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GRADATIONAL ACCURACY AND NONCLASSICAL SEMANTICS

Published online by Cambridge University Press:  03 October 2012

J. ROBERT G. WILLIAMS
J. ROBERT G. WILLIAMS*
Affiliation:
University of Leads
*
*DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF LEEDS, WOODHOUSE LANE, LEEDS, LS2 9JT, UK. E-mail: [email protected]
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Abstract

This paper gives a generalization of Jim Joyce’s 1998 argument for probabilism, dropping his background assumption that logic and semantics are classical. Given a wide variety of nonclassical truth-value assignments, Joyce-style arguments go through, allowing us to identify in each case a class of “nonclassically coherent” belief states. To give a local characterization of coherence, we need to identify a notion of logical consequence to use in an axiomatization. There is a very general, ‘no drop in truth-value’ characterization that will do the job. The result complements Paris’s 2001discussion of generalized forms of Dutch books appropriate to nonclassical settings.

Type
Research Articles
Information
The Review of Symbolic Logic , Volume 5 , Issue 4 , December 2012 , pp. 513 - 537
Copyright
Copyright © Association for Symbolic Logic 2012

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