This paper deals with the question of what it is for a quantifier expression to be vague. First it draws a distinction between two senses in which quantifier expressions may be said to be vague, and provides an account of the distinction which rests on independently grounded assumptions. Then it suggests that, if some further assumptions are granted, the difference between the two senses considered can be represented at the formal level. Finally, it outlines some implications of the account provided (...) which bear on three debated issues concerning quantification. (shrink)

This paper proposes a new dialetheic logic, a Dialetheic Logic with Exclusive Assumptions and Conclusions ), including classical logic as a particular case. In \, exclusivity is expressed via the speech acts of assuming and concluding. In the paper we adopt the semantics of the logic of paradox extended with a generalized notion of model and we modify its proof theory by refining the notions of assumption and conclusion. The paper starts with an explanation of the adopted philosophical perspective, then (...) we propose our \ logic. Finally, we show how \ supports the dialetheic solution of the liar paradox. (shrink)

This thesis explores the possibility of composite consciousness: phenomenally conscious states belonging to a composite being in virtue of the consciousness of, and relations among, its parts. We have no trouble accepting that a composite being has physical properties entirely in virtue of the physical properties of, and relations among, its parts. But a long­standing intuition holds that consciousness is different: my consciousness cannot be understood as a complex of interacting component consciousnesses belonging to parts of me. I ask why: (...) what is it about consciousness that makes us think it so different from matter? And should we accept this apparent difference? (shrink)

Neutralism is the broad view that philosophical progress can take place when (and sometimes only when) a thoroughly neutral, non-specific theory, treatment, or methodology is adopted. The broad goal here is to articulate a distinct, specific kind of sorites paradox (The Observational Sorites Paradox) and show that it can be effectively treated via Neutralism.

I argue that there can be no such thing as a borderline case of the predicate ‘phenomenally conscious’: for any given creature at any given time, it cannot be vague whether that creature is phenomenally conscious at that time. I first defend the Positive Characterization Thesis, which says that for any borderline case of any predicate there is a positive characterization of that case that can show any sufficiently competent speaker what makes it a borderline case. I then appeal to (...) the familiar claim that zombies are conceivable, and I argue that this claim entails that there can be no positive characterizations of borderline cases of ‘phenomenally conscious’. By the Positive Characterization Thesis, it follows that ‘phenomenally conscious’ can not have any borderline cases. (shrink)

This paper proposes a novel method of identifying the nature of vague sentences and a novel solution to the sorites paradox. The theory is motivated by patterns of use that language users display when using vague predicates. Identifying a coherent cause of this behaviour provides us with a theory of vague sentences that is behaviour- rather than paradox-led. The theory also provides a solution to the sorites paradox and is therefore more explanatory than other available theories of vagueness.

Kilimanjaro is an example of what some philosophers would call a ‘vague object’: it is only roughly 5895 m tall, its weight is not precise and its boundaries are fuzzy because some particles are neither determinately part of it nor determinately not part of it. It has been suggested that this vagueness arises as a result of semantic indecision: it is because we didn’t make up our mind what the expression “Kilimanjaro” applies to that we can truthfully say such things (...) as “It is indeterminate whether this particle is part of Kilimanjaro”. After reviewing some of the limitations of this approach, I will propose an alternative account, based on a new semantic relation—multiple reference—capable of holding in a one-many pattern between a term and several objects in the domain. I will explain how multiple reference works, what differentiates it from plural reference and how it might be used to accommodate at least some aspects of our ordinary discourse about vague objects. (shrink)

It’s not clear what supervaluationists should say about propositional content. Does a vague sentence, e.g., ‘Harry is bald’, express one proposition, or a barrage of propositions, or none at all? Or is the matter indeterminate? The supervaluationist canon is not decisive on the issue; authoritative passages can be cited in favor of each of the proposals just mentioned. Furthermore, some detractors have argued that supervaluationism is incapable of providing any coherent account of propositional content. This paper considers each of the (...) proposals for how many propositions are expressed by a vague sentence: none, some, all, or it’s indeterminate. Most of these proposals turn out to be unworkable in the metalanguage. I conclude that orthodox supervaluationists—those who identify truth with supertruth—must either relax the standard requirement that propositions be bivalent, or else alter the standard relation between sentences and propositions in which a sentence inherits its truth-conditions from the proposition it expresses. The best option going forward for the orthodox supervaluationist is perhaps the most surprising—amend the requirement that propositions be bivalent. I argue that propositions having supervaluational truth-conditions are best suited to fill the propositional roles in the semantic theory of a vague language. These propositions admit of truth-value gaps, and gappy propositions are controversial, but I argue that they earn their keep. (shrink)

This paper presents a novel semantic analysis of unit names (like pound and meter) and gradable adjectives (like tall, short and happy), inspired by measurement theory (Krantz et al. In Foundations of measurement: Additive and Polynomial Representations, 1971). Based on measurement theory’s four-way typology of measures, I claim that different adjectives are associated with different types of measures whose special characteristics, together with features of the relations denoted by unit names, explain the puzzling limited distribution of measure phrases, as well (...) as unit-based comparisons between predicates (as in the table is longer than it is wide). All considered, my analyses support the view that the grammar of natural languages is sensitive to features of measurement theory. (shrink)

What the world needs now is another theory of vagueness. Not because the old theories are useless. Quite the contrary, the old theories provide many of the materials we need to construct the truest theory of vagueness ever seen. The theory shall be similar in motivation to supervaluationism, but more akin to many-valued theories in conceptualisation. What I take from the many-valued theories is the idea that some sentences can be truer than others. But I say very different things to (...) the ordering over sentences this relation generates. I say it is not a linear ordering, so it cannot be represented by the real numbers. I also argue that since there is higher-order vagueness, any mapping between sentences and mathematical objects is bound to be inappropriate. This is no cause for regret; we can say all we want to say by using the comparative truer than without mapping it onto some mathematical objects. From supervaluationism I take the idea that we can keep classical logic without keeping the familiar bivalent semantics for classical logic. But my preservation of classical logic is more comprehensive than is normally permitted by supervaluationism, for I preserve classical inference rules as well as classical sequents. And I do this without relying on the concept of acceptable precisifications as an unexplained explainer. The world does not need another guide to varieties of theories of vagueness, especially since Timothy Williamson (1994) and Rosanna Keefe (2000) have already provided quite good guides. I assume throughout familiarity with popular theories of vagueness. (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)

Die gegenwärtig unter dem Titel ›Realismus‹ geführten Debatten in der Philosophie befinden sich nach allgemeiner Ansicht in einem Zustand größter Verwirrung, so daß es nützlich erscheint, ein wenig Ordnung in die theoretischen Optionen zu bringen bevor man für die eine oder andere Auffassung Partei ergreift. In der vorliegenden Arbeit wird dafür argumentiert, daß sich ein systematisch zusammenhängendes Zentrum dieser Debatten mit Hilfe des Begriffes der Referenz ordnen läßt. Nach der Analyse einiger klassischer Positionen soll ein Rahmen erstellt werden, innerhalb dessen (...) die Positionen eingeordnet und die zentralen Probleme fruchtbar diskutiert werden können. Zu diesem Zwecke ist es erforderlich, für die Einordnung der Positionen theoretische Kriterien zu benennen, die sich an den Problemen orientieren von denen hier argumentiert wird, das sie zentral seien. Sehr knapp ausgedrückt wird hier die Auffassung vertreten, Realismus sei als metaphysische These aufzufassen, welche eine von menschlichen epistemischen und semantischen Möglichkeiten unabhängige Existenz behauptet; in den gegenwärtigen Debatten typischerweise die Existenz einer Art von Dingen, nicht die eines individuellen Gegenstandes. Diese metaphysische These wird jedoch in der gegenwärtigen Debatte mit semantischen Argumenten untermauert, bzw. angegriffen und jene semantischen Argumente wiederum verwenden epistemische Erwägungen – die Frage betreffend, was man wissen kann und was nicht. Der Beginn der gegenwärtigen Realismusdebatten mit der soeben skizzierten zentralen Stellung semantischer Argumente ist, der hier vertretenen Auffassung zufolge, die Kritik am traditionellen Fregeschen Referenzbegriff durch Kripke und den frühen Putnam um 1970 (Kap. 2). Aus dieser neu zu bewertenden Kritik und der von den Autoren daraus entwickelten externalistischen realistischen Semantik für Artausdrücke läßt sich das erste Kriterium für eine Position in einer Realismusdebatte ableiten und klären (Kap. 3): Hält man die fragliche Art für eine natürliche Art und meint also, sie habe ihren ›Zusammenhalt‹ von Natur aus? Wenn ja, dann ist die fragliche Position eine realistische (das Kriterium ist dank des engen Zusammenhangs von Realismus und Externalismus sowohl hinreichend als auch notwendig). Hält man die Art nicht für eine natürliche Art, ist man Antirealist. Damit geht jeweils not- wendig eine bestimmte Semantik für den auf die Art referierenden Ausdruck einher. Es zeigt sich zugleich, daß es zwei Varianten des Realismus zu unterscheiden gilt, die hier als klassischer bzw. als moderater Realismus bezeichnet werden. Im folgenden (Kap. 4.1) wird argumentiert, daß der Begriff der Wahrheit nicht eigentlich der zentrale Punkt in den in Frage stehenden Realismusdebatten sein sollte, wie vielfach behauptet wurde, sondern seine Brisanz vielmehr aus zugrundeliegenden semantischen Fragen gewinnt die also in der weiteren Aufdeckung der Kriterien die zentrale Rolle spielen müssen. In der Analyse der Kritik an der in Kap. 3 entwickelten Position des ›klassischen Realismus‹ läßt sich ein zweites unterscheidendes Kriterium für Positionen in Realismusdebatten entwickeln: begriffliche Relativität. Nach der Ablehnung von Putnams Auffassungen zu diesem Thema, werden zwei Varianten vorgeschlagen, starke und schwache begriffliche Relativität (Kap. 4.2). Die Anwendung dieses Merkmals zwingt, so wird argumentiert, in einigen Fällen zu einer Kombination einer realistischen Auffassung von Arten als natürliche mit begrifflicher Relativität. Diese mittlere Position zwischen klassischem Realismus und Antirealismus wird als »moderater Realismus« bezeichnet. Der im ersten Kriterium verwendete Begriff der natürlichen Art, und damit die Optionen in den Debatten, wird schließlich mittels einer Dis- kussion des Phänomens der Vagheit noch weiter verdeutlicht (Kap. 4.3). Ab- schließend werden die drei Optionen zusammenfassend dargestellt und ein Versuch unternommen, ihre Fruchtbarkeit für diverse Realismusdebatten anzudeuten. (shrink)

Sex determines much about one's life, but what determines one's sex? The answer is complicated and incomplete: on close examination, ordinary notions of female and male are vague. In 2012, the International Olympic Committee further specified what they mean by woman in response to questions about who, exactly, is eligible to compete in women's Olympic events. I argue, first, that their stipulation is evidence that the use of vague terms is better described by semantic approaches to vagueness than by epistemic (...) approaches. In addition, the IOC's 2012 stipulation was made with sensitivity to its practical consequences. Linguistic actions often have morally relevant consequences, and I contend that, other things equal, we should adopt theories about language that acknowledge the responsibility we bear for what we say. Taking vagueness to be an epistemic phenomenon precludes the sense of agency needed for moral responsibility; taking it to be semantic does not. Thus I advance two arguments for semantic approaches to vagueness, as against epistemic approaches: one descriptive and one normative. (shrink)

Este artigo apresenta a teoria supervalorativista da vagueza e discute a objecção, que frequentemente lhe é dirigida, segundo a qual essa teoria não consegue dar conta do fenómeno da vagueza de ordem superior.

Most words in natural language are vague, that is to say, they lack sharp boundaries and, hence, they have (actual or potential) borderline cases, where the word in question neither definitely applies nor definitely fails to apply. Vagueness gives rise to paradoxes, the best known of which is the sorites (concerned with how many grains of sand are needed to make a heap). Besides offering a solution to such paradoxes, a theory of vagueness should systematically describe how the truth conditions (...) of sentences with vague terms are determined; and it should also define the right logical principles for reasoning with such sentences. This article offers an introduction to the main theories of vagueness and to the problems they have to face. (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)

This paper considers a now familiar argument that the ubiquity of context -dependence threatens the project of natural language semantics, at least as that project has usually been conceived: as concerning itself with `what is said' by an utterance of a given sentence. I argue in response that the `anti-semantic' argument equivocates at a crucial point and, therefore, that we need not choose between semantic minimalism, truth-conditional pragmatism, and the like. Rather, we must abandon the idea, familiar from Kaplan and (...) others, that utterances express propositions `relative to contexts' and replace it with the Strawonian idea that speakers express propositions by making utterances in contexts. The argument for this claim consists in a detailed investigation of the particular case of demonstratives, which I argue demand such a Strawsonian treatment. I then respond to several objections, the most important of which allege that the Strawsonian account somehow undermines the project of natural language semantics, or threatens the semantics -pragmatics distinction. Please note that the paper posted here is an extended version of what was published. (shrink)

Bob Hale’s distinguished record of research places him among the most important and influential contemporary analytic metaphysicians. In his deep, wide ranging, yet highly readable book Necessary Beings, Hale draws upon, but substantially integrates and extends, a good deal his past research to produce a sustained and richly textured essay on — as promised in the subtitle — ontology, modality, and the relations between them. I’ve set myself two tasks in this review: first, to provide a reasonably thorough (if not (...) exactly comprehensive) overview of the structure and content of Hale’s book and, second, to a limited extent, to engage Hale’s book philosophically. I approach these tasks more or less sequentially: Parts I and 2 of the review are primarily expository; in Part 3 I adopt a somewhat more critical stance and raise several issues concerning one of the central elements of Hale’s account, his essentialist theory of modality. (shrink)

Eleonore Stump claims in her book "Wandering in Darkness" that the problem of evil can be solved best by the help of narratives. This - so Stump - is due to the fact that narratives allow one to get a general view about relevant parts of the discussion of suffering. In this context she distinguishes the more detailed view of the discussion from a more general one by two different modes of cognition: the mode of gathering "knowledge that" and that (...) one of gathering "knowledge how". Knowledge by narratives is a subcategory of the last-mentioned one. In the paper I argue for the thesis that this distinction is not really crucial for Stump's argumentation and that in fact only "knowledge that" is relevant for her proposed solution. (shrink)

Sergio Tenenbaum and Diana Raffman contend that ‘vague projects’ motivate radical revisions to orthodox, utility-maximising rational choice theory. Their argument cannot succeed if such projects merely ground instances of the paradox of the sorites, or heap. Tenenbaum and Raffman are not blind to this, and argue that Warren Quinn’s Puzzle of the Self-Torturer does not rest on the sorites. I argue that their argument both fails to generalise to most vague projects, and is ineffective in the case of the Self-Torturer (...) itself. (shrink)

In a recent paper, Lee Kerckhove and Sara Waller (hereafter K & W) argue that the concept of personhood is irrelevant for the abortion debate.1 Surprisingly, this irrelevance is due merely to the fact that the predicate ‘being a person’ — hereafter ‘personhood’ — is inherently vague. This vagueness, they argue, reduces ‘personhood’ to incoherency and disqualifies the notion from being a useful moral concept. In other words, if ‘personhood’ isn’t a precise notion with well-defined boundaries, then it cannot be (...) of any use in the debate over the permissibility of abortion. This argument is mistaken. While it may be true that ‘personhood’ is irrelevant for the debate over abortion (a substantive issue not dealt with in this paper), it is not true that ‘personhood’ should be disqualified merely because it is vague. Section 2 of the paper is a quick survey in which I briefly review the importance of ‘personhood’ in some of the more recent literature concerning the moral status of abortion. Section 3 is a reconstruction of K & W’s argument against the relevancy of ‘personhood’ and a criticism showing why their argument fails. Section 4 approaches the use of a vague predicate in moral debate and explores the application of ‘personhood’ given three contemporary solutions to vagueness: degree theory, epistemicism and supervaluationism. (shrink)

The essay is a study of phenomenal specificity. By ‘phenomenal’ here we mean conscious awareness, which needs to be cashed out in detail throughout the study. Intuitively, one dimension of phenomenology is along with specificity. For example it seems appropriate to say that one’s conscious awareness in the middle of the visual field is in some sense more specific than the awareness in the periphery under normal circumstances. However, it is difficult to characterise the nature of phenomenal specificity in an (...) accurate way. This essay seeks to do just that. In the introduction, I set up the discussion by invoking a threefold Campbellian framework. Chapter 1 introduces a key notion of the analogue, its roots in sciences, and its applications in philosophy. Chapter 2 focuses on the major case study – the Sperling iconic memory paradigm – and explains how the relevant notion of the analogue can be used to explain phenomenal specificity involved in the Sperling case. Chapter 3 discusses functions of attention, as it is a crucial element in the Sperling case. Chapter 4 extends the project by explaining how visual demonstratives fit into the present picture. Finally chapter 5 discusses several directions for future researches. This essay is not an attempt to discuss all the issues concerning the Sperling case, but to provide a new angle in seeing the issue: most people agree that visual phenomenology is in some sense specific, but there are not enough attempts to model phenomenal specificity explicitly. On this occasion we use a notion of the analogue and related ideas to understand phenomenal specificity and how it applies to certain empirical cases. (shrink)

Most work on the semantic paradoxes within classical logic has centered around what this essay calls “linguistic” accounts of the paradoxes: they attribute to sentences or utterances of sentences some property that is supposed to explain their paradoxical or nonparadoxical status. “No proposition” views are paradigm examples of linguistic theories, although practically all accounts of the paradoxes subscribe to some kind of linguistic theory. This essay shows that linguistic accounts of the paradoxes endorsing classical logic are subject to a particularly (...) acute form of the revenge paradox: that there is no exhaustive classification of sentences into “good” and “bad” such that the T-schema holds when restricted to the “good” sentences unless it is also possible to prove some “bad” sentences. The foundations for an alternative classical nonlinguistic approach is outlined that is not subject to the same kinds of problems. Although revenge paradoxes of different strengths can be formulated, they are found to be indeterminate at higher orders and not inconsistent. (shrink)

Revisionary theories of logic or truth require revisionary theories of mind. This essay outlines nonclassically based theories of rational belief, desire, and decision making, singling out the supervaluational family for special attention. To see these nonclassical theories of mind in action, this essay examines a debate between David Lewis and Derek Parfit over what matters in survival. Lewis argued that indeterminacy in personal identity allows caring about psychological connectedness and caring about personal identity to amount to the same thing. The (...) essay argues that Lewis's treatment of two of Parfit's puzzle cases—degreed survival and fission—presuppose different nonclassical treatments of belief and desire. (shrink)

Time passes, and the inexorability of its passing has deep emotional significance. One of the main themes of this thesis involves an investigation into the metaphysical nature of the passage of time. What sort of metaphysical account of passage should be given? And do our emotional responses to temporal passage have metaphysical implications? The other main theme of the thesis is the issue of the metaphysics of persistence. When a thing is present at more than one time, what is the (...) metaphysical underpinning of its persistence? Some subsidiary issues, which are nevertheless important in their own right, are also discussed. There are interesting connections between the issues of persistence and these further issues, which include the nature of vagueness, and the distinction between intrinsic and extrinsic properties. (shrink)

This article deals with supervaluationism and the failure of truth-functionality. It draws some distinctions that may contribute to a better understanding of this semantic framework.

Agent relativists about vagueness (henceforth ‘agent relativists’) hold that whether or not an object x falls in the extension of a vague predicate ‘P’ at a time t depends on the judgemental dispositions of a particular competent agent at t. My aim in this paper is to critically examine arguments that purport to support agent relativism by appealing to data from forced-march Sorites experiments. The most simple and direct versions of such forced-march Sorites arguments rest on the following (implicit) premise: (...) If competent speakers' judgements vary in a certain way, then the extensions of ‘P’ as used by these speakers must vary in the same way. This premise is in need of independent support, since otherwise opponents of agent relativism can simply reject it. In this paper, I focus on the idea that one cannot plausibly reject this premise, as that would commit one to implausible claims about linguistic competence. Against this, I argue that one can accommodate the data from forced-march Sorites experiments in a way that is compatible with a plausible picture of linguistic competence, without going agent relativist. Thus, there is reason to be sceptical of the idea that such data paired with considerations about linguistic competence can be invoked in order to lend any solid support to agent relativism. Forced-march Sorites arguments of this kind can, and should be, resisted. (shrink)

Decisions are made under uncertainty when there are distinct outcomes of a given action, and one is uncertain to which the act will lead. Decisions are made under indeterminacy when there are distinct outcomes of a given action, and it is indeterminate to which the act will lead. This paper develops a theory of (synchronic and diachronic) decision-making under indeterminacy that portrays the rational response to such situations as inconstant. Rational agents have to capriciously and randomly choose how to resolve (...) the indeterminacy relevant to a given choice-situation, but such capricious choices once made constrain how they will choose in the future. The account is illustrated by the case of self-interested action in situations where it is indeterminate whether you yourself will survive to benefit or suffer the consequences. The conclusion emphasizes some distinctive anti-hedging predictions of the account. (shrink)

Substructural pluralism about the meaning of logical connectives is best understood as the view that natural language connectives have all (and only) the properties conferred by classical logic, but that particular occurrences of these connectives cannot simultaneously exhibit all these properties. This is just a more sophisticated way of saying that while natural language connectives are ambiguous, they are not so in the way classical logic intends them to be. Since this view is usually framed as a means to resolve (...) paradoxes, little attention is paid to the logical properties of the ambiguous connectives themselves. The present paper sets out to fill this gap. First, I argue that substructural logicians should care about these connectives; next, I describe a consequence relation between a set of ambiguous premises and an ambiguous conclusion, and review the logical properties of ambiguous connectives; and finally, I highlight how ambiguous connectives can explain our intuitions about logical rivalry. (shrink)

This paper offers an analysis of metalinguistic comparatives such as more dumb than crazy in which they differ from ordinary comparatives in the scale on which they compare: ordinary comparatives use scales lexically determined by particular adjectives, but metalinguistic ones use a generally-available scale of imprecision or ‘pragmatic slack’. To implement this idea, I propose a novel compositional implementation of the Lasersohnian pragmatic-halos account of imprecision—one that represents clusters of similar meanings as Hamblin alternatives. In the theory that results, existential (...) closure over alternatives mediates between alternative-sets and meanings in which imprecision has been resolved. I then articulate a version of this theory in which the alternatives are not related meanings but rather related utterances, departing significantly from Lasersohn’s original conception. Although such a theory of imprecision is more clearly ‘metalinguistic’, the evidence for it from metalinguistic comparatives in English is surprisingly limited. The overall picture that emerges is one in which the grammatical distinction between ordinary and metalinguistic comparatives tracks the independently motivated distinction between vagueness and imprecision. (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)

John Broome has argued that value incommensurability is vagueness, by appeal to a controversial about comparative indeterminacy. I offer a new counterexample to the collapsing principle. That principle allows us to derive an outright contradiction from the claim that some object is a borderline case of some predicate. But if there are no borderline cases, then the principle is empty. The collapsing principle is either false or empty.

We propose a new account of vagueness and approximation in terms of the theory of granular partitions. We distinguish different kinds of crisp and non-crisp granular partitions and we describe the relations between them, concentrating especially on spatial examples. We describe the practice whereby subjects use regular grid-like reference partitions as a means for tempering the vagueness of their judgments, and we demonstrate how the theory of reference partitions can yield a natural account of this practice, which is referred to (...) in the literature as ‘approximation’. (shrink)

The topic of this paper is whether there is metaphysical vagueness. It is shown that it is important to distinguish between the general phenomenon of indeterminacy and the more narrow phenomenon of vagueness (the phenomenon that paradigmatically rears its head in sorites reasoning). Relatedly, it is important to distinguish between metaphysical indeterminacy and metaphysical vagueness. One can wish to allow metaphysical indeterminacy but rule out metaphysical vagueness. As is discussed in the paper, central argument against metaphysical vagueness, like those of (...) Gareth Evans and Mark Sainsbury, would if successful rule out metaphysical indeterminacy. One way to argue specifically against the possibility of metaphysical vagueness might be thought to be to argue for a specific theory of the nature of vagueness according to which vagueness is a semantic phenomenon. But it is shown that there are complications also pertaining to arguments with that structure. Toward the end of the paper, I discuss Trenton Merricks’ well-known argument against a semantic view on vagueness and for a metaphysical view. (shrink)

This dissertation explores several illuminating points of intersection between the philosophy of perception and the philosophy of vagueness. Among other things, I argue: (i) that it is entirely unhelpful to theorize about perception or consciousness using Nagelian "what it's like" talk; (ii) that a popular recent account of perceptual phenomenology (representationalism) conflicts with our best theory of vagueness (supervaluationism); (iii) that there are no vague properties, for Evans-esque reasons; (iv) that it is impossible to insert "determinacy" operators into representationalism in (...) a truth-preserving manner; and (v) that strong versions of dualism are unable to accommodate the possibility of borderline consciousness. (shrink)

A dynamic semantics for epistemically modalized sentences is an attractive alternative to the orthodox view that our best theory of meaning ascribes to such sentences truth-conditions relative to what is known. This essay demonstrates that a dynamic theory about might and must offers elegant explanations of a range of puzzling observations about epistemic modals. The first part of the story offers a unifying treatment of disputes about epistemic modality and disputes about matters of fact while at the same time avoiding (...) the complexities of alternative theories. The second part of the story extends the basic framework to cover some complicated data about retraction and the interaction between epistemic modality and tense. A comparison between the suggestion made in this essay and current versions of the orthodoxy is provided. (shrink)

Supervaluationism is a well known theory of vagueness. Subvaluationism is a less well known theory of vagueness. But these theories cannot be taken apart, for they are in a relation of duality that can be made precise. This paper provides an introduction to the subvaluationist theory of vagueness in connection to its dual, supervaluationism. A survey on the supervaluationist theory can be found in the Compass paper of Keefe (2008); our presentation of the theory in this paper will be short (...) to get rapidly into the logical issues. This paper is relatively self-contained. A modest background on propositional modal logic is, though not strictly necessary, advisable. The reader might find useful the Compass papers Kracht (2011) and Negri (2011) (though these papers cover issues of more complexity than what is demanded to follow this paper). (shrink)

According to anti-atomism, we represent color properties (e.g., red) in virtue of representing color relations (e.g., redder than). I motivate anti-atomism with a puzzle involving a series of pairwise indistinguishable chips. I then develop two versions of anti-atomism.

This paper develops a novel problem for representationalism (also known as "intentionalism"), a popular contemporary account of perception. We argue that representationalism is incompatible with supervaluationism, the leading contemporary account of vagueness. The problem generalizes to naive realism and related views, which are also incompatible with supervaluationism.

Abstract. As a general theory of reasoning—and as a general theory of what holds true under every possible circumstance—logic is supposed to be ontologically neutral. It ought to have nothing to do with questions concerning what there is, or whether there is anything at all. It is for this reason that traditional Aristotelian logic, with its tacit existential presuppositions, was eventually deemed inadequate as a canon of pure logic. And it is for this reason that modern quantification theory, too, with (...) its residue of existentially loaded theorems and patterns of inference, has been claimed to suffer from a defect of logical purity. The law of non-contradiction rules out certain circumstances as impossible—circumstances in which a statement is both true and false, or perhaps circumstances where something both is and is not the case. Is this to be regarded as a further ontological bias? (shrink)

One feature of vague predicates is that, as far as appearances go, they lack sharp application boundaries. I argue that we would not be able to locate boundaries even if vague predicates had sharp boundaries. I do so by developing an idealized cognitive model of a categorization faculty which has mobile and dynamic sortals (`classes', `concepts' or `categories') and formally prove that the degree of precision with which boundaries of such sortals can be located is inversely constrained by their flexibility. (...) Given the literature, it is plausible that we are appropriately like the model. Hence, an inability to locate sharp boundaries is not necessarily because there are none; boundaries could be sharp and it is plausible that we would nevertheless be unable to locate them. (shrink)

There are well-known quasi-formal arguments that identity is a "strict" relation in at least the following three senses: (1) There is a single identity relation and a single distinctness relation; (2) There are no contingent cases of identity or distinctness; and (3) There are no vague or indeterminate cases of identity or distinctness. However, the situation is less clear cut than it at first may appear. There is a natural formal theory of identity that is very close to the standard (...) classical theory but which does not validate the formal analogues of (1)-(3). The core idea is simple: We weaken the Principle of the Indiscernibility of Identicals from a conditional to an entailment and we adopt a weakly classical logic. This paper investigates this weakly classical theory of identity (and related theories) and discusses its philosophical ramifications. It argues that we can accept a reasonable theory of identity without committing ourselves to the uniqueness, necessity, or determinacy of identity. (shrink)

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)

Jeff Paris proves a generalized Dutch Book theorem. If a belief state is not a generalized probability then one faces ‘sure loss’ books of bets. In Williams I showed that Joyce’s accuracy-domination theorem applies to the same set of generalized probabilities. What is the relationship between these two results? This note shows that both results are easy corollaries of the core result that Paris appeals to in proving his dutch book theorem. We see that every point of accuracy-domination defines a (...) dutch book, but we only have a partial converse. (shrink)