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A Measure for the Distance between an Interval Hypothesis and the Truth

Roberto Festa
Synthese
Vol. 67, No. 2, Causation and Scientific Inference and Related Matters (May, 1986), pp. 273-320
Published by: Springer
Stable URL: http://www.jstor.org/stable/20116273
Page Count: 48
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A Measure for the Distance between an Interval Hypothesis and the Truth
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Abstract

The problem of distance from the truth, and more generally distance between hypotheses, is considered here with respect to the case of quantitative hypotheses concerning the value of a given scientific quantity. Our main goal consists in the explication of the concept of distance D(I, Θ) between an interval hypothesis I and a point hypothesis Θ. In particular, we attempt to give an axiomatic foundation of this notion on the basis of a small number of adequacy conditions. Moreover, the distance function introduced here is employed for the reformulation of the approach to scientific inference -- developed by Hintikka, Levi and other scholars -- labelled "cognitive decision theory". In this connection, we supply a concrete illustration of the rules for inductive acceptance of interval hypotheses that can be obtained on the basis of D(I, Θ). Lastly, our approach is compared with other proposals made in literature about verisimilitude and distance from the truth.

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