observer‐relative chances and the doomsday argument

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This article was downloaded by: [York University Libraries] On: 14 November 2014, At: 14:59 Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Inquiry: An Interdisciplinary Journal of Philosophy Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/sinq20 Observerrelative chances and the doomsday argument John Leslie a a Department of Philosophy , University of Guelph , Guelph, Ontario, NIG 2W1, Canada Published online: 29 Aug 2008. To cite this article: John Leslie (1997) Observerrelative chances and the doomsday argument, Inquiry: An Interdisciplinary Journal of Philosophy, 40:4, 427-436, DOI: 10.1080/00201749708602461 To link to this article: http://dx.doi.org/10.1080/00201749708602461 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

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Page 1: Observer‐relative chances and the doomsday argument

This article was downloaded by: [York University Libraries]On: 14 November 2014, At: 14:59Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

Inquiry: An Interdisciplinary Journal of PhilosophyPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/sinq20

Observer‐relative chances and the doomsday argumentJohn Leslie aa Department of Philosophy , University of Guelph , Guelph, Ontario, NIG 2W1, CanadaPublished online: 29 Aug 2008.

To cite this article: John Leslie (1997) Observer‐relative chances and the doomsday argument, Inquiry: An InterdisciplinaryJournal of Philosophy, 40:4, 427-436, DOI: 10.1080/00201749708602461

To link to this article: http://dx.doi.org/10.1080/00201749708602461

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in thepublications on our platform. However, Taylor & Francis, our agents, and our licensors make no representationsor warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Anyopinions and views expressed in this publication are the opinions and views of the authors, and are not theviews of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should beindependently verified with primary sources of information. Taylor and Francis shall not be liable for any losses,actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoevercaused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Page 2: Observer‐relative chances and the doomsday argument

Inquiry, 40, 427-36

Observer-relative Chances and theDoomsday Argument

John LeslieUniversity of Guelph

Suppose various observers are divided randomly into two groups, a large and asmall. Not knowing into which group anyone has been sent, each can have stronggrounds for believing in being in the large group, although recognizing that everyobserver in the other group has equally powerful reasons for thinking of this othergroup as the large one. Justified belief can therefore be observer-relative in a ratherparadoxical way. Appreciating this allows one to reject an intriguing new objectionagainst Brandon Carter's 'doomsday argument'. Carter encourages us to doubt thatwe are among only the first hundredth, say, or first millionth, of all humans who willever have existed. He thereby reinforces whatever reasons we may have forsuspecting that, unless we take great care, the human race will not survive long.Admittedly his argument is weakened if our world is indeterministic, so that there isno suitably guaranteed 'fact of the matter' of how many humans will ever haveexisted. But even then, it can caution us against believing that a lengthy future forhumankind 'is as good as determined'. Of all the objections the argument has yetfaced, the new one is the most interesting.

Perhaps the human race will not exist for much longer. For one thing,population growth is moving the biosphere towards a pollution crisis. Therisk of human extinction can seem all too clear. Risks, however, are mattersof probability, and probability theory is full of traps. Perhaps the best way toavoid them is to consider simple stories about tossed coins, groups of varioussizes experiencing various things, and suchlike.

A hundred women are blindfolded. Selected at random, five form a firstgroup, and the ninety-five others a second. Each woman knows this, but notwhich group she is in. Suppose, though, that you are one of them. Veryprobably your group is larger: the odds in favour of it are ninety-five to five.

However, how do matters look to some woman in the other group? In hereyes, the odds are ninety-five to five that her group is larger.

You will have to say to yourself: 'All in the other group have strongevidence, just as powerful as my own evidence for thinking my group larger,for thinking theirs larger; yet even so, I'm virtually certain they are wrong.'Now, may this not seem a trifle odd? Just by increasing the size of the largergroup, we can construct a case in which you could be 99.99999 per cent surethat your group was larger, although thinking that people in the other groupwho were 99.99999 per cent sure that theirs was larger had evidence andreasons entirely as good as yours.

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Matters could come to look still odder. Imagine that some man, let us callhim 'the external observer', learns just that there are these two groups ofninety-five and five, and that one of them taken at random was named 'theHeads group' when a tossed coin fell Heads, its partner then automaticallybeing called 'the Tails group'. Nobody informs him or any of the womenwhether it was the large or the small group which became the Heads group.Can he tell which group is probably the larger? Clearly not, granted that heknows that no bias could have entered into the naming. (The coin was fair.The naming process took account simply of how the coin landed, and not ofeach group's size.) He can reflect that every woman in the Heads group hasexcellent grounds for thinking that hers is the larger group. But the groundsare of no use to him personally, for he must see that members of the Tailsgroup can point to equivalent grounds for thinking theirs the larger.

The situation, then, is as follows. All these persons - the women in theHeads group, those in the Tails group, and the external observer - are fullyaware that there are two groups, and that each woman has a ninety-five percent chance of having entered the larger. Yet the conclusions they ought toderive differ radically. The external observer ought to conclude that theprobability is fifty per cent that the Heads group is the larger of the two. Anywoman actually in the Heads group, however, ought to judge the oddsninety-five to five that her group, identified as 'the group I am in', is thelarger, regardless of whether she has been informed of its name. (Herestimated odds for 'the size of the group I am in' ought to be the same even ifshe thought the information wrong. Bear in mind always that the names wereallocated without taking account of group sizes, and that only the coin tosserknows whether the large group or the small group became the Heads group.)Similarly, any woman in the Tails group ought to judge the odds ninety-fiveto five that the group she is in is the larger one. Now, may this not disprovethe commonly accepted thesis that estimated probabilities should be basedon available evidence?

Not so. Each woman can do something which the external observercannot. Although fully aware that each group contains people who can say 'Ipersonally am in one group or the other', the external observer cannothimself say this. His own evidence cannot include evidence of being himselfone of the hundred women. Hence none of it can be evidence specially likelyto have been acquired from inside the larger group. But part of eachwoman's evidence is indeed specially likely to have been acquired there. Theevidence in question is of being in a group. Sure enough, some women'sevidence of being in a group will be evidence possessed inside the group ofonly five; but as a woman among the hundred you can say 'I personally amvery unlikely to be one of those five'.

Any air of paradox must not prevent our accepting these things. True, anyreasons one possesses for thinking one's blindfolded self in the group of

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Observer-relative Chances and the Doomsday Argument 429

ninety-five must be reasons which are possessed by everybody among thefive; yet we must not jump to the conclusion that, after all, each womanshould judge the odds fifty-fifty that she is in the larger group. The odds areinstead ninety-five to five; for if every woman were to think herself in thegroup of ninety-five, then five of them would be wrong, ninety-five of themright.

In effect, each can treat herself as a sample drawn at random from thehundred. A few such samples would be unrepresentative. Coming from thegroup of five, they would mislead anyone who thought otherwise. If the Tailsgroup is actually the larger, then the women in the Heads group would besadly misled in concluding that theirs was the larger. But the reasoningcarrying them to their conclusion would not be poor reasoning. It wouldmislead a mere five women. For the ninety-five others it would deliver thecorrect result. (Yet is this truly so regardless of whether any woman learnsthe name of her group"? Indeed it is. For suppose, for argument's sake, thatlearning the name of one's group justified re-estimating the probability of itsbeing the larger one as only fifty per cent, in agreement with the externalobserver's estimate. It would follow, for a start, that if all the women learnedthe names of their groups, and if each woman were forced to guess whetherhers was the larger group or the smaller, then they might just as well all say'the smaller'; but then, unfortunately, ninety-five would have guessedwrongly, and only five rightly. Next, since the re-estimate of 'only fifty percent', or any other re-estimate, would, if justified at all, be equally justifiedno matter what one learned about the name of one's group, it would furtherfollow that this re-estimate could be made even before learning the name;but this conflicts with the fact that one ought, before learning the name ofone's group, to be rather confident that it was the larger of the two.Remember, though, that nothing important hangs on whether any womanever learns her group's name. Even without knowing her group's name, awoman could still appreciate that the external observer estimated its chanceof being the larger one as only fifty per cent - this being what his evidenceled him to estimate in the cases of both groups. The paradox is that sheherself would then have to say: 'In view of my evidence of being in one ofthe groups, ninety-five per cent is what I estimate.')

The external observer, although he knows all about the evidence which thewomen have in their possession - so that there is at least some sense inwhich he can say that he 'shares' all of this evidence - really can be regardedas deprived of useful information which each of them possesses, informationwhich can be treated as the equivalent of having sampled the hundredrandomly: the information, that is to say, that one is oneself among thehundred. It should be unsurprising, therefore, that he has no way of tellingwhich group is probably the larger. The situation could be very different if,for instance, he had known in advance that he would get information from

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just one of the women, Kate, who had been specified before the hundred hadbeen divided into the two groups. Evidently Kate would have been likely toenter the larger group. If Kate then phoned him that she had learned hers wasthe Heads group, he could conclude rather confidently that the Heads groupwas the larger. His being external to the two groups would no longer matter.As things stand, in contrast, he is at a loss. In imagination he can follow theentire process of being oneself blindfolded, of being told about the divisioninto groups of ninety-five and five, of being pushed into a group, and ofconcluding that this group is very probably the larger of the two. Yet all thisis useless to him.

Consider next a story about a lottery. The winner would be selected atrandom from among all who troubled to fill in a lengthy form. With thesuspicion that few would bother, Mr Smith filled in the form himself, andwon. Although his suspicion was not thereby proved correct, Mr Smith'sfaith in it rightly became greater.

People sometimes protest that somebody or other would have to have wonthe lottery, no matter how many had entered it. I suspect that their reasoningruns roughly as follows. The fact that someone had actually won, and was'me' to that person, ought to have no effect on an impartial externalobserver's estimate of the probability that there were only a few entrants, forit was known from the start that there would be some joyful 'me'. Well, twoconflicting probability estimates, if based on the very same evidence, cannotboth be right. As the external observer would have no cause to be impressedby the fact that somebody or other'had won, not even if able to see just whothis person was, it follows that the somebody or other in question wouldequally have no cause to be impressed by having won.

As can now be appreciated, this is faulty reasoning. It forgets that MrSmith, unlike any external observer, could justifiably treat himself as asample drawn at random from among all those who hoped to win.

Sure enough, there is some air of paradox here. Somebody or other wins alottery, at once becoming more confident than before that the number ofnames in the urn was small. The external observer, learning that somebodyor other has won and that this person has altered his or her degree ofconfidence, experiences no parallel change in confidence. However, neitherthe winner nor the external observer is correct at the expense of the other.Both are correct. Paradoxical or not, we simply have to accept this. Yes, thewinner must concede that the external observer has no good reason foraltered confidence. But yes, too, the external observer must concede that thewinner does have good reason for altered confidence. The truth that youpersonally have won a lottery is nothing very remarkable if the number ofnames in the urn was small, and as the winner you ought to remember this.

Such points are relevant to Brandon Carter's doomsday argument. Theyanswer the only really new objection I have come across since producing

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Observer-relative Chances and the Doomsday Argument 431

detailed defences of this argument.1 It is a 'But how would a Martian viewmatters?' objection tentatively suggested (private communication) by themathematical physicist Alex Vilenkin, who was otherwise strongly inclinedto accept Carter's reasoning. It can seem an extremely powerful objection.

Carter, a Fellow of the Royal Society for work in applied mathematics,views his doomsday argument as just an application of probability theory. Itruns as follows. On one possible scenario, the human race will soon becomeextinct. Population has grown so fast of late that in this case, of all humanswho would ever have been born, roughly ten per cent would have had livesoverlapping in time with yours and mine. But the human race might insteadovercome all the perils presently confronting it, surviving for many thousandcenturies and colonizing the galaxy. On the galactic colonization scenario,you and I are extremely unusual. Of all humans who would ever have beenborn perhaps one in a million would have had lives overlapping with ours.To simplify matters, suppose these were the only possible scenarios. Whichone do you think we actually inhabit? Although famous for his anthropicprinciple that reminds us that intelligent life can exist only in intelligent-life-permitting times and places, which may be extremely unusual ones, Carter israther reluctant to take seriously the idea that you and I find ourselves at atime at which only a very small proportion of all humans will have foundthemselves. For this could be like taking seriously the idea that the lotterywhich you had just won was a million-named lottery, although beforewinning you had judged it fairly probable that there were only ten names inthe urn.

Carter has never reasoned that the chances of our being in, for instance,the earliest ten per cent of all humans are no greater than ten per cent, so thatdoomsday is fairly sure to occur shortly. What he instead suggests is that youshould not be confident that the human race will have a very long futureunless you had been, before considering his doomsday argument, veryconfident indeed. But of course you might have been very confident indeed.Many people are totally unimpressed by the hazards of biological warfare,thinning of the ozone layer, and so forth. Carter respects Bayes's Rule of theprobability calculus, which tells us how to change our estimated probabilitiesin the light of newly considered evidence. Somebody who learns of havingwon a lottery has no right to move at once to the conclusion that the urncontained only a few names, for it might have been extremely likely tocontain, say, a million. If the prior probability of its containing a million was99.9999999999 per cent, then even winning ought to leave you veryconfident that it had contained a million.

Still, it ought at least to reduce your confidence somewhat, as Bayesiancalculation shows. It is absurd to argue that since you (a) know that you havewon, and (b) would be equally sure of this regardless of what youhypothesized about the number of names in the urn, it follows (c) that

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winning ought not to affect your estimate of how many names the urncontained. Taking account of how likely you would have been to win,against the background of competing theories about how many names theurn contained, is not a case of 'changing the rules of the probability game'through supposing, first, that you know for sure that you have won, andsecondly that you do not at all know it. Instead of giving the probability ofevidence e as unity, or close to unity, in a Bayesian calculation, just becauseyou are sure or close to sure that you have in fact got evidence e (evidence ofhaving won a lottery, or of being in the earliest hundred million humans, orwhatever), you need to remember that 'probability of evidence e' here meansthe probability that you would have got evidence e one way or the other. Youare not asking whether to trust the evidence of your eyes or of your scientificinstruments. (The lottery winner, for instance, is not concerned with whetherthe probability is unity, one hundred per cent, that the letter announcing thewin is genuine and not a hoax or hallucination.) Rather, you are asking howprobable it would have been that your eyes or scientific instruments wouldsupply this kind of evidence, against the background of competing theories:the theory, for example, that there were only ten names in the lottery urn, andits competitor that there were a million names.

For those interested in mathematics, the correct formula for calculating theprobability of evidence e is therefore

prob(e) = prob(A) prob(e given h) + prob(nof h) prob(e given not h)

where h and not h are hypotheses whose probabilities are to be adjustedwhen evidence e has been considered. Only after grasping this can you applythe Bayesian formula

prob(fc given e) = prob(/z) prob(e given h) divided by prob(e)

without getting a ludicrous result.One often meets with the objection that no relevant information could be

gained by finding yourself alive at such and such a time. Supposedly, thiswould be totally unlike finding yourself as, say, one of five lottery winnerswhose names were drawn from an urn before those of the ninety-five loserswhich had also been waiting to be drawn, or finding yourself as a womanamong a blindfolded hundred and then undergoing the new process of beingpushed into one (but you do not know which) of a group of five and a groupof ninety-five. However, the objection fails. Being alive first, and later beingpushed into one group or another, is inessential to the moral which Carterencourages us to draw. For imagine instead that each of the hundred womenhad been born into a group of five or a group of ninety-five. Just so long asnone knew which group she had been born into, the same moral could bedrawn.

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Observer-relative Chances and the Doomsday Argument 433

Before considering Carter's argument, I would have given humanity'schance of spreading through the galaxy as about ninety-five per cent. Aftertaking it into account, I say close to fifty per cent. There has been a shift inmy estimate, but not the huge shift produced when one puts complete trust inBayesian calculations. The reason for somewhat distrusting them concernsthe world's possible indeterminism: the fact that, whereas the number ofnames in an urn is something definite, the number of future humans may notyet be fixed.

Note, this is not a case of distrusting probabilistic calculations wheneverthey are applied to one's own observed position in time. Let me here retell astory which has usually managed to persuade people. Imagine a projectdesigned as follows. In one century, three emeralds were to be distributed. Insome much later century, five thousand would be distributed. Suppose youhave no clue as to the dates of the centuries in question, but can be sure thatthe project would one day have been carried out as planned. You are thengiven one of the emeralds. What are the odds that you live in the later of thetwo centuries? Answer: five thousand to three, for if the project were carriedout as planned, and if all emerald-getters judged they were in the later of thetwo centuries, then five thousand of them would be right. This is every bit aspowerful as the earlier argument that if one hundred blindfolded womenwere divided randomly into two groups, one of five and one of ninety-five,then each woman should judge it ninety-five per cent probable that she wasin the larger group. The fact that the women are distributed in space, theemerald-getters in time, is without relevance.

All this, though, is on the assumption that it was fully determined that theproject would be carried out as planned. What if we move to anindeterministic situation? Here I am influenced by a Shooting Room story,developed with the help of David Lewis. People are thrust into a room in oneor more batches: the first of ten people, the second (if there is one) of ahundred, the third of a thousand, the fourth of ten thousand, and so on. Aseach batch enters the room, two dice are thrown. If the result is a double-six,everyone in the batch is shot and the process ends. Otherwise the batchleaves the room safely and another, ten times larger, is thrust in. The roombeing infinitely large, the process can be continued indefinitely. Now,suppose you find yourself thrust into the room. What are the odds that youwill leave it safely? Answer: thirty-five out of thirty-six, if how the dice aregoing to fall is a radically indeterministic affair.

As Lewis has insisted - 'a good, hard paradox' (private communication) -this is intensely odd since at least ninety per cent of all those ever thrust intothe room must suffer shooting. Nevertheless, it would seem, you have tojudge that your chances of suffering shooting are only one in thirty-six,granted that the fall of the dice really is indeterministic in a radical way (nohidden determinism here). For in this case somebody thrust into the room

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simply cannot know that it is ninety per cent probable that double-six isabout to be thrown/There is a major distinction between knowing merelythat disaster is bound to strike, at some time which has still to be determined,the large majority of all who will ever have been in your present situation,and knowing instead that deterministic factors had fixed precisely when itwould strike, and precisely how many people would be in this unfortunatemajority, long before you yourself had entered the situation.

Ought this to destroy all confidence in Carter's argument? Does it provethat the case of living at a time at which, on one possible scenario, only onein a million of all humans will have lived, cannot be at all like winning alottery in which, on one possible theory, there were a million entrants? Not atall. For if the Shooting Room story is retold in a way involving fulldeterminism, then you must judge that your chances of suffering shootingare high. Now, the future of the human race may well be neither completelydetermined nor completely undetermined. To the extent that it is determined,Carter's argument can be powerfully applied to it. And, crucially, those whoare greatly confident in a long future for humankind are in effect saying thatsuch a future is as good as determined.

To see how determinism would affect matters, consider replacing the twodice by a computer which generates successive figures of pi, the ratio of acircle's circumference to its diameter. Starting at, say, the ninety-seventhfigure, the computer deterministically spews out two figures whenever abatch of people is thrust into the room. As before, the batch will exit safelyunless the figures are a six and a six. As before, any later batch would be tentimes larger than its predecessor. You find yourself thrust into the room, butwith a grasp of mathematics insufficient to allow you to do the computer'sjob for it. What should you say are your chances of exiting safely? Answer:not above ten per cent, for at least ninety per cent of those ever thrust into theroom will find themselves in the final batch, the batch which is shot. There isno escape from this frightening conclusion, granted that the successivefigures of pi are not random, but only pseudo-random. For now you cannotprotest that whether two sixes are about to appear has still to be settled byindeterministic factors.

Note that, even given a fully deterministic process which settles whichbatch is the very largest, the size of any batch (or your own contribution to itssize) could in no way cause the computer to generate a fatal six and six. Thecomputer is simply not influenced by batch sizes (or by your existence). Itjust calculates successive figures of pi. None the less, the frighteningconclusion remains inescapable. Finding yourself in the room really canindicate that, very probably, you are in the batch which will not exit safely,the largest batch which will ever have entered it. Indications need not becauses. Clock hands can show that a bomb is probably about to explode,without having to be parts of a triggering process. This point, by the way,

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mirrors ones made in my earlier writings, and it tries to answer just one of avery great number of objections which have been brought against thedoomsday argument, often with immense confidence. Since not even a verylong and repetitious article could deal with all such objections, let me appealto readers not to put complete trust in any which spring to mind.

The frightening and inescapable conclusion, however, concerns simplyhow people thrust into the room themselves ought to estimate the probabilityof exiting safely. Watching the experiment and equally unable to do thecomputer's job for it, an external observer ought instead to estimate that thechances of each particular batch exiting safely are ninety-nine per cent; forof the hundred possible ways of choosing two figures from the range 0-0 to9-9, only one is 6-6. If the external, observer decided to keep betting thateach group entering the room would be shot, until one group actually was,then he or she ought to expect to lose many bets before winning. Thedifference between what the external observer ought to predict about anygiven batch, namely that its members will (almost certainly) exit safely, andwhat people in this batch ought to predict, namely that they will (almost ascertainly) be shot, simply has to be accepted, paradoxical though it may be.For remember, the external observer, although knowing all the evidencewhich is known to the people in the room, can still be viewed as deprived ofevidence to which these people can rightly appeal. The external observerdoes not personally have evidence of having been thrust into the room. He orshe is like the observer external to the hundred blindfolded women, whocannot have acquired evidence of actually being in one of the two groups.

All this is relevant to what a Martian, an observer external to the humanrace, ought to predict about its future. As Vilenkin suspected, Carter'sdoomsday argument should entirely fail to change the Martian's estimate ofthe probability that humankind will survive for long. This, though, is nobasis for an objection against Carter. It does not say that the doomsdayargument ought to leave our own estimates entirely unaffected. Estimatedprobabilities can be observer-relative in a somewhat disconcerting way: away not depending on the fact that, obviously, various observers often areunaware of truths which other observers know. The case of the blindfoldedwomen provides a simple means of illustrating the point.2

NOTES

1 'Time and the Anthropic Principle', Mind 101 (1992), pp. 521-40; 'Testing the DoomsdayArgument', Journal of Applied Philosophy 11 (1994), pp. 31-44; and The End of the World:the Science and Ethics of Human Extinction (London/New York: Routledge, 1996), whichwas the topic of a Review Discussion, 'Doom Soon?', by T. Tännsjö in Inquiry 40 (1997),pp. 243-52.

2 A year after Vilenkin had raised his point, it reappeared on page 252 of W. Eckhardt's 'AShooting-room View of Doomsday' in The Journal of Philosophy 94 (1997), pp. 244-59.Eckhardt says simply that he 'cannot fathom' why, in the deterministic case, a spectator

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outside the shooting room ought to bet differently from somebody inside. I have here tried toshow that the matter is fathomable. Still, Eckhardt is right in thinking that what he calls 'thehuman randomness assumption', namely that 'We can validly consider our birth rank asgenerated by random or equiprobable sampling from the collection of all persons who everlive', is highly questionable. Any such assumption is indeed a mistake if the world isimportantly indeterministic. Where Eckhardt goes astray is in dismissing the distinctionbetween determinism and indeterminism as insignificant, on the grounds that a record ofindeterministic dice throws, for instance, can behave deterministically. Though they can, thisstrikes me as irrelevant I reject Eckhardt's question-begging claim that betting games are'the same games' regardless of whether they are played (a) with indeterministic dice or else(b) with records (which would behave always in a fixed way, no matter how often they wereused) of how such dice have fallen. If knowing, when part of a continually growingpopulation, not just that disaster was sure to overtake most people who would ever haveentered that population, but also that the precise number of victims had been fixed before youentered it, then you could have a right to be alarmed.

Received 2 October 1997

John Leslie, Department of Philosophy, University of Guelph, Guelph, Ontario, NIG 2W1,Canada

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14

Nov

embe

r 20

14