Reasoning about the future: Doom and beauty

Synthese 156 (3):427 - 439 (2007)
According to the Doomsday Argument we have to rethink the <span class='Hi'>probabilities</span> 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 <span class='Hi'>probabilities</span> 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 <span class='Hi'>probabilities</span> 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 <span class='Hi'>probabilities</span> 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 <span class='Hi'>probabilities</span>—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.
Keywords Doomsday  Sleeping Beauty  Bayes  Probability updating
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DOI 10.2307/27653528
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Chris Smeenk (2014). Predictability Crisis in Early Universe Cosmology. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 46 (1):122-133.

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