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A Better Way of Framing Williamson’s Coin-Tossing Argument, but It Still Does Not Work

Published online by Cambridge University Press:  01 January 2022

Colin Howson
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Abstract

Timothy Williamson claimed to prove with a coin-tossing example that hyperreal probabilities cannot save the principle of regularity. A premise of his argument is that two specified infinitary events must be assigned the same probability because, he claims, they are isomorphic. But as has been pointed out, they are not isomorphic. A way of framing Williamson’s argument that does not make it depend on the isomorphism claim is in terms of shifts in Bernoulli processes, the usual mathematical model of sequential coin tossing. But even so framed, the argument still fails.

Type
DISCUSSION
Information
Philosophy of Science , Volume 86 , Issue 2 , April 2019 , pp. 366 - 374
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

For helpful comments I thank the journal’s anonymous reviewers and Tim Childers and the other members of the Institute of Philosophy, Czech Academy of Sciences.

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