A Tale of Two Envelopes
Department of Philosophy, University of Toronto, Toronto, Ontario M5R 2M8, Canada bkatz{at}chass.utoronto.ca Department of Philosophy, Glendon College, York University, Toronto, Ontario M4N 3M6, Canada dolin{at}yorku.ca
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Abstract |
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This paper deals with the two-envelope paradox. Two main formulations of the paradoxical reasoning are distinguished, which differ according to the partition of possibilities employed. We argue that in the first formulation the conditionals required for the utility assignment are problematic; the error is identified as a fallacy of conditional reasoning. We go on to consider the second formulation, where the epistemic status of certain singular propositions becomes relevant; our diagnosis is that the states considered do not exhaust the possibilities. Thus, on our approach to the paradox, the fallacy, in each formulation, is found in the reasoning underlying the relevant utility matrix; in both cases, the paradoxical argument goes astray before one gets to questions of probability or calculations of expected utility.