Michael Glanzberg

Quantified terms are terms of generality. They are also provide some of our prime examples of the phenomenon of scope. The distinction between singular and general terms, as well as the ways that general terms enter into scope relations, are certainly fundamental to our understanding of language. Yet when we turn to natural language, we encounter a huge and apparently messy collection of general terms; not just every and some, but most, few, between five and ten, and many others. Natural-language sentences also display a complex range of scope phenomena; unlike first-order logic, which clearly and simply demarcates scope in its notation.

One of the great successes in the study of language has been the application of formal methods, including those of formal logic. Even so, this chapter argues against one way of accounting for this success, by arguing that the study of natural language semantics and of logical consequence relations are not the same. There is indeed a lot we can glean about logic from looking at our languages, and at our inferential practices, but the semantic properties of natural languages do not determine genuine logical consequence relations. We can get from natural language semantics to logical consequence, but only by a significant process of identification of logical constants, abstraction, and idealization. The chapter also discusses different approaches to the nature of logical consequence, and examines which allow logic and natural language to come closer together.

Quantification is haunted by the specter of paradoxes. Since Russell, it has been a persistent idea that the paradoxes show what might have appeared to be absolutely unrestricted quantification to be somehow restricted. In the contemporary literature, this theme is taken up by Dummett (1973, 1993) and Parsons (1974a,b). Parsons, in particular, argues that both the Liar and Russell’s paradoxes are to be resolved by construing apparently absolutely unrestricted quantifiers as appropriately restricted.

The Taming of the True continues the project Neil Tennant began in Anti-realism and Logic of investigating and defending anti-realism. Tennant’s earlier book anticipated a second volume, in which issues related to empirical discourse would be addressed in greater detail. The Taming of the True provides this sequel. It also attempts a ground-clearing project, by addressing challenges to some of the presuppositions and implications of Tennant’s anti-realist position. Finally, it takes an opportunity to revisit some of the issues examined in the earlier book, in light of the evolving debate over realism and anti-realism.

This paper argues for the thesis that, roughly put, it is impossible to talk about absolutely everything. To put the thesis more precisely, there is a particular sense in which, as a matter of semantics, quantifiers always range over domains that are in principle extensible, and so cannot count as really being ‘absolutely everything’. The paper presents an argument for this thesis, and considers some important objections to the argument and to the formulation of the thesis. The paper also offers an assessment of just how implausible the thesis really is. It argues that the intuitions against the thesis come down to a few special cases, which can be given special treatment. Finally, the paper considers some metaphysical ideas that might surround the thesis. Particularly, it might be maintained that an important variety of realism is incompatible with the thesis. The paper argues that this is not the case.

Cappelen and Hawthorne’s Relativism and Monadic Truth (2009) offers an extended defense of a thesis they call simplicity, which, in brief, holds that propositions are true or false simpliciter. Propositions are cast in their traditional roles as the contents of assertions, and as the semantic values of declarative sentences in contexts. Simplicity stands in sharp contrast to forms of relativism including, for instance, a form that hold that our claims are true or false only relative to a judge. This applies especially to claims of taste, which come out true or false only relative to the judge who finds things tasty (e.g. Glanzberg 2007, Lasersohn 2005). But simplicity also rejects the more widespread temporalist view that propositions are true or false only relative to a time, and it rejects the even more widely held view that propositions are true or false only relative to a world. One reason that has been advanced for temporalism, e.g. by Kaplan (1989), is that our languages seem to contain non-trivial temporal operators. Hence, the argument goes, the semantic values of sentences need to be temporally neutral, i.e. vary for truth or falsehood with time. The same goes for possible worlds and modal operators. Hence, Kaplan and many others think of the semantic values of sentences as sets of world-time pairs. It has been tempting to apply this sort of argument much more widely, to see the semantic values of sentences as varying not just with world and time, but perhaps with location and other parameters as well. Kaplan..

This paper presents an approach to truth and the Liar paradox which combines elements of context dependence and hierarchy. This approach is developed formally, using the techniques of model theory in admissible sets. Special attention is paid to showing how starting with some ideas about context drawn from linguistics and philosophy of language, we can see the Liar sentence to be context dependent. Once this context dependence is properly understood, it is argued, a hierarchical structure emerges which is neither ad hoc nor unnatural

About twenty-five years ago, Charles Parsons published a paper that began by asking why we still discuss the Liar Paradox. Today, the question seems all the more apt. In the ensuing years we have seen not only Parsons’ work (1974), but seminal work of Saul Kripke (1975), and a huge number of other important papers. Too many to list. Surely, one of them must have solved it! In a way, most of them have. Most papers on the Liar Paradox offer some explanation of the behavior of paradoxical sentences, and most also offer some extension for the predicate ‘true’ that they think is adequate, at least in some restricted setting. But if this is a solution, then the problem we face is far from a lack of solutions; rather, we have an overabundance of conflicting ones. Kripke’s work alone provides us with uncountably many different extensions for the truth predicate. Even if it so happens that one of these is a conclusive solution, we do not seem to know which one, or why. We should also ask, given that we are faced with many technically elegant but contradictory views, if they are really all addressing the same problem. What we lack is not solutions, but a way to compare and evaluate the many ones we have.

The study of quantification in natural language has made remarkable progress. Quantification in natural language has been investigated extensively by philosophers, logicians, and linguists. The result has been an elegant and far-reaching theory. This article presents a survey of some of the important components of this theory. The first section presents the core of the theory of generalized quantifiers. This theory explores the range of expressions of generality in natural language, and studies some of their logical properties. The second section turns to issues of how quantifiers enter into scope relations. Here there is less unanimity than in the theory of generalized quantifiers. Two basic approaches, representative of the main theories in the literature, are sketched and compared. The final section turns briefly to the general question of what a quantifier is.

This paper argues against minimalism about truth. It does so by way of acomparison of the theory of truth with the theory of sets, and considerationof where paradoxes may arise in each. The paper proceeds by asking twoseemingly unrelated questions. First, what is the theory of truth about?Answering this question shows that minimalism bears important similaritiesto naive set theory. Second, why is there no strengthened version ofRussell's paradox, as there is a strengthened Liar paradox? Answering thisquestion shows that like naive set theory, minimalism is unable to makeadequate progress in resolving the paradoxes, and must be replaced by adrastically different sort of theory. Such a theory, it is shown, must befundamentally non-minimalist.

This paper argues against relativism, focusing on relativism based on the semantics of predicates of personal taste. It presents and defends a contextualist semantics for these predicates, derived from current work on gradable adjectives. It then considers metasemantic questions about the kinds of contextual parameters this semantics requires. It argues they are not metasemantically different from those in other gradable adjectives, and that contextual parameters of this sort are widespread in natural language. Furthermore, this paper shows that if such parameters are rejected, it leads to an unacceptably rampant form of relativism, that relativizes truth to an open-ended list of parameters.

The discussion of supervenience is replete with the use of in?nitary logical operations. For instance, one may often ?nd a supervenient property that corresponds to an in?nite collection of supervenience-base properties, and then ask about the in?nite disjunction of all those base properties. This is crucial to a well-known argument of Kim (1984) that supervenience comes nearer to reduction than many non-reductive physicalists suppose. It also appears in recent discussions such as Jackson (1998).