A condition for transitivity in high probability

Authors
William Roche
Texas Christian University
Abstract
There are many scientific and everyday cases where each of Pr and Pr is high and it seems that Pr is high. But high probability is not transitive and so it might be in such cases that each of Pr and Pr is high and in fact Pr is not high. There is no issue in the special case where the following condition, which I call “C1”, holds: H 1 entails H 2. This condition is sufficient for transitivity in high probability. But many of the scientific and everyday cases referred to above are cases where it is not the case that H 1 entails H 2. I consider whether there are additional conditions sufficient for transitivity in high probability. I consider three candidate conditions. I call them “C2”, “C3”, and “C2&3”. I argue that C2&3, but neither C2 nor C3, is sufficient for transitivity in high probability. I then set out some further results and relate the discussion to the Bayesian requirement of coherence.
Keywords High Probability  Krauss  Multiverse Hypothesis  Screening-off  Super-high probability  Transitivity
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DOI 10.1007/s13194-017-0172-6
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References found in this work BETA

Further Results on the Intransitivity of Evidential Support.Igor Douven - 2011 - Review of Symbolic Logic 4 (4):487-497.
A Weaker Condition for Transitivity in Probabilistic Support.William Roche - 2012 - European Journal for Philosophy of Science 2 (1):111-118.
A Condition for Transitivity in Probabilistic Support.Tomoji Shogenji - 2003 - British Journal for the Philosophy of Science 54 (4):613-616.

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