Abstract
This project deals with vague expressions: adjectives like 'tall', quantifiers like 'many', adverbs like 'very' and prepositions like 'about' (as in 'about three o?clock'). In other words, it deals with expressions that give rise to borderline cases -- cases where it is not clear whether or not the expression applies. The pervasive vagueness of natural language has often been regarded as a deficiency. But vagueness is a central ingredient in successful communication. Being precise is costly and most of the time there is no need to be so. Often vague indications are enough. Moreover, vagueness is unavoidable in ordinary discourse. Our powers of discrimination are limited, and therefore it is not always possible to draw sharp borderlines. Sometimes we cannot be more precise even if we would want to. There is no way to draw a precise borderline between yellow and orange just using your eyes. The main goal of the project is to develop a formal framework within which the characteristic semantic and pragmatic properties of vague expressions can be systematically explored. One such property is context-dependence. An object that is 'small' in one context can be considered 'large' in another (for example, even small elephants are large animals). This context-dependence radically affects the logical behavior of vague adjectives, and one of the sub-goals of the project is to map out these logical properties, and to study the logical properties of modifying adverbs like 'very', measurement phrases like 'two meters' and approximators like 'about'. A second phenomenon that we intend to study concerns the level of granularity used to interpret precise terms. Thus, we typically interpret round numbers as approximations to an actual quantity, whereas other, non-round numbers are taken more literally. Someone who talks about 'a hundred peopl'? or 'two meters' normally means 'approximately 100 people' and 'roughly two meters'. (If we want to make an exception to this rule, we need to say 'exactly 100 people' and 'exactly two meters'.) But the phrases '103 people' or '1.92 meters' are taken to refer to precise quantities. The question then is what kind of mechanism is responsible for this difference in interpretation, and more generally what factors determine the level of granularity that is understood during a conversation or other discourse.