The purpose of this paper is to challenge some widespread assumptions about the role of the modal axiom 4 in a theory of vagueness. In the context of vagueness, axiom 4 usually appears as the principle ‘If it is clear (determinate, definite) that A, then it is clear (determinate, definite) that it is clear (determinate, definite) that A’, or, more formally, CA → CCA. We show how in the debate over axiom 4 two different notions of clarity are in play (...) (Williamson-style "luminosity" or self-revealing clarity and concealeable clarity) and what their respective functions are in accounts of higher-order vagueness. On this basis, we argue first that, contrary to common opinion, higher-order vagueness and S4 are perfectly compatible. This is in response to claims like that by Williamson that, if vagueness is defined with the help of a clarity operator that obeys axiom 4, higher-order vagueness disappears. Second, we argue that, contrary to common opinion, (i) bivalence-preservers (e.g. epistemicists) can without contradiction condone axiom 4 (by adopting what elsewhere we call columnar higher-order vagueness), and (ii) bivalence-discarders (e.g. open-texture theorists, supervaluationists) can without contradiction reject axiom 4. Third, we rebut a number of arguments that have been produced by opponents of axiom 4, in particular those by Williamson. (The paper is pitched towards graduate students with basic knowledge of modal logic.). (shrink)

ABSTRACT: Stewart Shapiro recently argued that there is no higher-order vagueness. More specifically, his thesis is: (ST) ‘So-called second-order vagueness in ‘F’ is nothing but first-order vagueness in the phrase ‘competent speaker of English’ or ‘competent user of “F”’. Shapiro bases (ST) on a description of the phenomenon of higher-order vagueness and two accounts of ‘borderline case’ and provides several arguments in its support. We present the phenomenon (as Shapiro describes it) and the accounts; then discuss Shapiro’s arguments, arguing that (...) none is compelling. Lastly, we introduce the account of vagueness Shapiro would have obtained had he retained compositionality and show that it entails true higher-order vagueness. (shrink)

On standard versions of supervaluationism, truth is equated with supertruth, and does not satisfy bivalence: some truth-bearers are neither true nor false. In this paper I want to confront a well-known worry about this, recently put by Wright as follows: ‘The downside . . . rightly emphasized by Williamson . . . is the implicit surrender of the T-scheme’. I will argue that such a cost is not high: independently motivated philosophical distinctions support the surrender of the T- scheme, and (...) suggest acceptable approximations. (shrink)

Truth-value gaps have received little attention from a foundational perspective, a fact which has rightfully opened up gap theories to charges of vacuousness. This paper develops an account of the foundations of gap-like behavior which has some hope of avoiding such charges. I begin by reviewing and sharpening a powerful argument of Dummett’s to constrain the options that gap theorists have to make sense of their views. I then show that within these strictures, we can give an account of gaps (...) by drawing on elements of a broadly Stalnakerian framework for assertion and using gaps to track an amalgamation of assertoric effects. The discussion reveals that we may need special resources in our theories of assertion to posit gaps, that gaps may be unusable in characterizing the structure of mental states, and that gaps may have heterogeneous linguistic sources that result in equally heterogeneous projective and inferential behavior. (shrink)

Scientific anti-realists who appeal to the pessimistic induction (PI) claim that the theoretical terms of past scientific theories often fail to refer to anything. But on standard views in philosophy of language, such reference failures prima facie lead to certain sentences being neither true nor false. Thus, if these standard views are correct, then the conclusion of the PI should be that significant chunks of current theories are truth-valueless. But that is semantic anti-realism about scientific discourse—a position most philosophers of (...) science, anti-realists included, consider anathema today. Therefore, proponents of the PI confront a dilemma: either accept semantic anti-realism or reject common semantic views. I examine strategies (with particular emphasis on supervaluations) for the PI proponent to either lessen the sting of this argument, or learn to live with it. 1 Introduction2 Designation Failure 2.1 Designation failure leads to truth-valueless sentences2.1.1 Direct reference theory2.1.2 Fregeanism2.1.3 Accounts of reference-fixing: why ‘phlogiston’ fails to designate 2.2 Objection: sentences exhibiting designation failure are false not truth-valueless 2.3 Avoiding truth-valuelessness via controversial semantic positions3 What to do? Closing the Gaps4 Conclusion. (shrink)

In Category Mistakes, Ofra Magidor provides two arguments against the view that category mistakes express propositions that are not truth-evaluable at some world. I argue that her first, Williamsonian argument against this view begs the question, and that her second argument rests on a misleading conception of how semantic defect results in infelicity judgments. I conclude by conceding that she is still correct to stress that the view she opposes face noteworthy foundational and empirical challenges.

Truth is one of the central subjects in philosophy. It is also one of the largest. Truth has been a topic of discussion in its own right for thousands of years. Moreover, a huge variety of issues in philosophy relate to truth, either by relying on theses about truth, or implying theses about truth.

In this paper, we offer a theory of the role of the nominal in complex demonstrative expressions, such as 'this dog' or 'that glove with a hole in it'.

Logic: the Basics is an accessible introduction to the core philosophy topic of standard logic. Focussing on traditional Classical Logic the book deals with topics such as mathematical preliminaries, propositional logic, monadic quantified logic, polyadic quantified logic, and English and standard ‘symbolic transitions’. With exercises and sample answers throughout this thoroughly revised new edition not only comprehensively covers the core topics at introductory level but also gives the reader an idea of how they can take their knowledge further and the (...) philosophical questions around logic. -/- Logic: the Basics is essential reading for first-year undergraduate philosophy students on standard introductory logic courses. (shrink)