Reducing belief simpliciter to degrees of belief

Annals of Pure and Applied Logic 164 (12):1338-1389 (2013)

Authors
Hannes Leitgeb
Ludwig Maximilians Universität, München
Abstract
Is it possible to give an explicit definition of belief in terms of subjective probability, such that believed propositions are guaranteed to have a sufficiently high probability, and yet it is neither the case that belief is stripped of any of its usual logical properties, nor is it the case that believed propositions are bound to have probability 1? We prove the answer is ‘yes’, and that given some plausible logical postulates on belief that involve a contextual “cautiousness” threshold, there is but one way of determining the extension of the concept of belief that does the job. The qualitative concept of belief is not to be eliminated from scientific or philosophical discourse, rather, by reducing qualitative belief to assignments of resiliently high degrees of belief and a “cautiousness” threshold, qualitative and quantitative belief turn out to be governed by one unified theory that offers the prospects of a huge range of applications. Within that theory, logic and probability theory are not opposed to each other but go hand in hand
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DOI 10.1016/j.apal.2013.06.015
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References found in this work BETA

Reason and the Grain of Belief.Scott Sturgeon - 2008 - Noûs 42 (1):139–165.
What is the Normative Role of Logic?Hartry Field - 2009 - Aristotelian Society Supplementary Volume 83 (1):251-268.
Two Modellings for Theory Change.Adam Grove - 1988 - Journal of Philosophical Logic 17 (2):157-170.
Propositional Reasoning That Tracks Probabilistic Reasoning.Hanti Lin & Kevin Kelly - 2012 - Journal of Philosophical Logic 41 (6):957-981.

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Citations of this work BETA

Evidence: A Guide for the Uncertain.Kevin Dorst - forthcoming - Philosophy and Phenomenological Research.
Belief and Credence: Why the Attitude-Type Matters.Elizabeth Grace Jackson - 2019 - Philosophical Studies 176 (9):2477-2496.
Lockeans Maximize Expected Accuracy.Kevin Dorst - 2017 - Mind 128 (509):175-211.
A Tale of Two Epistemologies?Alan Hájek & Hanti Lin - 2017 - Res Philosophica 94 (2):207-232.

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