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FORMAL QUALITATIVE PROBABILITY

Part of: Foundations of probability theory

Published online by Cambridge University Press:  20 February 2020

DANIEL KIAN Mc KIERNAN
DANIEL KIAN Mc KIERNAN*
Affiliation:
INDEPENDENT RESEARCHER E-mail:[email protected]
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Abstract

Choices rarely deal with certainties; and, where assertoric logic and modal logic are insufficient, those seeking to be reasonable turn to one or more things called “probability.” These things typically have a shared mathematical form, which is an arithmetic construct. The construct is often felt to be unsatisfactory for various reasons. A more general construct is that of a preordering, which may even be incomplete, allowing for cases in which there is no known probability relation between two propositions or between two events. Previous discussion of incomplete preorderings has been as if incidental, with researchers focusing upon preorderings for which quantifications are possible. This article presents formal axioms for the more general case. Challenges peculiar to some specific interpretations of the nature of probability are brought to light in the context of these propositions. A qualitative interpretation is offered for probability differences that are often taken to be quantified. A generalization of Bayesian updating is defended without dependence upon coherence. Qualitative hypothesis testing is offered as a possible alternative in cases for which quantitative hypothesis testing is shown to be unsuitable.

Keywords

axiomatic probabilityformal epistemologyhypothesis testingqualitative probabilityBayes’ TheoremBayesian updating

MSC classification

Primary: 60A05: Axioms; other general questions
Type
Research Article
Information
The Review of Symbolic Logic , Volume 14 , Issue 4 , December 2021 , pp. 882 - 909
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Copyright
© Association for Symbolic Logic, 2020

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