A measure for the distance between an interval hypothesis and the truth

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, ) between an interval hypothesis I and a point hypothesis . 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, ).Lastly, our approach is compared with other proposals made in literature about verisimilitude and distance from the truth.I am grateful for the possibility of spending a period of some months at the Department of Philosophy of University of Gröningen. I profited there a lot from the supervision by Dr. Theo Kuipers. I am also grateful to Prof. Ilkka Niiniluoto who gave rise to my interest in this kind of research during a period spent at Department of Philosophy of University of Helsinki, and who made a number of useful suggestions in the final stage of this paper. Moreover, I would like to thank Dr. Carlo Buttasi for suggesting a better formulation of the proof of (T.24).