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Mind 2000 109(435):415-442; doi:10.1093/mind/109.435.415
© 2000 by Mind Association
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The two-envelope paradox

M Clark and N ShackelA

Department of Philosophy, University of Nottingham, University Park, Nottingham NG7 2RD, UK E-mail: michael.clark@nottingham.ac.uk A Department of Mathematics, De Montfort University, The Gateway, Leicester LE1 9BH, UK E-mail: nshackel@dmu.ac.uk

Previous claims to have resolved the two-envelope paradox have been premature. The paradoxical argument has been exposed as manifestly fallacious if there is an upper limit to the amount of money that may be put in an envelope; but the paradoxical cases which can be described if this limitation is removed do not involve mathematical error, nor can they be explained away in terms of the strangeness of infinity. Only by taking account of the partial sums of the infinite series of expected gains can the paradox be resolved.


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