GRADATIONAL ACCURACY AND NONCLASSICAL SEMANTICS

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 2001 discussion of generalized forms of Dutch books appropriate to nonclassical settings.