The Review of Symbolic Logic

Research Article

DEGREE SUPERVALUATIONAL LOGIC

J. ROBERT G. WILLIAMSa1 c1

a1 Department of Philosophy, University of Leeds

Abstract

Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There’s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic that norms belief as classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterize degrees of determinacy. It applies the methodology above to focus on degree logic. This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allow degrees of consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical—all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail.

(Received July 04 2010)

(Online publication August 16 2010)

Correspondence:

c1 DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF LEEDS, WOODHOUSE LANE, LEEDS, WEST YORKSHIRE, LS2 9JT, UNITED KINGDOM. Email: j.r.g.williams@leeds.ac.uk