This paper is a tribute to Delia Graff Fara. It extends her work on failures of meta-rules for validity as truth-preservation under a supervaluationist identification of truth with supertruth. She showed that such failures occur even in languages without special vagueness-related operators, for standards of deductive reasoning as materially rather than purely logically good, depending on a context-dependent background. This paper extends her argument to: quantifier meta-rules like existential elimination; ambiguity; deliberately vague standard mathematical notation. Supervaluationist (...) attempts to qualify the meta-rules impose unreasonable cognitive demands on reasoning and underestimate her challenge. (shrink)

In this paper I criticize a version of supervaluation semantics. This version is called "Region-Valuation" semantics. It's developed by Pablo Cobreros. I argue that all supervaluationists, regionalists in particular, and truth-value gap theorists of vagueness more generally, are commited to the validity of D-intro, the principle that every sentence entails its definitization (the truth of "Paul is tall" guarantees the truth of "Paul is definitely tall"). The principle embroils one in a paradox that's distinct from, but related to, the sorites (...) paradox. I call it the "gap-principles paradox". -/- . (shrink)

• Suppose we try to “solve” the sorites paradox (i.e., say either why the premises aren’t both true or why the reasoning isn’t valid reasoning) by denying the sorites premise: by saying that it’s *not* the case that any man 1mm shorter than a tall man is tall (for a man).

I propose that the meanings of vague expressions render the truth conditions of utterances of sentences containing them sensitive to our interests. For example, 'expensive' is analyzed as meaning 'costs a lot', which in turn is analyzed as meaning 'costs significantly greater than the norm'. Whether a difference is a significant difference depends on what our interests are. Appeal to the proposal is shown to provide an attractive resolution of the sorites paradox that is compatible with classical logic and semantics.

Philosophers disagree about whether vagueness requires us to admit truth-value gaps, about whether there is a gap between the objects of which a given vague predicate is true and those of which it is false on an appropriately constructed sorites series for the predicate---a series involving small increments of change in a relevant respect between adjacent elements, but a large increment of change in that respect between the endpoints. There appears, however, to be widespread agreement that there is some sense (...) in which vague predicates are gappy which may be expressed neutrally by saying that on any appropriately constructed sorites series for a given vague predicate there will be a gap between the objects of which the predicate is denitely true and those of which it is denitely false. Taking as primitive the operator ‘it is denitely the case that’, abbreviated as ‘D’, we may stipulate that a predicate F is denitely true (or denitely false) of an object just in case ‘DF (a)’, where a is a name for the object, is true (or false) simpliciter.1 This yields the following conditional formulation of a ‘gap principle’: (D Φ (x) ∧ D¬ Φ (y)) → ¬R(x, y). Here ‘ Φ ’ is to be replaced with a vague predicate, while ‘R’ is to stand for a sorites relation for that predicate: a relation that can be used to construct a sorites series for the predicate---such as the relation of being just one millimetre shorter than for the predicate ‘is tall’. Disagreements about the sense in which it is correct to say that vague predicates are gappy can then be recast as disagreements about how to understand the denitely operator. One might give it, for example, a pragmatic construal such as ‘it would not be misleading to assert that’; or an epistemic construal such as ‘it is known that’ or ‘it is knowable that’; or a semantic construal such as ‘it is true that’. (shrink)

This paper discusses Fara's so-called 'Paradox of Higher-Order Vagueness' concerning supervaluationism. In the paper I argue that supervaluationism is not committed to global validity, as it is largely assumed in the literature, but to a weaker notion of logical consequence I call 'regional validity'. Then I show that the supervaluationist might solve Fara's paradox making use of this weaker notion of logical consequence. The paper is discussed by Delia Fara in the same volume.

This paper discusses Fara's so-called 'Paradox of Higher-Order Vagueness' concerning supervaluationism. In the paper I argue that supervaluationism is not committed to global validity, as it is largely assumed in the literature, but to a weaker notion of logical consequence I call 'regional validity'. Then I show that the supervaluationist might solve Fara's paradox making use of this weaker notion of logical consequence. The paper is discussed by Delia Fara in the same volume.

One reason to think that names have a predicate-type semantic value is that they naturally occur in count-noun positions: ‘The Michaels in my building both lost their keys’; ‘I know one incredibly sharp Cecil and one that's incredibly dull’. Predicativism is the view that names uniformly occur as predicates. Predicativism flies in the face of the widely accepted view that names in argument position are referential, whether that be Millian Referentialism, direct-reference theories, or even Fregean Descriptivism. But names are predicates (...) in all of their occurrences; they are predicates that are true of their bearers. When a name appears as a bare singular in argument position, it really occupies the predicate position of what in this essay is called a denuded definite description: a definite description with an unpronounced definite article. Sloat provided good evidence for this. The definite article is sometimes pronounced with names in the singular: ‘The Ivan we all love doesn't feel well’. Sloat proposed a disjunctive generalization of when the definite article must be pronounced with a singular name. This essay shows that by slightly revising Sloat's generalization, we arrive at a simple, nondisjunctive, syntactic rule that governs the overt appearance of the definite article with singular names. But Ivan does not necessarily bear the name ‘Ivan’, so one might worry that the sentence “Ivan might not have had ‘Ivan’ as a name” would incorrectly be predicted false. This essay shows that Predicativism does not have this consequence by showing that incomplete definite descriptions in general and incomplete denuded descriptions, such as ‘Øthe Ivan’, in particular are rigid designators. (shrink)

I argue that, contrary to widespread philosophical opinion, phenomenal indiscriminability is transitive. For if it were not transitive, we would be precluded from accepting the truisms that if two things look the same then the way they look is the same and that if two things look the same then if one looks red, so does the other. Nevertheless, it has seemed obvious to many philosophers (e.g. Goodman, Armstrong and Dummett) that phenomenal indiscriminability is not transitive; and, moreover, that this (...) non-transitivity is straightforwardly revealed to us in experience. I show this thought to be wrong. All inferences from the character of our experience to the non-transitivity of indiscriminability involve either a misunderstanding of continuity, a mistaken interpretation of the idea that we have limited powers of discrimination, or tendentious claims about what our experience is really like; or such inferences are based on inadequately supported premisses, which though individually plausible are jointly implausible. (shrink)

Let us say that the proposition that p is transparent just in case it is known that p, and it is known that it is known that p, and it is known that it is known that it is known that p, and so on, for any number of iterations of the knowledge operator ‘it is known that’. If there are transparent propositions at all, then the claim that any man with zero hairs is bald seems like a good candidate. (...) We know that any man with zero hairs is bald. And it also does not seem completely implausible that we know that we know it, and that we know that we know that we know it, and so on. (shrink)

If you’ve read the first five hundred pages of this book, you’ve read most of it (we assume that ‘most’ requires more than ‘more than half’). The set of natural numbers n such that the first n pages are most of this book is nonempty. Therefore, by the least number principle, it has a least member k. What is k? We do not know. We have no idea how to find out. The obstacle is something about the term ‘most’. It (...) is recognisably the same feature as the feature of ‘heap’ that prevents us from finding an answer to the question ‘How many grains make a heap?’ and the feature of many other expressions that prevents us from finding answers to similar questions involving them. Call this feature, whatever its underlying nature, vagueness. (shrink)

Draft (Version 1.1, October 2007): (PDF file) A reply to Jason Stanley’s Analysis criticism of my interest-relative view on vagueness.

Many classically valid meta-inferences fail in a standard supervaluationist framework. This allegedly prevents supervaluationism from offering an account of good deductive reasoning. We provide a proof system for supervaluationist logic which includes supervaluationistically acceptable versions of the classical meta-inferences. The proof system emerges naturally by thinking of truth as licensing assertion, falsity as licensing negative assertion and lack of truth-value as licensing rejection and weak assertion. Moreover, the proof system respects well-known criteria for the admissibility of inference rules. (...) Thus, supervaluationists can provide an account of good deductive reasoning. Our proof system moreover brings to light how one can revise the standard supervaluationist framework to make room for higher-order vagueness. We prove that the resulting logic is sound and complete with respect to the consequence relation that preserves truth in a model of the non-normal modal logic _NT_. Finally, we extend our approach to a first-order setting and show that supervaluationism can treat vagueness in the same way at every order. The failure of conditional proof and other meta-inferences is a crucial ingredient in this treatment and hence should be embraced, not lamented. (shrink)

W3C: The World Wide Web Consortium. Introduction to HTML: A Self Paced Course on Web Authoring : This is now my favorite online HTML tutorial (which is not to say that I've searched exhaustively, or even extensively). I especially like its Table of HTML (4.01) Character Entities , which gives names and ascii codes for special characters, such as the em-dash, section sign, greek letters, etc. Publishing a Personal Web Page using CU People : Basic information for Cornell people who (...) want to create a personal Web Page. Creating Course Web sites : Cornell faculty wanting to create course websites should look here if they need more space than the 5MB allotted by CU People. Wade's HTML Tutorial : This tutorial makes it easy to get started creating web pages by writing html. Beginner's Guide to HTML : Another good introduction; from the NCSA (National Center for Supercomputing Applications). W3C HTML Validator : Check your web pages for errors and compliance with HTML standards. HTML With Style : Biweekly tutorials on making web-pages. Each tutorial contains lots of interesting, opinionated details about the right and wrong way to produce web pages. (shrink)

ABSTRACT: If an event of one kind does not always lead to an event of a second given kind, it does not follow (of course) that the occurrence of an event of the first kind can never explain the occurrence of an event of the second kind. I’m concerned here with cases of belief. In the service of defending a plausible “boundary-shifting” solution to the sorites paradox, I argue that a certain paradoxical belief(in the universally-generalized premise of the sorites paradox) (...) can be explained by our having reasonable beliefs that entail it (beliefs in the instances of that generalization). Some have argued against boundary-shifting solutions on the grounds that beliefs in instances do not always lead to beliefs in generalizations over those instances. I argue that the objection flounders. An event of one kind can explain an event of another kind even if events of the first kind do not always lead to events of the second kind. One does not impugn an explanation merely by pointing to its defeasibility. (shrink)

Intuitively, vagueness involves some sort of indeterminacy: if Plato is a borderline case of baldness, then there is no fact of the matter about whether or not he’s bald—he’s neither bald nor not bald. The leading formal treatments of such indeterminacy—three valued logic, supervaluationism, etc.—either fail to validate the classical theorems, or require that various classically valid inference rules be restricted. Here we show how a fully classical, yet indeterminist account of vagueness can be given within natural semantics, an alternative (...) semantics for classical proof theory. The key features of the account are: there is a single notion of truth—definite truth—and a single notion of validity; sentences can be true, false, or undetermined; all classical theorems and all classical inference rule are valid; the sorites argument is unsound; ‘definitely’ is treated as a meta-language predicate; higher-order vagueness is handled via semantic ascent. (shrink)

Though it is standardly assumed that supervaluationism applied to vagueness is committed to global validity, Achille Varzi (2007) argues that the supervaluationist should take seriously the idea of adopting local validity instead. Varzi’s motivation for the adoption of local validity is largely based on two objections against the global notion: that it brings some counterexamples to classically valid rules of inference and that it is inconsistent with unrestricted higher-order vagueness. In this discussion I review these objections and point (...) out ways to address them not considered in Varzi’s paper. (shrink)

Although Strawson’s main aim in “On Referring” was to argue that definite descriptions can be used referentially – that is, “to mention or refer to some individual person or single object . . . , in the course of doing what we should normally describe as making a statement about that person [or] object” (1950, p. 320) – he denied that definite descriptions are always used referentially. The description in ‘Napoleon was the greatest French soldier’ is not used referentially, says (...) Strawson, since it is used not to mention an individual, but only “to say something about an individual already mentioned” (p. 320). This is an example of what we may call a predicative use of a definite description, though such uses might be better illustrated by considering the false sentence.. (shrink)

Here I propose a coherent way of preserving the identity of material objects with the matter that constitutes them. The presentation is formal, and intended for RSL. An informal presentation is in preliminary draft! -/- Relative-sameness relations—such as being the same person as—are like David Lewis's "counterpart" relations in the following respects: (i) they may hold between objects that aren't identical (I propose), and (ii) there are a multiplicity of them, different ones of which may be variously invoked in different (...) contexts. They differ from counterpart relations, however, in that they are weak equivalence relations (transitive, symmetric and weakly reflexive). The likenesses to counterpart relations make them suitable for an analysis of de-re temporal and modal predications. The difference renders the resulting counterpart theory immune to standard criticisms of Lewis's Counterpart Theory (e.g., in Hazen 1979, and Fara and Williamson 2005). (shrink)

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)

Vague expressions are omnipresent in natural language. As such, their use in legal texts is virtually inevitable. If a law contains vague terms, the question whether it applies to a particular case often lacks a clear answer. One of the fundamental pillars of the rule of law is legal certainty. The determinacy of the law enables people to use it as a guide and places judges in the position to decide impartially. Vagueness poses a threat to these ideals. In (...) borderline cases, the law seems to be indeterminate and thus incapable of serving its core rule of law value. -/- In the philosophy of language, vagueness has become one of the hottest topics of the last two decades. Linguists and philosophers have investigated what distinguishes "soritical " vagueness from other kinds of linguistic indeterminacy, such as ambiguity, generality, open texture, and family resemblance concepts. There is a vast literature that discusses the logical, semantic, pragmatic, and epistemic aspects of these phenomena. Legal theory has hitherto paid little attention to the differences between the various kinds of linguistic indeterminacy that are grouped under the heading of "vagueness ", let alone to the various theories that try to account for these phenomena. -/- Bringing together leading scholars working on the topic of vagueness in philosophy and in law, this book fosters a dialogue between philosophers and legal scholars by examining how philosophers conceive vagueness in law from their theoretical perspective and how legal theorists make use of philosophical theories of vagueness. The chapters of the book are organized into three parts. The first part addresses the import of different theories of vagueness for the law, referring to a wide range of theories from supervaluationist to contextualist and semantic realist accounts in order to address the question of whether the law can learn from engaging with philosophical discussions of vagueness. The second part of the book examines different vagueness phenomena. The contributions in part 2 suggest that the greater awareness to different vagueness phenomena can make lawyers aware of specific issues and solutions so far overlooked. The third part deals with the pragmatic aspects of vagueness in law, providing answers to the question of how to deal with vagueness in law and with the professional, political, moral, and ethical issues such vagueness gives rise to. (shrink)

In this paper I argue that names are predicates when they occur in the appellation position of 'called'-predications. This includes not only proper names, but all names -- including quote-names of proper names and quote-names of other words or phrases. Thus in "You can call me Al", the proper name 'Al' is a predicate. And in "You can call me 'Al'," the quote-name of 'Al' -- namely ' 'Al' ' -- is also a predicate.

Consider the following sentences: In every race, the colt won; In every race, John won.John Hawthorne and David Manley say that the difference between these two sentences raises a problem for Predicativism about names. According to the currently more standard version of Predicativism, a bare singular name in argument position, like ‘John’ in , is embedded in a definite description with an unpronounced definite article. The problem is supposed to be that permits a covarying reading that allows for different races (...) to have been won by different colts, while does not permit a covarying reading—it can be true only if there is a single John that won every race. But, the objection runs, if the name ‘John’ is really embedded in a definite description with an unpronounced definite article, then the two sentences are structurally parallel and should not differ with respect to covariation. Appealing to Jason Stanley's ‘Nominal Restriction’ , I show that the difference between the two sentences above not only does not raise a problem for Predicativism but also is actually predicted by it. (shrink)

Vague expressions are omnipresent in natural language. Their use in legal texts is inevitable. A law phrased in vague terms will often leave it indeterminate whether it applies to a particular case. This places the law at odds with legal values. One of the fundamental pillars of the rule of law is legal certainty. The determinacy of the law enables people to use it as a guide and allows judges make impartial decisions. Vagueness poses a threat to these ideals. (...) In borderline cases, the law seems to be indeterminate and thus incapable of serving its core rule of law value. -/- In the philosophy of language, vagueness has become one of the hottest topics of the past two decades. Linguists and philosophers have investigated what distinguishes ‘soritical’ vagueness from other kinds of linguistic indeterminacy, such as ambiguity, generality, open texture, and family resemblance concepts. There is a vast literature that discusses the logical, semantic, pragmatic, and epistemic aspects of these phenomena. Legal theory has hitherto paid little attention to the differences between the various kinds of linguistic indeterminacy that are grouped under the heading of ‘vagueness’, let alone to the various theories that try to account for these phenomena. -/- Bringing together leading scholars working on the topic of vagueness in philosophy and in law, this book fosters a dialogue between philosophers and legal scholars by examining how philosophers conceive legal ambiguity from their theoretical perspective and how legal theorists make use of philosophical theories of vagueness. -/- The chapters of the book are organized into three parts. The first part addresses the import of different theories of vagueness for the law, referring to a wide range of theories from supervaluationist to contextualist and semantic realist accounts in order to address the question of whether the law can learn from engaging with philosophical discussions of vagueness. The second part of the book examines different vagueness phenomena. The contributions suggest that paying greater attention to these phenomena can make lawyers aware of specific issues and solutions as yet overlooked. The third part deals with the pragmatic aspects of vagueness in law and with the professional, political, and moral issues to which such vagueness gives rise. (shrink)

In “Descriptions as Predicates” (Fara 2001) I argued that definite and indefinite descriptions should be given a uniform semantic treatment as predicates rather than as quantifier phrases. The aim of the current paper is to clarify and elaborate one of the arguments for the descriptions-aspredicates view, one that concerns the interaction of descriptions with adverbs of quantification.

A report of a person's desire can be true even if its embedded clause underspecifies the content of the desire that makes the report true. It is true that Fiona wants to catch a fish even if she has no desire that is satisfied if she catches a poisoned minnow. Her desire is satisfied only if she catches an edible, meal-sized fish. The content of her desire is more specific than the propositional content of the embedded clause in our true (...) report of her desires. Standard semantic accounts of belief reports require, however, that the embedded clause of a true belief report specify precisely the content of the belief that makes it true. Such accounts of belief reports therefore face what I call "the problem of underspecification" if they are extended to desire reports. Such standard accounts are sometimes refined by requiring that a belief report can be true not only if its subject has a belief with precisely the propositional content specified by its embedded clause, but also only if its subject grasps that content in a particular way. Such refinements do not, however, help to address the problem of underspecification for desire reports. (shrink)

This paper is an informal presentation of the ideas presented formally in ”Relative-Sameness Counterpart Theory”. Relative-sameness relations -- such as being the same person as -- are like David Lewis’s “counterpart” relations in the following respects: (i) they may hold over time or across worlds between objects that aren’t cross-time or cross-world identical (I propose), and (ii) there are a multiplicity of them, different ones of which may be variously invoked in different contexts. They differ from his counterpart relations, however, (...) in that they are weak equivalence relations (transitive, symmetric and weakly reflexive). The likenesses to counterpart relations make them suitable for an analysis of de-re temporal and modal predications. The difference renders the resulting counterpart theory immune to standard criticisms of Lewis’s Counterpart Theory (e.g., in Hazen 1979, and Fara and Williamson 2005). The use of sameness as opposed to similarity relations in the analysis of de-re temporal and modal predication renders the resulting truth conditions as statable in terms that proponents of Kripke’s identity-based analysis can accept. (shrink)

If a counterpart theorist’s understanding of the counterpart relation precludes haecceitist differences between possible worlds, as David Lewis’s does, how can he admit haecceitist possibilities, as Lewis wants to? Lewis (Philosophical Review 3–32, 1983; On the Plurality of Worlds, 1986) devised what he called a ‘cheap substitute for haecceitism,’ which would allow for haecceitist possibilities while preserving the counterpart relation as a purely qualitative one. The solution involved lifting an earlier (Journal of Philosophy 65(5):113–126, 1968; 68(7):203–211, 1971) ban on there (...) being multiple intra-world counterparts. I argue here that serious problems for ‘cheap haecceitism’ lurk very close to its surface, and they emerge when we consider the effect of using an actuality operator in our language. Among the most serious of the problems is the result that being the case in some possible world does not always suffice for possibly being the case. The result applies to any counterpart theory that employs a purely qualitative counterpart relation. The upshot is that if we are to admit haecceitist possibilities, as we should, then we must reject any purely qualitative relation as the one involved in the analysis of what might have been for an individual. (shrink)

In this paper I trace Quine's early development of his treatment of names, first as abbreviations for definite descriptions with "Frege-Rusell" style substantive content, then as abbreviations for definite descriptions containing simple predicative content, through to a treatment of names themselves as predicates rather than as abbreviations for this or that type of more complex expression. Along the way, I explain why—despite ubiquitous claims and suggestions to the contrary—Quine never actually uses the verbized name "Socratizes".

Descriptions are predicates. Here, I'll take this to mean either of two basically equivalent things: that they have extensions as their semantic values, sets of entities, in the broadest sense; or that they have type-〈e,t〉 functions as their semantic values, functions from entities, in the broadest sense, to truth values. An entity in the broadest sense is anything that can be the subject of a first-order predication. Examples are individuals, pluralities, masses, and kinds. Here I'm including entities in this broadest (...) sense because my thesis that descriptions are predicates applies to all sorts of descriptions: singular descriptions, plural definite descriptions, mass descriptions, kind descriptions, and indefinite descriptions as well. (shrink)

Arguing About Language presents a comprehensive selection of key readings on fundamental issues in the philosophy of language. It offers a fresh and exciting introduction to the subject, addressing both perennial problems and emerging topics. Classic readings from Frege, Russell, Kripke, Chomsky, Quine, Grice, Lewis and Davidson appear alongside more recent pieces by philosophers or linguists such as Robyn Carston, Delia Graff Fara, Frank Jackson, Ernie Lepore & Jerry Fodor, Nathan Salmon, Zoltán Szabó, Timothy Williamson and Crispin Wright. (...) Organised into clear sections, readings have been chosen that engage with one another and often take opposing views on the same question, helping students to get to grips with the key areas of debate in the philosophy of language, including: sense and reference definite descriptions linguistic conventions language and behaviour descriptivism and rigidity contextualism vagueness rule-following and normativity fictional discourse. Each article selected is clear, thought-provoking and free from unnecessary jargon. The editors provide lucid introductions to each section in which they give an overview of the debate and outline the arguments of the papers. Arguing About Language is an ideal reader for students looking for a balanced yet up-to-date introduction to the philosophy of language. Darragh Byrne is lecturer in philosophy at the University of Birmingham, UK. Max Kölbel is ICREA Research Professor at the University of Barcelona, Spain. He is the author of Truth without Objectivity (Routledge, 2002) and co-editor of Wittgenstein's Lasting Significance (Routledge, 2004) with Bernhard Weiss, as well as Relative Truth (Oxford, 2008) with Manuel García-Carpintero. (shrink)

Stewart Shapiro's aim in Vagueness in Context is to develop both a philosophical and a formal, model-theoretic account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases. A person can be tall with respect to male accountants and not tall with respect to professional basketball players. The main feature (...) of Shapiro's account is that the extensions of vague terms also vary in the course of a conversation, even after the external contextual features, such as the comparison class, are fixed. A central thesis is that in some cases, a competent speaker of the language can go either way in the borderline area of a vague predicate without sinning against the meaning of the words and the non-linguistic facts. Shapiro calls this open texture, borrowing the term from Friedrich Waismann.The formal model theory has a similar structure to the supervaluationist approach, employing the notion of a sharpening of a base interpretation. In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity. The ultimate goal of the technical aspects of the work is to delimit a plausible notion of logical consequence, and to explore what happens with the sorites paradox.Later chapters deal with what passes for higher-order vagueness - vagueness in the notions of 'determinacy' and 'borderline' - and with vague singular terms, or objects. In each case, the philosophical picture is developed by extending and modifying the original account. This is followed with modifications to the model theory and the central meta-theorems.As Shapiro sees it, vagueness is a linguistic phenomenon, due to the kinds of languages that humans speak. But vagueness is also due to the world we find ourselves in, as we try to communicate features of it to each other. Vagueness is also due to the kinds of beings we are. There is no need to blame the phenomenon on any one of those aspects. (shrink)

Philosophy for the 21st Century, an introductory anthology, is an extraordinarily comprehensive collection of historical and contemporary readings. It covers all major fields, including not only metaphysics, epistemology, ethics, and philosophy of religion, but also philosophy of science, philosophy of mind, philosophy of language, political philosophy, and philosophy of art. This volume is unique in drawing on the judgments of a new generation of scholars, each of whom has chosen the articles and provided the introduction for one section of the (...) book. These associate editors--Delia Graff, Robin Jeshion, L. A. Paul, Jesse Prinz, Stuart Rachels, Gabriela Sakamoto, David Sosa, and Cynthia A. Stark--are at the forefront of 21st-century philosophy. Their selections include the work of such leading contemporary thinkers as Nancy Cartwright, Saul Kripke, David Lewis, Thomas Nagel, Robert Nozick, Derek Parfit, and Sydney Shoemaker, along with classic works from 2500 years of philosophy. The book has been structured to maximize continuity, and an introductory essay by Simon Blackburn explains the tools of symbolic logic. This groundbreaking volume sets a new standard for introducing students to the importance and fascination of philosophical inquiry. (shrink)

Philosophy of language is the branch of philosophy that examines the nature of meaning, the relationship of language to reality, and the ways in which we use, learn, and understand language. _The Routledge Companion to Philosophy of Language _provides a comprehensive and up-to-date survey of the field, charting its key ideas and movements, and addressing contemporary research and enduring questions in the philosophy of language. Unique to this _Companion _is clear coverage of research from the related disciplines of formal logic (...) and linguistics, and discussion of the applications in metaphysics, epistemology, ethics and philosophy of mind. Organized thematically, the _Companion _is divided into seven sections: Core Topics; Foundations of Semantics; Parts of Speech; Methodology; Logic for Philosophers of Language; Philosophy of Language for the Rest of Philosophy; and Historical Perspectives. Comprised of 70 never-before-published essays from leading scholars--including Sally Haslanger, Jeffrey King, Sally McConnell-Ginet, Rae Langton, Kit Fine, John MacFarlane, Jeff Pelletier, Scott Soames, Jason Stanley, Stephen Stich and Zoltan Gendler Szabo--the _Routledge Companion to Philosophy of Language_ promises to be the most comprehensive and authoritative resource for students and scholars alike. (shrink)

If you’ve read the first five hundred pages of this book, you’ve read most of it (we assume that ‘most’ requires more than ‘more than half’). The set of natural numbers n such that the first n pages are most of this book is nonempty. Therefore, by the least number principle, it has a least member k. What is k? We do not know. We have no idea how to find out. The obstacle is something about the term ‘most’. It (...) is recognisably the same feature as the feature of ‘heap’ that prevents us from finding an answer to the question ‘How many grains make a heap?’ and the feature of many other expressions that prevents us from finding answers to similar questions involving them. Call this feature, whatever its underlying nature, vagueness. (shrink)

Of the many families of words that are thought to be vague, so-called observational predicates may be both the most fascinating and the most confounding. Roughly, observational predicates are terms that apply to objects on the basis of how those objects appear to us perceptually speaking. ‘Red’, ‘loud’, ‘sweet’, ‘acrid’, and ‘smooth’ are good examples. Delia Graff explains that a “predicate is observational just in case its applicability to an object (given a fixed context of evaluation) depends only (...) on the way that object appears” (2001, 3). By the same token observational predicates are, as Crispin Wright observes, terms “whose senses are taught entirely by ostension” (1976). Like other vague predicates, observational words appear to generate sorites paradoxes. Consider for example a series of 20 colored patches progressing from a clearly red one to a clearly orange one, so ordered that each patch is just noticeably different in hue from the one before. The following argument then seems forced upon us: (1) Patch #1 is red. (2) Any patch that differs only slightly in hue from a red patch is itself red. (3) Therefore patch #20 is red. Premise (2) expresses what Wright has called the tolerance of ‘red’: the application of the predicate tolerates small changes in a decisive parameter (here, hue). Of course, most vague predicates, hence most versions of the sorites, are not observational. For instance, given a series of. (shrink)

This is a discussion of Delia Fara’s theory of vagueness, and of its solution to the Sorites paradox, criticizing some of the details of the account, but agreeing that its central insight will be a part of any solution to the problem. I also consider a wider range of philosophical puzzles that involve arguments that are structurally similar to the argument of the Sorites paradox, and argue that the main ideas of her account of vagueness helps to respond to (...) some of those puzzles. (shrink)

In her recent defense of predicativism for proper names, Delia Graff Fara proposes the following non-metalinguistic being-called condition for the applicability of names as predicates: A name ‘N’ is true of a thing if and only if it is called N. The BCC is supposed to hold for names only. In this essay I criticize Fara’s BCC by arguing that the word ‘called’ is ambiguous, and that the BCC holds only for the particular sense of ‘calling’ as naming. (...) I revise accordingly Fara’s BCC and propose in its place a non-metalinguistic being-named condition. I also argue, against Fara, that being-named conditions are not unique to proper names: they hold for mass nouns, common count nouns, as well as for family names, which I distinguish from surnames. Finally, I discuss honorific titles and propose a being-entitled condition according to which a title ‘T’ is true of a thing just in case it is dubbed T. I conclude the paper with pragmatic, syntactic, as well as semantic considerations in favor of the thesis that names are a subspecies of non-hereditary, honorific titles. (shrink)

Vagueness is a familiar but deeply puzzling aspect of the relation between language and the world. It is highly controversial what the nature of vagueness is -- a feature of the way we represent reality in language, or rather a feature of reality itself? May even relations like identity or parthood be affected by vagueness? Sorites arguments suggest that vague terms are either inconsistent or have a sharp boundary. The account we give of such paradoxes plays a pivotal role for (...) our understanding of natural languages. If our reasoning involves any vague concepts, is it safe from contradiction? Do vague concepts really lack any sharp boundary? If not, why are we reluctant to accept the existence of any sharp boundary for them? And what rules of inference can we validly apply, if we reason in vague terms? Cuts and Clouds presents the latest work towards a clearer understanding of these old puzzles about the nature and logic of vagueness. The collection offers a stimulating series of original essays on these and related issues by some of the world's leading experts. (shrink)

equiv: (¬ DEF T (x) & ¬ DEF ¬ T (x)). equiv: ¬(DEF T (x) ∨ DEF ¬T (x)). equiv: ¬∆ T (x) (“not determinate whether x is tall”).

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 collective harm cases, bad consequences follow if enough people act in a certain way even though no such individual act makes a difference for the worse. Global warming, overfishing and Derek Parfit’s famous case of the harmless torturers are some examples of such harm. Shelly Kagan argues that there is a threshold such that one single act might trigger harm in all collective harm cases. Julia Nefsky points to serious shortcomings in Kagan’s argument, but does not show that (...) his conclusion is incorrect. I argue that our best theories of vagueness (the epistemic view of vagueness, three-valued logic, and supervaluationism) entail that there is a threshold in all collective harm cases. However, my analysis points to another problem with Kagan’s argument: the thresholds are not necessarily perceptible. Given the assumption that only perceptible differences matter morally, passing such a threshold does not necessarily trigger morally relevant harm, pace Kagan. Last, I consider two variants of Kagan’s argument and find both problematic. One controversially assumes that observational relations like ‘cannot perceive the difference between’ are transitive. The other problematically assumes that so called triangulation always is possible. (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)

According to James McCawley (1981) and Richard Larson and Gabriel Segal (1995), the following sentence is three-ways ambiguous: -/- Harry wants to be the mayor of Kenai. -/- According to them also, the three-way ambiguity cannot be accommodated on the Russellian view that definite descriptions are quantified noun phrases. In order to capture the three-way ambiguity of the sentence, these authors propose that definite descriptions must be ambiguous: sometimes they are predicate expressions; sometimes they are Russellian quantified noun phrases. After (...) explaining why the McCawley-Larson-Segal solution contains an obvious flaw, I discuss how an effort to correct the flaw brings to light certain puzzles about the individuation of desires, about quantifying in, and about the disambiguation of desire ascriptions. (shrink)

Vague expressions are omnipresent in natural language. As such, their use in legal texts is virtually inevitable. If a law contains vague terms, the question whether it applies to a particular case often lacks a clear answer. One of the fundamental pillars of the rule of law is legal certainty. The determinacy of the law enables people to use it as a guide and places judges in the position to decide impartially. Vagueness poses a threat to these ideals. In (...) borderline cases, the law seems to be indeterminate and thus incapable of serving its core rule of law value. -/- In the philosophy of language, vagueness has become one of the hottest topics of the last two decades. Linguists and philosophers have investigated what distinguishes "soritical " vagueness from other kinds of linguistic indeterminacy, such as ambiguity, generality, open texture, and family resemblance concepts. There is a vast literature that discusses the logical, semantic, pragmatic, and epistemic aspects of these phenomena. Legal theory has hitherto paid little attention to the differences between the various kinds of linguistic indeterminacy that are grouped under the heading of "vagueness ", let alone to the various theories that try to account for these phenomena. -/- The paper is an introduction to a book of the same title. Bringing together leading scholars working on the topic of vagueness in philosophy and in law, the book fosters a dialogue between philosophers and legal scholars by examining how philosophers conceive legal ambiguity from their theoretical perspective and how legal theorists make use of philosophical theories of vagueness. (shrink)

This paper is concerned with the claim that supervaluationist consequence is not classical for a language including an operator for definiteness. Although there is some sense in which this claim is uncontroversial, there is a sense in which the claim must be qualified. In particular I defend Keefe's position according to which supervaluationism is classical except when the inference from phi to Dphi is involved. The paper provides a precise content to this claim showing that we might provide complete (and (...) sound) systems of deduction for supervaluationist consequence in which proofs are completely classical with the exception of a single last step (involving the above mentioned inference). (shrink)