Counterexamples to a Likelihood Theory of Evidence

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Forster, Malcolm R.
preprint description
The Likelihood Theory of Evidence (LTE) says, roughly, that all the information relevant to the bearing of data on hypotheses (or models) is contained in the likelihoods. There exist counterexamples in which one can tell which of two hypotheses is true from the full data, but not from the likelihoods alone. These examples suggest that some forms of scientific reasoning, such as the consilience of inductions (Whewell, 1858), cannot be represented within Bayesian and Likelihoodist philosophies of science.