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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 cla...