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Problems with the simplified account and some unnatural features of the model theory lead to refinements of the philosophical account, the model theoretic semantics, and perhaps the logic as well. This chapter deals with what passes for higher-order vagueness — vagueness in the notions of ‘determinacy’ and ‘borderline’. The philosophical picture is developed, by extending and modifying the account presented in Chapter 1. This is followed with the required modifications to the model theory, and the central meta-theorems.

This chapter provides a simplified account of how vagueness arises in language and is manifested in the use of language. It is a commonplace that the extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases. A person can be tall with respect to male accountants and not tall (or even short) with respect to professional basketball players. A person can be wealthy with respect to local business tycoons, but not wealthy with respect to CEOs of major software companies. The main feature of the present account is that the extensions (and anti-extensions) of vague terms also vary in the course of a conversation, even after the external contextual features, such as the comparison class, are fixed. A central thesis of the view is that, in some cases, a competent speaker of the language can go either way in the borderline area of a vague predicate without sinning against the meaning of the words and the non-linguistic facts.

This chapter provides a technical model theory, using the resources of mathematical logic, for vagueness in some formalized languages. The system has a similar structure to the supervaluationist approach, employing the notion of a sharpening (or precisification) of a base interpretation. In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity. The model theory is much like that of the Kripke semantics for intuitionistic logic, except that both extensions and anti-extensions vary, in concert with each other, throughout a given frame. And the system does not rely on completely sharp interpretations.

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.

This chapter examines the connections between these three notions: philosophical open texture, Hartian open texture, and defeasibility in legal reasoning. Section A begins by exploring the origins of the idea of ‘open texture’. Section B looks at the way the concept works within Hart's analysis, Section C offers a brief overview of defeasibility while Section D compares open texture with defeasibility. The primary conclusion is that Hartian open texture and defeasibility are, at best, only broadly analogous, in that both create circumstances in which judges have discretion to create new law or exceptions to existing law.

This paper challenges some widespread assumptions about the role of the modal axiom S4 in theories of vagueness. In the context of vagueness, S4 usually appears as the principle ‘If it’s clear (determinate, definite) that A, then it’s clear that it’s clear that A’, or, formally, CA→CCA. We argue first that contrary to common opinion, higher-order vagueness and S4 are perfectly compatible. This is in response to claims such as Williamson’s that if vagueness is defined using a clarity operator that obeys S4, higher-order vagueness disappears. Second, we argue that contrary to common opinion, bivalence-preservers (such as epistemicists) can without contradiction condone S4, and bivalence-discarders (such as open-texture theorists and supervaluationists) can without contradiction reject S4. To this end, we show how in the debate over S4 two different notions of clarity are in play, and elucidate their respective functions in accounts of higher-order vagueness. Third, we rebut several arguments produced by opponents of S4, including those by Williamson.

This chapter articulates a tentative thesis that the foregoing matter of meaning-shift, concerning the logical terminology, is itself context-sensitive, and, indeed, interest-relative. Whether the logical terms have the same meaning, or different meanings, in the different structures or theories (with different logics) depends on what is salient in a conversation comparing the structures or theories. For some purposes, it makes sense—it is all but demanded—to insist that the classical connectives and quantifiers have different meanings than their counterparts in intuitionistic, paraconsistent, quantum, etc. systems. For other purposes, in other conversational contexts, it makes more sense to say that the meaning of the logical terminology is the same in the different systems. This sort of meta-contextualist thesis raises deep and vexing questions concerning meaning. The thesis of this chapter is situated within some general issues concerning language, such as vagueness, open-texture, and verbal disputes.

The criteria for statehood are of a special character, in that their application conditions the application of most other international laws. As a result, existing States have tended to retain for themselves as much freedom of action with regard to new States as possible. At the empirical level, the question is whether, given the existence of international laws determining what ‘States’ are, those rules are sufficiently certain to be applied in specific cases or have been kept so uncertain or open to manipulation as not to provide any standards at all. This question is independent of the point that States may on occasions recognise as a State an entity that does not come within the accepted definition of the term. Rather, the question is whether States can effectively refuse, under cover of the ‘open texture’ of the rules, to treat entities as States that do in truth qualify as such.

Ronald Dworkin's earlier work advocated that there exists a unique right answer for a vast majority of cases. However the nature of this ‘right answer thesis’ was a direct response to Hart's argument on ‘open texture’ and judicial discretion. In addition, Dworkin did not include the limitations and complexities of language as an obstacle to his thesis. His more recent work provided a more helpful scrutiny on ambiguous, open-textured, or unclear applications, and argument of relevant legal language. This chapter investigates the effectiveness of the ‘right answer thesis’, inquiring into the strengths and weaknesses of the thesis argument, from the offered critique by A.D. Woozley. Dworkin's interpretative (holistic) approach did not fit the practice.

Vagueness of language is commonly supposed to pose problems for the law insofar as it is a source of indeterminacy, and indeterminacy results in borderline or ‘hard’ cases. This chapter argues that in legal cases where soritical vagueness (the vagueness associated with borderline cases) occurs, specifically where the court appears obliged to draw sharp boundaries between cases that are only incrementally different, the difficulty derives not from the vagueness of the language in which the law is expressed, but rather from the relationship between the law and the seamless character of the phenomena (properties, actions, states of affairs, etc.) to which it must apply. Soritical vagueness provides the resources to avoid drawing sharp boundaries in a continuous environment; but the law, insofar as it demands ‘sharp’ decisions, cannot make use of those resources. Only ordinary speakers can make use of them, and so the legal difficulties remain.

Most of the writing about clear cases is not about sociology of chances of convergences but rather about language-based determinacy. Clear cases may give the appearance of a predictable or obvious nature and basis, but one can't deny a possible facade. A close analysis reveals a variety of problems. Other influences that can make a clear case unclear or a hard case easy includes the issue of speakers' intention, dialects and idiolects, context, community practices and assumption, views about justice, ideas about rule-application, as well as the issues of vagueness and ‘open texture’.

Most of the philosophical literature on vagueness starts with the identification of the term whose vagueness is at issue—tall, short, night, day, bald, tadpole, etc. But in legal interpretation an additional problem arises, because it is not always obvious which term in a legal text, or even which legal text, is the operative one. H.L.A. Hart’s idea of a rule of recognition conceptualizes the way in which some second-order rule is necessary to identify which first-order rule is applicable to some form of conduct, but it is often the case that the second-order rule itself exhibits various forms of vagueness. When that is so, vagueness appears as a distinct problem with important but often unrecognized implications.

This chapter explores the ramifications of a relativist view of logic with respect to the meanings of logical terms. It is a twist on the old question of whether classicists and intuitionists have any substantial disagreement, or whether they are merely talking past each other as they attach different meanings to the crucial logical terminology. The author argues that the very question of whether the meanings are the same or different is itself a context sensitive matter: it depends on what aspects of the situation are salient.

This chapter examines how the Athenians attempted to cope with law's “open texture,” that is, the potential ambiguity of statutes. Some scholars have claimed that the Athenian courts were not interested in consistency and tended to judge cases on an ad hoc basis. While it is true that litigants did not often cite previous cases in forensic oratory, this was because most trials concerned questions of fact. When questions concerning the interpretation of statute arose, it was not unusual for litigants to appeal to precedents or to the intent of the lawgiver to support their legal arguments. Litigants used precedents to show that their interpretation of the law was the traditional one, accepted by other citizens.