Vagueness and Central Gaps
This chapter proposes a new account of the semantics of vague expressions in natural language. It assumes that vague expressions are semantically tolerant. It is observed that the intuitive statement of tolerance corresponds to two different first-order formalizations. Both yield the Sorites contradiction for domains that contain a Sorites sequence of object with respect to some predicate /F/ in the language. But suppose there is a /significant central gap/, i.e. an area in the scale that is larger than the tolerance margin (in the context of use) such that objects with measures above the gap satisfy /F/ and objects with measures below that gap do not, while no object has a measure in the gap. Then one of the two tolerance principles is false. The other is true, but does not induce a Sorites contradiction. The main idea of the proposal is to use the idea of /domain restriction/ so that utterances are interpreted as concerning domains of object so restricted that they contain central gaps. This allows us to retain tolerance, consistency, and bivalence.
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