The first part of the book provides a conceptual map of theories of vagueness. At the centre of the map is the classical view of vagueness, according to which the semantics of vague language is exactly the same as the semantics of precise language. This view applies the standard model theory for precise mathematical language to vague language. The key elements of this classical model theory then give the axes of the space of possible theories of vagueness. This chapter deals with preliminaries. Section 1.1 introduces some basic formal tools. Section 1.2 presents the classical semantic picture which will be located at the origin of the map.
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