Some disagreements are serious, others are footling. There are two disagreements about dreaming. They concern the questions ‘Do we wake or dream?’ and ‘Should we have confidence in dreams or in waking experience?’. The answer, said the Sceptics, is in each case: ‘Who knows?’. According to Galen, the sceptics aren’t serious, and no-one is genuinely puzzled by the questions — the disagreements are of the footling sort. That is true, and philosophically uninteresting. But the sceptical arguments which have exercised philosophers are, as Galen suggests, trifles; and in this case at least it is not difficult to let the fly out of the fly-bottle.

The epistemicist solution to the Sorites Paradox consists of two key components. First, vague terms, just as non-vague ones, have ordinary classical semantic-values and do not require any revision of classical logic or semantics. In the case of ‘tall’, each person is either tall or not tall, and there is a specific number k such that someone is tall if and only if they are over k metres in height, thus ensuring that one of the premises of the paradox is just plainly false. Second, although words like ‘tall’ have such sharp boundaries, we do not and cannot know what these boundaries are, and this explains why we might be tempted to (falsely) conclude that such boundaries do not exist.

Epistemicm faces four principle challenges: addressing the counterintuitiveness of the view; accounting for how the sharp meanings of vague terms are determined; explaining why we are principally ignorant of the sharp-boundaries of vague terms; and explaining what makes vagueness into a distinctive phenomenon, different than other kinds of ignorance. The chapter focuses on discussion of these four challenges, presents the most prominent defence of Epistemicism - Timothy Williamson’s- and discusses a range of objections from recent literature to these responses.

Degree-theoretical approaches to vagueness attempt to flesh out the idea that properties referred to by vague predicates come in degrees, and that sentences containing such predicates can be true to a degree in between absolute truth and absolute falsity. This many-valued semantics is wedded either to some fuzzy logic, or to a non-truth-functional logic, or even to classical logic. The first part of the chapter is devoted to surveying these different alternatives. Subsequently, we discuss the standard fuzzy approach (SFA) to the Sorites, based on infinite-valued Łukasiewicz logic. The mainstream objections to the SFA are then dispelled from a perspective that views classical logic as an ambiguous logic. Next, we address the status of the Tolerance principle in the SFA. We provide a semantics for vague predicates within Rational Pavelka Logic (RPL), contending that the conditional premisses in a Sorites are ambiguous between a reading as Łukasiewicz conditionals and a reading as 'tolerance conditionals'. In conclusion, we formalise in RPL a purely structural version of the paradox, where no logical constant is involved. We ascribe this paradox to an equivocation over consequence.

Incoherentism about vagueness is the view that vague expressions/concepts are incoherent due to their vagueness. This chapter elaborates on what incoherentism is, and defends a particular incoherentist view. It presents an overview of important arguments for and against incoherentism. Among arguments for the view are claims that it provides an attractive account of the nature of vagueness, and of the way in which vagueness is associated with indeterminacy. Among arguments against the view are claims that it presupposes a mistaken view on semantic/conceptual competence, and that the view sits ill with how ubiquitous vagueness is. The specific view defended is compared to the views of Michael Dummett, Terence Horgan and Peter Unger.

The chapter presents a traditional model of partially defined predicates, its rejection of bivalence, and its responses to versions of the Sorites. An intractable problem with the model is then identified as arising from three assumptions: (i) the language containing the predicates is spoken by a vast but ill-defined community, (ii) the linguistic rules make fine-grained distinctions that go unnoticed by speakers, and (iii) the rules are abstracted from uses of the predicates. Progress, it is argued, requires dispensing with (i), embracing a plurality of micro-languages, and using them to construct perfected versions of (ii) and (iii). The resulting model defines the micro-language centered on an individual x at a time in terms of the dispositions of x to affirm or deny certain predicates of objects. Coordinated languages constructed from micro-languages centered on different individuals in a communicative situation allow one to assign assertive contents to uses of sentences. Given this, one can show how precise, knowable (though unknown) demarcations between items in the range of a vague predicate are determined. The technique, available to both defenders and opponents of excluded middle, can be used to reconstruct attractive responses to the Sorites, without some important defects.