In an interesting experimental study, Bonini et al. (1999) present partial support for truth-gap theories of vagueness. We say this despite their claim to find theoretical and empirical reasons to dismiss gap theories and despite the fact that they favor an alternative, epistemic account, which they call ‘vagueness as ignorance’. We present yet more experimental evidence that supports gap theories, and argue for a semantic/pragmatic alternative that unifies the gappy supervaluationary approach together with its glutty relative, the subvaluationary approach.

In §2-4, I survey three extant ways of making sense of indeterminate truth and find each of them wanting. All the later sections of the paper are concerned with showing that the most promising way of making sense of indeterminate truth is via either a theory of truthmaker gaps or via a theory of truthmaking gaps. The first intimations of a truthmaker–truthmaking gap theory of indeterminacy are to be found in Quine (1981). In §5, we see how Quine proposes to (...) solve Unger’s problem of the many via positing the possibility of groundless truth. In §6, I elaborate the truthmaker gap model of indeterminacy first sketched by Sorensen (2001, ch.11) and use it to give a reductive analysis of indeterminate truth. In §7, I briefly assess what kind of formal framework can best express the possibility of truthmaker gaps. In §8, I contrast what I dub ‘the ordinary conception of worldly indeterminacy’ with Williamson’s conception of worldly indeterminacy. In §9, I show how one can distinguish linguistic from worldly indeterminacy on a truthmaker gap conception. In §10, I briefly sketch the relationship between truthmaker gaps and ignorance. In §11, I assess whether a truthmaker gap conception of vagueness is really just a form of epistemicism. In §12, I propose that truthmaker gaps can yield a plausible model of (semantic) presupposition failure. In §13, in response to the worry that a truthmaker gap conception of indeterminacy is both parochial and controversial—since it commits us to an implausibly strong theory of truthmaking—I set forth a truthmaking gap conception of indeterminacy. In §14, I answer the worry that groundless truths, of whatever species, are just unacceptably queer. A key part of this answer is that a truthmaker–truthmaking gap model of indeterminacy turns out to be considerably less queer than any model of indeterminacy which gives up on Tarski’s T-schema for truth (and cognate schemas). (shrink)

Fallibilists about looks deny that the relation of looking the same as is non-transitive. Regarding familiar examples of coloured patches suggesting that such a relation is non-transitive, they argue that, in fact, indiscriminable adjacent patches may well look different, despite their perceptual indiscriminability: it’s just that we cannot notice the relevant differences in the chromatic appearances of such patches. In this paper, I present an argument that fallibilism about looks requires commitment to an empirically false consequence. To succeed in deflecting (...) putative cases of non-transitivity, fallibilists would have to claim that there can’t be any perceptual limitations of any kind on human chromatic discrimination. But there are good reasons to think such limitations exist. (shrink)

Might it be that world itself, independently of what we know about it or how we represent it, is metaphysically indeterminate? This article tackles in turn a series of questions: In what sorts of cases might we posit metaphysical indeterminacy? What is it for a given case of indefiniteness to be 'metaphysical'? How does the phenomenon relate to 'ontic vagueness', the existence of 'vague objects', 'de re indeterminacy' and the like? How might the logic work? Are there reasons for postulating (...) this distinctive sort of indefiniteness? Conversely, are there reasons for denying that there is indefiniteness of this sort? (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)

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)

Unrestricted Composition (UC) is, roughly, the claim that given any objects at all, there is something which those objects compose. (UC) conflicts in an obvious way with common sense. It has as a consequence, for instance, that there is something which has as parts my nose and the moon. One of the more influential arguments for (UC) is Theodore Sider’s version of the Argument from Vagueness. (A version of the Argument from Vagueness was first presented by David Lewis (1986), pp. (...) 212–213). That argument purports to show that some plausible claims concerning the nature of vagueness entail (UC). In this paper I will suggest a response to this argument. I will show that the proponent of Supersubstantivalism (SS)—the view that material objects are identical to regions of spacetime—can reject a premise of Sider’s argument without denying the plausible claims concerning vagueness. Doing so requires only rejecting a certain view concerning the relationship between the proper sub-region relation and the proper parthood relation. So, proponents of (SS) are in a better position than many of us to side with common sense regarding composition. In the first section of the paper, I will present Sider’s argument. In the second section, I will introduce (SS) and briefly discuss some reasons one might have to believe that it is true. In the third section, I will show how the proponent of (SS) can avoid commitment to (UC) and reject a premise of Sider’s argument. Last, I’ll briefly consider and respond to some objections. (shrink)

This paper presents a new theory of vagueness, which is designed to retain the virtues of the fuzzy theory, while avoiding the problem of higher-order vagueness. The theory presented here accommodates the idea that for any statement S₁ to the effect that 'Bob is bald' is x true, for x in [0, 1], there should be a further statement S₂ which tells us how true S₁ is, and so on - that is, it accommodates higher-order vagueness without resorting to the (...) claim that the metalanguage in which the semantics of vagueness is presented is itself vague, and without requiring us to abandon the idea that the logic - as opposed to the semantics - of vague discourse is classical. I model the extension of a vague predicate P as a blurry set, this being a function which assigns a degree of membership or degree function to each object o, where a degree function in turn assigns an element of [0, 1] to each finite sequence of elements of [0, 1]. The idea is that the assignment to the sequence (0.3, 0.2), for example, represents the degree to which it is true to say that it is 0.2 true that o is P to degree 0.3. The philosophical merits of my theory are discussed in detail, and the theory is compared with other extensions and generalisations of fuzzy logic in the literature. (shrink)

From Fine and Kamp in the 70’s—through Osherson and Smith in the 80’s, Williamson, Kamp and Partee in the 90’s and Keefe in the 00’s—up to Sauerland in the present decade, the objection continues to be run that fuzzy logic based theories of vagueness are incompatible with ordinary usage of compound propositions in the presence of borderline cases. These arguments against fuzzy theories have been rebutted several times but evidently not put to rest. I attempt to do so in this (...) paper. (shrink)

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. (shrink)

To get to grips with what Shapiro does and can say about higher-order vagueness, it is first necessary to thoroughly review and evaluate his conception of (first-order) vagueness, a conception which is both rich and suggestive but, as it turns out, not so easy to stabilise. In Sections I–IV, his basic position on vagueness (see Shapiro [2003]) is outlined and assessed. As we go along, I offer some suggestions for improvement. In Sections V–VI, I review two key paradoxes of higher-order (...) vagueness, while in Section VII, I explore a possible line of response to such paradoxes given by Keefe [2000]. In Section VIII, I assess whether which Shapiro might adapt Keefe’s response to combat both paradoxes. (shrink)

Although arguments for and against competing theories of vagueness often appeal to claims about the use of vague predicates by ordinary speakers, such claims are rarely tested. An exception is Bonini et al. (1999), who report empirical results on the use of vague predicates by Italian speakers, and take the results to count in favor of epistemicism. Yet several methodological difficulties mar their experiments; we outline these problems and devise revised experiments that do not show the same results. We then (...) describe three additional empirical studies that investigate further claims in the literature on vagueness: the hypothesis that speakers confuse ‘P’ with ‘definitely P’, the relative persuasiveness of different formulations of the inductive premise of the Sorites, and the interaction of vague predicates with three different forms of negation. (shrink)

Individual semiotic systems interpreting their environment are not well understood from the externalist approach typical of the scientific method. Science constructs probabilities describing large populations of systems, not individuals. The Umwelt, as the individually experienced/created aspects of the habitat aspect of its population’s ecological niche, is given an internalist understanding within the framework of the compositional hierarchy. Vagueness is an important aspect of the internalist condition. It is selectively reduced momentarily by creative choices that can have a Peircean semiotic formulation, (...) and which are often unpredictable externally, thereby appearing to be chance events. (shrink)

Levels of reality reflect one kind of complexity, which can be modeled using a specification hierarchy. Levels emerged during the Big Bang, as physical degrees of freedom became increasingly fixed as the expanding universe developed, and new degrees of freedom associated with higher levels opened up locally, requiring new descriptive semantics. History became embodied in higher level entities, which are increasingly individuated, aggregate patterns of lower level entities. Development is an epigenetic trajectory from vaguer to more definite and individuated embodiment, (...) punctuated by the emergence of new integrative levels. It is constrained by being subsumed by lower levels (e.g., physical dynamics) and may be guided by structural attractors as well as by internally stored information (e.g., genes) in the higher levels. I conjecture, on a thermodynamic basis, that the number of levels that become manifest in an expanding universe depends upon its rate of expansion. (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)

According to the fitting-attitude analysis of value , to be valuable is to be a fitting object of a pro-attitude. In earlier publications, setting off from this format of analysis, I proposed a modelling of value relations which makes room for incommensurability in value. In this paper, I first recapitulate the value modelling and then move on to suggest adopting a structurally similar analysis of probability. Indeed, many probability theorists from Poisson onwards did adopt an analysis of this kind. This (...) move allows to formally model probability and probability relations in essentially the same way as value and value relations. One of the advantages of the model is that we get a new account of Keynesian incommensurable probabilities, which goes beyond Keynes in distinguishing between different types of incommensurability. It also becomes possible to draw a clear distinction between incommensurability and vagueness in probability comparisons. (shrink)

The vagueness view holds that when evaluative comparisons are hard, there is indeterminacy about which comparative relation holds. It is sceptical about whether there are any incommensurate items (in some domain). The sceptical element of John Broome’s version of this view rests on a controversial principle. Robert Sugden advances a similar view which does not depend on this principle. Sugden’s argument fails as a vagueness view because it assumes rather than shows that there are no incommensurate items (in some domain). (...) Nonetheless, I argue that an interpretation of his argument constitutes a defensible vagueness view which is supported by intuition about examples. On this interpretation Sugden’s view can be mapped onto Broome’s application of a supervaluationist view of vagueness. It is also (on this reading) a close relative of James Griffin’s ‘rough equality’ view when this is interpreted in terms of vagueness. On an alternative interpretation Sugden’s view is not sceptical about incommensurateness. On this interpretation he does not defend a vagueness view and is ‘sceptical’ about the contribution of the philosophical literature to our understanding of rational choice. (shrink)

The idea of higher-order vagueness is usually associated with conceptions of vagueness that focus on the existence of borderline cases. What sense can be made of it within a conception of vagueness that focuses on tolerance instead? A proposal is offered here. It involves understanding ‘definitely’ not as a sentence operator but as a predicate modifier, and more precisely as an intensifier, that is, an operator that shifts the predicate extension along a scale. This idea is combined with the author’s (...) earlier approach to the semantics of vague expressions, which builds on the idea of a central gap associated with a predicate. The central gap approach is generalized to handle arbitrarily many iterations of ‘definitely’. (shrink)

This paper deals with the possibility of faultless disagreement in law. It does this by looking to other spheres in which faultless disagreement appears to be possible, mainly in matters of taste and ethics. Three possible accounts are explored: the realist account, the relativist account, and the expressivist account. The paper tries to show that in the case of legal disagreements, there is a place for an approach that can take into account our intuitions in the sense that legal disagreements (...) are genuine and at times faultless. (shrink)

The problem of artificial precision is a major objection to any theory of vagueness based on real numbers as degrees of truth. Suppose you are willing to admit that, under sufficiently specified circumstances, a predication of “is red” receives a unique, exact number from the real unit interval [0, 1]. You should then be committed to explain what is it that determines that value, settling for instance that my coat is red to degree 0.322 rather than 0.321. In this note (...) I revisit the problem in the important case of Łukasiewicz infinite-valued propositional logic that brings to the foreground the rôle of maximally consistent theories. I argue that the problem of artificial precision, as commonly conceived of in the literature, actually conflates two distinct problems of a very different nature. (shrink)

Timothy Williamson claims that margin for error principles govern all cases of inexact knowledge. I show that this claim is unfounded: there are cases of inexact knowledge where Williamson’s argument for margin for error principles does not go through. The problematic cases are those where the value of the relevant parameter is fixed across close cases. I explore and reject two responses to my objection, before concluding that Williamson’s account of inexact knowledge is not compelling.

What is the proper attitude toward what is expressed by a vague sentence in the face of borderline evidence? Some call this attitude “ambivalence” and distinguish it from uncertainty. It has been argued that Classical Epistemicism conjoined with classical probability theory fails to characterize this attitude, and that we must therefore abandon classical logic or classical probabilities in the presence of vagueness. In this paper, I give a characterization of ambivalence assuming a supervaluationist semantics for vague terms that does not (...) revise either. The theory, which I call the theory of Superprobabilities, identifies the proper attitude toward a vague sentence, in the presence of exact borderline evidence, as the set of classical probabilities of the evidence on each member of the set of all precisifications of a vague sentence. I defend the use of sets of probabilities against objections by generalizing the theory of Superprobabilities to a decision theory called Superrationality. I then compare the merits of the theory of Superprobabilities to Classical Epistemicism and nonclassical probabilities theories with respect to the problem of ambivalence. (shrink)

This article argues that the decision problem in the original position should be characterized as a decision problem under uncertainty even when it is assumed that the denizens of the original position know that they have an equal chance of ending up in any given individual’s place. It supports this claim by arguing that (a) the continuity axiom of decision theory does not hold between all of the outcomes the denizens of the original position face and that (b) neither us (...) nor the denizens of the original position can know the exact point at which discontinuity sets in, because the language we employ in comparing different outcomes is ineradicably vague. It is also argued that the account underlying (b) can help proponents of superiority in value theory defend their view against arguments offered by Norcross and Griffin. (shrink)

We argue that a semantics for counterfactual conditionals in terms of comparative overall similarity faces a formal limitation due to Arrow’s impossibility theorem from social choice theory. According to Lewis’s account, the truth-conditions for counterfactual conditionals are given in terms of the comparative overall similarity between possible worlds, which is in turn determined by various aspects of similarity between possible worlds. We argue that a function from aspects of similarity to overall similarity should satisfy certain plausible constraints while Arrow’s impossibility (...) theorem rules out that such a function satisfies all the constraints simultaneously. We argue that a way out of this impasse is to represent aspectual similarity in terms of ranking functions instead of representing it in a purely ordinal fashion. Further, we argue against the claim that the determination of overall similarity by aspects of similarity faces a difficulty in addition to the Arrovian limitation, namely the incommensurability of different aspects of similarity. The phenomena that have been cited as evidence for such incommensurability are best explained by ordinary vagueness. (shrink)

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)

During the last couple of decades, several attempts have been made to come up with a theory that can handle the various semantic, logical and philosophical problems raised by the vagueness of natural languages. One of the most influential ideas that have come into fashion in recent years is the idea that vagueness should be analysed as a form of context sensitivity. Such contextualist theories of vagueness have gained some popularity, but many philosophers have remained sceptical of the prospects of (...) finding a tenable contextualist solution to the problems of vagueness. This paper provides an introduction to the most popular contextualist accounts, and a discussion of some of the most important arguments for and against them. (shrink)

This piece gives an overview of the supervaluationist theory of vagueness. According to that theory, a sentence is true if and only if it is true on all ways of making it precise. This yields borderline case predications that are neither true nor false, but yet classical logic is preserved almost entirely. The article presents the view and some of its merits and briefly compares it with other theories of vagueness. It raises issues about higher-order vagueness and the definitely operator (...) and about the supervaluationist's accounts of truth and validity. (shrink)

Logical Pluralists maintain that there is more than one genuine/true logical consequence relation. This paper seeks to understand what the position could amount to and some of the challenges faced by its formulation and defence. I consider in detail Beall and Restall’s Logical Pluralism—which seeks to accommodate radically different logics by stressing the way that they each fit a general form, the Generalised Tarski Thesis (GTT)—arguing against the claim that different instances of GTT are admissible precisifications of logical consequence. I (...) then consider what it is to endorse a logic within a pluralist framework and criticise the options Beall and Restall entertain. A case study involving many-valued logics is examined. I next turn to issues of the applications of different logics and questions of which logic a pluralist should use in particular contexts. A dilemma regarding the applicability of admissible logics is tackled and it is argued that application is a red herring in relation to both understanding and defending a plausible form of logical pluralism. In the final section, I consider other ways to be and not to be a logical pluralist by examining analogous positions in debates over religious pluralism: this, I maintain, illustrates further limitations and challenges for a very general logical pluralism. Certain less wide-ranging pluralist positions are more plausible in both cases, I suggest, but assessment of those positions needs to be undertaken on a case-by-case basis. (shrink)

Taking a series of colour patches, starting with one that clearly looks red, and making each so similar in colour to the previous one that it looks the same as it, we appear to be able to show that a yellow patch looks red. I ask whether phenomenal sorites paradoxes, such as this, are subject to a unique kind of solution that is unavailable in relation to other sorites paradoxes. I argue that they do not need such a solution, nor (...) do they succumb to one. In particular, I reject the claim made by Fara and Raffman that looks the same is a transitive relation, which would allow us to solve phenomenal sorites paradoxes by denying the possibility of the required kind of sorites series. (shrink)

A theory of vagueness gives a model of vague language and of reasoning within the language. Among the models that have been offered are Degree Theorists’ numerical models that assign values between 0 and 1 to sentences, rather than simply modelling sentences as true or false. In this paper, I ask whether we can benefit from employing a rich, well-understood numerical framework, while ignoring those aspects of it that impute a level of mathematical precision that is not present in the (...) modelled phenomenon of vagueness. Can we ignore apparent implications for the phenomena by pointing out that it is just a model and that the unwanted features are mere artefacts? I explore the distinction between representors and artefacts and criticise the strategy of appealing to features as mere artefacts in defence of a theory. I focus largely on theories using numerical resources, but also consider other, related theories and strategies, including theories appealing to non-linear structures. (shrink)

According to columnar higher-order vagueness, all orders of vagueness coincide: any borderline case is a borderline borderline case, and a third-order borderline case, etc. Bobzien has worked out many details of such a theory and models it with a modal logic closely related to S4. I take up a range of questions about the framework and argue that it is not suitable for modelling the structure of vagueness and higher-order vagueness.

I offer a reconstruction of contemporary medical procedures of sex assignment for infants with intersex conditions. In the perspective adopted, sex assignment to intersexed newborns can be understood as a procedure that imposes determinate sex predicates. The account describes two stages of sex assignment. At the first stage of the process, the sex predicates ‘female’, ‘male’, or ‘intersexed’ are taken to denote genital morphology. Initial genital assessment of newborns imposes clear boundaries upon the extensions of these predicates through diagnostic schemes (...) of precisification. At the second stage, the sex predicates ‘female’ and ‘male’ denote sex of rearing, a therapeutic and pedagogical project aimed at producing stable and psycho-socially well-adjusted gender identity. The multi-dimensional indeterminacy of prognosticating sex of rearing at the second stage is mitigated through the prioritization of some subsets of the medical data. (shrink)

A number of epistemologists have recently concluded that a piece of reasoning may be epistemically permissible even when it is impossible for the reasoning subject to present her reasoning as an argument without begging the question. I agree with these epistemologists, but argue that none has sufficiently divorced the notion of begging the question from epistemic notions. I present a proposal for a characterization of begging the question in purely pragmatic terms.

There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an agent reports that two things are indistinguishable are both carefully modeled, the problems disappear, and indistinguishability can indeed be taken to be an equivalence relation. Moreover, this model also suggests a logic of vagueness that seems (...) to solve many of the problems related to vagueness discussed in the philosophical literature. In particular, it is shown here how the logic can handle the sorites paradox. (shrink)

In an alleged counter-example to the completeness of rational preferences, a career as a clarinettist is compared with a career in law. It seems reasonable to neither want to judge that the law career is at least as preferred as the clarinet career nor want to judge that the clarinet career is at least as preferred as the law career. The two standard interpretations of examples of this kind are, first, that the examples show that preferences are rationally permitted to (...) be incomplete and, second, that the examples show that preferences are rationally permitted to be indeterminate. In this paper, I shall argue that the difference between these interpretations is crucial for the money-pump argument for transitivity, which is the standard argument that rational preferences are transitive. I shall argue that the money-pump argument for transitivity fails if preferences are rationally permitted to be incomplete but that it works if preferences are rationally permitted to be indeterminate and rationally required to be complete. (shrink)

Michael Tye responds to the problem of higher-order vagueness for his trivalent semantics by maintaining that truth-value predicates are “vaguely vague”: it’s indeterminate, on his view, whether they have borderline cases and therefore indeterminate whether every sentence is true, false, or indefinite. Rosanna Keefe objects (1) that Tye’s argument for this claim tacitly assumes that every sentence is true, false, or indefinite, and (2) that the conclusion is any case not viable. I argue – contra (1) – that Tye’s argument (...) needn’t make that assumption. A version of her objection is in fact better directed against other arguments Tye advances, though Tye can absorb this criticism without abandoning his position’s core. On the other hand, Keefe’s second objection does hit the mark: embracing ‘vaguely vague’ truth-value predicates undermines Tye’s ability to support validity claims needed to defend his position. To see this, however, we must develop Keefe’s remarks further than she does. (shrink)

Various writers have proposed that the notion of a possible world is a functional concept, yet very little has been done to develop that proposal. This paper explores a particular functionalist account of possible worlds, according to which pluralities of possible worlds are the bases for structures which provide occupants for the roles which analyse our ordinary modal concepts. It argues that the resulting position meets some of the stringent constraints which philosophers have placed upon accounts of possible worlds, while (...) also trivializing the question what possible worlds are. The paper then discusses a range of problems facing the functionalist position. (shrink)

In 1907 Borel published a remarkable essay on the paradox of the Heap (“Un paradoxe économique: le sophisme du tas de blé et les vérités statistiques”), in which Borel proposes what is likely the first statistical account of vagueness ever written, and where he discusses the practical implications of the sorites paradox, including in economics. Borel’s paper was integrated in his book Le Hasard, published 1914, but has gone mostly unnoticed since its publication. One of the originalities of Borel’s essay (...) is that it puts forward a model of vagueness as imprecision, making particular use of the Gaussian law of measurement errors to model categorization. The aim of our paper is to give a presentation of the historical context of Borel’s essay, to spell out the mathematical details of his model, and to provide a critical assessment of his theory. Three aspects of Borel’s account are particularly discussed: the first concerns the comparison between Borel’s statistical account and posterior degree-theoretic accounts of vagueness. The second concerns the anti-epistemicist flavor of Borel’s approach, whereby the idea of statistical fluctuation is used to undermine the notion of sharp boundary for vague predicates. The third concerns the problematic link between Borel’s model of vagueness as imprecision and the notion of semantic indeterminacy. An English translation of Borel’s original essay is appended to this paper (Erkenntnis, this issue). (shrink)

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

The main question of the paper is that ofwhat vagueness consists in. This question must be distinguished from other questions about vagueness discussed in the literature. It is argued that familiar accounts of vagueness for general reasons failto answer the question ofwhat vagueness consists in. A positive view is defended, according to which, roughly, the vagueness of an expression consists in it being part ofsemantic competence to accept a tolerance principle for the expression. Since tolerance principles are inconsistent, this is (...) an inconsistency view on vagueness. (shrink)

Nicholas Smith argues that an adequate account of vagueness must involve\ndegrees of truth. The basic idea of degrees of truth is that while\nsome sentences are true and some are false, others possess intermediate\ntruth values: they are truer than the false sentences, but not as\ntrue as the true ones. This idea is immediately appealing in the\ncontext of vagueness--yet it has fallen on hard times in the philosophical\nliterature, with existing degree-theoretic treatments of vagueness\nfacing apparently insuperable objections. Smith seeks to turn the\ntide in (...) favor of a degree-theoretic treatment of vagueness, by motivating\nand defending the basic idea that truth can come in degrees, by arguing\nthat no theory of vagueness that does not countenance degrees of\ntruth can be correct, and by developing a new degree-theoretic treatment\nof vagueness--fuzzy plurivaluationism--that solves the problems plaguing\nearlier degree theories. (shrink)

It is often assumed that indeterminacy in mereological relations—in particular, indeterminacy in which collections of objects have fusions—leads immediately to indeterminacy in what objects there are in the world. This assumption is generally taken as a reason for rejecting mereological vagueness. The purpose of this paper is to examine the link between mereological vagueness and existential vagueness. I hope to show that the connection between the two forms of vagueness is not nearly so clear-cut as has been supposed.

After presenting a negative characterization of metaphysical vagueness and the main tenets of the view of vagueness as semantic indecision, the paper critically discusses the objection that such a view requires that at least some vagueness not be just constituted by semantic indecision—but rather by the metaphysical vagueness of some semantic relations themselves submitted by Trenton Merricks and, more recently, Nathan Salmon.

Consider a cat on a mat. On the one hand, there seems to be just one cat, but on the other there seem to be many things with as good a claim as anything in the vicinity to being a cat. Hence, the problem of the many. In his ‘Many, but Almost One,’ David Lewis offered two solutions. According to the first, only one of the many is indeed a cat, although it is indeterminate exactly which one. According to the (...) second, the many are all cats, but they are almost identical to each other, and hence they are almost one. For Lewis, the two solutions do not compete with each other but are mutually complementary, as each one can assist the other. This paper has two aims: to give some reasons against the first of these two solutions, but then to defend the second as a self-standing solution from Lewis’s considerations to the contrary. (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)

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.

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. (shrink)