Saturday, June 1, 2013
The Objective Conception of Context and Its Logic CHRISTOPHERMENZEL Department of Philosophy, Texas AhIM University, College Station, Texas 77843-4237 U.S.A. (email: email@example.com) Abstract. In this paper, an “objective” conception of contexts based loosely upon situation theory is developed and formalized. Unlike “subjective” conceptions, which take contexts to be something like sets of beliefs, contexts on the objective conception are taken to be complex, structured pieces of the world that (in general) contain individuals, other contexts, and propositions about them. An extended first-order language for this account is developed. The language contains complex terms for propositions, and the standard predicate ‘ist’ that expresses the relation that holds between a context and a proposition just in case the latter is true in the former. The logic for the objective conception features a “global” classical predicate calculus, a “local” logic for reasoning within contexts, and axioms for propositions. The specter of paradox is banished from the logic by allowing ‘ist’ to be nonbivalent in problematic cases: it is not in general the case, for any context c and proposition p, that either ist(c,p) or ist.c;:p/. An important representational capability of the logic is illustrated by proving an appropriately modified version of an illustrative theorem from McCarthy’s classic Blocks World example.