Possible Worlds and Possible Meanings: A Semantics for the Interpretation of Vague Languages

The paper develops a formal model for interpreting vague languages based on a variant of "supervaluation" semantics. Two modes of semantic variability are modelled, corresponding to different aspects of vagueness: one mode arises where there can be multiple definitions of a term; and the other relates to the threshold of applicability of a vague term with respect to the magnitude of relevant observable values. The truth of a proposition depends on both the possible world and the "precisification" with respect to which it is evaluated. Structures representing possible worlds and precisifications are both specified in terms of primitive functions representing observable measurements, so that the semantics is grounded upon an underlying theory of physical reality. On the basis of this semantics, the acceptability of a proposition to an agent is characterised in terms of a combination of agent's beliefs about the world and their attitude to admissible interpretations of vague predicates.