A Theory of Belief for Scientific Refutations

Synthese 145 (3):397-423 (2005)
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Abstract

A probability function on an algebra of events is assumed. Some of the events are scientific refutations in the sense that the assumption of their occurrence leads to a contradiction. It is shown that the scientific refutations form a a boolean sublattice in terms of the subset ordering. In general, the restriction of to the sublattice is not a probability function on the sublattice. It does, however, have many interesting properties. In particular, (i) it captures probabilistic ideas inherent in some legal procedures; and (ii) it is used to argue against the commonly held view that behavioral violations of certain basic conditions for qualitative probability are indicative of irrationality. Also discussed are (iii) the relationship between the formal development of scientific refutations presented here and intuitionistic logic, and (iv) an interpretation of a belief function used in the behavioral sciences to explain empirical results about subjective, probabilistic estimation, including the Ellsberg paradox.

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Citations of this work

Logic in reality.Joseph E. Brenner - 2008 - Dordrecht: Springer.

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References found in this work

The mathematics of metamathematics.Helena Rasiowa - 1963 - Warszawa,: Państwowe Wydawn. Naukowe. Edited by Roman Sikorski.
Risk, ambiguity, and the Savage axioms.Daniel Ellsberg - 1961 - Quarterly Journal of Economics:643–69.
Zur Deutung der intuitionistischen Logik.Andrey N. Kolmogorov - 1932 - Mathematische Zeitschrift 35:58-65.

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