Notre Dame Journal of Formal Logic 44 (2):111-123 (2003)

Authors
Brian Weatherson
University of Michigan, Ann Arbor
Abstract
We generalize the Kolmogorov axioms for probability calculus to obtain conditions defining, for any given logic, a class of probability functions relative to that logic, coinciding with the standard probability functions in the special case of classical logic but allowing consideration of other classes of "essentially Kolmogorovian" probability functions relative to other logics. We take a broad view of the Bayesian approach as dictating inter alia that from the perspective of a given logic, rational degrees of belief are those representable by probability functions from the class appropriate to that logic. Classical Bayesianism, which fixes the logic as classical logic, is only one version of this general approach. Another, which we call Intuitionistic Bayesianism, selects intuitionistic logic as the preferred logic and the associated class of probability functions as the right class of candidate representions of epistemic states (rational allocations of degrees of belief). Various objections to classical Bayesianism are, we argue, best met by passing to intuitionistic Bayesianism—in which the probability functions are taken relative to intuitionistic logic—rather than by adopting a radically non-Kolmogorovian, for example, nonadditive, conception of (or substitute for) probability functions, in spite of the popularity of the latter response among those who have raised these objections. The interest of intuitionistic Bayesianism is further enhanced by the availability of a Dutch Book argument justifying the selection of intuitionistic probability functions as guides to rational betting behavior when due consideration is paid to the fact that bets are settled only when/if the outcome bet on becomes known
Keywords probability   intuitionistic logic
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DOI 10.1305/ndjfl/1082637807
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References found in this work BETA

The Foundations of Statistics.Leonard J. Savage - 1954 - Wiley Publications in Statistics.
Truth and Probability.Frank Ramsey - 1926 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge. pp. 52-94.
The Probable and the Provable.Laurence Jonathan Cohen - 1977 - Oxford and New York: Clarendon Press.
A Mathematical Theory of Evidence.Glenn Shafer - 1976 - Princeton University Press.
The Foundations of Statistics.Leonard J. Savage - 1956 - Philosophy of Science 23 (2):166-166.

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Citations of this work BETA

Imprecise Probabilities.Anna Mahtani - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 107-130.
Dutch Book Arguments.Susan Vineberg - 2011 - Stanford Encyclopedia of Philosophy.
Gradational Accuracy and Nonclassical Semantics.J. Robert G. Williams - 2012 - Review of Symbolic Logic 5 (4):513-537.
Degree Supervaluational Logic.J. Robert G. Williams - 2011 - Review of Symbolic Logic 4 (1):130-149.

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