A consequence relation is strongly classical if it has all the theorems and entailments of classical logic as well as the usual meta-rules (such as Conditional Proof). A consequence relation is weakly classical if it has all the theorems and entailments of classical logic but lacks the usual meta-rules. The most familiar example of a weakly classical consequence relation comes from a simple supervaluational approach to modelling vague language. This approach is formally equivalent to an account of logical consequence according (...) to which α1, ..., αn entails β just in case □α1, ..., □αn entails □β in the modal logic S5. This raises a natural question: If we start with a different underlying modal logic, can we generate a strongly classical logic? This paper explores this question. In particular, it discusses four related technical issues: (1) Which base modal logics generate strongly classical logics and which generate weakly classical logics? (2) Which base logics generate themselves? (3) How can we directly characterize the logic generated from a given base logic? (4) Given a logic that can be generated, which base logics generate it? The answers to these questions have philosophical interest. They can help us to determine whether there is a plausible supervaluational approach to modelling vague language that yields the usual meta-rules. They can also help us to determine the feasibility of other philosophical projects that rely on an analogous formalism, such as the project of defining logical consequence in terms of the preservation of an epistemic status. (shrink)

Logical form has always been a prime concern for philosophers belonging to the analytic tradition. For at least one century, the study of logical form has been widely adopted as a method of investigation, relying on its capacity to reveal the structure of thoughts or the constitution of facts. This book focuses on the very idea of logical form, which is directly relevant to any principled reflection on that method. Its central thesis is that there is no such thing as (...) a correct answer to the question of what is logical form: two significantly different notions of logical form are needed to fulfil two major theoretical roles that pertain respectively to logic and to semantics. This thesis has a negative and a positive side. The negative side is that a deeply rooted presumption about logical form turns out to be overly optimistic: there is no unique notion of logical form that can play both roles. The positive side is that the distinction between two notions of logical form, once properly spelled out, sheds light on some fundamental issues concerning the relation between logic and language. (shrink)

What sort of logic do we get if we adopt a supervaluational semantics for vagueness? As it turns out, the answer depends crucially on how the standard notion of validity as truth preservation is recasted. There are several ways of doing that within a supervaluational framework, the main alternative being between “global” construals (e.g., an argument is valid iff it preserves truth-under-all-precisifications) and “local” construals (an argument is valid iff, under all precisifications, it preserves truth). The former alternative is by (...) far more popular, but I argue in favor of the latter, for (i) it does not suffer from a number of serious objections, and (ii) it makes it possible to restore global validity as a defined notion. (shrink)

In a paper called 'Definiteness and Knowability', Tim Williamson addresses the question whether one must accept that vagueness is an epistemic phenomenon if one adopts classical logic and a disquotational principle for truth. Some have suggested that one must not, hence that classical logic and the disquotational principle may be preserved without endorsing epistemicism. Williamson’s paper, however, finds ‘no plausible way of substantiating that possibility’. Its moral is that ‘either classical logic fails, or the disquotational principle does, or vagueness is (...) an epistemic phenomenon’. The moral of this paper, on the contrary, is that there is a plausible way of substantiating that possibility. The option it contemplates looks like a view that Williamson dismisses at the beginning of his paper, and that others regard as unworthy of serious consideration. (shrink)

Logical Pluralists maintain that there is more than one genuine/true logical consequence relation. This paper seeks to understand what the position could amount to and some of the challenges faced by its formulation and defence. I consider in detail Beall and Restall’s Logical Pluralism—which seeks to accommodate radically different logics by stressing the way that they each fit a general form, the Generalised Tarski Thesis (GTT)—arguing against the claim that different instances of GTT are admissible precisifications of logical consequence. I (...) then consider what it is to endorse a logic within a pluralist framework and criticise the options Beall and Restall entertain. A case study involving many-valued logics is examined. I next turn to issues of the applications of different logics and questions of which logic a pluralist should use in particular contexts. A dilemma regarding the applicability of admissible logics is tackled and it is argued that application is a red herring in relation to both understanding and defending a plausible form of logical pluralism. In the final section, I consider other ways to be and not to be a logical pluralist by examining analogous positions in debates over religious pluralism: this, I maintain, illustrates further limitations and challenges for a very general logical pluralism. Certain less wide-ranging pluralist positions are more plausible in both cases, I suggest, but assessment of those positions needs to be undertaken on a case-by-case basis. (shrink)

This piece gives an overview of the supervaluationist theory of vagueness. According to that theory, a sentence is true if and only if it is true on all ways of making it precise. This yields borderline case predications that are neither true nor false, but yet classical logic is preserved almost entirely. The article presents the view and some of its merits and briefly compares it with other theories of vagueness. It raises issues about higher-order vagueness and the definitely operator (...) and about the supervaluationist's accounts of truth and validity. (shrink)

It is often assumed that the supervaluationist theory of vagueness is committed to a global notion of logical consequence, in contrast with the local notion characteristic of modal logics. There are, at least, two problems related to the global notion of consequence. First, it brings some counterexamples to classically valid patterns of inference. Second, it is subject to an objection related to higher-order vagueness . This paper explores a third notion of logical consequence, and discusses its adequacy for the supervaluationist (...) theory. The paper proceeds in two steps. In the first step, the paper provides a deductive notion of consequence for global validity using the tableaux method. In the second step, the paper provides a notion of logical consequence which is an alternative to global validity, and discusses i) whether it is acceptable to the supervaluationist and ii) whether it plays a better role in a theory of vagueness in the face of the problems related to the global notion. (shrink)

The supervaluationist theory of vagueness is committed to a particular notion of logical consequence known as global validity. According to a recent objection, this notion of consequence is more problematic than is usually thought since i) it bears a commitment to some sort of bizarre inferences, ii) this commitment threatens the internal coherence of the theory and iii) we might find counterexamples to classically valid pat- terns of inference even in the absence of a definitely-operator (or similar device). As a (...) consequence, the supervaluationist theory itself is in trou- ble. This paper discusses the objection. (shrink)

How to handle vagueness? One way is to introduce the machinery of acceptable sharpenings, and reinterpret truth as truth-in-all-sharpenings or truth-in-some-sharpenings. A major selling point has been the conservativism of the resulting systems with respect to classical theoremhood and inference. Supervaluationism and subvaluationism possess interesting formal symmetries, a fact that has been used to argue for the subvaluationist approach. However, the philosophical motivation behind each is a different matter. Subvaluationism comes with a standard story that is difficult to sign up (...) to. In this paper, I make use of a variant of Putnam’s well-known idea of linguistic deference, and some results in voting theory, to answer this criticism of subvaluationism. The acceptability intuitions of each member of a linguistic community amount to their voting for one or more acceptable sharpenings, with truth then characterised as truth-in-a--sufficiency-of-sharpenings. This produces a family of logical systems that are close relations of subvaluationism, share its conservatism results, yet have stronger philosophical foundations in the workings of externalist content. (shrink)