the doomsday argument

129

copy 2006 The Author Journal compilation copy 2006 Blackwell Publishing Ltd 9600 Garsington Road Oxford OX4 2DQ UK and 350 Main Street Malden MA 02148 USA

Blackwell Publishing LtdOxford UKPHIBPhilosophical Books0031-8051copy Blackwell Publishers Ltd 2006472

RECENT WORK

XXXX

THE DOOMSDAY ARGUMENT

The University of Edinburgh

1 Introduction Carter-Leslie Doomsday

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

The term lsquoDoomsday Argumentrsquo (lsquoDArsquo henceforth) was first proposed byFrank J Tipler John Leslie subsequently adopted and popularised lsquoDArsquo as ahandy shorthand name for a family of Bayesian arguments about our speciesrsquolikely survival prospects

1

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

2

andeven forms the basis of a science fiction novel

3

Unlike other arguments aboutthe future DA does not issue in a prophecy or straightforward projectionDA 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 Lesliersquos

The End of the World The Science and Ethics of HumanExtinction

(Routledge 1996) Lesliersquos other works that discuss or mention DA include lsquoRisking the Worldrsquos Endrsquo

Bulletin of the Canadian Nuclear Society

10 (1989) pp 10ndash15

Universes

(Routledge 1989) p 214 fn 1lsquoIs the End of the World Nighrsquo

The Philosophical Quarterly

40 (1990) pp 65ndash72lsquoDoomsday Revisitedrsquo


42 (1992) pp 85ndash9lsquoThe Doomsday Argumentrsquo

Mathematical Intelligencer

14 (1992) pp 48ndash51lsquoBayes Urns and Doomsdayrsquo

Interchange

23 (1992) pp 289ndash95lsquoTime and the Anthropic Principlersquo

Mind

101 (1992) pp 521ndash540lsquoDoom and Probabilitiesrsquo

Mind

102 (1993) pp 489ndash91lsquoMore About Doomrsquo

Mathematical Intelligencer

15 (1993) pp 5ndash7lsquoTesting the Doomsday Argumentrsquo

Journal of Applied Philosophy

11 (1994) pp 31ndash44lsquoObserver-Relative Chances and the Doomsday Argumentrsquo

Inquiry

40 (1997) pp 427ndash36lsquoOur Place in the Cosmosrsquo

Philosophy

75 (2000) pp 10ndash122 Eg Paul Daviesrsquo

About Time

(Penguin 1995 pp 258ndash64) 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 lsquothe Carter Catastrophersquo is the keystone of Stephen Baxterrsquos novel

Time Manifold 1

(HarperCollins 2000)

Philosophical Books Vol 47 No 2 April 2006 pp 129ndash142

130

copy 2006 The Author Journal compilation copy 2006 Blackwell Publishing Ltd

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 lsquoAnthropic Principlersquo to denote the inter-relationsbetween our existence as observers and the physical conditions we observe

4

Besides familiar anthropic topics like cosmic fine-tuning and Diracrsquos 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

5

Thepublished version of his lecture

6

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 lsquocut-off rsquo mightplay

7

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

8

If humanity survives and the all-time human total rises much higherour birth-ranks will be unusually early in human history ie 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 humansGranted some lsquolotteryrsquo assumptions our birth-ranks receive higher posteriorprobabilities with lsquoDoom Soonrsquo than they do with lsquoDoom Deferredrsquo

9

4 See lsquoLarge Number Coincidences and the Anthropic Principle in Cosmologyrsquo in MS Longair(ed)

Confrontation of Cosmological Theories With Observational Data

(Reidel 1974) pp 291ndash985 For more on Carterrsquos lsquocrucial stepsrsquo formula see John D Barrow and Frank J Tipler

TheAnthropic Cosmological Principle

(Oxford University Press 1986) pp 562ndash46 lsquoThe Anthropic Principle and its Implications for Biological Evolutionrsquo

Philosophical Transactionsof the Royal Society of London

Series A 310 1983 pp 347ndash63 Carter (ibid pp 358 ff) alsooffers anthropic explanations for why we observe neither advanced extra-terrestrials nornatural analogues of the wheel

7 Eg ldquoa man-made ecological disaster is an eventuality which might well be discussed withreference to the anthropic principlerdquo lsquoThe Anthropic Principle and Its Implicationsrsquo 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 lsquolotteryrsquo 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

i

conditional on the total population being

j

is equal to 1

j

where

i

le

j

and otherwise equals zero

131


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 Doommdashas in any subjectivist Bayesian argumentthe 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 lsquoDoomrsquo posteriorprobability if your lsquoDoomrsquo prior is non-negligible Even if DA increases yourprobability for Doom a thousand-fold this shouldnrsquot trouble you if yourprior for human extinction was only around one in ten billion say

Leslie often illustrates DA-reasoning with lsquoUrnrsquo stories Imagine your nameis written on a slip of paper and dropped into an urn Your prior probabilityfor the urn holding 10 names is 002 while your prior probability for itholding 1000 names is 098 Slips of paper are withdrawn from the urnwithout subsequently being replaced Your name appears on the third drawShould your name appearing so early in the draw affect your probabilitiesIf you assume the draw was random itrsquos easy to demonstrate that you shouldchange your probabilities Indeed Bayesrsquos Theorem suggests that your priorof 002 should yield to a posterior probability around 067

10

Oddly enough some DA variants started life as objections to DA Thusbegan the lsquoShooting Roomrsquo DA which Leslie first proposed as a problem forDA

11

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 simultaneouslyboth 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 alarming110 or a more comfortable 3536 Leslie says the answer hinges on thetruth or falsity of determinism if determinism is true your survival-chancesare 110 but if the world is significantly indeterministic your chances are 3536 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

12

10 Thus P(H|e) = (P(e|H)P(H))(P(e|H) P(H) + P(e|

not

H) P(|

not

H))Here P(H

|

e) = (002

times

03)((002

times

03) + (098

times

0003))

asymp

067 (Cf Leslie lsquoTime andthe Anthropic Principlersquo p 526)

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

The End of the World

pp 235ndash612 lsquoA Shooting-Room View of Doomsdayrsquo

Journal of Philosophy

94 (1997) pp 244ndash59 Eckhardtalso accuses DA-reasoning (a) of conflating Bayesrsquos Theorem with Bayesianism and (b) of

always

increasing any (non-extreme) probability for extinction

132


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 importantdifferences from it Nielsenrsquos investigation into random dynamics

14

led him toconsider the notion of random location in time In particular he consideredthe pair ltnow yougt as randomly selected from all the lsquohuman momentsrsquothere will be Assuming the total of humans will be finite

15

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 Nielsenrsquos 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

16

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 ltnow megt pairing is atypical

Paul Franceschi claims to have a third form of DA whose method ofpopulation-sampling differs from both Carter-Leslie lsquoUrnrsquo and EckhardtSowers lsquoball dispenserrsquo versions

17

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 Franceschirsquos diagnosis of DA is that neither scenario above strikes theright balance between temporal and atemporal population-sampling Insteadhe proposes that something like either sampling method could apply to oursituation so that a DA probability-shift

might

be possible Thus Franceschirsquoslsquothird routersquo uncertainty as to how our birth-ranks are assigned means DABayesian shifts are permissible but non-obligatory

13 lsquoRandom Dynamics and Relations between the Number of Fermion Generations and the FineStructure Constantrsquo

Acta Physica Polonica

Series B 20 (1989) pp 427ndash68 (SPIRES HEPreprint at httpwwwslacstanfordeduspiresfindhepwwwindexer=1amprawcmd=find+j+APPOAB20427)

14 Ie that naturersquos fundamental laws are of such complexity that they can be treated as

de facto

random15 Nielsen makes this stipulation so we can take a Lebesque measure on our class of person-

moments16 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 double17 See Franceschi lsquoA Third Route to the Doomsday Argumentrsquo original (2003) preprint at

httpcogprintsorg2990 later (2005) preprint at httpcogprintsorg4519 See alsoWilliam Eckhardt lsquoProbability Theory and the Doomsday Argumentrsquo

Mind

102 (1993)pp 483ndash88 and George F Sowers Jr lsquoThe Demise of the Doomsday Argumentrsquo

Mind

111(2002) pp 37ndash45 NB the latter do not accept DA and offer their alternative birth-rankmechanisms as

objections

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

133


J Richard Gott III has proposed a lsquodelta

t

rsquo DA using the CopernicanPrinciple of Mediocrity

18

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 beUsing the usual 95 confidence interval deployed in scientific contextsGott argues there is a 95 chance we are not observing human historyfrom within its first (or last) 25 Thus humanityrsquos future should be between139

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 ofwhich he observed in 1969) If humanityrsquos past

asymp

200000 years Gott suggestswe can be 95 confident humanity will last another 5100 to (78

times

10

6

) moreyears Some critics find this too broad-brush a prediction and think Gottrsquosmethod 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 priorprobabilities for his argument and (b) ignoring a significant constraint on ourprior probabilities for duration ie 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 lsquovague priorrsquoP(N) = kN where N is the all-time total of humans and k is a normalizingconstant

21

Bradley Monton and Sherrilyn Roush

22

charge Gottrsquos 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 Gottrsquos method topple into self-contradiction

23

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

24

18 Gottrsquos DA was first presented in lsquoImplications of the Copernican Principle for Our FutureProspectsrsquo

Nature

363 (1993) pp 315ndash9 He offered some replies to objections in lsquoFutureProspects Discussed Gott Repliesrsquo

Nature

368 (1994) p 108 A popular exposition of GottrsquosDA appears in his book

Time Travel in Einsteinrsquos Universe

(Houghton Mifflin 2001)19 For this and other objections to Gott see Carlton M Cavesrsquo lsquoPredicting Future Duration from

Present Age A Critical Assessmentrsquo

Contemporary Physics

41 (2000) pp 143ndash153 archivedby

arXivorg

at httparxivorgpdfastro-ph0001414 Cavesrsquo paper ends with a challengeto Gott to test the lsquodelta

t

rsquo argument with a $1000 bet on the longevity of a sample of dogs20 lsquoThe Doomsday Argument and the Number of Possible Observersrsquo


52 (2002) pp 164ndash84 at pp 174ndash79

21 Lesliersquos 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 onersquos priorprobability for extinction sufficiently low onersquos probability for extinction might still be loweven after using Lesliersquos DA

22 lsquoGottrsquos Doomsday Argumentrsquo at httpphilsci-archivepitteduarchive0000120501gott1fpdf

23 lsquoA Probable Paradoxrsquo

Nature

389 (1997) p 77924 lsquoHow to Predict Future Duration from Present Agersquo


56 (2006)pp 16ndash38

134


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 ldquoGiven twentyseconds many people believe they have found crushing objections to Carterrsquosline of thoughtrdquo

25

Some can be dealt with quite quickly Many people belietheir own uniqueness by protesting lsquoBut Irsquom uniquersquo on first hearing DADoomsayers can reply lsquoYou are unique but it is not an explanatory desider-atum that you appear improbablersquo 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 lsquoontological proof rsquo 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 DArsquos anthropic appeal to our location as observers Likewise DArequires no commitment to lsquofour-dimensionalismrsquo about time rather thanpresentismmdashDA is

not

meant to address the question lsquoWhy is it this moment

now

rsquo but rather lsquoWhy are we alive with this segment of humanityrsquo Carterand Leslie are not pondering whether or not they lived c 2000

mdashratherDA invites us to consider where creatures like ourselves are

likely

to be Asample of major objections follows

A hardy perennial is the lsquoNeanderthalrsquo or lsquoancient Romanrsquo objection ieearlier observers could have used DA to reach an erroneous result Any earlierDA must have failed so itrsquos likely present-day DA will too We might beunlucky enough to be the unique generation of correct Doomsayers but weshouldnrsquot think thus of ourselves Leslie offers several replies to this objection(of varying plausibility) (1) Any probabilistic reasoning will fail for someonewho is improbably locatedmdashprior to the result being announced the eventualwinner of a million-ticket lottery should still rationally expect to lose

26

(2)Perhaps the preponderance of moments in history where DA fails could beoffset by the number of successful users of DA ldquoReasoning which lsquofailedrsquo 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 extinctrdquo27 (3) nocave man shared the Earth with six billion contemporaries plus H-bombsozone depletion and biological weapons (4) Maybe not all earlier applicationsof DA were wrong after all28

In a meta-inductive spin on lsquocave manrsquo objections Kevin Korb and JonathanJ Oliver invoke a targeting truth (TT) principle ldquono good inductive method

25 lsquoTime and the Anthropic Principlersquo p 52826 ldquoIt would not be a defect in probabilistic reasoning if it encouraged an erroneous conclusion

in the mind of someone who happened to be improbably situatedrdquo (Torbjoumlrn TaumlnnsjoumllsquoDoom Soonrsquo Inquiry 40 (1997) pp 243ndash52) at p 247)

27 Leslie The End of the World p 23 original emphasis28 ldquoAny 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 timesrdquo (The Endof the World p 205)

135


shouldmdashin this worldmdashprovide no more guidance to the truth than doesflipping a coinrdquo29 They argue that if ldquothe total population is bounded bytwo times the sample value then 499 inferences using the Doomsdayargument are wrong and 501 inferences are rightrdquo hence ldquoin a perfectlyreasonable metainduction we should conclude that there is something verywrong with this form of inferencerdquo30 Bostrom replies (a) odds of 501499 arestill better than 5050 and (b) we can easily run DA with a bounded value threeor more times the sample-size31 Korb and Oliver retort DArsquos success-ratecan be made arbitrarily small ldquosimply by increasing the population size in theexamplerdquo32 and that DA-inferences tend asymptotically to a success-rate nobetter than random

Bostrom argues that itrsquos a mistake to read the conclusion of DA as neces-sarily implying human extinction33 Instead he maintains even if DA succeedsit 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 lsquoDoomSoonrsquo 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 DArsquos 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 lsquosupernovarsquo objection alleges that DA seemingly grants us paranormalpowers such as non-local and retroactive causation34 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 doesnrsquot occur then neither will the crashcolonization programme) Thus if DA gives us reason to think wersquore latehumans it also gives us reason to believe the supernova wonrsquot occur or hasnrsquotoccurred We seemingly have some paranormal non-local connection withevents outside our direct causal control or events that have already occurredHowever 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 event35

29 Korb and Oliver lsquoA Refutation of the Doomsday Argumentrsquo Mind 107 (1998) pp 403ndash410 at p 404

30 lsquoA Refutation of the Doomsday Argumentrsquo p 40531 See Bostromrsquos lsquoThe Doomsday Argument is Alive and Kickingrsquo Mind 108 (1999) pp 539ndash550

Also Nick Bostromrsquos PhD dissertation Observational Selection Effects and Probability (LSE 2000)(Chapter 6) pp 121ndash122) available at httpwwwanthropic-principlecomphd The TTobjection is also discussed in the (substantially expanded) book-version of Bostromrsquos PhDAnthropic Bias Observation Selection Effects in Science and Philosophy (Routledge 2002) pp 109ndash110

32 Korb and Oliver lsquoComment on Nick Bostromrsquos ldquoThe Doomsday Argument is Alive andKickingrdquorsquo Mind 108 (1999) pp 551ndash553 at p 551

33 Anthropic Bias pp 107ndash0834 See Olum lsquoThe Doomsday Argument and the Number of Possible Observersrsquo pp 172ndash7335 lsquoThe Doomsday Argument Adam and Eve UN++ and Quantum Joersquo Synthese 127 (2001)

pp 359ndash387

136


Surely the Urn model fallaciously reduces all possible human futures totwo artificial scenarios36 This objection may mistake a pedagogical devicefor part of DArsquos logical and probabilistic scaffolding The Urn model can workwith many urns of widely differing sizes We neednrsquot 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 cases37

Carter and Lesliersquos 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 lsquoDeath Soonrsquo makes your presentlocation more probable than lsquoDeath Laterrsquo and you should not expect tocomplete this article38 However this lsquolongevityrsquo 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 lsquono outsiderrsquo requirement ie that in applying the samplingintuitions behind DA ldquothere must be no outsidersmdashbeings who are ignoredin the reasoning but who really belong in the reference classrdquo39 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 thelsquoUssherian Corollaryrsquo after Bishop Ussherrsquos demonstration that Creationoccurred in 4004 He says the Urn Model can equally generate a lowprobability for an old human race so DA ldquoentails a parallel Ussherian moralthat we have systematically underestimated the chance that the human racebegan fairly recentlyrdquo40 Even if we grant Chambers that his UssherianCorollary and DA are probabilistically symmetrical this symmetry is morethan offset by a glaring evidential asymmetry Chambersrsquos 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 lsquoDoom Soonrsquo shift The idea is this if we consider only

36 ldquoWe 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 lsquoharmless simplificationrsquo which better revealsthe logic of the argumentrdquo (Korb and Oliver lsquoA Refutation of the Doomsday Argumentrsquop 407)

37 lsquoNo One Knows the Date or the Hour an Unorthodox Application of Rev Bayesrsquos TheoremrsquoPhilosophy of Science (Proceedings) 66 (1999) Supplementary volume pp 339ndash53 352

38 Seemingly first developed in J-P Delahayersquos lsquoRecherche de Modegraveles pour lrsquoArgument delrsquoApocalypse de Carter-Lesliersquo unpublished MS A version of this objection is also given byKorb and Oliver lsquoA Refutation of the Doomsday Argumentrsquo p 405

39 Anthropic Bias p 11240 lsquoDo Doomsdayrsquos Proponents Think We Were Born Yesterdayrsquo Philosophy 76 (2001) pp 443ndash

50 at p 446

137


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 DAldquoOne should reason as if one were a random sample from the set of allobservers in onersquos reference classrdquo41 On the other we have the Self-IndicationAssumption (SIA) ldquoGiven the fact that you exist you should (other thingsequal) favour hypotheses according to which many observers exist overhypotheses on which few observers existrdquo42 Its exponents claim invoking SIAmeans lsquoDoom Soonrsquo is offset by the fact that our existing at all favours lsquoDoomLaterrsquo Paul Bartha and Christopher Hitchcock think DA can be evaded if wetake into account the probability of our own existence43 While they grant thatit seems odd to discus the probability of something we know occurred andabout which scepticism seems impossible (ie the fact we exist) giving a prob-ability to our own existence is perfectly permissible and invites a variant ofthe lsquohypothetical priorsrsquo solution to the traditional lsquoproblem of old evidencersquo44

There seems to be a consensus that invoking SIA will successfully nullifythe lsquoDoom Soonrsquo 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 absurditiesHowever Bostrom for example has notably insisted that SIA leads to allmanner of counter-intuitive consequences if applied alone45

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 Bostromrsquos criticisms) Montonrsquos DA runs thus let lsquoH1rsquo and lsquoH2rsquo betwo population hypotheses such that H1 lt H2

46 Furthermore let lsquoK rsquo stand

41 Nick Bostrom and Milan M Cirkovic lsquoThe Doomsday Argument and the Self-IndicationAssumption Reply to Olumrsquo The Philosophical Quarterly 53 (2003) pp 83ndash91 at p 84

42 Bostrom Anthropic Bias p 66 Bostrom says a version of SIA (albeit not under this name) firstappeared in Dennis Dieksrsquos lsquoDoomsdaymdashor the Dangers of Statisticsrsquo The PhilosophicalQuarterly 42 (1992) pp 78ndash85 Another version appears in Tomaacutes Kopf Pavel Krtous andDon N Page lsquoToo Soon for Doom Gloomrsquo archived by arXivorg at httparxivorgabsgr-qc9407002 Interestingly the Kopf (et al) version of SIA refers to ldquoThe 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 historyrdquo (lsquoToo Soon for Doom Gloomrsquo p 7emphasis added)

43 lsquoNo One Knows the Date or the Hourrsquo passim44 For both the lsquoold evidencersquo problem and its lsquohypothetical priorsrsquo solution see Colin Howson and

Peter Urbach Scientific Reasoning The Bayesian Approach (Open Court 2nd edn 1993) pp 403 ff45 See Bostromrsquos lsquoPresumptuous Philosopherrsquo thought-experiment Anthropic Bias pp 124 ff

Bostrom also rebuts charges that SSA leads to conflicts with Lewisrsquos Principal Principle(ibid pp 141ndash58)

46 Montonrsquos H1and H2 have total human populations of 200 billion and 200 trillion with priorsof 005 and 095 respectively see lsquoThe Doomsday Argument Without Knowledge of BirthRankrsquo The Philosophical Quarterly 53 (2003) pp 79ndash82 at p 80

138


for the proposition that someone has property k where k is a property unlikelyto have multiple instantiations47 P(K ) is independent of whether H1 or H2

obtains ie K is not conditional on overall population-size If lsquoMrsquo is the pro-position that I have property k and I know M it follows that P(M | H1) gtP(M | H2) for any values of H1 or H2 Montonrsquos conclusions have beenresisted DJ Bradley claims Montonrsquos DA implicitly relies on birth-rankinformation and that no suitable alternative property has been proposed48

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 Hempelrsquos paradox of the ravens In bothcases he maintains the problem arises through lack of an objective criterionfor determining the proper reference class50

Bostromrsquos 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 computers51 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 LestBostromrsquos reasoning sound too much like a version of DA itrsquos important tonote that Bostrom argues that DA uses a flawed overly-ambitious indifferenceprinciple ie 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 Bostromrsquos Simulation Argumentuses a lsquobland principle of indifferencersquo (BPI) which counsels ldquoindifference

47 Eg ldquobeing alone in 323 Main Street in Lexington Kentucky from 2041 to 2042 GMTon April 9 2002rdquo (ibid)

48 lsquoNo Doomsday Argument Without Knowledge of Birth Rank A Defense of BostromrsquoSynthese 144 (2005) pp 91ndash100

49 lsquoComment lrsquoUrne de Carter et Leslie se Deacuteverse dans Celle de Hempelrsquo The Canadian Journalof Philosophy 29 (1999) pp 139ndash156 Also in translation as lsquoThe Doomsday Argument andHempelrsquos Problemrsquo at httpwwwanthropic-principlecompreprintsfrafranceschihtml

50 See also Franceschirsquos lsquoUne Solution pour lrsquoArgument de lrsquoApocalypsersquo Canadian Journal ofPhilosophy 28 (1998) pp 227ndash46 Also relevant to Franceschirsquos DA is his lsquoUne Solution pourle Paradoxe de Goodmanrsquo Dialogue 40 (2001) pp 99ndash123 English translation at httpcogprintsorg2176

51 See lsquoAre We Living in a Computer Simulationrsquo The Philosophical Quarterly 53 (2003) pp 243ndash55First presented in lsquoAre You Living in a Computer Simulationrsquo 2001 at httpwwwsimulation-argumentcomclassicpdf See also Bostromrsquos popular exposition in lsquoThe SimulationArgument Why the Probability that You Are Living in a Matrix is Quite Highrsquo Times HigherEducation Supplement May 16th 2003 at httpwwwsimulation-argumentcommatrixhtml

139


only between hypotheses about which observer one is when one has noinformation about which of these observers one isrdquo52 If we think a fraction xof all minds are computer-simulations and our experiential content might bethe same whether we are simulations or not Bostromrsquos BPI suggests that ourcredence for our being simulation minds should equal x53

Perhaps the most ambitious attempt at offering a new diagnosis and rebuttalof DA while also newly applying the probabilistic intuitions behind DA comesfrom John FG Eastman54 Eastmanrsquos 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 lifetimeon 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 lsquomany worldsrsquo quantum superposition of individuallydeterministic lsquoquasi-classicalrsquo 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

Irsquove 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 Descartesrsquos 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 DA55

Darren Bradley and Branden Fitelson outline a posterior-probabilisticlsquolotteryrsquo DA They suggest that such lsquolotteryrsquo DArsquos 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 lsquolotteryrsquo DA of limited appeal they suggest ways to create a more robust

52 lsquoAre We Living in a Computer Simulationrsquo p 25053 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 assumptionsSee his lsquoAre You a Simrsquo The Philosophical Quarterly 53 (2003) pp 425ndash31 But see alsoBostromrsquos lsquoThe Simulation Argument Reply to Weathersonrsquo The Philosophical Quarterly 55(2005) pp 90ndash97

54 lsquoThe Doomsday Argument Consciousness and Many Worldsrsquo General Relativity and QuantumCosmology archived at httparxivorgabsgr-qc0208038

55 Alasdair Richmond lsquoImmortality and Doomsdayrsquo American Philosophical Quarterly 41 (2004)pp 235ndash247

140


confirmation-theoretic DA that skirts many obstacles that face traditionalposterior-probabilistic formulations56 They argue that DA can be betterexpressed using ratios of likelihoods rather than ratios of posterior probabilitiesOn 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 lsquoPrinciple of Indifferencersquo 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 lsquoMonty Hallrsquo problem (In this case the doors lsquoMontyHallrsquo opens are treated like DArsquos birth-ranked humans) Thus the oft-contestedconclusion that you should switch your choice of doors in the Monty Hallproblem (after the gamersquos host has eliminated one possibility) receives supportfrom an unexpected quarter However a direct challenge to DA likelihoodndashratio arguments comes from Elliot Sober ldquoThoroughly 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 probablerdquo57 Soberrsquos 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 doesnrsquot say

(1) Besides expounding DA Lesliersquos 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 outreacute dangers ranging from vacuum metastability disastersthrough to Schopenhauerian pessimism and moral relativism (At leasttime has taken Y2K bugs off Lesliersquos 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 ldquoBy2020 bioterror or bioerror will lead to one million casualties in a singleeventrdquo Taking all likely threats into account he thinks we have only a 05chance of surviving the 21st century58

56 lsquoMonty Hall Doomsday and Confirmationrsquo Analysis 63 (2003) pp 23ndash3157 lsquoAn Empirical Critique of Two Versions of the Doomsday ArgumentmdashGottrsquos Line and

Lesliersquos Wedgersquo Synthese 135 (2003) pp 415ndash430 at p 42458 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 Scientistrsquos Warning (Basic Books2004) His bioterror wager can be found at httpwwwlongbetsorg At the time of writing(December 15th 2005) Reesrsquos bet had logged 181 votes in its favour to 190 against

141


(3) Another approach to Doomsday treats technological progress as aPascalian Wager whose pay-offs include possible extinction59 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 use60

(4) Heinz von Foerster et al61 treat population-growth as approximatedby the two-body collision equation so birth-rate is proportional to total popu-lation dPdt = kP1+r (P and t are population and time respectively k and rare positive constants) This model predicts human population will becomeinfinite (ie hit a singularity) on Friday 13th November 2026 This model wasused by von Foersterrsquos 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 Foersterrsquos model apparently ceased to resemble our true populationcurve c 197362

(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 lsquoPrisonersrsquo Dilemmarsquo analyses of international relations nuclearcrises etc63

(6) Using Kolmogorovrsquos axioms Martin H Krieger argues that Doom(personal social or planetary extinction for example) should receive eitherprobability 0 or 164 Alexander and Michael Scott use Kolmogorovrsquos infinitycondition to criticize Kriegerrsquos notions of randomness and independence65

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 doesnrsquot intervene DA will probably keep attracting refutationsOne interesting endeavour might be to investigate how DA relates to differentmeasures of confirmation As Bradley and Fitelsonrsquos confirmation-theoretic

59 For a critique of Pascalian Wagers about extinction see Neil A Manson lsquoThe PrecautionaryPrinciple the Catastrophe Argument and Pascalrsquos Wagerrsquo Ends and Means Journal of theUniversity of Aberdeen Centre for Philosophy Technology and Society 4 (1999) available at httpwwwabdnacukphilosophyendsandmeansvol4no1mansonshtml

60 lsquoThe Recombinant DNA Debatersquo Philosophy and Public Affairs 7 (1978) pp 187ndash20561 Heinz von Foerster PM Mora and LW Amiot lsquoDoomsday Friday November 13 2026rsquo

Science 132 (1960) pp 1291ndash1295 and lsquoDoomsdayrsquo Science 133 (1961) pp 936ndash94662 See J Serrin lsquoIs Doomsday on Targetrsquo Science 189 (1975) pp 86ndash8863 See eg Robert Axelrod The Evolution of Co-operation (Basic Books 1984) and Nigel Howard

lsquoDrama Theory and Its Relationship to Game Theoryrsquo Group Decision and Negotiation 3 (1994)pp 187ndash206 and 207ndash53

64 lsquoCould the Probability of Doom be Zero or Onersquo The Journal of Philosophy 92 (1995)pp 382ndash387

65 lsquoTaking the Measure of Doomrsquo The Journal of Philosophy 95 (1998) pp 133ndash141

142


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

Bostromrsquos 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 Bostromrsquos Simulation Argument uses aversion of SSA Bostrom does not accept this version unreservedly Insteadhe 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 ldquoA 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 itrdquo66 Using BostromrsquosSSSA DA does not prompt any clear conclusions about humanityrsquos expecta-tions It seems clear that any neo-Doomsayer must pay heed to Bostromrsquosreservations 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 SSAAny conclusion to this debate might prove to have far-reaching consequencesAs noted above attempts have been made to apply DA intuitions to lsquomanyworldsrsquo 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 Carterrsquos DA So far mostanthropic arguments about time have concentrated on DA but Carterrsquos 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 159ndash83 and 202ndash05 As noted above Nielsendefined his original DA reference-classes in terms of human-moments rather than birth-ranked humans

130


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 lsquoAnthropic Principlersquo to denote the inter-relationsbetween our existence as observers and the physical conditions we observe

4

Besides familiar anthropic topics like cosmic fine-tuning and Diracrsquos 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

5

Thepublished version of his lecture

6

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 lsquocut-off rsquo mightplay

7

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

8

If humanity survives and the all-time human total rises much higherour birth-ranks will be unusually early in human history ie 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 humansGranted some lsquolotteryrsquo assumptions our birth-ranks receive higher posteriorprobabilities with lsquoDoom Soonrsquo than they do with lsquoDoom Deferredrsquo

9

4 See lsquoLarge Number Coincidences and the Anthropic Principle in Cosmologyrsquo in MS Longair(ed)

Confrontation of Cosmological Theories With Observational Data

(Reidel 1974) pp 291ndash985 For more on Carterrsquos lsquocrucial stepsrsquo formula see John D Barrow and Frank J Tipler

TheAnthropic Cosmological Principle

(Oxford University Press 1986) pp 562ndash46 lsquoThe Anthropic Principle and its Implications for Biological Evolutionrsquo

Philosophical Transactionsof the Royal Society of London

Series A 310 1983 pp 347ndash63 Carter (ibid pp 358 ff) alsooffers anthropic explanations for why we observe neither advanced extra-terrestrials nornatural analogues of the wheel

7 Eg ldquoa man-made ecological disaster is an eventuality which might well be discussed withreference to the anthropic principlerdquo lsquoThe Anthropic Principle and Its Implicationsrsquo 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 lsquolotteryrsquo 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

i

conditional on the total population being

j

is equal to 1

j

where

i

le

j

and otherwise equals zero

131





10


11


12


not

H) P(|

not

H))Here P(H

|

e) = (002

times

03)((002

times

03) + (098

times

0003))

asymp







always


132




13


14


15



16



17


only then


might






de facto





Mind


Mind


objections


133



t


18


th


asymp


times

10

6


19

Ken D Olum

20


21


22


23


24


Nature


Nature







arXivorg


t







Nature



56 (2006)pp 16ndash38

134




25


not


now



likely



26







135










pp 359ndash387

136










50 at p 446

137












138












139














140










141















142






131





10


11


12


not

H) P(|

not

H))Here P(H

|

e) = (002

times

03)((002

times

03) + (098

times

0003))

asymp







always


132




13


14


15



16



17


only then


might






de facto





Mind


Mind


objections


133



t


18


th


asymp


times

10

6


19

Ken D Olum

20


21


22


23


24


Nature


Nature







arXivorg


t







Nature



56 (2006)pp 16ndash38

134




25


not


now



likely



26







135










pp 359ndash387

136










50 at p 446

137












138












139














140










141















142






132




13


14


15



16



17


only then


might






de facto





Mind


Mind


objections


133



t


18


th


asymp


times

10

6


19

Ken D Olum

20


21


22


23


24


Nature


Nature







arXivorg


t







Nature



56 (2006)pp 16ndash38

134




25


not


now



likely



26







135










pp 359ndash387

136










50 at p 446

137












138












139














140










141















142






133



t


18


th


asymp


times

10

6


19

Ken D Olum

20


21


22


23


24


Nature


Nature







arXivorg


t







Nature



56 (2006)pp 16ndash38

134




25


not


now



likely



26







135










pp 359ndash387

136










50 at p 446

137












138












139














140










141















142






134




25


not


now



likely



26







135










pp 359ndash387

136










50 at p 446

137












138












139














140










141















142






135










pp 359ndash387

136










50 at p 446

137












138












139














140










141















142






136










50 at p 446

137












138












139














140










141















142






137












138












139














140










141















142






138












139














140










141















142






139














140










141















142






140










141















142






141















142






142






the doomsday argument

Documents