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Doomsday Argument

Edited by Yann Benétreau-Dupin (University of Western Ontario, Rotman Institute of Philosophy)
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Summary

The Doomsday argument is a family of arguments about humanity’s likely survival. There are mainly two versions of the argument discussed in the literature, both of which appeal to a form of Copernican principle (or principle of typicality or mediocrity). A first version of the argument (endorsed by, e.g., John Leslie) dictates a probability shift in favor of theories that predict earlier end dates for our species assuming that we are a typical—rather than atypical—member of that group.

The other main version of the argument is sometimes referred to as the ‘delta-t argument,’ and it has provoked both outrage and genuine scientific interest. It claims to allow one to make a prediction about the total duration of any process of indefinite duration based only on the assumption that the moment of observation is randomly selected. A variant of this argument, which gives equivalent predictions, reasons in terms of one’s rank in a sequential process.

Key works An early version of the Doomsday argument, referred to as the 'Carter catastrophe', appeared in Carter & McCrea 1983. The Doomsday argument was then popularized by John Leslie 1990. The 'delta-t argument' was put forth by Richard Gott (1993, 1994). Several attempts to block the conclusions of this argument have been offered. In order to counter the consequence of what he called the 'self-sampling assumption,' Nick Bostrom 2002 suggested to adopt the 'self-indicating assumption.' In order to avoid conclusions that are entirely dependent on our reference class, Radford Neal 2006 argued that we ought to appeal to fully non-indexical conditioning to block the conclusions of the Doomsday argument. Benétreau-Dupin argued that only imprecise probabilities can avoid the conclusions of all versions of the Doomsday argument.
Introductions See Bostrom 2002 (§6-7) and Richmond 2006 for reviews. See Monton & Roush 2001 for Gott's version of the Doomsday argument.
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  1. Tom Adams (2007). Sorting Out the Anti-Doomsday Arguments: A Reply to Sowers. Mind 116 (462):269-273.
    claim that his thought experiment shows that a currently living person is not a random sample is refuted. His thought experiment is reduced to a probability model, and is shown to be identical to one previously developed by Dieks. The status of the Doomsday Argument is left unresolved, since Dieks's refutation attempt is disputed in the literature.
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  2. Mr István A. Aranyosi, The Doomsday Simulation Argument. Or Why Isn't the End Nigh, and You're Not Living in a Simulation.
    According to the Carter-Leslie Doomsday Argument, we should assign a high probability to the hypothesis that the human species will go extinct very soon. The argument is based on the application of Bayes’s theo-rem and a certain indifference principle with respect to the temporal location of our observed birth rank within the totality of birth ranks of all humans who will ever have lived. According to Bostrom’s Simulation Argument, which appeals to a weaker indifference principle than the Doomsday Argument, at (...)
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  3. Paul Bartha & Christopher Hitchcock (1999). No One Knows the Date or the Hour: An Unorthodox Application of Rev. Bayes's Theorem. Philosophy of Science 66 (3):353.
    Carter and Leslie (1996) have argued, using Bayes's theorem, that our being alive now supports the hypothesis of an early 'Doomsday'. Unlike some critics (Eckhardt 1997), we accept their argument in part: given that we exist, our existence now indeed favors 'Doom sooner' over 'Doom later'. The very fact of our existence, however, favors 'Doom later'. In simple cases, a hypothetical approach to the problem of 'old evidence' shows that these two effects cancel out: our existence now yields no information (...)
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  4. Paul Bartha & Christopher Hitchcock (1999). The Shooting-Room Paradox and Conditionalizing on Measurably Challenged Sets. Synthese 118 (3):403-437.
    We provide a solution to the well-known “Shooting-Room” paradox, developed by John Leslie in connection with his Doomsday Argument. In the “Shooting-Room” paradox, the death of an individual is contingent upon an event that has a 1/36 chance of occurring, yet the relative frequency of death in the relevant population is 0.9. There are two intuitively plausible arguments, one concluding that the appropriate subjective probability of death is 1/36, the other that this probability is 0.9. How are these two values (...)
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  5. Yann Benétreau-Dupin (forthcoming). Blurring Out Cosmic Puzzles. Philosophy of Science.
    The Doomsday argument and anthropic reasoning are two puzzling examples of probabilistic confirmation. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, they constitute a challenge to Bayesianism. Several attempts, some successful, have been made to avoid these conclusions, but some versions of these arguments cannot be dissolved within the framework of orthodox Bayesianism. I show that adopting an imprecise framework of probabilistic reasoning allows for a more adequate representation of (...)
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  6. Yann Benétreau-Dupin (2015). The Bayesian Who Knew Too Much. Synthese 192 (5):1527-1542.
    In several papers, John Norton has argued that Bayesianism cannot handle ignorance adequately due to its inability to distinguish between neutral and disconfirming evidence. He argued that this inability sows confusion in, e.g., anthropic reasoning in cosmology or the Doomsday argument, by allowing one to draw unwarranted conclusions from a lack of knowledge. Norton has suggested criteria for a candidate for representation of neutral support. Imprecise credences (families of credal probability functions) constitute a Bayesian-friendly framework that allows us to avoid (...)
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  7. N. Bostrom (1999). The Doomsday Argument is Alive and Kicking. Mind 108 (431):539-551.
    A recent paper by Korb and Oliver in this journal attempts to refute the Carter-Leslie Doomsday argument. I organize their remarks into five objections and show that they all fail. Further efforts are thus called upon to find out what, if anything, is wrong with Carter and Leslie's disturbing reasoning. While ultimately unsuccessful, Korb and Oliver's objections do however in some instances force us to become clearer about what the Doomsday argument does and doesn't imply.
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  8. Nick Bostrom, A Doomsday Argument Primer.
    Rarely does philosophy produce empirical predictions. The Doomsday argument is an important exception. From seemingly trivial premises it seeks to show that the risk that humankind will go extinct soon has been systematically underestimated. Nearly everybody's first reaction is that there must be something wrong with such an argument. Yet despite being subjected to intense scrutiny by a growing number of philosophers, no simple flaw in the argument has been identified.
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  9. Nick Bostrom, Beyond the Doomsday Argument: Reply to Sowers and Further Remarks.
    George Sowers tries to refute the Doomsday argument on grounds that true random sampling requires all possible samples to be equally probable the time when the sample is taken. Yet the Doomsday argument does not rely on true random sampling. It presupposes random sampling only in a metaphorical sense. After arguing that Sowers’ critique fails, I outline my own view on the matter, which is that the Doomsday argument is inconclusive and that by developing a theory of observation selection effects (...)
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  10. Nick Bostrom (2008). The Doomsday Argument. Think 6 (17-18):23-28.
    A recent paper by Korb and Oliver in this journal attempts to refute the Carter-Leslie Doomsday argument. I organize their remarks into five objections and show that they all fail. Further efforts are thus called upon to find out what, if anything, is wrong with Carter and Leslie’s disturbing reasoning. While ultimately unsuccessful, Korb and Oliver’s objections do however in some instances force us to become clearer about what the Doomsday argument does and doesn’t imply.
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  11. Nick Bostrom (2003). The Mysteries of Self-Locating Belief and Anthropic Reasoning. The Harvard Review of Philosophy 11 (1):59-73.
    1. How big is the smallest fish in the pond? You take your wide-meshed fishing net and catch one hundred fishes, every one of which is greater than six inches long. Does this evidence support the hypothesis that no fish in the pond is much less than six inches long? Not if your wide-meshed net can’t actually catch smaller fish...
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  12. Nick Bostrom (2002). Anthropic Bias: Observation Selection Effects in Science and Philosophy. Routledge.
    Anthropic Bias explores how to reason when you suspect that your evidence is biased by "observation selection effects"--that is, evidence that has been filtered by the precondition that there be some suitably positioned observer to "have" the evidence. This conundrum--sometimes alluded to as "the anthropic principle," "self-locating belief," or "indexical information"--turns out to be a surprisingly perplexing and intellectually stimulating challenge, one abounding with important implications for many areas in science and philosophy. There are the philosophical thought experiments and paradoxes: (...)
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  13. Nick Bostrom (2001). The Doomsday Argument Adam & Eve, UN++, and Quantum Joe. Synthese 127 (3):359 - 387.
    The Doomsday argument purports to show that the risk of the human species going extinct soon has been systematically underestimated. This argument has something in common with controversial forms of reasoning in other areas, including: game theoretic problems with imperfect recall, the methodology of cosmology, the epistemology of indexical belief, and the debate over so-called fine-tuning arguments for the design hypothesis. The common denominator is a certain premiss: the Self-Sampling Assumption. We present two strands of argument in favor of this (...)
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  14. Nick Bostrom (2000). Observer-Relative Chances in Anthropic Reasoning? Erkenntnis 52 (1):93-108.
    John Leslie presents a thought experiment to show that chances are sometimes observer-relative in a paradoxical way. The pivotal assumption in his argument – a version of the weak anthropic principle – is the same as the one used to get the disturbing Doomsday argument off the ground. I show that Leslie's thought experiment trades on the sense/reference ambiguity and is fallacious. I then describe a related case where chances are observer-relative in an interesting way. But not in a paradoxical (...)
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  15. Nick Bostrom & Milan M. Cirković (2003). The Doomsday Argument and the Self–Indication Assumption: Reply to Olum. Philosophical Quarterly 53 (210):83-91.
    In a recent paper in this journal, Ken Olum attempts to refute the doomsday argument by appealing to the self–indication assumption (SIA) that your very existence gives you reason to think that there are many observers. Unlike earlier users of this strategy, Olum tries to counter objections that have been made against (SIA). We argue that his defence of (SIA) is unsuccessful. This does not, however, mean that one has to accept the doomsday argument (or the other counter–intuitive results that (...)
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  16. Nick Bostrom & Milan M. Cirković (2003). The Doomsday Argument and the Self–Indication Assumption: Reply to Olum. Philosophical Quarterly 53 (210):83–91.
    In a recent paper in this journal, Ken Olum attempts to refute the Doomsday argument by appealing to the self-indication assumption (SIA), the idea that your very existence gives you reason to think that there are many observers. In contrast to earlier refutation attempts that use this strategy, Olum confronts and try to counter some of the objections that have been made against SIA. We argue that his defense of SIA is unsuccessful. This does not, however, mean that one has (...)
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  17. D. J. Bradley (2012). Four Problems About Self-Locating Belief. Philosophical Review 121 (2):149-177.
    This article defends the Doomsday Argument, the Halfer Position in Sleeping Beauty, the Fine-Tuning Argument, and the applicability of Bayesian confirmation theory to the Everett interpretation of quantum mechanics. It will argue that all four problems have the same structure, and it gives a unified treatment that uses simple models of the cases and no controversial assumptions about confirmation or self-locating evidence. The article will argue that the troublesome feature of all these cases is not self-location but selection effects.
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  18. D. J. Bradley (2005). No Doomsday Argument Without Knowledge of Birth Rank: A Defense of Bostrom. Synthese 144 (1):91 - 100.
    The Doomsday Argument says we should increase our subjective probability that Doomsday will occur once we take into account how many humans have lived before us. One objection to this conclusion is that we should accept the Self-Indication Assumption (SIA): Given the fact that you exist, you should (other things equal) favor hypotheses according to which many observers exist over hypotheses on which few observers exist. Nick Bostrom argues that we should not accept the SIA, because it can be used (...)
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  19. Darren Bradley (2007). Bayesianism And Self-Locating Beliefs. Dissertation, Stanford University
    How should we update our beliefs when we learn new evidence? Bayesian confirmation theory provides a widely accepted and well understood answer – we should conditionalize. But this theory has a problem with self-locating beliefs, beliefs that tell you where you are in the world, as opposed to what the world is like. To see the problem, consider your current belief that it is January. You might be absolutely, 100%, sure that it is January. But you will soon believe it (...)
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  20. Darren Bradley & Branden Fitelson (2003). Monty Hall, Doomsday and Confirmation. Analysis 63 (277):23–31.
    We give an analysis of the Monty Hall problem purely in terms of confirmation, without making any lottery assumptions about priors. Along the way, we show the Monty Hall problem is structurally identical to the Doomsday Argument.
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  21. Nicola Bruno (1999). Millenarismo secolarizzato e percezione del rischio. Etica E Politica 1 (1).
    According to the Carter-Leslie "doomsday argument", the probability of the world ending soon is larger than people think. The argument exploits Bayesian reasoning to compute the posterior probability of the world ending at some near point in the future, given the rank of our generation in the human race, and given assumptions about the prior probability of the world ending at that point. The doomsday argument appears flawed both in its logical structure and in its assumptions about millenaristic beliefs . (...)
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  22. Brandon Carter & William H. McCrea (1983). The Anthropic Principle and its Implications for Biological Evolution [and Discussion]. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 310 (1512):347-363.
    In the form in which it was originally expounded, the anthropic principle was presented as a warning to astrophysical and cosmological theorists of the risk of error in the interpretation of astronomical and cosmological information unless due account is taken of the biological restraints under which the information was acquired. However, the converse message is also valid: biological theorists also run the risk of error in the interpretation of the evolutionary record unless they take due heed of the astrophysical restraints (...)
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  23. Timothy Chambers (2001). Do Doomsday's Proponents Think We Were Born Yesterday? Philosophy 76 (3):443-450.
    In a recent article, John Leslie has defended the intriguing Carter-Leslie ‘Doomsday Argument’ (Philosophy, January 2000). I argue that an essential presupposition of the argument—that ‘the case of one's name coming out of [an] urn is sufficiently similar to the case of being born into the world’—engenders, in turn, a parallel ‘Ussherian Corollary’. The dubiousness of this Corollary, coupled with independent considerations, casts doubt upon the Carter-Leslie presupposition, and hence, dooms the Doomsday argument.
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  24. Dennis Dieks (2007). Reasoning About the Future: Doom and Beauty. [REVIEW] Synthese 156 (3):427 - 439.
    According to the Doomsday Argument we have to rethink the probabilities we assign to a soon or not so soon extinction of mankind when we realize that we are living now, rather early in the history of mankind. Sleeping Beauty finds herself in a similar predicament: on learning the date of her first awakening, she is asked to re-evaluate the probabilities of her two possible future scenarios. In connection with Doom, I argue that it is wrong to assume that our (...)
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  25. Dennis Dieks, The Probability of Doom.
    According to the Doomsday Argument the probability of an impending extinction of mankind is much higher than we think. The adduced reason is that in our assignment of probabilities to soon or not so soon doom we have not fully taken into account that we live in the specific year 2001. This is relevant information, because if I consider myself as an arbitrary member of the human race I have a much higher probability of finding myself living in 2001 on (...)
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  26. Dennis Dieks (1992). Doomsday--Or: The Dangers of Statistics. Philosophical Quarterly 42 (166):78-84.
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  27. William Eckhardt (1997). A Shooting-Room View of Doomsday. Journal of Philosophy 94 (5):244-259.
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  28. William Eckhardt (1993). Probability Theory and the Doomsday Argument. Mind 102 (407):483-488.
    John Leslie has published an argument that our own birth rank among all who have lived can be used to make inferences about all who will ever live, and hence about the expected survival time for the human race. It is found to be shorter than usually supposed. The assumptions underpinning the argument are criticized, especially the unwarranted one that the argument's sampling is equiprobable from among all who ever live. A mathematical derivation shows that Leslie's argument is correct only (...)
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  29. Arthur Falk (1993). Summer 1991: The "Monty Hall" Problem; Fall 1993: The Two Envelopes Puzzle; And Now: Doomsday. Proceedings of the Heraclitean Society 17:64.
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  30. Antony Flew (1997). The End of the World: The Science and Ethics of Human Extinction By John Leslie. [REVIEW] Philosophy 72 (279):158-.
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  31. Dr Paul Franceschi, Elements of Dialectical Contextualism.
    In what follows, I strive to present the elements of a philosophical doctrine, which can be defined as dialectical contextualism. I proceed first to define the elements of this doctrine: dualities and polar contraries, the principle of dialectical indifference and the one-sidedness bias. I emphasize then the special importance of this doctrine in one specific field of meta-philosophy: the methodology for solving philosophical paradoxes. Finally, I describe several applications of this methodology on the following paradoxes: Hempel's paradox, the surprise examination (...)
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  32. P. Franceschi (1998). A Solution to the Doomsday Argument. Canadian Journal of Philosophy 28 (2):227-246.
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  33. Paul Franceschi (2009). A Third Route to the Doomsday Argument. Journal of Philosophical Research 34:263-278.
    In this paper, I present a solution to the Doomsday argument based on a third type of solution, by contrast to, on the one hand, the Carter-Leslie view and, on the other hand, the Eckhardt et al. analysis. I begin by strengthening both competing models by highlighting some variations of their original models, which renders them less vulnerable to several objections. I then describe a third line of solution, which incorporates insights from both Leslie and Eckhardt’s models and fits more (...)
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  34. Paul Franceschi, Une Application Des N-Univers a l'Argument de l'Apocalypse Et au Paradoxe de Goodman.
    Several philosophical problems are based on an analogy between a real situation and a probabilistic model. Such problems are based on urn analogies. The present dissertation aims to describe and implement a methodology oriented towards the resolution of philosophical problems based on an urn analogy. This methodology is based on the use of the n-universes. To this end, I describe first the n-universes in a detailed way. I also discuss the difficulties of the theory of n-universes related to the demultiplication (...)
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  35. Paul Franceschi (1999). Comment l'Urne de Carter et Leslie se Déverse dans celle de Hempel. Canadian Journal of Philosophy 29 (1):139-156.
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  36. Paul Franceschi (1999). The Doomsday Argument and Hempel's Problem. [Journal (on-Line/Unpaginated)] 29 (1).
    English translation of a paper originally pupblished in French in the Canadian Journal of Philosophy under the title 'Comment l'urne de Carter et Leslie se déverse dans celle de Hempel'. In this paper, I present firstly a solution to Hempel's Problem. I recall secondly the solution to the Doomsday Argument described in my previous Une Solution pour l'Argument de l'Apocalypse (Canadian Journal of Philosophy 1998-2) and remark that both solutions are based on a similar line of reasoning. I show thirdly (...)
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  37. Paul Franceschi (1998). Une solution pour l'argument de l'apocalypse. Canadian Journal of Philosophy 28 (2):227-246.
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  38. Paul Franceschi (1998). Une Solution Pour l'Argument de l'Apocalypse. Canadian Journal of Philosophy 28 (2):227 - 246.
    Attribué à Brandon Carter, l' argument de l'Apocalypse Doomsday Argument , soit DA, dans ce qui suit) a été décrit par John Leslie (1992). On peut formuler ainsi cet argument. Soit A l'événement: l'Apocalypse se produira avant l'an 2150 ; et B l'événement: l'Apocalypse ne se produira pas avant 2150 . Soit également Z l'événement: j'ai connu les années 1990 . On peut par ailleurs estimer à 40 milliards le nombre d'humains ayant existé depuis la naissance de l'humanité, jusqu'à notre (...)
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  39. Austin Gerig, The Doomsday Argument in Many Worlds.
    You and I are highly unlikely to exist in a civilization that has produced only 70 billion people, yet we find ourselves in just such a civilization. Our circumstance, which seems difficult to explain, is easily accounted for if (1) many other civilizations exist and if (2) nearly all of these civilizations (including our own) die out sooner than usually thought, i.e., before trillions of people are produced. Because the combination of (1) and (2) make our situation likely and alternatives (...)
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  40. J. Richard Gott (1994). Future Prospects Discussed. Nature 368:108.
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  41. J. Richard Gott (1993). Implications of the Copernican Principle for Our Future Prospects. Nature 363:315-319.
    Making only the assumption that you are a random intelligent observer, limits for the total longevity of our species of 0.2 million to 8 million years can be derived at the 95% confidence level. Further consideration indicates that we are unlikely to colonize the Galaxy, and that we are likely to have a higher population than the median for intelligent species.
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  42. Mark Greenberg (1999). Apocalypse Not Just Now. London Review of Books 21 (13):19-22.
    John Leslie comes to tell us that the end of the world is closer than we think. His book is no ordinary millennial manifesto, however. Leslie is a sophisticated philosopher of science, and the source of his message is not divine revelation, apocalyptic fantasy or anxiety about the year-2000 computer problem, but ‘the Doomsday Argument’ – an a priori argument that seeks support in probability..
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  43. How Long Do We Have, Every Conscious Machine Brings Us Closer to Death.
    The Doomsday Argument is alive and kicking, and since its formulation in the beginning of the Eighties by the astrophysicist Brandon Carter it has gained wide attention, been strongly criticized and has been described in many different, and sometimes non-interchangeable analogies. I will briefly present the argument here, and departing from Nick Bostrom's interpretation, I will defend that doom may be sooner than we think if we start building conscious machines soon in the future.
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  44. Marcus Hutter (2010). A Complete Theory of Everything (Will Be Subjective). Algorithms 3 (4):329-350.
    Increasingly encompassing models have been suggested for our world. Theories range from generally accepted to increasingly speculative to apparently bogus. The progression of theories from ego- to geo- to helio-centric models to universe and multiverse theories and beyond was accompanied by a dramatic increase in the sizes of the postulated worlds, with humans being expelled from their center to ever more remote and random locations. Rather than leading to a true theory of everything, this trend faces a turning point after (...)
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  45. George F. Sowers Jr (2002). The Demise of the Doomsday Argument. Mind 111 (441):37 - 45.
    A refutation of the doomsday argument is offered. Through a simple thought experiment analysed in Bayesian terms the fallacy is shown to be the assumption that a currently living person represents a random sample from the population of all persons who will ever have existed. A more general version of the counter argument is then given. Previous arguments that purport to answer this concern are also addressed. One result is determining criteria for the applicability of time sampling arguments, i.e., under (...)
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  46. Brian Kierland & Bradley Monton (2006). How to Predict Future Duration From Present Age. Philosophical Quarterly 56 (January):16-38.
    Physicist J. Richard Gott has given an argument that, if good, allows one to make accurate predictions for the future longevity of a process, based solely on its present age. We show that there are problems with some of the details of Gott’s argument, but we defend the crucial insight: in many circumstances, the greater the present age of a process, the more likely a longer future duration.
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  47. Jaegwon Kim (1989). References. Semiotics 5 (3):401-431.
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  48. Joshua Knobe, Ken D. Olum & And Alexander Vilenkin (2006). Philosophical Implications of Inflationary Cosmology. British Journal for the Philosophy of Science 57 (1):47-67.
    Recent developments in cosmology indicate that every history having a non-zero probability is realized in infinitely many distinct regions of spacetime. Thus, it appears that the universe contains infinitely many civilizations exactly like our own, as well as infinitely many civilizations that differ from our own in any way permitted by physical laws. We explore the implications of this conclusion for ethical theory and for the doomsday argument. In the infinite universe, we find that the doomsday argument applies only to (...)
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  49. KB Korb & JJ Oliver (1999). Comment on Nick Bostrom's 'the Doomsday Argument is Alive and Kicking'. Mind 108 (431):551-553.
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  50. Kevin B. Korb & Jonathan J. Oliver (1998). A Refutation of the Doomsday Argument. Mind 107 (426):403-410.
    Carter and Leslie's Doomsday Argument maintains that reflection upon the number of humans born thus far, when that number is viewed as having been uniformly randomly selected from amongst all humans, past, present and future, leads to a dramatic rise in the probability of an early end to the human experiment. We examine the Bayesian structure of the Argument and find that the drama is largely due to its oversimplification.
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