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 explains and defends a dialetheic account of vagueness and its solution to the Sorites Paradox. According to this, statements in the middle of a Sorites progression are both true and false. After an explanation of an appropriate paraconsistent logic, detailed models of Sorites transitions are provided. Crucial to any supposed solution to the Sorites Paradox is how it handles the matter of cut-offs. Much of the chapter concerns how a dialetheic solution handles this.

This Introduction provides the tools necessary for understanding the Sorites Paradox as well as a first orientation concerning its solutions and influence. After presenting the aims and the structure of the book and characterising the notion of vagueness, the Introduction presents the Sorites Paradox in its two main versions: the lack-of-boundaries version and the tolerance version. The Introduction proceeds with an overview of the solutions to the Sorites Paradox that will be developed in the volume: the ones that preserve classical logic (epistemicism, supervaluationism, contextualism, incoherentism) and the ones that do not (intuitionism, rejection of excluded middle, dialetheism, Degree theory and non-transitivism). Finally, after presenting and briefly discussing the Forced-March Paradox, the Introduction ends with a survey of the main areas in which the influence of the Sorites Paradox has been important, which are discussed in the second part of the volume.

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.

Contextualist accounts of the Sorites Paradox are sometimes taken as claiming that vagueness just is (a form of) context-sensitivity, and that the paradox is solvable by appeal to that context-sensitivity alone.We argue that this interpretation is misleading.Certainly contextualist accounts often provide plausible diagnoses of the intuitive pull of the soritical premise, and, due to their dynamical nature, they are well-suited to explain linguistic behaviour in so-called forced-march versions of the puzzle.However, they usually have to be coupled with non-contextualist accounts in order to resolve the paradox proper.We begin by distinguishing various contextualist explanations of the appeal of the soritical premise.Then we point out three main virtues of these approaches and discusssome objections.Lastly we consider the prospects for a recent descendant of contextualism that is meant to solve the paradox proper as well as the forced march puzzle.

When students tell their parents or friends that they are about to take a course in argumentation, the response very likely may be amazement. “We have too much argumentation as it is,” the parent or friend might reply. “Why would anyone want to study that?”

How would we know an argument when we saw one?

That is a tricky question because we don’t actually “see” arguments. They are embedded in conversation, speeches, writings, nonverbal expressions – in the interactions we have when we try to influence other people and to justify the claims we make on their belief or action. In fact, they are what people produce during these interactions. They are sets of statements arranged in the proper relationship to each other. But compared with what is actually said or written, they may need to be reworded, divided or combined, and maybe even made explicit rather than assumed.

When you advance an assertion in conversation with another person, that person might accept it immediately. Or the person might reject it out of hand, refusing even to listen to any more about it. Most reactions, however, fall somewhere between these two extremes. The other person is not yet satisfied that you are correct in what you assert but is willing to give the matter some more thought. Such a person might respond by asking, “What do you have to go on?” or “What makes you say so?” Questions of this sort are requests for evidence that will back up the assertion you have advanced. This chapter is concerned with evidence and its role in argumentation.

Except for the realms of symbolic logic and mathematics, where content-free symbols are often employed, argumentation usually is expressed in language. In fact, arguments typically cannot be separated from the language in which they are cast. This means that language is not just “added on” to an argument for ornamentation, but is an intrinsic part of the argument’s substance, shaping what the argument “means” to people and how they will respond to it. But language is inexact. Its meanings and uses cannot be fixed with precision, and it does not completely match the thinking of either arguer or audience. Understanding how language works is a critical aspect of knowing how an argument will proceed.