Williams, JRG orcid.org/0000-0003-4831-2954 (2016) Probability and nonclassical logic. In: Hajek, A and Hitchcock, C, (eds.) The Oxford Handbook of Probability and Philosophy. Oxford Handbooks . Oxford University Press ISBN 9780199607617
Abstract
Classical tautologies have probability. Classical contradictions have probability. These familiar features reflect a connection between standard probability theory and classical logic. In contexts in which classical logic is questioned—to deal with the paradoxes of self-reference, or vague propositions, for the purposes of scientific theory or metaphysical anti-realism—we must equally question standard probability theory. Section 1 covers the intended interpretation of ‘nonclassical logic’ and ‘probability’. Section 2 reviews the connection between classical logic and classical probability. Section 3 briefly reviews salient aspects of nonclassical logic, laying out a couple of simple examples to fix ideas. Section 4 explores modifications of probability theory. The variations laid down will be motivated initially by formal analogies to the classical setting. In section 5, however, we look at two foundational justifications for the presentations of ‘nonclassical probabilities’ that are arrived at. Sections 6-7 describe extensions of the nonclassical framework: to conditionalization and decision theory in particular. Section 8 will consider some alternative approaches, and section 9 evaluates progress.
Metadata
Item Type: | Book Section |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2016, OUP. This is an author produced version of a book chapter published in The Oxford Handbook of Probability and Philosophy . Uploaded in accordance with the publisher's self-archiving policy |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Arts, Humanities and Cultures (Leeds) > School of Philosophy, Religion and History of Science (Leeds) > School of Philosophy (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 30 Sep 2016 11:46 |
Last Modified: | 15 Jan 2018 18:54 |
Status: | Published |
Publisher: | Oxford University Press |
Series Name: | Oxford Handbooks |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:104891 |