Abstract

The main goal of this paper is to present and compare two approaches to formalizing cross-world comparisons like John might have been taller than he is in quantified modal logics. One is the standard method employing degrees and graded positives, according to which the example just given is to be paraphrased as something like The height that John has is such that he might have had a height greater than it, which is amenable to familiar formalization strategies with respect to quantified modal logic. The other approach, based on subjunctive modal logic, mimics the mixed indicative-subjunctive patterns typical of cross-world comparisons in many natural languages by means of explicit mood markers. This latter approach is new and should, for various reasons, appeal to linguists and philosophers. Along the way, I argue that attempts to capture cross-world comparison by means of sentential operators are either inadequate or subject to substantive logical and philosophical objections.