Sleeping Beauty: Exploring a Neglected Solution

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The strong law of large numbers and considerations concerning additional information strongly suggest that Beauty upon awakening has probability 1⁄3 to be in a heads-awakening but should still believe the probability that the coin landed heads in the Sunday toss to be 1⁄2. The problem is that she is in a heads-awakening if and only if the coin landed heads. So, how can she rationally assign different probabilities or credences to propositions she knows imply each other? This is the problem we address in this article. We suggest that ‘p whenever q and vice versa’ may be consistent with p and q having different probabilities if one of them refers to a sample space containing ordinary possible worlds and the other to a sample space containing centred possible worlds, because such spaces may fail to combine into one composite probability space and, as a consequence, ‘whenever’ may not be well-defined; such is the main contribution of this paper.
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