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    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




    The University of Edinburgh

    1. Introduction: Carter-Leslie Doomsday

    Despite humankinds perennial fascination with its own extinction, theDoomsday Argument was only comparatively rarely discussed before c. 1990.Consequently, rather than cover the last few years work on Doomsday, thisarticle tries to survey all of at least the major Doomsday discussions since thetopic was first aired in 1983.

    The term Doomsday Argument (DA henceforth) was first proposed byFrank J. Tipler. John Leslie subsequently adopted and popularised DA as ahandy shorthand name for a family of Bayesian arguments about our specieslikely survival prospects.


    Besides frequently appearing in philosophical andscientific journals, DA has been expounded in popular science books


    andeven forms the basis of a science fiction novel.


    Unlike other arguments aboutthe future, DA does not issue in a prophecy or straightforward projection.DA aims to raise our personal probabilities for human extinction, usuallyconditional on our birth-rank in history. One may think DA sound yet believe

    1. The

    locus classicus

    for DA is John Leslies

    The End of the World: The Science and Ethics of HumanExtinction

    , (Routledge: 1996). Leslies other works that discuss or mention DA include: Risking the Worlds End,

    Bulletin of the Canadian Nuclear Society

    , 10 (1989), pp. 1015;


    , (Routledge, 1989), p. 214, fn. 1;Is the End of the World Nigh?,

    The Philosophical Quarterly

    , 40 (1990), pp. 6572;Doomsday Revisited,

    The Philosophical Quarterly

    , 42 (1992), pp. 859;The Doomsday Argument,

    Mathematical Intelligencer

    , 14 (1992), pp. 4851;Bayes, Urns and Doomsday,


    , 23 (1992), pp. 28995;Time and the Anthropic Principle,


    , 101 (1992), pp. 521540;Doom and Probabilities,


    , 102 (1993), pp. 48991;More About Doom,

    Mathematical Intelligencer

    , 15 (1993), pp. 57;Testing the Doomsday Argument,

    Journal of Applied Philosophy

    , 11 (1994), pp. 3144;Observer-Relative Chances and the Doomsday Argument,


    , 40 (1997), pp. 42736;Our Place in the Cosmos,


    , 75 (2000), pp. 1012.2. E.g. Paul Davies

    About Time

    , (Penguin, 1995, pp. 25864) usefully summarises DA and somemajor 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 Baxters novel

    Time: Manifold 1

    , (HarperCollins, 2000).

    Philosophical Books Vol. 47 No. 2 April 2006 pp. 129142

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    in a long human future. One may reject DA but think the human race hasentered its last lap. Perhaps unsurprisingly, DA has been more criticized thanendorsed. However, a consensus over where DA fails has been slow to emergeand several objections to DA are mutually incompatible. (It seemed for a timethat almost any stick would do to beat a Doomsday.)

    DA sprang from the Anthropic Principle debate about observation-selectioneffects in science. Seeking a balance between excessive anthropocentrism andexcessive insistence on our typicality, physicist and mathematician BrandonCarter coined the term Anthropic Principle to denote the inter-relationsbetween our existence as observers and the physical conditions we observe.


    Besides familiar anthropic topics like cosmic fine-tuning and Diracs large-number coincidences, Carter also applied anthropic reasoning to our locationin time. He first aired DA in a 1983 lecture on the likely number of crucialsteps in our evolution and the striking similarity between the time it took lifeto evolve on Earth and the time remaining before the Sun burns out.


    Thepublished version of his lecture


    does not invoke DA. However, in a discussionappendix to the published paper, he outlines some anthropic speculations onthe likelihood of extinction and what explanatory roles a future cut-off mightplay.


    Carter mainly uses DA as a way of rebutting charges that anthropicreasoning doesnt yield testable predictions. However, he declines to discussDA in print and insists that Leslie should share any credit for DAs discovery.

    The Carter-Leslie DA can be encapsulated thus. Recent history has seenapparently unprecedented growth in human population. Our c. six billioncontemporaries may be a significant percentage of all humans there have everbeen.


    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 peoplewill have lived after us than lived before us. However, if human populationdrops irreversibly in the near future, we who live now will also be a significantfraction of the all-time human total. If Doom looms, our location seemsrelatively probable but if Doom is deferred, we are unusually early humans.Granted some lottery assumptions, our birth-ranks receive higher posteriorprobabilities with Doom Soon than they do with Doom Deferred.


    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. 29198.5. For more on Carters crucial steps formula, see John D. Barrow and Frank J. Tipler,

    TheAnthropic Cosmological Principle

    , (Oxford University Press, 1986), pp. 56246. The Anthropic Principle and its Implications for Biological Evolution,

    Philosophical Transactionsof the Royal Society of London

    , Series A, 310, 1983, pp. 34763. Carter (ibid., pp. 358 ff.) alsooffers anthropic explanations for why we observe neither advanced extra-terrestrials nornatural analogues of the wheel.

    7. E.g. a man-made ecological disaster . . . is an eventuality which might well be discussed withreference 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 alivenow, 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 humanpopulation receive the same prior probability and (b) that the likelihood of your havinga particular birth-rank


    , conditional on the total population being


    , is equal to 1/





    , and otherwise equals zero.

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    Assuming we should favour explanations that make our explanandumrelatively probable, we seemingly must favour impending Doom as the betterexplanation of our location.

    DA is thus a probabilistic force-multiplier: whatever personal probability wenow accord imminent extinction should be increased once we take anthropicexplanations of our birth-rank into account. Carter-Leslie DA does not attemptto derive a precise probability for Doom. Leslie says only that DA should act toincrease our probability for Doomas in any subjectivist Bayesian argument,the precise priors to be fed in have to be derived from elsewhere. DA is notan alternative to empirical arguments about Doom but requires empiricalinput in order to work. Thus, DA can only yield a high Doom posteriorprobability if your Doom prior is non-negligible. Even if DA increases yourprobability for Doom a thousand-fold, this shouldnt trouble you if yourprior for human extinction was only around one in ten billion, say.

    Leslie often illustrates DA-reasoning with Urn stories. Imagine your nameis written on a slip of paper and dropped into an urn. Your prior probabilityfor the urn holding 10 names is 0.02, while your prior probability for itholding 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, its easy to demonstrate that you shouldchange your probabilities. Indeed, Bayess Theorem suggests that your priorof 0.02 should yield to a posterior probability around 0.67.


    Oddly enough, some DA variants started life as objections to DA. Thusbegan the Shooting Room DA, which Leslie first proposed as a problem forDA.


    Imagine you are placed in a room with several other people and toldthat 90% of those who enter the room will be shot. However, you are alsotold you will leave unharmed unless two fair dice, thrown simultaneously,both yield sixes. How are these claims reconciled? The answer is that, at eachthrow of the dice, ten times more people occupy the Shooting Room than didon the round before. Are your chances of leaving the room alive an alarming1/10 or a more comfortable 35/36? Leslie says the answer hinges on thetruth or falsity of determinism; if determinism is true, your survival-chancesare 1/10 but if the world is significantly indeterministic, your chances are 35/36. Leslie maintains that the only really threatening criticism of DA hithertohas been that DA requires the truth of determinism. Few critics agree withLeslie that DA requires determinism. William Eckhardt objects that if DA didhinge on how deterministic the world is, we could effectively test determinismby seeing how far DA yields successful predictions.


    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) + (0.98


    0.67. (Cf. Leslie, Time andthe Anthropic Principle, p. 526.)

    11. Based on a query about DA from David Lewis. See Leslie,

    The End of the World

    , pp. 2356.12. A Shooting-Room View of Doomsday,

    Journal of Philosophy

    , 94 (1997), pp. 24459. Eckhardtalso accuses DA-reasoning (a) of conflating Bayess Theorem with Bayesianism, and (b) of


    increasing any (non-extreme) probability for extinction.

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    2. Doomsday according to Nielsen, Franceschi and Gott

    In 1988, physicist Holger Bech Nielsen independently proposed another DA,


    which somewhat resembles the Carter-Leslie version but also shows importantdifferences from it. Nielsens investigation into random dynamics


    led him toconsider the notion of random location in time. In particular, he consideredthe pair as randomly selected from all the human momentsthere will be. Assuming the total of humans will be finite


    and that weshould favour the most probable location for our present moment, weshould conclude that we are at, or near, the maximum human population. Ifmaximal population is still to come, or our population endures near itspresent level, our location is unlikely. Nielsens DA thus predicts probableDoom within a period commensurable with the time it takes our populationto double. Therefore, humans should either be extinct or greatly reduced innumbers

    within a hundred years



    Nielsen also discusses some objections to hisDA: (1) reference-classes of humans and times might be too subjective to yieldconcrete predictions, (2) our present location may be a statistical fluctuation;(3) if you have an unusual property, (for example, having a birthday today or beingmore than 95 years old), you can suspect your pairing is atypical.

    Paul Franceschi claims to have a third form of DA, whose method ofpopulation-sampling differs from both Carter-Leslie Urn and Eckhardt/Sowers ball dispenser versions.


    Rather than birth-ranks being generated asnames drawn from an urn, Sowers imagines human births as unmarked ballswhich are dispensed from a machine and

    only then

    have numbers added tothem. Franceschis diagnosis of DA is that neither scenario above strikes theright balance between temporal and atemporal population-sampling. Instead,he proposes that something like either sampling method could apply to oursituation, so that a DA probability-shift


    be possible. Thus, Franceschisthird route: uncertainty as to how our birth-ranks are assigned means DABayesian shifts are permissible but non-obligatory.

    13. Random Dynamics and Relations between the Number of Fermion Generations and the FineStructure Constant,

    Acta Physica Polonica

    , Series B, 20 (1989), pp. 42768 (SPIRES HEPreprint at:,B20,427).

    14. I.e. that natures 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 alsoWilliam Eckhardt, Probability Theory and the Doomsday Argument,


    , 102 (1993),pp. 48388 and George F. Sowers Jr, The Demise of the Doomsday Argument,


    , 111(2002), pp. 3745. NB: the latter do not accept DA and offer their alternative birth-rankmechanisms as


    to the Carter-Leslie DA. Eckhardt thinks DA errs by treating actualand non-existent humans the same way, while Sowers thinks birth-ranks must be indexed onour temporal position and so fail to be random.

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    J. Richard Gott III has proposed a delta


    DA, using the CopernicanPrinciple of Mediocrity.


    Gott says we should not expect to find ourselveslocated anywhere special in human history. Thus, if we assume that all loca-tions in history are a priori equiprobable, we can calculate from observationsof 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 historyfrom within its first (or last) 2.5%. Thus, humanitys future should be between1/39


    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 ofwhich he observed in 1969.) If humanitys past

    200,000 years, Gott suggestswe can be 95% confident humanity will last another 5,100 to (7.8



    ) moreyears. Some critics find this too broad-brush a prediction and think Gottsmethod has implausible empirical consequences if applied (as Gott suggests)more generally, to human lifespans, for instance.


    Ken D. Olum


    accuses Gott of (a) failing to justify any choice of priorprobabilities for his argument and (b) ignoring a significant constraint on ourprior probabilities for duration, i.e. that the longer a process lasts, the morelikely we are to be observing it. Gott claims his method does not neglect theneed 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 normalizingconstant.


    Bradley Monton and Sherrilyn Roush


    charge Gotts argumentwith (amongst other failings) invalidly excluding an infinite human futureand being self-refuting. An intriguing twist to Gott-criticism comes fromP. T. Landsberg and J. N. Dewynne, who propose a meta-DA which threatensto make Gotts method topple into self-contradiction.


    In a (qualified) defenceof Gott, Bradley Monton and Brian Kierland argue that his argument mayfail in many contexts but that it can be defended against many previouscriticisms and that its general methodology (for estimating future durationfrom past duration) is sound.


    18. Gotts DA was first presented in Implications of the Copernican Principle for Our FutureProspects,


    , 363 (1993), pp. 3159. He offered some replies to objections in FutureProspects Discussed: Gott Replies,


    , 368 (1994), p. 108. A popular exposition of GottsDA appears in his book

    Time Travel in Einsteins 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. 143153, archivedby

    at: Caves paper ends with a challengeto Gott to test the delta


    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. 16484, at pp. 17479.

    21. Leslies DA does not seek to justify a choice of priors; rather, Leslie says, the force of DAresides in the effect it has on any existing priors for extinction. Thus, were ones priorprobability for extinction sufficiently low, ones probability for extinction might still be loweven after using Leslies DA.

    22. Gotts Doomsday Argument, at:

    23. A Probable Paradox,


    , 389 (1997), p. 779.24. How to Predict Future Duration from Present Age,

    The Philosophical Quarterly

    , 56 (2006),pp. 1638.

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    3. Objections to Carter-Leslie Doomsday

    DA has received many ripostes, some of them independently-discoveredmany times. Leslie sounds a cautionary note for DA sceptics: Given twentyseconds, many people believe they have found crushing objections to Cartersline of thought.


    Some can be dealt with quite quickly. Many people belietheir own uniqueness by protesting But Im 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 butthis does not prevent them being typical in others. (It seems a safe bet thatmost readers of these pages are carbon-based and oxygen-breathing.) DA isnot an a priori ontological proof of human extinction, but requires empiricalfacts 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 DAs anthropic appeal to our location as observers. Likewise DArequires no commitment to four-dimensionalism about time rather thanpresentismDA is


    meant to address the question Why is it this moment


    ? but rather Why are we alive with this segment of humanity?. Carterand Leslie are not pondering whether or not they lived c. 2000

    rather,DA invites us to consider where creatures like ourselves are


    to be. Asample 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 earlierDA must have failed so its likely present-day DA will too. We might beunlucky enough to be the unique generation of correct Doomsayers but weshouldnt think thus of ourselves. Leslie offers several replies to this objection,(of varying plausibility): (1) Any probabilistic reasoning will fail for someonewho is improbably locatedprior to the result being announced, the eventualwinner of a million-ticket lottery should still rationally expect to lose.


    (2)Perhaps the preponderance of moments in history where DA fails could beoffset by the number of successful users of DA: Reasoning which failed forpeople at most points in human history by suggesting wrong predictions to themmight still suggest a correct prediction to most humans who could use it if humannumbers expanded rapidly soon before humankind became extinct.27 (3) nocave man shared the Earth with six billion contemporaries plus H-bombs,ozone depletion and biological weapons. (4) Maybe not all earlier applicationsof DA were wrong after all.28

    In a meta-inductive spin on cave man objections, Kevin Korb and JonathanJ. 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 (Torbjrn Tnnsj,Doom Soon?, Inquiry, 40 (1997), pp. 24352), 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 Endof the World, p. 205).

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    shouldin this worldprovide no more guidance to the truth than doesflipping a coin.29 They argue that if the total population is bounded bytwo times the sample value . . . , then 499 inferences using the Doomsdayargument are wrong and 501 inferences are right, hence in a perfectlyreasonable metainduction we should conclude that there is something verywrong with this form of inference.30 Bostrom replies (a) odds of 501/499 arestill 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: DAs success-ratecan be made arbitrarily small simply by increasing the population size in theexample,32 and that DA-inferences tend asymptotically to a success-rate nobetter than random.

    Bostrom argues that its 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 disjunctiveconclusion. Besides updating our probabilities for Doom, DA reasoning iscompatible with the following alternative conclusions: (1) our having a DoomSoon prior so low that our posterior probability for Doom is still negligibleeven after applying DA; (2) the all-time total of humans being infinite and somaking DAs conclusion ill-defined; (3) human population starting to dwindlesoon 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 paranormalpowers, such as non-local and retroactive causation.34 Imagine that a nearbystar has a high probability of becoming a supernova and killing most ofhumanity. 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 doesnt occur then neither will the crashcolonization programme.) Thus, if DA gives us reason to think were latehumans, it also gives us reason to believe the supernova wont occur or hasntoccurred. We seemingly have some paranormal, non-local connection withevents 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 likelyto happen with the causes of that event.35

    29. Korb and Oliver, A Refutation of the Doomsday Argument, Mind, 107 (1998), pp. 403410, at p. 404.

    30. A Refutation of the Doomsday Argument, p. 405.31. See Bostroms The Doomsday Argument is Alive and Kicking, Mind, 108 (1999), pp. 539550.

    Also, Nick Bostroms Ph.D. dissertation, Observational Selection Effects and Probability, (LSE, 2000),(Chapter 6), pp. 121122), available at The TTobjection is also discussed in the (substantially expanded) book-version of Bostroms Ph.D.,Anthropic Bias: Observation Selection Effects in Science and Philosophy, (Routledge, 2002), pp. 109110.

    32. Korb and Oliver, Comment on Nick Bostroms The Doomsday Argument is Alive andKicking, Mind, 108 (1999), pp. 551553, at p. 551.

    33. Anthropic Bias, pp. 10708.34. See Olum, The Doomsday Argument and the Number of Possible Observers, pp. 17273.35. The Doomsday Argument, Adam and Eve, UN++ and Quantum Joe, Synthese, 127 (2001),

    pp. 359387.

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    Surely the Urn model fallaciously reduces all possible human futures totwo, artificial scenarios?36 This objection may mistake a pedagogical devicefor part of DAs logical and probabilistic scaffolding. The Urn model can workwith many urns, of widely differing sizes. We neednt even confine ourselvesto considering finite numbers of urns or human beings. Paul Bartha andChristopher Hitchcock discuss the use of nonstandard measures for infiniteconfirmation-theoretic DA cases.37

    Carter and Leslies DA has had a life-expectancy parody. If your life is nearits end, there will be few moments after this one and your present is notunusually early. However, if your death is distant, then this moment is unusu-ally near the beginning of your life. Hence, Death Soon makes your presentlocation more probable than Death Later and you should not expect tocomplete 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 havea clear-cut way of defining appropriate reference-classes for the moments ofour lives and (b) it falls foul of an important restriction on DA inferencesBostrom calls the no outsider requirement, i.e. that in applying the samplingintuitions behind DA, there must be no outsidersbeings who are ignoredin the reasoning but who really belong in the reference class.39 In the DAcase, we have no relevant data about the longevity of human species but dataabout lifespans is in plentiful supply.

    Timothy Chambers argues DA faces a probabilistic mirror he calls theUssherian Corollary, after Bishop Usshers demonstration that Creationoccurred in 4004 . He says the Urn Model can equally generate a lowprobability for an old human race, so DA entails a parallel Ussherian moral:that we have systematically underestimated the chance that the human racebegan fairly recently.40 Even if we grant Chambers that his UssherianCorollary and DA are probabilistically symmetrical, this symmetry is morethan offset by a glaring evidential asymmetry. Chamberss argument mightthreaten DA if DA tried to derive our likely future purely from the fact thatwe exist now, prior to, or in the absence of, any information about pastpopulation. However, DA has rather more empirical input to it than simplynoting 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 revealsthe 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. Bayess Theorem,Philosophy of Science (Proceedings), 66 (1999), Supplementary volume, pp. 33953, 352.

    38. Seemingly first developed in J.-P. Delahayes Recherche de Modles pour lArgument delApocalypse de Carter-Leslie, unpublished MS. A version of this objection is also given byKorb and Oliver, A Refutation of the Doomsday Argument, p. 405.

    39. Anthropic Bias, p. 112.40. Do Doomsdays Proponents Think We Were Born Yesterday?, Philosophy, 76 (2001), pp. 443

    50, at p. 446.

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    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 opportunitiesfor being human a larger human polity affords. Thus, the fact that you existshould incline you to favour hypotheses according to which many humansexist, rather than few. The result is a contest between two assumptions. Onthe 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 allobservers in ones reference class.41 On the other, we have the Self-IndicationAssumption (SIA): Given the fact that you exist, you should (other thingsequal) favour hypotheses according to which many observers exist overhypotheses on which few observers exist.42 Its exponents claim invoking SIAmeans Doom Soon is offset by the fact that our existing at all favours DoomLater. Paul Bartha and Christopher Hitchcock think DA can be evaded if wetake into account the probability of our own existence.43 While they grant thatit seems odd to discus the probability of something we know occurred andabout 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 ofthe hypothetical priors solution to the traditional problem of old evidence.44

    There seems to be a consensus that invoking SIA will successfully nullifythe Doom Soon shift produced by using SSA. However, controversy attendsthe consequences of applying SIA on its own, the worry being that SIA appealssimply because it seems to offer an easy way to defeat DA and not becauseof any intrinsic merit it may possess. It seems reasonable to demand of eitherassumption that it could be applied in isolation without creating absurdities.However, Bostrom, for example, has notably insisted that SIA leads to allmanner of counter-intuitive consequences if applied alone.45

    Bradley Monton argues that DA can be formulated without our knowinganything about our birth-ranks. (His aim is not to defend DA but to defendSIA from Bostroms criticisms.) Montons DA runs thus: let H1 and H2 betwo population hypotheses, such that H1 < H2.

    46 Furthermore, let K stand

    41. Nick Bostrom and Milan M. Cirkovic, The Doomsday Argument and the Self-IndicationAssumption: Reply to Olum, The Philosophical Quarterly, 53 (2003), pp. 8391, at p. 84.

    42. Bostrom, Anthropic Bias, p. 66. Bostrom says a version of SIA (albeit not under this name) firstappeared in Dennis Diekss Doomsdayor the Dangers of Statistics, The PhilosophicalQuarterly, 42 (1992), pp. 7885. Another version appears in Toms Kopf, Pavel Krtous andDon N. Page, Too Soon for Doom Gloom, archived by at: Interestingly, the Kopf (et al.) version of SIA refers to The probability forthe observer to exist somewhere in a history of length N is proportional to the probability ofthat 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 Bostroms Presumptuous Philosopher thought-experiment, Anthropic Bias, pp. 124 ff.

    Bostrom also rebuts charges that SSA leads to conflicts with Lewiss Principal Principle,(ibid., pp. 14158).

    46. Montons H1and H2 have total human populations of 200 billion and 200 trillion, with priorsof 0.05 and 0.95 respectively, see The Doomsday Argument Without Knowledge of BirthRank, The Philosophical Quarterly, 53 (2003), pp. 7982, at p. 80.

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    for the proposition that someone has property k, where k is a property unlikelyto have multiple instantiations.47 P(K ) is independent of whether H1 or H2obtains, 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. Montons conclusions have beenresisted. D.J. Bradley claims Montons DA implicitly relies on birth-rankinformation 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 atextending DA methodology to other philosophical areas or problems. PaulFranceschi49 argues that there are important similarities between thereference-class problem in DA and Hempels paradox of the ravens. In bothcases, he maintains, the problem arises through lack of an objective criterionfor determining the proper reference class.50

    Bostroms Simulation Argument uses DA-inspired reasoning to suggest anovel disjunctive conclusion. Bostrom argues that if we accept a broadly func-tionalist conception of the mind and also believe that advanced civilizationswill run many computer-simulations of minds, we should expect to be simu-lated minds running inside advanced computers.51 Thus, we must distributeour credences between one of three options: (a) few civilizations survive toattain simulation-level technology, (b) few advanced civilizations care tosimulate their ancestors or (c) we are probably simulated minds ourselves. LestBostroms reasoning sound too much like a version of DA, its important tonote that Bostrom argues that DA uses a flawed, overly-ambitious indifferenceprinciple, i.e. one which requires us to treat all birth-ranks as equiprobableand to consider ourselves as randomly-selected humans even though we knowwe live c. 2005 . Knowing our approximate birth-ranks precludes us treat-ing ourselves as random humans. Instead, Bostroms Simulation Argumentuses 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 GMTon April 9, 2002, (ibid.).

    48. No Doomsday Argument Without Knowledge of Birth Rank: A Defense of Bostrom,Synthese, 144 (2005), pp. 91100.

    49. Comment lUrne de Carter et Leslie se Dverse dans Celle de Hempel, The Canadian Journalof Philosophy, 29 (1999), pp. 139156. Also in translation as: The Doomsday Argument andHempels Problem, at

    50. See also Franceschis Une Solution pour lArgument de lApocalypse, Canadian Journal ofPhilosophy, 28 (1998), pp. 22746. Also relevant to Franceschis DA is his Une Solution pourle Paradoxe de Goodman, Dialogue, 40 (2001), pp. 99123; English translation at

    51. See Are We Living in a Computer Simulation?, The Philosophical Quarterly, 53 (2003), pp. 24355.First presented in Are You Living in a Computer Simulation?, 2001, at See also Bostroms popular exposition in The SimulationArgument: Why the Probability that You Are Living in a Matrix is Quite High, Times HigherEducation Supplement, May 16th, 2003, at

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    only between hypotheses about which observer one is, when one has noinformation about which of these observers one is.52 If we think a fraction xof all minds are computer-simulations and our experiential content might bethe same whether we are simulations or not, Bostroms BPI suggests that ourcredence for our being simulation minds should equal x.53

    Perhaps the most ambitious attempt at offering a new diagnosis and rebuttalof DA, while also newly applying the probabilistic intuitions behind DA, comesfrom John F.G. Eastman.54 Eastmans paper attempts to demonstrate thefollowing 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 socannot be described fully by deterministic laws.

    The impossibility of an infinite conscious lifetime suggests consciousnessis generated through a many worlds quantum superposition of individuallydeterministic quasi-classical histories.

    The ultimate failure of DA arises because DA assumes the existence of onlyone (classical) history. Consequently, DA fails through not recognizing thateach observer-moment is associated with multiple (quasi-classical) histories.

    Ive argued that DA inferences are only plausible in cases where our reference-classes are more circumscribed by the hypotheses under consideration thanthey are in the standard DA case. In support of this thesis, I deployed DAintuitions against Descartess doctrine of immortality, arguing (a) Cartesiandualism is unusual in making embodied human souls appear unusually locatedand (b) this anti-Cartesian off-shoot of DA escapes many of the reference-classproblems associated with traditional DA.55

    Darren Bradley and Branden Fitelson outline a posterior-probabilisticlottery DA. They suggest that such lottery DAs do yield non-negligibleshifts in probabilities for Doom but they also think the lottery version needssubstantial and controversial probabilistic assumptions. (For example, that wecan apply the Principle of Indifference to the various population-hypothesesand treat them all as a priori equiprobable.) Granting that such assumptionsmake 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. 42531. But see alsoBostroms The Simulation Argument: Reply to Weatherson, The Philosophical Quarterly, 55(2005), pp. 9097.

    54. The Doomsday Argument, Consciousness and Many Worlds, General Relativity and QuantumCosmology, archived at

    55. Alasdair Richmond, Immortality and Doomsday, American Philosophical Quarterly, 41 (2004),pp. 235247.

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    confirmation-theoretic DA that skirts many obstacles that face traditionalposterior-probabilistic formulations.56 They argue that DA can be betterexpressed using ratios of likelihoods, rather than ratios of posterior probabilities.On this view, all DA requires is that the likelihood of our having a givenbirth-rank is a strictly decreasing function of the total number of humanspostulated. (This assumption requires no precise numerical likelihoods forbirth-ranks or any Principle of Indifference to generate equal probabilitiesfor population-hypotheses.) In addition, they suggest that their confirmation-likelihood DA can yield a more robust descendant which aptly illustrates thereasoning behind the Monty Hall problem. (In this case, the doors MontyHall opens are treated like DAs birth-ranked humans.) Thus, the oft-contestedconclusion that you should switch your choice of doors in the Monty Hallproblem (after the games host has eliminated one possibility) receives supportfrom an unexpected quarter. However, a direct challenge to DA likelihoodratio arguments comes from Elliot Sober: Thoroughly preposterous hypothesescan have high likelihoods. . . . If I hear noises in my attic, the hypothesis thatthere are gremlins bowling up there has a likelihood of unity, but few of uswould say that this hypothesis is very probable.57 Sobers verdict on theCarter-Leslie DA is that the admissibility of its assignment of likelihoodscan only be assessed empirically in particular situations and hence there is nogeneral DA inference.

    5. Doom Without Doomsday

    There are many non-Bayesian arguments about extinction. Some mention ofalternative approaches might help to clarify what DA does and doesnt say:

    (1) Besides expounding DA, Leslies 1996 The End of the World is also acomprehensive guide to mechanisms that might trigger, or hasten, humanextinction. Besides war, pandemic and environmental collapse, Leslie alsosurveys more outr dangers, ranging from vacuum metastability disastersthrough to Schopenhauerian pessimism and moral relativism. (At leasttime has taken Y2K bugs off Leslies list.)

    2) Some generate Doom-predictions by projecting current environmentaland technological trends. Sir Martin Rees is so confident that biotechnologyposes high risks of near-future disaster that he has publicly wagered that By2020, bioterror or bioerror will lead to one million casualties in a singleevent. Taking all likely threats into account, he thinks we have only a 0.5chance of surviving the 21st century.58

    56. Monty Hall, Doomsday and Confirmation, Analysis, 63 (2003), pp. 2331.57. An Empirical Critique of Two Versions of the Doomsday ArgumentGotts Line and

    Leslies Wedge, Synthese, 135 (2003), pp. 415430, 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 Scientists Warning (Basic Books,2004). His bioterror wager can be found at At the time of writing(December 15th 2005), Reess bet had logged 181 votes in its favour, to 190 against.

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    (3) Another approach to Doomsday treats technological progress as aPascalian Wager whose pay-offs include possible extinction.59 Stephen P. Stichcompares Pascalian with Bayesian threat-analyses for recombinant DNA tech-nology. He claims the former founder over the plethora of relevant alternativeswe 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 approximatedby 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 rare positive constants.) This model predicts human population will becomeinfinite (i.e. hit a singularity) on Friday 13th November, 2026. This model wasused by von Foersters critics as a lesson in the dangers of projecting fromdata. However, von Foerster seems to have laid more stress on predicting apopulation singularity, or discontinuity, rather than a literally infinitehumanity. However, whatever the likelihood of population-singularity in2026, von Foersters model apparently ceased to resemble our true populationcurve c. 1973.62

    (5) Not strictly DA as such, but still relevant to human prospects, are thefamilies of attempts to apply evolutionary modelling, game theory and dramatheory to Prisoners Dilemma analyses of international relations, nuclearcrises, etc.63.

    (6) Using Kolmogorovs axioms, Martin H. Krieger argues that Doom(personal, social or planetary extinction, for example), should receive eitherprobability 0 or 1.64 Alexander and Michael Scott use Kolmogorovs infinitycondition to criticize Kriegers notions of randomness and independence.65

    Krieger must, they say, either model behaviour in infinitely many humanagents or treat human behaviour as a Zeno supertask of random choices.

    6. Prospects for Doomsday

    If Doomsday doesnt intervene, DA will probably keep attracting refutations.One interesting endeavour might be to investigate how DA relates to differentmeasures of confirmation. As Bradley and Fitelsons confirmation-theoretic

    59. For a critique of Pascalian Wagers about extinction, see Neil A. Manson, The PrecautionaryPrinciple, the Catastrophe Argument and Pascals Wager, Ends and Means: Journal of theUniversity of Aberdeen Centre for Philosophy, Technology and Society, 4 (1999), available at:

    60. The Recombinant DNA Debate, Philosophy and Public Affairs, 7 (1978), pp. 187205.61. Heinz von Foerster, P.M. Mora and L.W. Amiot, Doomsday: Friday, November 13, 2026,

    Science 132 (1960), pp. 12911295 and Doomsday, Science, 133 (1961), pp. 936946.62. See J. Serrin, Is Doomsday on Target?, Science, 189 (1975), pp. 8688.63. 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. 187206 and 20753.

    64. Could the Probability of Doom be Zero or One?, The Journal of Philosophy, 92 (1995),pp. 382387.

    65. Taking the Measure of Doom, The Journal of Philosophy, 95 (1998), pp. 133141.

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    DA suggests, there may be different ways to employ Bayesian intuitions in DAcontexts. DAs plausibility (or otherwise) may prove to be measure-sensitive.

    Bostroms ultimate verdict on DA is that its reference-classes are too ill-defined to prompt any unambiguous moral. However, having made thisdiagnosis, he goes on to suggest ways of finessing and extending the notionof observer-relative chances. While Bostroms Simulation Argument uses aversion of SSA, Bostrom does not accept this version unreservedly. Instead,he sees it as a special case of a strengthened SSA which quantifies overobserver-moments, rather than observers. Indeed, he defines reference classesin terms of observer-moments: A reference class definition is a partition ofpossible observer-moments; each equivalence class in the partition is the ref-erence class for all the observer-moments included in it.66 Using BostromsSSSA, DA does not prompt any clear conclusions about humanitys expecta-tions. It seems clear that any neo-Doomsayer must pay heed to Bostromsreservations 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 manyworlds hypotheses in quantum mechanics, the apparent paradoxes of con-firmation theory and widely differing metaphysical hypotheses about mindand body. It might also be interesting to pursue the original anthropic invest-igations of our location in time that prompted Carters DA. So far, mostanthropic arguments about time have concentrated on DA but Carters rea-soning may have far wider applications. For all that its conclusions have oftenbeen strenuously resisted, DA has prompted searching examinations of prob-abilistic and anthropic reasoning, and the debates that it has engenderedlook far from being extinct just yet.

    66. Bostrom, Anthropic Bias, p. 181. See also pp. 15983 and 20205. As noted above, Nielsendefined his original DA reference-classes in terms of human-moments rather than birth-ranked humans.