Everett, Anthony [2000] 'A Simple Logic for Comparisons and Vagueness', Synthèse 123, pp. 263-8.
Abstract: I provide an intuitive, semantic account of a new logic for comparisons
(CL), in which atomic statements are assigned both a classical truth-value
and a ``how much'' value or extension in the range [0, 1]. The truth-value
of each comparison is determined by the extensions of its component
sentences; the truth-value of each atomic depends on whether its extension
matches a separate standard for its predicate; everything else is computed
classically. CL is less radical than Casari's comparative logics, in that it
does not allow for the formation of comparative statements out of
truth-functional molecules. I argue that CL provides a better analysis of
comparisons and predicate vagueness than classical logic, fuzzy logic or
supervaluation theory. CL provides a model for descriptions of the world in
terms of comparisons only. The sorites paradox can be solved by the
elimination of atomic sentences.