Is a Possible-Worlds Semantics of Modality Possible? A Problem for Kratzer's Semantics

Modal sentences like ( 1 ) and (2) concern what is necessary or possible and delineating their truth conditions in tenns of possible worlds therefore seems intuitive. Modal logicians--among others, Kripke (1963)--have done this, suggesting that ( 1 ) is equivalent to saying that it is necessary that Britney drink Pepsi, the truth of which requires that in every accessible possible world, Britney drink Pepsi, while (2) is equivalent to saying that it is possible that Britney eat spinach, merely requiring that in some accessible possible world, Britney eat spinach. English auxiliary verbs signifying necessity include 'must', 'ought to', 'have to' and 'should'; those signifying possibility include 'may', 'might', 'can', 'is able to' . Accessibility is relative to some base world with respect to which a given sentence's truth value is determined (usually the actual world). The interpretation of modal sentences is relative in a further way: depending on the kind of modality invoked, the accessible worlds should do the following: • make true what is known ( epistemic reading), • make true some relevant facts of the base world (circumstantial reading), • fulfill what is required (deontic reading), or • fulfill what is desired (bouletic reading), or • obey conditions on a "normal" course of events (stereotypical reading), etc . . Thus a deontic reading o f ( 1 ) with respect to the actual world h as it that given what is required by a certain law(s) or contract (Britney's advertisement contract with Pepsi, say), Britney must drink Pepsi, i .e . , will drink Pepsi in every possible world in which the actual law or contract is fulfilled (these are the deontically possible worlds with respect to the actual world). The kind of modality invoked depends in part on the choice of lexical item (e.g. 'might' allows an epistemic reading but not a deontic one), and in part on the context of utterance (which can decide even among several, say, deontic readings--what is required by U.S . law, by Britney's contract, or by Britney's health) . This standard approach to modality has deficiencies that Kratzer ( 1 977, 1 98 1 , 1 99 1 ) aimed to correct while retaining much of the possible worlds framework posited by the standard analysis. But in the process, she left untouched a stubborn problem. In what follows, I will first explicate the problem (Section 2) and then identify its source and scope (Section 3). After examining two current attempts to solve the problem (Section 4), I will argue that a genuine solution calls for a