About this topic
Summary In this category belong a range of puzzles that are analysed using probabililty and have philosophical implications. Perhaps the best known is Goodman's New Riddle of Induction (Grue), which can be seen as a strengthened version of Hume's problem of induction. The Paradox of the Ravens (the paradox of confirmation) is one of the central problems for theories of confirmation. It seems to show that obvious principles of confirmation generate the result that a white sneaker confirms that all ravens are black. The Sleeping Beauty problem concerns an agent who is woken on either one day or two, and faces the question of whether the current waking is part of the single waking or the double waking. This raises the issue of incorporating self-locating beliefs into the Bayesian framework. The Doomsday Argument purports to show that humans will die out sooner than we previously thought, based merely on our own birth rank among humans. The Monty Hall Problem is about whether you should swap doors, after tentatively choosing one of the three doors, one of which contains a prize, and finding that the door you selected does not have the prize.
Key works The New Riddle of Induction was introduced in Goodman 1954. The Paradox of the Ravens was introduced by Hosiasson-Lindenbaum 1940 and influentially discussed by Hempel 1945 I and Hempel 1945 II. Sleeping Beauty was introduced by Elga 2000, shortly followed by Lewis 2001. The Doomsday Argument was popularized largely by Leslie 1989.
Introductions The new riddle of induction and the paradox of the ravens are explained in section 5 of Vickers 2008. This Bostrom manuscript explains the Doomsday Argument and Titelbaum forthcoming gives a summary of the responses to Sleeping Beauty
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Doomsday Argument
  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. 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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  3. 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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  4. Yann Benétreau-Dupin (forthcoming). Blurring Out Cosmic Puzzles. Philosophy of Science.
    The Doomsday argument and anthropic arguments are illustrations of a paradox. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, the paradox constitutes a challenge to Bayesianism. Several attempts, some successful, have been made to avoid these conclusions, but some versions of the paradox 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 ignorance (...)
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  5. 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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  6. 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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  7. 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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  8. 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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  9. 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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  10. 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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  11. 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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  12. 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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  13. 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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  14. 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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  15. 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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  16. 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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  17. 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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  18. 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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  19. 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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  20. Dennis Dieks (1992). Doomsday--Or: The Dangers of Statistics. Philosophical Quarterly 42 (166):78-84.
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  21. William Eckhardt (1997). A Shooting-Room View of Doomsday. Journal of Philosophy 94 (5):244-259.
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  22. 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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  23. 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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  24. 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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  25. 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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  26. 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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  27. 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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  28. 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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  29. 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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  30. 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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  31. 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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  32. John Leslie (2008). Infinitely Long Afterlives and the Doomsday Argument. Philosophy 83 (4):519-524.
    A recent book of mine defends three distinct varieties of immortality. One of them is an infinitely lengthy afterlife; however, any hopes of it might seem destroyed by something like Brandon Carter's 'doomsday argument' against viewing ourselves as extremely early humans. The apparent difficulty might be overcome in two ways. First, if the world is non-deterministic then anything on the lines of the doomsday argument may prove unable to deliver a strongly pessimistic conclusion. Secondly, anything on those lines may break (...)
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  33. John Leslie (1997). Observer-Relative Chances and the Doomsday Argument. Inquiry 40 (4):427 – 436.
    Suppose various observers are divided randomly into two groups, a large and a small. Not knowing into which group anyone has been sent, each can have strong grounds for believing in being in the large group, although recognizing that every observer in the other group has equally powerful reasons for thinking of this other group as the large one. Justified belief can therefore be observer-relative in a rather paradoxical way. Appreciating this allows one to reject an intriguing new objection against (...)
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  34. John Leslie (1994). Testing the Doomsday Argument. Journal of Applied Philosophy 11 (1):31-44.
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  35. John Leslie (1992). Doomsday Revisited. Philosophical Quarterly 42 (166):85-89.
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  36. Peter J. Lewis (2013). The Doomsday Argument and the Simulation Argument. Synthese 190 (18):4009-4022.
    The Simulation Argument and the Doomsday Argument share certain structural similarities, and hence are often discussed together (Bostrom 2003, Aranyosi 2004, Richmond 2008, Bostrom and Kulczycki 2011). Both are cases where reflecting on one’s location among a set of possibilities yields a counter-intuitive conclusion—in one case that the end of humankind is closer than you initially thought, and in the second case that it is more likely than you initially thought that you are living in a computer simulation. Indeed, the (...)
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  37. Peter J. Lewis (2010). A Note on the Doomsday Argument. Analysis 70 (1):27-30.
    I argue that the Doomsday argument fails because it fails to take into account the lesson of the Sleeping Beauty puzzle.
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  38. Bradley Monton (2003). The Doomsday Argument Without Knowledge of Birth Rank. Philosophical Quarterly 53 (210):79–82.
    The Carter-Leslie Doomsday argument, as standardly presented, relies on the assumption that you have knowledge of your approximate birth rank. I demonstrate that the Doomsday argument can still be given in a situation where you have no knowledge of your birth rank. This allows one to reply to Bostrom's defense of the Doomsday argument against the refutation based on the idea that your existence makes it more likely that many observers exist.
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  39. Bradley Monton & Sherri Roush, Gott's Doomsday Argument.
    Physicist J. Richard Gott uses the Copernican principle that “we are not special” to make predictions about the future lifetime of the human race, based on how long the human race has been in existence so far. We show that the predictions which can be derived from Gott’s argument are less strong than one might be inclined to believe, that Gott’s argument illegitimately assumes that the human race will not last forever, that certain versions of Gott’s argument are incompatible with (...)
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  40. John D. Norton (2010). Cosmic Confusions: Not Supporting Versus Supporting Not. Philosophy of Science 77 (4):501-523.
    Bayesian probabilistic explication of inductive inference conflates neutrality of supporting evidence for some hypothesis H (“not supporting H”) with disfavoring evidence (“supporting not-H”). This expressive inadequacy leads to spurious results that are artifacts of a poor choice of inductive logic. I illustrate how such artifacts have arisen in simple inductive inferences in cosmology. In the inductive disjunctive fallacy, neutral support for many possibilities is spuriously converted into strong support for their disjunction. The Bayesian “doomsday argument” is shown to rely entirely (...)
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  41. Ken D. Olum (2002). The Doomsday Argument and the Number of Possible Observers. Philosophical Quarterly 52 (207):164-184.
    If the human race comes to an end relatively shortly, then we have been born at a fairly typical time in the history of humanity; if trillions of people eventually exist, then we have been born in the first surprisingly tiny fraction of all people. According to the 'doomsday argument' of Carter, Leslie, Gott and Nielsen, this means that the chance of a disaster which would obliterate humanity is much larger than usually thought. But treating possible observers in the same (...)
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  42. Ronald Pisaturo (2011). The Longevity Argument. self.
    J. Richard Gott III (1993) has used the “Copernican principle” to derive a probability density function for the total longevity of any phenomenon, based solely on the phenomenon’s past longevity. John Leslie (1996) and others have used an apparently similar probabilistic argument, the “Doomsday Argument,” to claim that conventional predictions of longevity must be adjusted, based on Bayes’ Theorem, in favor of shorter longevities. Here I show that Gott’s arguments are flawed and contradictory, but that one of his conclusions—his delta (...)
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  43. Ronald Pisaturo (2009). Past Longevity as Evidence for the Future. Philosophy of Science 76 (1):73-100.
    Gott ( 1993 ) has used the ‘Copernican principle’ to derive a probability distribution for the total longevity of any phenomenon, based solely on the phenomenon’s past longevity. Leslie ( 1996 ) and others have used an apparently similar probabilistic argument, the ‘Doomsday Argument’, to claim that conventional predictions of longevity must be adjusted, based on Bayes’s Theorem, in favor of shorter longevities. Here I show that Gott’s arguments are flawed and contradictory, but that one of his conclusions is plausible (...)
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  44. Joel Pust (2007). Cartesian Knowledge and Confirmation. Journal of Philosophy 104 (6):269-289.
    Bayesian conceptions of evidence have been invoked in recent arguments regarding the existence of God, the hypothesis of multiple physical universes, and the Doomsday Argument. Philosophers writing on these topics often claim that, given a Bayesian account of evidence, our existence or something entailed by our existence (perhaps in conjunction with some background knowledge or assumption) may serve as evidence for each of us. In this paper, I argue that this widespread view is mistaken. The mere fact of one's existence (...)
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  45. Alasdair Richmond (2006). The Doomsday Argument. Philosophical Books 47 (2):129-142.
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  46. Alasdair Richmond (2004). Immortality and Doomsday. American Philosophical Quarterly 41 (3):235 - 247.
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  47. Alasdair M. Richmond (2008). Doomsday, Bishop Ussher and Simulated Worlds. Ratio 21 (2):201–217.
    This paper attempts three tasks in relation to Carter and Leslie's Doomsday Argument. First, it criticises Timothy Chambers' 'Ussherian Corollary', a striking but unsuccessful objection to standard Doomsday arguments. Second, it reformulates the Ussherian Corollary as an objection to Bradley Monton's variant Doomsday and Nick Bostrom's Simulation Argument. Finally, it tries to diagnose the epistemic/metaphysical problems facing Doomsday-related arguments.1.
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  48. E. Sober (2003). An Empirical Critique of Two Versions of the Doomsday Argument – Gott's Line and Leslie's Wedge. Synthese 135 (3):415 - 430.
    I discuss two versions of the doomsday argument. According to ``Gott's Line'',the fact that the human race has existed for 200,000 years licences the predictionthat it will last between 5100 and 7.8 million more years. According to ``Leslie'sWedge'', the fact that I currently exist is evidence that increases the plausibilityof the hypothesis that the human race will come to an end sooner rather than later.Both arguments rest on substantive assumptions about the sampling process thatunderlies our observations. These sampling assumptions have (...)
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  49. George F. Sowers Jr (2002). The Demise of the Doomsday Argument. Mind 111 (441):37-46.
    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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  50. G. F. Sowers (2002). The Demise of the Doomsday Argument. Mind 111 (441):37-46.
    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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