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This chapter distinguishes two approaches to vagueness. The vagueness-in-language approach sees the world as exact, and all vagueness as inherent in our means of representing the world. By contrast, the vagueness-in-the-world approach sees the world itself as fuzzy, in the sense that for some things and some attributes of things, there is allegedly no fact of the matter whether those things possess or lack those attributes. The former approach is criticized on several grounds. The vagueness-in-language approach is either incoherent or collapses into vagueness-in-the-world. A recent objection to direct-reference theory, based upon the criticized approach, is shown to be fundamentally mistaken.

This introductory chapter begins with a brief exposition of two types of puzzling issues that the philosophical discussion centres on and that also play a pivotal role in this collection: (i) the question of what vagueness consists in; and (ii) the problem of giving a convincing resolution to the Sorites paradox. This is followed by summaries of the individual chapters, along with an outline of some more specific questions regarding the nature and logic of vagueness raised in them: What sort of facts vagueness is grounded in? Is there vagueness in reality? What sort of similiarity relation is in play in the Sorites paradox? What do we do when using vague expressions in communication? If vagueness calls for a revisionism about logic, what sort of non-classical logic ought we adopt? Is there higher-order vagueness?

It is common among philosophers who take an interest in the phenomenon of vagueness in natural language not merely to acknowledge higher-order vagueness but to take its existence as a basic datum; so that views that lack the resources to account for it, or that put obstacles in the way, are regarded as deficient just on that score. This chapter aims to loosen the hold of this deeply misconceived idea. Higher-order vagueness is no basic datum but an illusion, fostered by misunderstandings of the nature of ordinary (if you will, ‘first-order’) vagueness itself. To see through the illusion is to take a step that is prerequisite for a correct understanding of vagueness, and for any satisfying dissolution of its attendant paradoxes.

Both Hart and Weismann wrote on the existence of ‘open texture’ within the circumstantial gaps of human-flawed rules and practical perception. Weismann derived the term from his approach to Wittgenstein's philosophy, and argued on the general vagueness of the language. H.L.A. Hart argued on judicial interpretation between formalism and rule-scepticism that legal rules have an applicable meaning in accordance with the depending situation, but the problem lies within the language vagueness in interpreted application. The chapter discusses Hart's view on the nature of language, rules and rule application.