Angelika Kratzer

In this paper I offer an account of the meaning of 'must' and 'can' within the framework of possible worlds semantics. The paper consists of two parts: the first argues for a relative concept of modality underlying modal words like 'must' and 'can' in natural language. I give preliminary definitions of the meaning of these words which are formulated in terms of logical consequence and compatibility, respectively. The second part discusses one kind of insufficiency in the meaning definitions given in the first part, which arise from the ex falso quodlibet paradox of logical consequence. In stepwise fashion, I make an attempt to avoid most of the consequences of this paradox for the meaning definitions of 'must' and 'can'. My goal for this paper was to give a truth-conditional account of modals based on a mechanism for drawing conclusions from premises. Premise sets can be inconsistent, so the mechanism I was after had to be able to resolve inconsistencies. There are many areas in human cognition where inconsistencies arise and need to be resolved. Theories of belief revision have attracted most of the attention here, culminating in the 1980s with Alchourrón, Gärdenfors, and Makinson (1985). As Makinson (2003) explains, he and his co-workers were motivated by David Lewis’s work on counterfactuals, but they found possible worlds semantics ontologically unacceptable. My work from the 1970s also took off from Lewis's work on counterfactuals, but I saw no need to escape from possible worlds.