SCIENCE AND SEMANTICS: THE CASE OF VAGUENESS AND SUPERVALUATION*

Abstract: It is widely assumed that the methods and results of science have no place among the data to which our semantics of vague predicates must answer. This despite the fact that it is well known that such prototypical vague predicates as ‘is bald’ play a central role in scientific research (e.g. the research that established Rogaine as a treatment for baldness). I argue here that the assumption is false and costly: in particular, I argue one cannot accept either supervaluationist semantics, or the criticism of that semantics offered by Fodor and Lepore, without having to abandon accepted, and unexceptionable, scientific methodology.     

Vagueness and revision sequences

Theories of truth and vagueness are closely connected; in this article, I draw another connection between these areas of research. Gupta and Belnap’s Revision Theory of Truth is converted into an approach to vagueness. I show how revision sequences from a general theory of definitions can be used to understand the nature of vague predicates. The revision sequences show how the meaning of vague predicates are interconnected with each other. The approach is contrasted with the similar supervaluationist approach.     

What makes it a heap?

On the epistemic view of vagueness, a vague expression has sharp boundaries whose location speakers of the language cannot recognize. The paper argues that one of the deepest sources of resistance to the epistemic view is the idea that all truths are cognitively accessible from truths in a language for natural science, conceived as precise, in a sense explained. The implications of the epistemic view for issues about the relations between vague predicates and scientific predicates are investigated.     

Reasoning with Slippery Predicates

It is a commonplace that the extensions of most, perhaps all, vague predicates vary with such features as comparison class and paradigm and contrasting cases. My view proposes another, more pervasive contextual parameter. Vague predicates exhibit what I call open texture: in some circumstances, competent speakers can go either way in the borderline region. The shifting extension and anti-extensions of vague predicates are tracked by what David Lewis calls the “conversational score”, and are regulated by what Kit Fine calls penumbral connections, including a principle of tolerance. As I see it, vague predicates are response-dependent, or, better, judgement-dependent, at least in their borderline regions. This raises questions concerning how one reasons with such predicates. In this paper, I present a model theory for vague predicates, so construed. It is based on an overall supervaluationist-style framework, and it invokes analogues of Kripke structures for intuitionistic logic. I argue that the system captures, or at least nicely models, how one ought to reason with the shifting extensions (and anti-extensions) of vague predicates, as borderline cases are called and retracted in the course of a conversation. The model theory is illustrated with a forced march sorites series, and also with a thought experiment in which vague predicates interact with so-called future contingents. I show how to define various connectives and quantifiers in the language of the system, and how to express various penumbral connections and the principle of tolerance. The project fits into one of the topics of this special issue. In the course of reasoning, even with the external context held fixed, it is uncertain what the future extension of the vague predicates will be. Yet we still manage to reason with them. The system is based on that developed, more fully, in my Vagueness in Context, Oxford, Oxford University Press, 2006, but some criticisms and replies to critics are incorporated.     

FREGE'S CONCEPT PARADOX AND THE MIRRORING PRINCIPLE

Frege held that singular terms can refer only to objects, not to concepts. I argue that the counter-intuitive consequences of this claim ('the concept paradox') arise from Frege's mirroring principle that an incomplete expression can only express an incomplete sense and stand for an incomplete reference. This is not, as is sometimes thought, merely because predicates and singular terms cannot be intersubstituted salva veritate ( congruitate ). The concept paradox, properly understood, poses therefore a different, harder, challenge. An investigation of the foundations of the mirroring principle also sheds light on the role which language plays in Frege's epistemology of logic.     

The Thesis of Vague Objects and Unger's Problem of the Many

Abstract

Peter Unger argues that his puzzle of the problem of the many leaves us with having to accept either countless embedded objects of the same kind or a Parmenidean rejection of distinct entities. This dilemma can be avoided if objects truly have vague boundaries. It is metaphysically impossible for an entity with a vague boundary to be embedded within an entity of the same kind. A cloud's parts (that is, cloud stuff) cannot be clearly embedded within the vague boundary region of another cloud, for the latter region is defined as possessing neither cloud-stuff nor non-cloud-stuff. Likewise, there cannot be a cloud with a vague boundary embedded in the middle of another cloud because there would then have to be a population of water droplets dense enough to compose part of the larger cloud which was nevertheless insufficient in density to compose part of the embedded cloud.     

Do Differences in Grammatical Form between Languages Explain Differences in Ontology between Different Philosophical Traditions?: A Critique of the Mass-Noun Hypothesis

It is an assumed view in Chinese philosophy that the grammatical differences between English or Indo-European languages and classical Chinese explain some of the differences between the Western and Chinese philosophical discourses. Although some philosophers have expressed doubts about the general link between classical Chinese philosophy and syntactic form of classical Chinese, I discuss a specific hypothesis, i.e., the mass-noun hypothesis, in this essay. The mass-noun hypothesis assumes that a linguistic distinction such as between the singular terms and the predicates is sufficient to justify or necessarily leads to a specific ontological distinction such as the distinction between the particular and the universal. I argue that one cannot read off semantic properties simply from syntactic ones and hence the syntactic differences do not automatically translate into the semantic differences between languages, that the syntactic features of Chinese nouns do not have explanatory significance in explaining why the particular-universal problem does not arise in the classical period of Chinese philosophy, and that the part-whole ontology allegedly informed by the mass-noun-like semantics does not provide a natural or intuitive picture of the language-world relation.     

God’s silence

Vagueness manifests itself (among other things) in our inability to find boundaries to the extension of vague predicates. A semantic theory of vagueness plans to justify this inability in terms of the vague semantic rules governing language and thought. According to a supporter of semantic theory, the inability to find such a boundary is not dependent on epistemic limits and an omniscient being like God would be equally unable. Williamson (Vagueness, 1994) argued that cooperative omniscient beings adequately instructed would find a precise boundary in a sorites series and that, for this reason, the semantic theory misses its target, while Hawthorne (Philosophical Studies 122:1–25, 2005) stood with the semantic theorists and argued that the linguistic behaviour of a cooperative omniscient being like God would clearly demonstrate that he does not find a precise boundary in the sorites series. I argue that Hawthorne’s definition of God’s cooperative behaviour cannot be accepted and that, contrary to what has been assumed by both Williamson and Hawthorne, an omniscient being like God cannot be a cooperative evaluator of a semantic theory of vagueness.     

Proto-Rigidity*

What is it for a predicate or a general term to be a rigid designator? Two strategies for answering this question can be found in the literature, but both run into severe difficulties. In this paper, it is suggested that proper names and the usual examples of rigid predicates share a semantic feature which does the theoretical work usually attributed to rigidity. This feature cannot be equated with rigidity, but in the case of singular terms this feature entails their rigidity, as understood in the standard characterisation. Hence, it is appropriate to call this feature proto-rigidity.     

I—Stewart Shapiro

ABSTRACT After a brief account of the problem of higher-order vagueness, and its seeming intractability, I explore what comes of the issue on a linguistic, contextualist account of vagueness. On the view in question, predicates like'borderline red'and'determinately red'are, or at least can be, vague, but they are different in kind from'red'. In particular,'borderline red'and'determinately red'are not colours. These predicates have linguistic components, and invoke notions like'competent user of the language'. On my view, so-called'higher-order vagueness'is actually ordinary, first-order vagueness in different predicates. I explore the possibility that, nevertheless, a pernicious regress ensues.     

Denoting and Disquoting

Fregeans hold that predicates denote things, albeit things different in kind from what singular terms denote. This leads to a familiar problem: it seems impossible to say what any given predicate denotes. One strategy for avoiding this problem reduces the Fregean position to form of nominalism. I develop an alternative strategy that lets the Fregean hold on to the view that predicate denote things by reconceiving the nature of singular denotation and of Fregean objects.     

Almost‐Ontology: Why Epistemicism Cannot Help Us Avoid Unrestricted Composition or Diachronic Plenitude

That any filled location of spacetime contains a persisting thing has been defended based on the ‘argument from vagueness.’ It is often assumed that since the epistemicist account of vagueness blocks the argument from vagueness it facilitates a conservative ontology without gerrymandered objects. It doesn't. The epistemic vagueness of ordinary object predicates such as ‘bicycle’ requires that objects that can be described as almost‐but‐not‐quite‐bicycle exist even though they fall outside the predicate's sharp extension. Since the predicates that begin with ‘almost’ are vague as well, epistemicism's ontological backdrop is far from the conservative picture it is thought to enable.     

Vagueness and Context

A number of recent accounts for vague terms postulate a kind of context-sensitivity, one that kicks in after the usual ‘external’ contextual factors like comparison class are established and held fixed. In a recent paper, ‘Vagueness without Context Change’(Mind 116 (2007): 275–92), Rosanna Keefe criticizes all such accounts. The arguments are variations on considerations that have been brought against context-sensitive accounts of knowledge, predicates of personal taste, epistemic modals, and the like. The issues are well known and there are variety of options available in reply. More important, the arguments rely on an overly narrow conception of context-sensitivity, suggesting that one size fits all. If Keefe’s arguments were cogent, they would tell against the context-sensitivity of just about any expression, beyond the typical indexicals, including the variation of vague terms with comparison class. However, the criticisms raised by Keefe do highlight certain questions that must be answered by an advocate of a context-sensitive account of vagueness, essentially the same sorts of questions that must be answered by a contextualist or relativist about knowledge, epistemic modals, predicates of personal taste, etc. The main purpose of this paper is to use replies to the relevant objections raised by Keefe as a springboard for further articulation of the underlying view of vagueness.     

Tolerant, Classical, Strict

In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases.     

Vagueness: Why Do We Believe in Tolerance?

The tolerance principle, the idea that vague predicates are insensitive to sufficiently small changes, remains the main bone of contention between theories of vagueness. In this paper I examine three sources behind our ordinary belief in the tolerance principle, to establish whether any of them might give us a good reason to revise classical logic. First, I compare our understanding of tolerance in the case of precise predicates and in the case of vague predicates. While tolerance in the case of precise predicates results from approximation, tolerance in the case of vague predicates appears to originate from two more specific sources: semantic indeterminacy on the one hand, and epistemic indiscriminability on the other. Both give us good and coherent grounds to revise classical logic. Epistemic indiscriminability, it is argued, may be more fundamental than semantic indeterminacy to justify the intuition that vague predicates are tolerant.     

Vagueness and Margin for Error Principles*

Timothy Williamson's potentially most important contribution to epistemicism about vagueness lies in his arguments for the basic epistemicist claim that the alleged cut‐off points of vague predicates are not knowable. His arguments for this are based on so‐called ‘margin for error principles’. This paper argues that these principles fail to provide a good argument for the basic claim. Williamson has offered at least two kinds of margin for error principles applicable to vague predicates. A certain fallacy of equivocation (on the meaning of ‘knowable’) seems to underlie his justification for both kinds of principles. Besides, the margin for error principles of the first kind can be used in the derivation of unacceptable consequences, while the margin for error principles of the second kind can be shown to be compatible with the falsity of epistemicism, under a number of assumptions acceptable to the epistemicist.     

Solving the Heap

The present offers a pragmatic solution of the Heap Paradox, based on the idea that vague predicates are “indexical” in the sense that their denotation does not only depend on the context of their use, but it is a function of the context. The analysis is based on the following three claims. The borderlines of vague terms are undetermined in the sense that though they may be determined in some contexts, they may differ from one context to the next. Vagueness serves the important communicative function, enabling speakers to identify entities as objects (as things we can talk about) in terms of some quantitative differences between the “object” and its background in the context. Thus, in some contexts we can naturally partition the group of men uniquely so as to distinguish the bald from the not-bald. Whether a man with a given hair number is among the bald in a given context depends not only on his own hair number but also on the hair number of others in that context. This provides the background for the claim that when we assert that John is bald, we presuppose that there is a unique demarcation to the bald in that context. I consider the truth of the Paradox’s statements in contexts where the presupposition is true and in contexts where it is false. The analysis yields that the contradiction is avoided because though each of the statements is often true, never are all the sentences in the Paradox true together.     

Paradox lost: Understanding vague predicates

Abstract

The paper is concerned with the status of vague predicates. It is argued that they are for the most part ‘classifiers’, which are covertly comparatives and name not monadic properties but relations. The Sorites Paradox, it is claimed, is thus defused and a verdict theory of vague predicates is presented. Our practice in using vague words is described and it is contended that in our use of these predicates we always have a permanent possibility of independent demarcation. Wittgenstein's picture of the wall and the swamp is deployed to avoid the Transition Problem and it is argued against Fregeans that we need vague language for the advancement of knowledge and understanding.