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- Dennis Dieks (2007). Reasoning About the Future: Doom and Beauty. 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 ordinary probability judgements do not already reflect our place in history: we justify the predictive use we make of the probabilities yielded by science (or other sources of information) by our knowledge of the fact that we live now, a certain time before the possible occurrence of the events the probabilities refer to. Our degrees of belief should change drastically when we forget the date—importantly, this follows without invoking the “Self Indication Assumption”. Subsequent conditionalization on information about which year it is cancels this probability shift again. The Doomsday Argument is about such probability shifts, but tells us nothing about the concrete values of the probabilities—for these, experience provides the only basis. Essentially the same analysis applies to the Sleeping Beauty problem. I argue that Sleeping Beauty “thirders” should be committed to thinking that the Doomsday Argument is ineffective; whereas “halfers” should agree that doom is imminent—but they are wrong.Reading list | Discuss | Edit | Categorize |My bibliography
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All parties to the Sleeping Beauty debate agree that it shows that some cherished principle of rationality has to go. Thirders think that it is Conditionalization and Reflection that must be given up or modified; halfers think that it is the Principal Principle. I offer an analysis of the Sleeping Beauty puzzle that allows us to retain all three principles. In brief, I argue that Sleeping Beauty’s credence in the uncentered proposition that the coin came up heads should be 1/2, but her credence in the centered proposition that the coin came up heads and it is Monday should be 1/3. I trace the source of the earlier mistakes to an unquestioned assumption in the debate, namely that an uncentered proposition is just a special kind of centered proposition. I argue that the falsity of this assumption is the real lesson of the Sleeping Beauty case.
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| | Other links: springerlink.com | Scholar | At my library | More options ... I describe in this paper a solution to the Sleeping Beauty problem. I begin with the consensual emerald case and discuss then Bostrom's Incubator gedanken. I address then the Sleeping Beauty problem. I argue that the root cause of the flaw in the argument for 1/3 is an erroneous assimilation with a repeated experiment. I show that the same type of analysis also applies to Elga's version of the argument for 1/3. Lastly, I show that the core of the Sleeping Beauty problem is related to the problem of world reduction.
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| | Other links: philsci-archive.pitt.edu | Scholar | More options ... 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 about the coming of Doom. More complex cases suggest a move from countably additive to non-standard probability measures.
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| | Other links: jstor.org journals.uchicago.edu dx.doi.org | Scholar | At my library | More options ... The Sleeping Beauty problem—first presented by A. Elga in a philosophical context—has captured much attention. The problem, we contend, is more aptly regarded as a paradox: apparently, there are cases where one ought to change one’s credence in an event’s taking place even though one gains no new information or evidence, or alternatively, one ought to have a credence other than 1/2 in the outcome of a future coin toss even though one knows that the coin is fair. In this paper we argue for two claims. First, that Sleeping Beauty does gain potentially new relevant information upon waking up on Monday. Second, his credence shift is warranted provided it accords with a calculation that is a result of conditionalization on the relevant information: “this day is an experiment waking day” (a day within the experiment on which one is woken up). Since Sleeping Beauty knows what days d could refer to, he can calculate the probability that the referred to waking day is a Monday or a Tuesday providing an adequate resolution of the paradox.
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| | Scholar | At my library | More options ... We present a new argument for the claim that in the Sleeping Beauty problem, the probability that the coin comes up heads is 1/3. Our argument depends on a principle for the updating of probabilities that we call ‘generalized conditionalization’, and on a species of generalized conditionalization we call ‘synchronic conditionalization on old information’. We set forth a rationale for the legitimacy of generalized conditionalization, and we explain why our new argument for thirdism is immune to two attacks that Pust (Synthese 160:97–101, 2008 ) has leveled at other arguments for thirdism.
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| | Other links: dx.doi.org springerlink.com | Scholar | At my library | More options ... I describe in this paper an ontological solution to the Sleeping Beauty problem. I begin with describing the Entanglement urn experiment. I restate first the Sleeping Beauty problem from a wider perspective than the usual opposition between halfers and thirders. I also argue that the Sleeping Beauty experiment is best modelled with the Entanglement urn. I draw then the consequences of considering that some balls in the Entanglement urn have ontologically different properties form normal ones. In this context, considering a Monday-waking (drawing a red ball) leads to two different situations that are assigned each a different probability. This leads to a two-sided account of the Sleeping Beauty problem. On the one hand, the first situation is handled by the argument for 1/3. On the other hand, the second situation corresponds to a reasoning that echoes the argument for 1/2 but that leads however, to different conclusions.
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| | Scholar | More options ... I describe in this paper an ontological solution to the Sleeping Beauty problem. I begin with describing the Entanglement urn experiment. I restate first the Sleeping Beauty problem from a wider perspective than the usual opposition between halfers and thirders. I also argue that the Sleeping Beauty experiment is best modelled with the Entanglement urn. I draw then the consequences of considering that some balls in the Entanglement urn have ontologically different properties form normal ones. The upshot is that I endorse the halfer conclusion on the probability of Heads once beauty is awaken and the thirder conclusion on conditional probabilities, and that original conclusions ensue on the probability of waking on Monday.
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| | Scholar | More options ... One argument for the thirder position on the Sleeping Beauty problem rests on direct inference from objective probabilities. In this paper, I consider a particularly clear version of this argument by John Pollock and his colleagues (The Oscar Seminar 2008). I argue that such a direct inference is defeated by the fact that Beauty has an equally good reason to conclude on the basis of direct inference that the probability of heads is 1/2. Hence, neither thirders nor halfers can find direct support in an appeal to objective probabilities.
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| | Other links: analysis.oxfordjournals.org | Scholar | At my library | More options ... 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 the hypothesis of a soon extinction, Doom Soon, than on the hypothesis of Doom Late---according to the latter hypothesis there are so many more years I could have found myself living in. Accordingly, Bayesian reasoning leads to a posterior probability of the Doom Soon hypothesis, after I have taken the evidence of my birth date fully into account, that is much higher than the prior probability. I show that the Argument is nothing but a rather trivial mathematical exercise in the calculation of posterior from prior probabilities; it is only about the relation between these probabilities and is silent about the concrete values these probabilities should have. Nothing in the Argument supports the conclusion its proponents think it supports, namely that Doom Soon is much more probable than we ordinarily think. The Argument is formally valid, but ineffective.
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| | Scholar | More options ... 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 ordinary probability judgements do not already reflect our place in history: we justify the predictive use we make of the probabilities yielded by science (or other sources of information) by our knowledge of the fact that we live now, a certain time before the possible occurrence of the events the probabilities refer to. Our degrees of belief should change drastically when we forget the date—importantly, this follows without invoking the "Self Indication Assumption". Subsequent conditionalization on information about which year it is cancels this probability shift again. The Doomsday Argument is about such probability shifts, but tells us nothing about the concrete values of the probabilities—for these, experience provides the only basis. Essentially the same analysis applies to the Sleeping Beauty problem. I argue that Sleeping Beauty "thirders" should be committed to thinking that the Doomsday Argument is ineffective; whereas "halfers" should agree that doom is imminent—but they are wrong.
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| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: jstor.org | Scholar | At my library | More options ...
| | Other links: jstor.org | Scholar | At my library | More options ... Discussion of Dennis Dieks, Reasoning about the future: Doom and beauty
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