussher’s demonstration that Creation occurred in 4004 . He says the Urn Model can equally generate a low probability for an old human race, so DA “entails a parallel Ussherian moral: that we have systematically underestimated the chance that the human race began fairly recently”.40 Even if we grant Chambers that his Ussherian Corollary and DA are probabilistically symmetrical, this symmetry is more than offset by a glaring evidential asymmetry. Chambers’s argument might threaten DA if DA tried to derive our likely future purely from the fact that we exist now, prior to, or in the absence of, any information about past population. However, DA has rather more empirical input to it than simply noting the fact that we live now. A very popular counter-DA move is to invoke a compensating probability- shift to counteract any ‘Doom Soon’ shift. The idea is this: if we consider only 36. “We do not accept that there are only two plausible candidate sizes for the ultimate popu- lation of humans. Nor . . . that the substitution of only two hypotheses for the many billions (trillions?) of a priori available hypotheses is a ‘harmless simplification’ which better reveals the logic of the argument”, (Korb and Oliver, ‘A Refutation of the Doomsday Argument’, p. 407). 37. ‘No One Knows the Date or the Hour: an Unorthodox Application of Rev. Bayes’s Theorem’, Philosophy of Science (Proceedings), 66 (1999), Supplementary volume, pp. 339–53, 352. 38. Seemingly first developed in J.-P. Delahaye’s ‘Recherche de Modèles pour l’Argument de l’Apocalypse de Carter-Leslie’, unpublished MS. A version of this objection is also given by Korb and Oliver, ‘A Refutation of the Doomsday Argument’, p. 405. 39. Anthropic Bias, p. 112. 40. ‘Do Doomsday’s Proponents Think We Were Born Yesterday?’, Philosophy, 76 (2001), pp. 443– 50, at p. 446.
  • 137 © 2006 The Author. Journal compilation © 2006 Blackwell Publishing Ltd. birth-ranks then we can get a DA shift in favour of imminent Doom. How- ever, this shift effectively disappears if we consider the increased opportunities for being human a larger human polity affords. Thus, the fact that you exist should incline you to favour hypotheses according to which many humans exist, rather than few. The result is a contest between two assumptions. On the one hand, we have the Self-Sampling Assumption (SSA) that fuels DA: “One should reason as if one were a random sample from the set of all observers in one’s reference class”.41 On the other, we have the Self-Indication Assumption (SIA): “Given the fact that you exist, you should (other things equal) favour hypotheses according to which many observers exist over hypotheses on which few observers exist”.42 Its exponents claim invoking SIA means ‘Doom Soon’ is offset by the fact that our existing at all favours ‘Doom Later’. Paul Bartha and Christopher Hitchcock think DA can be evaded if we take into account the probability of our own existence.43 While they grant that it seems odd to discus the probability of something we know occurred and about which scepticism seems impossible (i.e. the fact we exist), giving a prob- ability to our own existence is perfectly permissible and invites a variant of the ‘hypothetical priors’ solution to the traditional ‘problem of old evidence’.44 There seems to be a consensus that invoking SIA will successfully nullify the ‘Doom Soon’ shift produced by using SSA. However, controversy attends the consequences of applying SIA on its own, the worry being that SIA appeals simply because it seems to offer an easy way to defeat DA and not because of any intrinsic merit it may possess. It seems reasonable to demand of either assumption that it could be applied in isolation without creating absurdities. However, Bostrom, for example, has notably insisted that SIA leads to all manner of counter-intuitive consequences if applied alone.45 Bradley Monton argues that DA can be formulated without our knowing anything about our birth-ranks. (His aim is not to defend DA but to defend SIA from Bostrom’s criticisms.) Monton’s DA runs thus: let ‘H1’ and ‘H2’ be two population hypotheses, such that H1 < H2. 46 Furthermore, let ‘K ’ stand 41. Nick Bostrom and Milan M. Cirkovic, ‘The Doomsday Argument and the Self-Indication Assumption: Reply to Olum’, The Philosophical Quarterly, 53 (2003), pp. 83–91, at p. 84. 42. Bostrom, Anthropic Bias, p. 66. Bostrom says a version of SIA (albeit not under this name) first appeared in Dennis Dieks’s ‘Doomsday—or the Dangers of Statistics’, The Philosophical Quarterly, 42 (1992), pp. 78–85. Another version appears in Tomás Kopf, Pavel Krtous and Don N. Page, ‘Too Soon for Doom Gloom’, archived by at: gr-qc/9407002. Interestingly, the Kopf (et al.) version of SIA refers to “The probability for the observer to exist somewhere in a history of length N is proportional to the probability of that history and to the number of people in that history” (‘Too Soon for Doom Gloom’, p. 7, emphasis added). 43. ‘No One Knows the Date or the Hour’, passim. 44. For both the ‘old evidence’ problem and its ‘hypothetical priors’ solution, see Colin Howson and Peter Urbach, Scientific Reasoning: The Bayesian Approach (Open Court, 2nd edn. 1993), pp. 403 ff. 45. See Bostrom’s ‘Presumptuous Philosopher’ thought-experiment, Anthropic Bias, pp. 124 ff. Bostrom also rebuts charges that SSA leads to conflicts with Lewis’s Principal Principle, (ibid., pp. 141–58). 46. Monton’s H1and H2 have total human populations of 200 billion and 200 trillion, with priors of 0.05 and 0.95 respectively, see ‘The Doomsday Argument Without Knowledge of Birth Rank’, The Philosophical Quarterly, 53 (2003), pp. 79–82, at p. 80.
  • 138 © 2006 The Author. Journal compilation © 2006 Blackwell Publishing Ltd. for the proposition that someone has property k, where k is a property unlikely to have multiple instantiations.47 P(K ) is independent of whether H1 or H2 obtains, i.e. K is not conditional on overall population-size. If ‘M’ is the pro- position that I have property k and I know M, it follows that P(M | H1) > P(M | H2) for any values of H1 or H2. Monton’s conclusions have been resisted. D.J. Bradley claims Monton’s DA implicitly relies on birth-rank information and that no suitable alternative property has been proposed.48 4. What Doomsday Did Next Besides critiques and defences of DA, there have been several attempts at extending DA methodology to other philosophical areas or problems. Paul Franceschi49 argues that there are important similarities between the reference-class problem in DA and Hempel’s paradox of the ravens. In both cases, he maintains, the problem arises through lack of an objective criterion for determining the proper reference class.50 Bostrom’s Simulation Argument uses DA-inspired reasoning to suggest a novel disjunctive conclusion. Bostrom argues that if we accept a broadly func- tionalist conception of the mind and also believe that advanced civilizations will run many computer-simulations of minds, we should expect to be simu- lated minds running inside advanced computers.51 Thus, we must distribute our credences between one of three options: (a) few civilizations survive to attain simulation-level technology, (b) few advanced civilizations care to simulate their ancestors or (c) we are probably simulated minds ourselves. Lest Bostrom’s reasoning sound too much like a version of DA, it’s important to note that Bostrom argues that DA uses a flawed, overly-ambitious indifference principle, i.e. one which requires us to treat all birth-ranks as equiprobable and to consider ourselves as randomly-selected humans even though we know we live c. 2005 . Knowing our approximate birth-ranks precludes us treat- ing ourselves as random humans. Instead, Bostrom’s Simulation Argument uses a ‘bland principle of indifference’ (BPI), which counsels “indifference 47. E.g., “being alone in 323 Main Street in Lexington, Kentucky, from 20:41 to 20:42 GMT on April 9, 2002”, (ibid.). 48. ‘No Doomsday Argument Without Knowledge of Birth Rank: A Defense of Bostrom’, Synthese, 144 (2005), pp. 91–100. 49. ‘Comment l’Urne de Carter et Leslie se Déverse dans Celle de Hempel’, The Canadian Journal of Philosophy, 29 (1999), pp. 139–156. Also in translation as: ‘The Doomsday Argument and Hempel’s Problem’, at 50. See also Franceschi’s ‘Une Solution pour l’Argument de l’Apocalypse’, Canadian Journal of Philosophy, 28 (1998), pp. 227–46. Also relevant to Franceschi’s DA is his ‘Une Solution pour le Paradoxe de Goodman’, Dialogue, 40 (2001), pp. 99–123; English translation at http:// 51. See ‘Are We Living in a Computer Simulation?’, The Philosophical Quarterly, 53 (2003), pp. 243–55. First presented in ‘Are You Living in a Computer Simulation?’, 2001, at http://www.simulation- See also Bostrom’s popular exposition in ‘The Simulation Argument: Why the Probability that You Are Living in a Matrix is Quite High’, Times Higher Education Supplement, May 16th, 2003, at
  • 139 © 2006 The Author. Journal compilation © 2006 Blackwell Publishing Ltd. only between hypotheses about which observer one is, when one has no information about which of these observers one is”.52 If we think a fraction x of all minds are computer-simulations and our experiential content might be the same whether we are simulations or not, Bostrom’s BPI suggests that our credence for our being simulation minds should equal x.53 Perhaps the most ambitious attempt at offering a new diagnosis and rebuttal of DA, while also newly applying the probabilistic intuitions behind DA, comes from John F.G. Eastman.54 Eastman’s paper attempts to demonstrate the following conclusions: DA is intimately related to the nature of consciousness and can be re- formulated to show that there is no possibility of an infinite conscious lifetime, on pain of otherwise generating contradictions. As a corollary to the above, consciousness cannot be generated, or under- stood, through any classical instantiation of a computer programme and so cannot be described fully by deterministic laws. The impossibility of an infinite conscious lifetime suggests consciousness is generated through a ‘many worlds’ quantum superposition of individually deterministic ‘quasi-classical’ histories. The ultimate failure of DA arises because DA assumes the existence of only one (classical) history. Consequently, DA fails through not recognizing that each observer-moment is associated with multiple (quasi-classical) histories. I’ve argued that DA inferences are only plausible in cases where our reference- classes are more circumscribed by the hypotheses under consideration than they are in the standard DA case. In support of this thesis, I deployed DA intuitions against Descartes’s doctrine of immortality, arguing (a) Cartesian dualism is unusual in making embodied human souls appear unusually located and (b) this anti-Cartesian off-shoot of DA escapes many of the reference-class problems associated with traditional DA.55 Darren Bradley and Branden Fitelson outline a posterior-probabilistic ‘lottery’ DA. They suggest that such ‘lottery’ DA’s do yield non-negligible shifts in probabilities for Doom but they also think the lottery version needs substantial and controversial probabilistic assumptions. (For example, that we can apply the Principle of Indifference to the various population-hypotheses and treat them all as a priori equiprobable.) Granting that such assumptions make ‘lottery’ DA of limited appeal, they suggest ways to create a more robust 52. ‘Are We Living in a Computer Simulation?’, p. 250. 53. Brian Weatherson delineates four versions of BPI, arguing that only one of them supports the Simulation Argument, and only then if conjoined with dubious epistemic assumptions. See his ‘Are You a Sim?’, The Philosophical Quarterly, 53 (2003), pp. 425–31. But see also Bostrom’s ‘The Simulation Argument: Reply to Weatherson’, The Philosophical Quarterly, 55 (2005), pp. 90–97. 54. ‘The Doomsday Argument, Consciousness and Many Worlds’, General Relativity and Quantum Cosmology, archived at 55. Alasdair Richmond, ‘Immortality and Doomsday’, American Philosophical Quarterly, 41 (2004), pp. 235–247.
  • 140 © 2006 The Author. Journal compilation © 2006 Blackwell Publishing Ltd. confirmation-theoretic DA that skirts many obstacles that face traditional posterior-probabilistic formulations.56 They argue that DA can be better expressed using ratios of likelihoods, rather than ratios of posterior probabilities. On this view, all DA requires is that the likelihood of our having a given birth-rank is a strictly decreasing function of the total number of humans postulated. (This assumption requires no precise numerical likelihoods for birth-ranks or any ‘Principle of Indifference’ to generate equal probabilities for population-hypotheses.) In addition, they suggest that their confirmation- likelihood DA can yield a more robust descendant which aptly illustrates the reasoning behind the ‘Monty Hall’ problem. (In this case, the doors ‘Monty Hall’ opens are treated like DA’s birth-ranked humans.) Thus, the oft-contested conclusion that you should switch your choice of doors in the Monty Hall problem (after the game’s host has eliminated one possibility) receives support from an unexpected quarter. However, a direct challenge to DA likelihood– ratio arguments comes from Elliot Sober: “Thoroughly preposterous hypotheses can have high likelihoods. . . . If I hear noises in my attic, the hypothesis that there are gremlins bowling up there has a likelihood of unity, but few of us would say that this hypothesis is very probable”.57 Sober’s verdict on the Carter-Leslie DA is that the admissibility of its assignment of likelihoods can only be assessed empirically in particular situations and hence there is no general DA inference. 5. Doom Without Doomsday There are many non-Bayesian arguments about extinction. Some mention of alternative approaches might help to clarify what DA does and doesn’t say: (1) Besides expounding DA, Leslie’s 1996 The End of the World is also a comprehensive guide to mechanisms that might trigger, or hasten, human extinction. Besides war, pandemic and environmental collapse, Leslie also surveys more outré dangers, ranging from vacuum metastability disasters through to Schopenhauerian pessimism and moral relativism. (At least time has taken Y2K bugs off Leslie’s list.) 2) Some generate Doom-predictions by projecting current environmental and technological trends. Sir Martin Rees is so confident that biotechnology poses high risks of near-future disaster that he has publicly wagered that “By 2020, bioterror or bioerror will lead to one million casualties in a single event”. Taking all likely threats into account, he thinks we have only a 0.5 chance of surviving the 21st century.58 56. ‘Monty Hall, Doomsday and Confirmation’, Analysis, 63 (2003), pp. 23–31. 57. ‘An Empirical Critique of Two Versions of the Doomsday Argument—Gott’s Line and Leslie’s Wedge’, Synthese, 135 (2003), pp. 415–430, at p. 424. 58. Our Final Century: Will the Human Race Survive the Twenty-First Century? (Heinemann, 2003). Rees has since upped the ante in a further book: Our Final Hour: A Scientist’s Warning (Basic Books, 2004). His bioterror wager can be found at At the time of writing (December 15th 2005), Rees’s bet had logged 181 votes in its favour, to 190 against.
  • 141 © 2006 The Author. Journal compilation © 2006 Blackwell Publishing Ltd. (3) Another approach to Doomsday treats technological progress as a Pascalian Wager whose pay-offs include possible extinction.59 Stephen P. Stich compares Pascalian with Bayesian threat-analyses for recombinant DNA tech- nology. He claims the former founder over the plethora of relevant alternatives we must consider and the latter founder over choosing whose subjective prob- abilities we should use.60 (4) Heinz von Foerster et al.61 treat population-growth as approximated by the two-body collision equation, so birth-rate is proportional to total popu- lation: dP/dt = kP1+r. (P and t are population and time respectively; k and r are positive constants.) This model predicts human population will become infinite (i.e. hit a singularity) on Friday 13th November, 2026. This model was used by von Foerster’s critics as a lesson in the dangers of projecting from data. However, von Foerster seems to have laid more stress on predicting a population singularity, or discontinuity, rather than a literally infinite humanity. However, whatever the likelihood of population-singularity in 2026, von Foerster’s model apparently ceased to resemble our true population curve c. 1973.62 (5) Not strictly DA as such, but still relevant to human prospects, are the families of attempts to apply evolutionary modelling, game theory and drama theory to ‘Prisoners’ Dilemma’ analyses of international relations, nuclear crises, etc.63. (6) Using Kolmogorov’s axioms, Martin H. Krieger argues that Doom (personal, social or planetary extinction, for example), should receive either probability 0 or 1.64 Alexander and Michael Scott use Kolmogorov’s infinity condition to criticize Krieger’s notions of randomness and independence.65 Krieger must, they say, either model behaviour in infinitely many human agents or treat human behaviour as a Zeno supertask of random choices. 6. Prospects for Doomsday If Doomsday doesn’t intervene, DA will probably keep attracting refutations. One interesting endeavour might be to investigate how DA relates to different measures of confirmation. As Bradley and Fitelson’s confirmation-theoretic 59. For a critique of Pascalian Wagers about extinction, see Neil A. Manson, ‘The Precautionary Principle, the Catastrophe Argument and Pascal’s Wager’, Ends and Means: Journal of the University of Aberdeen Centre for Philosophy, Technology and Society, 4 (1999), available at: http:// 60. ‘The Recombinant DNA Debate’, Philosophy and Public Affairs, 7 (1978), pp. 187–205. 61. Heinz von Foerster, P.M. Mora and L.W. Amiot, ‘Doomsday: Friday, November 13,  2026’, Science 132 (1960), pp. 1291–1295 and ‘Doomsday’, Science, 133 (1961), pp. 936–946. 62. See J. Serrin, ‘Is Doomsday on Target?’, Science, 189 (1975), pp. 86–88. 63. See, e.g., Robert Axelrod, The Evolution of Co-operation (Basic Books, 1984) and Nigel Howard, ‘Drama Theory and Its Relationship to Game Theory’, Group Decision and Negotiation, 3 (1994), pp. 187–206 and 207–53. 64. ‘Could the Probability of Doom be Zero or One?’, The Journal of Philosophy, 92 (1995), pp. 382–387. 65. ‘Taking the Measure of Doom’, The Journal of Philosophy, 95 (1998), pp. 133–141.
  • 142 © 2006 The Author. Journal compilation © 2006 Blackwell Publishing Ltd. DA suggests, there may be different ways to employ Bayesian intuitions in DA contexts. DA’s plausibility (or otherwise) may prove to be measure-sensitive. Bostrom’s ultimate verdict on DA is that its reference-classes are too ill- defined to prompt any unambiguous moral. However, having made this diagnosis, he goes on to suggest ways of finessing and extending the notion of observer-relative chances. While Bostrom’s Simulation Argument uses a version of SSA, Bostrom does not accept this version unreservedly. Instead, he sees it as a special case of a strengthened SSA which quantifies over observer-moments, rather than observers. Indeed, he defines reference classes in terms of observer-moments: “A reference class definition is a partition of possible observer-moments; each equivalence class in the partition is the ref- erence class for all the observer-moments included in it.”66 Using Bostrom’s SSSA, DA does not prompt any clear conclusions about humanity’s expecta- tions. It seems clear that any neo-Doomsayer must pay heed to Bostrom’s reservations about the choice of reference classes made in the classical Carter- Leslie DA. Whether DA can be re-formulated with a truly robust reference- class remains to be seen. Debate will probably continue over the relative merits of SIA and SSA. Any conclusion to this debate might prove to have far-reaching consequences. As noted above, attempts have been made to apply DA intuitions to ‘many worlds’ hypotheses in quantum mechanics, the apparent paradoxes of con- firmation theory and widely differing metaphysical hypotheses about mind and body. It might also be interesting to pursue the original anthropic invest- igations of our location in time that prompted Carter’s DA. So far, most anthropic arguments about time have concentrated on DA but Carter’s rea- soning may have far wider applications. For all that its conclusions have often been strenuously resisted, DA has prompted searching examinations of prob- abilistic and anthropic reasoning, and the debates that it has engendered look far from being extinct just yet. 66. Bostrom, Anthropic Bias, p. 181. See also pp. 159–83 and 202–05. As noted above, Nielsen defined his original DA reference-classes in terms of human-moments rather than birth- ranked humans.