Sleeping Beauty, evidential support and indexical knowledge: reply to Horgan

Synthese 190 (9):1489-1501 (2013)
Terence Horgan defends the thirder position on the Sleeping Beauty problem, claiming that Beauty can, upon awakening during the experiment, engage in “synchronic Bayesian updating” on her knowledge that she is awake now in order to justify a 1/3 credence in heads. In a previous paper, I objected that epistemic probabilities are equivalent to rational degrees of belief given a possible epistemic situation and so the probability of Beauty’s indexical knowledge that she is awake now is necessarily 1, precluding such updating. In response, Horgan maintains that the probability claims in his argument are to be taken, not as claims about possible rational degrees of belief, but rather as claims about “quantitative degrees of evidential support.” This paper argues that the most plausible account of quantitative degree of support, when conjoined with any of the three major accounts of indexical thought in such a way as to plausibly constrain rational credence, contradicts essential elements of Horgan’s argument
Keywords Sleeping Beauty problem  Logical probability  Epistemic probability  Indexical knowledge
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DOI 10.1007/s11229-011-9888-6
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Logical Foundations of Probability.Rudolf Carnap - 1950 - Chicago]University of Chicago Press.
Attitudes de Dicto and de Se.David Lewis - 1979 - Philosophical Review 88 (4):513-543.

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