Parameters
However the linguistic theorist cashes out this linguistic notion, it is not obvious that an adequate theory can be stated using a simple monadic predicate such as ‘S is borderline’ or ‘S is vague’.
For one thing there is no sense in which the sentence ‘Harry is tall’, on its own, is borderline without further qualification. There are a range of heights such that if Harry is within that range then, in ordinary contexts, it is not permissible to assert the sentence ‘Harry is tall’ or its negation; relative to these contexts, the sentence is intuitively borderline. In a context where we are talking about basketball players, however, it may be perfectly acceptable to outright assert the sentence ‘Harry is not tall’. Presumably the sentence ‘Harry is not tall’ is not borderline in this context, even though it is in the former context: whether a sentence is borderline can depend on the context of utterance. Thus a linguistic theorist cannot take as her basic theoretical term a simple monadic predicate; she must take a relation which holds between a sentence and some parameters that includes, at the very least, the context of utterance.What must these parameters include other than the context of utterance? It is natural to think that we must also relativize to disambiguations of a given sentence. The sentence ‘some banks treat their customers well’ might be borderline if ‘bank’ means a financial institution but definitely false if it means the bank of a stream or river.[43]
Presumably we must also specify a language; if ‘Harry is tall’ means that 1=1 in some language L at context c then this sentence is borderline in English at c but not in L at c. Similarly, sentences within a single language change their meaning over time— some terms start off vague and become more precise, and vice versa.[44] For similar reasons one ought to relativize to dialects. Last, but not least, we must relativize to a world—the sentence ‘Harry is bald' could have been used in exactly the same way as the sentence ‘5 is prime’ is actually used. Even though there is an intuitive sense in which the sentence ‘Harry is bald’ would not be borderline at such a world, it is clear that we need a way of ascribing vagueness to a sentence that does not depend on how that sentence is used in the world of evaluation. In this sense we will say that at the world x, ‘Harry is bald’ is borderline as used at w and parameters... even if this sentence is used in a precise way at x (what this means is that the sentence ‘Harry is bald’ counts as borderline at x according to the way that sentence is used at w).
4.3