Counterexamples to a likelihood theory of evidence

Minds and Machines 16 (3):319-338 (2006)
Abstract
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. In Novum organon renovatum (Part II of the 3rd ed.). The philosophy of the inductive sciences. London: Cass, 1967), cannot be represented within Bayesian and Likelihoodist philosophies of science.
Keywords The likelihood principle  The law of likelihood  Evidence  Bayesianism  Likelihoodism  Curve fitting  Regression  Asymmetry of cause and effect
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Steven Orla Kimbrough (1980). On the Use of Likelihood as a Guide to Truth. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:117 - 128.
Barry Loewer, Robert Laddaga & Roger Rosenkrantz (1978). On The Likelihood Principle and a Supposed Antinomy. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:279 - 286.
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