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How probable is an infinite sequence of heads?

By Timothy Williamson

Abstract

Isn't probability 1 certainty? If the probability is objective, so is the certainty: whatever has chance 1 of occurring is certain to occur. Equivalently, whatever has chance 0 of occurring is certain not to occur (it has no chance of occurring). If the probability is subjective, so is the certainty: if you give credence 1 to an event, you are certain that it will occur. Equivalently, if you give credence 0 to an event, you are certain that it will not occur (it has no weight in your calculations of expected outcomes). And so on for other kinds of probability, such as evidential probability. The formal analogue of this picture is the regularity constraint: a probability distribution over sets of possibilities is regular just in case it assigns probability 0 only to the null set, and therefore probability 1 only to the set of all possibilities.The full-text of this article is not currently avaiable in ORA, but you may be able to access the article via the publisher copy link on this record page. Citation: Williamson, T. (2007). 'How probable is an infinite sequence of heads?', Analysis 67(3), 173-180. [The definitive publisher-authenticated version is available online at: http://analysis.oxfordjournals.org/cgi/content/extract/67/3/173]

Topics: Philosophy
Year: 2007
DOI identifier: 10.1093/analys
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