The Meaning of Modality

This paper describes a semantics for modal terms such as can and may that is intended to model the mental representation of their meaning. The basic assumption of the theory is that the evaluation of a modal assertion involves an attempted mental construction of a specified alternative to a given situation rather than the separate evaluation of each member of a set of possible alternatives as would be required by a "'possible worlds" semantics. The theory leads to the conclusion that, contrary to what is often assumed, modal auxiliary verbs are unambiguous. An influential account of the meaning of modality derives from the "possible worlds" semantics developed for modal logics by Kripke (1963) and Hintikka (1963). The central assumption in interpreting such models of modality is the Leibnizian idea that a proposition which is necessarily true is true in all possible worlds including the real world, whereas a proposition which is possibly true is true in some possible world(s). To make sense of certain modal logics, however, one need consider only certain possible worlds, namely, those that are "accessi-ble" to a given world. This notion may be taken to mean that there are only certain possible worlds that can be conceived of in a particular world, and hence for that world a necessary proposition is one that is true in all the worlds conceivable from within it, i.e., true in all the possible worlds that are accessible to it. The importance of the accessibility relation is simply that depending upon the assumptions made about its logic (whether it is deemed to be transitive, reflexive , etc.) so the resulting model captures the semantics of different modal logics. A number of theorists have used a "possible worlds" semantics in attempting to formalize the semantics of natural language (see, e.g., Montague, 1974; Partee, 1975). However, such formal models bear only a remote relation to the mental representation of meaning. Human beings show little aptitude in considering the complete set of alternatives to a given situation, even where He set is small (see Wason & Johnson-Laird, 1972, Chapters 13-15), and for many states of affairs the set of possible alternatives is vast. Moreover, before an individual can evaluate the truth of a proposition in a possible world, it is first necessary for