THE INDICATIVE CONDITIONAL. A PROBABILISTIC CRITERION OF SOUNDNESS FOR DEDUCTIVE INFERENCES Our objective in this section is to establish a prima facie case ...

This paper aims to identify the constitutive rule of assertion, conceived by analogy with the rules of a game. That assertion has such rules is by no means obvious; perhaps it is more like a natural phenomenon than it seems. One way to find out is by supposing that it has such rules, in order to see where the hypothesis leads and what it explains. That will be done here. The hypothesis is not perfectly clear, of course, but we have (...) at least a crude conception of constitutive rules, which we may refine as we elaborate the hypothesis. Although no attempt will be made here to define ‘rule’, some remarks on constitutive rules will focus the discussion. (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)

According to an old and attractive view, vagueness must be eliminated before semantic notions — truth, implication, and so on — may be applied. This view was accepted by Frege, but is rarely defended nowadays.1 This..

In the context of debates about truth, nihilism is the view that nothing is true. This is a very striking and (at first) implausible thesis, which is perhaps why it is seldom discussed. _Truth Without Truths_ applies nihilism to the philosophical debates on truth and paradox, and explores how a nihilist approach to truth is a serious contender. -/- ¶ -/- David Liggins demonstrates that a strong case for nihilism about truth is available. The main grounds for taking nihilism on (...) truth seriously are the solutions it provides to a wide range of paradoxes involving truth, and its epistemological superiority to theories that posit truths. The discussion considers a wider range of paradoxes than usual-including the truth-teller paradox and other paradoxes of underdetermination. -/- ¶ -/- Liggins shows how the debate over truth and paradox can be advanced by drawing on metaphysical debates about realism and anti-realism. _Truth Without Truths_ is also a challenge to deflationism. Deflationists provide an austere, metaphysically lightweight account of truth. But there is one posit that all contemporary deflationists make: they posit truths. By showing that we can well do without truths, Liggins argues that deflationism is actually too lavish a position. -/- ¶ -/- Liggins's preferred form of alethic nihilism includes a Ramseyan analysis of the concept of truth, which uses quantification into sentence position, conceived of as non-objectual and non-substitutional. This book is part of a wider movement exploring the implications of admitting forms of non-objectual, non-substitutional quantification – sometimes called 'higher-order metaphysics'. (shrink)

According to standard assumptions in semantics, ordinary users of a language have implicit beliefs about the truth-conditions of sentences in that language, and they often agree on those beliefs. For example, it is assumed that if Anna and John are both competent users of English and the former utters ‘grass is green’ in conversation with the latter, they will both believe that that sentence is true if and only if grass is green. These assumptions play an important role in an (...) intuitively compelling picture of communication, according to which successful communication through literal assertoric utterances is normally effected thanks to our shared beliefs about the truth-conditions of the sentences uttered in the course of the conversation. Against these standard assumptions, this paper argues that the participants in a conversation rarely have the same beliefs about the truth-conditions of the sentences involved in a linguistic interaction. More precisely, it argues for Variance, the thesis that nearly every utterance is such that there is no proposition which more than one language user believes to be that utterance’s truth-conditional content. If Variance is true, we must reject the standard picture of communication. Towards the end of the paper I identify three ways in which ordinary conversations can be communication-like despite the truth of Variance and argue that the most natural amendments to the standard picture fail to explain them. (shrink)

This paper articulates in formal terms a crucial distinction concerning future contingents, the distinction between what is true about the future and what is reasonable to believe about the future. Its key idea is that the branching structures that have been used so far to model truth can be employed to define an epistemic property, credibility, which we take to be closely related to knowledge and assertibility, and which is ultimately reducible to probability. As a result, two kinds of claims (...) about future contingents—one concerning truth, the other concerning credibility—can be smoothly handled within a single semantic framework. (shrink)

Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There’s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic thatnorms beliefas classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterizedegrees of determinacy. It applies the methodology above to focus ondegree logic. (...) This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allowdegreesof consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical—all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail. (shrink)

Say that an audience understands a given utterance perfectly only if she correctly identifies which proposition (or propositions) that utterance expresses. In ideal circumstances, the participants in a conversation will understand each other’s utterances perfectly; however, even if they do not, they may still understand each other’s utterances at least in part. Although it is plausible to think that the phenomenon of partial understanding is very common, there is currently no philosophical account of it. This paper offers such an account. (...) Along the way, I argue against two seemingly plausible accounts which use Stalnaker’s notion of common ground and Lewisian subject matters, respectively. (shrink)

A sorites argument is a symptom of the vagueness of the predicate with which it is constructed. A vague predicate admits of at least one dimension of variation (and typically more than one) in its intended range along which we are at a loss when to say the predicate ceases to apply, though we start out confident that it does. It is this feature of them that the sorites arguments exploit. Exactly how is part of the subject of this paper. (...) The majority of philosophers writing on vagueness take it to be a kind of semantic phenomenon. If we are right, they are correct in this assumption, which is surely the default position, but they have not so far provided a satisfactory account of the implications of this or a satisfactory diagnosis of the sorites arguments. Other philosophers have urged more exotic responses, which range from the view that the fault lies not in our language, but in the world, which they propose to be populated with vague objects which our semantics precisely reflects, to the view that the world and language are both perfectly in order, but that the fault lies with our knowledge of the properties of the words we use (epistemicism). In contrast to the exotica to which some philosophers have found themselves driven in an attempt to respond to the sorites puzzles, we undertake a defense of the commonsense view that vague terms are semantically vague. Our strategy is to take fresh look at the phenomenon of vagueness. Rather than attempting to adjudicate between different extant theories, we begin with certain pre-theoretic intuitions about vague terms, and a default position on classical logic. The aim is to see whether (i) a natural story can be told which will explain the vagueness phenomenon and the puzzling nature of soritical arguments, and, in the course of this, to see whether (ii) there arises any compelling pressure to give up the natural stance. We conclude that there is a simple and natural story to be told, and we tell it, and that there is no good reason to abandon our intuitively compelling starting point. The importance of the strategy lies in its dialectical structure. Not all positions on vagueness are on a par. Some are so incredible that even their defenders think of them as positions of last resort, positions to which we must be driven by the power of philosophical argument. We aim to show that there is no pressure to adopt these incredible positions, obviating the need to respond to them directly. If we are right, semantic vagueness is neither surprising, nor threatening. It provides no reason to suppose that the logic of natural languages is not classical or to give up any independently plausible principle of bivalence. Properly understood, it provides us with a satisfying diagnosis of the sorites argumentation. It would be rash to claim to have any completely novel view about a topic so well worked as vagueness. But we believe that the subject, though ancient, still retains its power to inform and challenge us. In particular, we will argue that taking seriously the central phenomenon of predicate vagueness—the “boundarylessness” of vague predicates—on the commonsense assumption that vagueness is semantic, leads ineluctably to the view that no sentences containing vague expressions (henceforth ‘vague sentences’) are truth-evaluable. This runs counter to much of the literature on vagueness, which commonly assumes that, though some applications of vague predicates to objects fail to be truth-evaluable, in clear positive and negative cases vague sentences are unproblematically true or false. It is clarity on this, and related points, that removes the puzzles associated with vagueness, and helps us to a satisfying diagnosis of why the sorites arguments both seem compelling and yet so obviously a bit of trickery. We give a proof that semantically vague predicates neither apply nor fail-to-apply to anything, and that consequently it is a mistake to diagnose sorites arguments, as is commonly done, by attempting to locate in them a false premise. Sorites arguments are not sound, but not unsound either. We offer an explanation of their appeal, and defend our position against a variety of worries that might arise about it. The plan of the paper is as follows. We first introduce an important distinction in terms of which we characterize what has gone wrong with vague predicates. We characterize what we believe to be our natural starting point in thinking about the phenomenon of vagueness, from which only a powerful argument should move us, and then trace out the consequences of accepting this starting point. We consider the charge that among the consequences of semantic vagueness are that we must give up classical logic and the principle of bivalence, which has figured prominently in arguments for epistemicism. We argue there are no such consequences of our view: neither the view that the logic of natural languages is classical, nor any plausible principle of bivalence, need be given up. Next, we offer a diagnosis of what has gone wrong in sorites arguments on the basis of our account. We then present an argument to show that our account must be accepted on pain of embracing (in one way or another) the epistemic view of “vagueness”, i.e., of denying that there are any semantically vague terms at all. Next, we discuss some worries that may arise about the intelligibility of our linguistic practices if our account is correct. We argue none of these worries should force us from our intuitive starting point. Finally, we cast a quick glance at other forms of semantic incompleteness. (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)

This paper explores several different accounts of validity within the supervaluationist framework that coincide in the absence of the D operator but differ once that operator is introduced. It argues that the alternatives have different advantages and suggests a form of a pluralism about notions of validity within the supervaluationist framework.