This paper offers the Boolean many-valued solution to the Sorites Paradox. According to the precisification-based Boolean many-valued theory, from which this solution arises, sentences have not only two truth values, truth (or 1) and falsity (or 0), but many Boolean values between 0 and 1. The Boolean value of a sentence is identified with the set of precisifications in which the sentence is true. Unlike degrees fuzzy logic assigns to sentences, Boolean many values are not linearly but only partially ordered; (...) so there are values that are incomparable. Despite this fact, the sentences in a sorites series can be taken as having values in a linear order, and losing (or gaining) value as we move from sentence to sentence in the series. So there is no sharp borderline between 0 and 1. Assigning Boolean many values instead of the two truth values to sentences for their vagueness values is analogous to assigning propositions instead of the truth values to sentences for their semantic values, as propositions are, from our viewpoint, also Boolean many values. (shrink)

This article presents an extension of Lewis’ analysis of counterfactuals to a graded framework. Unlike standard graded approaches, which use the probabilistic framework, we employ that of many-valued logics. Our principal goal is to provide an adequate analysis of the main background notion of Lewis’ approach—the one of the similarity of possible worlds. We discuss the requirements imposed on the analysis of counterfactuals by the imprecise character of similarity and concentrate in particular on robustness, i.e., the requirement that small changes (...) in the similarity relation should not significantly change the truth value of the counterfactual in question. Our second motivation is related to the logical analysis of natural language: analyzing counterfactuals in the framework of many-valued logics allows us to extend the analysis to counterfactuals that include vague statements. Unlike previous proposals of this kind in the literature, our approach makes it possible to apply gradedness at various levels of the analysis and hence provide a more detailed account of the phenomenon of vagueness in the context of counterfactuals. Finally, our framework admits a novel way of avoiding the Limit Assumption, keeping the core of Lewis’ truth condition for counterfactuals unchanged. (shrink)

Some find it plausible that a sufficiently long duration of torture is worse than any duration of mild headaches. Similarly, it has been claimed that a million humans living great lives is better than any number of worm-like creatures feeling a few seconds of pleasure each. Some have related bad things to good things along the same lines. For example, one may hold that a future in which a sufficient number of beings experience a lifetime of torture is bad, regardless (...) of what else that future contains, while minor bad things, such as slight unpleasantness, can always be counterbalanced by enough good things. Among the most common objections to such ideas are sequence arguments. But sequence arguments are usually formulated in classical logic. One might therefore wonder if they work if we instead adopt many-valued logic. I show that, in a common many-valued logical framework, the answer depends on which versions of transitivity are used as premises. We get valid sequence arguments if we grant any of several strong forms of transitivity of 'is at least as bad as' and a notion of completeness. Other, weaker forms of transitivity lead to invalid sequence arguments. The plausibility of the premises is largely set aside here, but I tentatively note that almost all of the forms of transitivity that lead to valid sequence arguments seem intuitively problematic. Still, a few moderately strong forms of transitivity that might be acceptable lead to valid sequence arguments, although weaker statements of the initial value claims avoid these arguments at least to some extent. (shrink)

This book proposes a new solution to the problem of vagueness. There are several different ways of addressing this problem and no clear agreement on which one is correct. The author proposes that it should be understood as the problem of explaining vague predicates in a way that systematizes six intuitions about the phenomenon and satisfies three criteria of adequacy for an ideal theory of vagueness. The third criterion, which is called the “criterion of precisification”, is the most controversial one. (...) It is based on the intuition that a predicate is vague only if it is imprecise. The author considers some different definitions of linguistic imprecision, proposing that a predicate is imprecise if and only if there is no sharp boundary between objects to which its application yields some particular truth-value and objects to which its application does not yield that truth-value. The volume critically reviews the current theories of vagueness and proposes a new one, the Theory of Vagueness as Arbitrariness, which defines a vague predicate as an arbitrary predicate that must be precisified in order to contribute to a sentence that has truth-conditions. The main advantages of this theory over the current alternatives are that it satisfies all three criteria and systematizes the relevant intuitions. (shrink)

I argue for two claims: that the ordinary English truth predicate is a gradable adjective and that truth is a property that comes in degrees. The first is a semantic claim, motivated by the linguistic evidence and the similarity of the truth predicate’s behavior to other gradable terms. The second is a claim in natural language metaphysics, motivated by interpreting the best semantic analysis of gradable terms as applied to the truth predicate. In addition to providing arguments for these two (...) claims, I draw out consequences for debates about deflationism and truth-based analyses of notions such as assertion and logical consequence. (shrink)

There are several types of truths. In this paper I focus on semantic truths, and within these on factual truths. These truths are attributed to statements. I review the theory of the truth proposed by Bunge and discuss some problems that it presents. I suggest that a theory of truth of factual statements should be complemented by a theory of relevance, and propose the basic tenets of it. Finally, I briefly discuss the nature of propositions and the problem of scientific (...) truth in the light of the presented semantic theory. (shrink)

Douglas Edwards is arguably the most prominent contemporary advocate of moderate alethic pluralism. Significantly influenced by Crispin Wright and Michael Lynch, his work on the nature of truth has become widely discussed in the topical literature. Edwards labels his version of moderate alethic pluralism determination pluralism. At first blush, determination pluralism appears philosophically promising. The position deserves thoughtful consideration, particularly because of its capacity to accommodate the scope problem. I argue, however, that upon analysis the view is better understood as (...) a form of metaphysical dualism or what I will call meta-dualism. Furthermore, determination pluralists face a dilemma; there appears to be an instability at the core of their dualistic model. On the one horn of the dilemma, they need a clear metaphysical demarcation at the interface of their two necessary domains. On the other horn, they seem to need to a metaphysically vague boundary at the interface of their two necessary domains. Determination pluralism needs substantial revision. (shrink)

In this dissertation, I argue that vagueness is a metaphysical phenomenon---that properties and objects can be vague---and propose a trivalent theory of vagueness meant to account for the vagueness in the world. In the first half, I argue against the theories that preserve classical logic. These theories include epistemicism, contextualism, and semantic nihilism. My objections to these theories are independent of considerations of the possibility that vagueness is a metaphysical phenomenon. However, I also argue that these theories are not capable (...) of accommodating metaphysical vagueness. As I move into my positive theory, I first argue for the possibility of metaphysical vagueness and respond to objections that charge that the world cannot be vague. One of these objections is Gareth Evans' much-disputed argument that vague identities are impossible. I then describe what I call the logic of states of affairs. The logic of states of affairs has as its atomic elements states of affairs that can obtain, unobtain, or be indeterminate. Finally, I argue that the logic of states of affairs is a better choice for a theory of vagueness than other logics that could accommodate metaphysical vagueness such as supervaluationism and degree theories. Preference should be given to the logic of states of affairs because it provides a better explanation of higher-order vagueness and does a better job of matching our ordinary understandings of logical operators than supervaluationism does and because it provides a more general account of indeterminacy than the account given by degree theories. Advisor: Reina Hayaki. (shrink)

ABSTRACT Issues concerning the putative perception/cognition divide are not only age-old, but also resurface in contemporary discussions in various forms. In this paper, I connect a relatively new debate concerning perceptual confidence to the perception/cognition divide. The term ‘perceptual confidence’ is quite common in the empirical literature, but there is an unsettled question about it, namely: are confidence assignments perceptual or post-perceptual? John Morrison in two recent papers puts forward the claim that confidence arises already at the level of perception. (...) In this paper, I first argue that Morrison’s case is unconvincing, and then develop one picture on perceptual precision with the notion of ‘matching profile’ and ‘supervaluation’ : 481–495.), highlighting the fact that this is a vagueness account, which is similar to but importantly different from indeterminacy accounts : 156–184.). With this model in hand, there can be rich resources with which to draw a theoretical line between perception and cognition. (shrink)

According to the plurivaluationist, our vague discourse doesn’t have a single meaning. Instead, it has many meanings, each of which is precise—and it is this plurality of meanings that is the source of vagueness. I believe plurivaluationist positions are underdeveloped and for this reason unpopular. This paper attempts to correct this situation by offering a particular development of plurivaluationism that I call supersententialism. The supersententialist leverages lessons from another area of research—the Problem of the Many—in service of the plurivaluationist position. (...) The Problem reveals theoretical reasons to accept that there are many cats where we thought there was one; the supersententialist claims that we are in a similar situation with respect to languages, propositions and sentences. I argue that the parallel suggested by the supersententialist reveals unappreciated advantages and lines of defense for plurivaluationism. (shrink)

According to Stewart Candlish, Russell and Moore had misunderstood F. H. Bradley’s monism. According to Jonathan Schaffer, they had misunderstood monism more generally. A key thread of the creation narrative of analytic philosophy, according to which Russell and Moore successfully undermined monism to give rise to a new movement is, therefore, in doubt. In this paper, I defend the standard narrative against those who seek to revise it.

Edgington has proposed a solution to the sorites paradox in terms of ‘verities’, which she defines as degrees of closeness to clear truth. Central to her solution is the assumption that verities are formally probabilities. She is silent on what verities might derive from and on why they should be probabilities. This paper places Edgington’s solution in the framework of a spatial approach to conceptualization, arguing that verities may be conceived of as deriving from how our concepts relate to each (...) other. Building on work by Kamp and Partee, this paper further shows how verities, thus conceived of, may plausibly be assumed to have probabilistic structure. The new interpretation of verities is argued to also help answer the question of what the verities of indicative conditionals are, a question which Edgington leaves open. Finally, the question of how to accommodate higher-order vagueness, given this interpretation, is addressed. (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.

This essay explores the thesis that for vague predicates, uncertainty over whether a borderline instance x of red/large/tall/good is to be understood as practical uncertainty over whether to treat x as red/large/tall/good. Expressivist and quasi-realist treatments of vague predicates due to John MacFarlane and Daniel Elstein provide the stalking-horse. It examines the notion of treating/counting a thing as F , and links a central question about our attitudes to vague predications to normative evaluation of plans to treat a thing as (...) F . The essay examines how the account applies to normatively defective or contested terms. The final section raises a puzzle about the mechanics of MacFarlane’s detailed implementation for the case of gradable adjectives. (shrink)

This paper explores the idea that vague predicates like “tall”, “loud” or “expensive” are applied based on a process of analog magnitude representation, whereby magnitudes are represented with noise. I present a probabilistic account of vague judgment, inspired by early remarks from E. Borel on vagueness, and use it to model judgments about borderline cases. The model involves two main components: probabilistic magnitude representation on the one hand, and a notion of subjective criterion. The framework is used to represent judgments (...) of the form “x is clearly tall” versus “x is tall”, as involving a shift of one’s criterion, and then to derive observed patterns of acceptance for borderline contradictions, namely sentences of the form “x is tall and not tall”, relative to the acceptance of their conjuncts. (shrink)

A framework of degrees of belief, or credences, is often advocated to model our uncertainty about how things are or will turn out. It has also been employed in relation to the kind of uncertainty or indefiniteness that arises due to vagueness, such as when we consider “a is F” in a case where a is borderline F. How should we understand degrees of belief when we take into account both these phenomena? Can the right kind of theory of the (...) semantics of vagueness help us answer this? Nicholas J.J. Smith defends a unified account, according to which “degree of belief is expected truth-value”; this builds on his Degree Theory of vagueness that offers an account of the semantics and logic of vagueness in terms of degrees of truth. I argue that his account fails. Degree theories of vagueness do not help us understand degrees of belief and, I argue, we shouldn’t expect a theory of vagueness to yield a detailed uniform story about this. The route from the semantics to psychological states needn’t be straightforward or uniform even before we attempt to combine vagueness with probabilistic uncertainty. (shrink)

There is a trade-off between specificity and accuracy in existing models of belief. Descriptions of agents in the tripartite model, which recognizes only three doxastic attitudes—belief, disbelief, and suspension of judgment—are typically accurate, but not sufficiently specific. The orthodox Bayesian model, which requires real-valued credences, is perfectly specific, but often inaccurate: we often lack precise credences. I argue, first, that a popular attempt to fix the Bayesian model by using sets of functions is also inaccurate, since it requires us to (...) have interval-valued credences with perfectly precise endpoints. We can see this problem as analogous to the problem of higher order vagueness. Ultimately, I argue, the only way to avoid these problems is to endorse Insurmountable Unclassifiability. This principle has some surprising and radical consequences. For example, it entails that the trade-off between accuracy and specificity is in-principle unavoidable: sometimes it is simply impossible to characterize an agent’s doxastic state in a way that is both fully accurate and maximally specific. What we can do, however, is improve on both the tripartite and existing Bayesian models. I construct a new model of belief—the minimal model—that allows us to characterize agents with much greater specificity than the tripartite model, and yet which remains, unlike existing Bayesian models, perfectly accurate. (shrink)

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)

In this paper we explain our pretense account of truth-talk and apply it in a diagnosis and treatment of the Liar Paradox. We begin by assuming that some form of deflationism is the correct approach to the topic of truth. We then briefly motivate the idea that all T-deflationists should endorse a fictionalist view of truth-talk, and, after distinguishing pretense-involving fictionalism (PIF) from error- theoretic fictionalism (ETF), explain the merits of the former over the latter. After presenting the basic framework (...) of our PIF account of truth-talk, we demonstrate a few advantages it offers over T-deflationist accounts that do not explicitly acknowledge pretense at work in the discourse. In turning to the Liar Paradox, we explain how the quasi-anaphoric functioning that our account attributes to truth-talk provides a diagnosis of the Liar Paradox (and other instances of semantic pathology) as having no content—in the sense of not specifying any of what we call M-conditions. At the same time, however, we vindicate the intuition that we can understand liar sentences, thereby avoiding one standard objection to “meaningless strategy” responses to the Liar Paradox. With this diagnosis in place, we then, by way of treatment, introduce a new predicate, ‘semantically defective’, and show how the explanation we give for its application allows for a consistent, yet revenge-immune, (dis)solution of the Liar Paradox, and semantic pathology generally. (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.

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

Can identity itself be vague? Can there be vague objects? Does a positive answer to either question entail a positive answer to the other? In this paper we answer these questions as follows: No, No, and Yes. First, we discuss Evans’s famous 1978 argument and argue that the main lesson that it imparts is that identity itself cannot be vague. We defend the argument from objections and endorse this conclusion. We acknowledge, however, that the argument does not by itself establish (...) either that there cannot be vague objects or that there cannot be identity statements that are indeterminate for ontic reasons. And we further acknowledge that it does not by itself establish that there cannot be identity statements that are indeterminate in virtue of the existence of vague objects. We then go on to argue that, despite this, one who believes in vague objects cannot endorse Evans’s argument. To establish this we offer supplementary arguments that show that if vague objects exist then identity is vague, and that if identity is vague then vague objects exist. Finally we draw attention to an argument parallel to that of Evans’s, but safer, which can be employed against the putative ontic indeterminacy in identity of vague objects which can be differentiated by identity-free properties. (shrink)

In the context of classical (crisp, precise) sets, there is a familiar connection between the notions of counting, ordering and cardinality. When it comes to vague collections, the connection has not been kept in central focus: there have been numerous proposals regarding the cardinality of vague collections, but these proposals have tended to be discussed in isolation from issues of counting and ordering. My main concern in this paper is to draw focus back onto the connection between these notions. I (...) propose a natural generalisation to the vague case of the familiar process of counting precise collections. I then discuss the relationships between this process of counting and various notions of ordering and cardinality for vague sets. Some existing views concerning the cardinality of vague collections fit better than others with my proposal about how to count the members of such a collection. In particular, the idea that we should approach cardinality via certain formulas of a logical language -- which has been prominent in the recent literature -- is less attractive than other existing proposals. (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)

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)

A decade ago, Harris Nover and I introduced the Pasadena game, which we argued gives rise to a new paradox in decision theory even more troubling than the St Petersburg paradox. Gwiazda's and Smith's articles in this volume both offer revisionist solutions. I critically engage with both articles. They invite reflections on a number of deep issues in the foundations of decision theory, which I hope to bring out. These issues include: some ways in which orthodox decision theory might be (...) supplemented; the role of simulations of such infinite games; the role of small probabilities, and of idealization, in decision theory; tolerance about practical norms; and alternative ways of understanding decision theory's job description. (shrink)

The paper presents both new data and a new analysis of the semantic and pragmatic properties of the class of absolute scalar adjectives within an extension of a well-known logical framework for the analysis of gradable predicates: the delineation semantics framework . It has been long observed that the context-sensitivity, vagueness and gradability features of absolute scalar predicates give rise to certain puzzles for their analysis within most, if not all, modern formal semantic frameworks. While there exist proposals for solving (...) these puzzles within other major frameworks , it has been argued that some of their aspects are particularly challenging for the analysis of absolute scalar predicates within the delineation approach. By combining insights into the relationship between context-sensitivity and scalarity from the DelS framework with insights into the relationship between tolerance/similarity relations and the Sorites paradox from Cobreros et al.’s Tolerant, Classical, Strict framework, I propose a new logical system, called Delineation TCS , in which to set analyses of four classes of adjectival predicates. I argue that this new framework allows for an analysis of absolute scalar adjectives that answers these challenges for delineation-based frameworks, while still preserving the heart of the Klein-ian approach. (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)

If we think, as Ramsey did, that a degree of belief that P is a stronger or weaker tendency to act as if P, then it is clear that not only uncertainty, but also vagueness, gives rise to degrees of belief. If I like hot coffee and do not know whether the coffee is hot or cold, I will have some tendency to reach for a cup; if I like hot coffee and know that the coffee is borderline hot, I (...) will have some tendency to reach for a cup. Suppose that we take degrees of belief arising from uncertainty to obey the laws of probability and that we model vagueness using degrees of truth. We then encounter a problem: it does not look as though degrees of belief arising from vagueness should obey the laws of probability. One response would be to countenance two different sorts of degrees of belief: degrees of belief arising from uncertainty, which obey the laws of probability; and degrees of belief arising from vagueness, which obey a different set of laws. I argue, however, that if a degree of belief that P is a stronger or weaker tendency to act as if P, then this option is not open. Instead, I propose an account of the behaviour of degrees of belief that integrates subjective probabilities and degrees of truth. On this account, degrees of belief are expectations of degrees of truth. The account explains why degrees of belief behave in accordance with the laws of probability in cases involving only uncertainty, while also allowing degrees of belief to behave differently in cases involving only vagueness, and in mixed cases involving both uncertainty and vagueness. Justifications of the account are given both via Dutch books and in terms of epistemic accuracy. (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)

This paper proposes an experimental investigation of the use of vague predicates in dynamic sorites. We present the results of two studies in which subjects had to categorize colored squares at the borderline between two color categories (Green vs. Blue, Yellow vs. Orange). Our main aim was to probe for hysteresis in the ordered transitions between the respective colors, namely for the longer persistence of the initial category. Our main finding is a reverse phenomenon of enhanced contrast (i.e. negative hysteresis), (...) present in two different tasks, a comparative task involving two color names, and a yes/no task involving a single color name, but not found in a corresponding color matching task. We propose an optimality-theoretic explanation of this effect in terms of the strict-tolerant framework of Cobreros et al. (J Philos Log 1–39, 2012), in which borderline cases are characterized in a dual manner in terms of overlap between tolerant extensions, and underlap between strict extensions. (shrink)

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)

ABSTRACT: This paper argues that the so-called paradoxes of higher-order vagueness are the result of a confusion between higher-order vagueness and the distribution of the objects of a Sorites series into extensionally non-overlapping non-empty classes.

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)

Philosophers, linguists and others interested in problems concerning natural language frequently employ tools from logic and model theory. The question arises as to the proper interpretation of the formal methods employed—of the relationship between, on the one hand, the formal languages and their set-theoretic models and, on the other hand, the objects of ultimate interest: natural language and the meanings and truth conditions of its constituent words, phrases and sentences. Two familiar answers to this question are descriptivism and instrumentalism. More (...) recently, a third answer has been proposed: the logic as modelling view. This paper seeks to clarify and assess this view of logic. The conclusion is that we can successfully adopt the modelling perspective on a given piece of logical machinery only if we have to hand some other machinery to which we take the descriptive attitude. Thus, logic as modelling is not a full-fledged alternative to the descriptive view— for it cannot stand alone: it can at best be an addition to the descriptive perspective. The paper first presents the argument in a general, abstract form, before working through a detailed case study. The case examined is the one with respect to which the logic as modelling view has been developed in the greatest detail in the literature: the case of fuzzy model theory as an account of vagueness in natural language. (shrink)

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)

The primary appeal of stakeholder theory in business ethics derives from its promise to help solve two large and often morally difficult problems: (1) how to manage people fairly and efficiently and (2) how to determine the extent of a firm's moral responsibilities beyond its obligations to enhance its profits and economic value. This article investigates a variety of conceptual quandaries that stakeholder theory faces in addressing these two general problems. It argues that these quandaries pose intractable obstacles for stakeholder (...) theory which prevent it from delivering on its large promises. Acknowledging that various versions of stakeholder theory have made a contribution in elucidating the complex nature of firms and business decision making, the article argues that it is time to move on. More precise explications of the nature of modern firms focusing on the application of basic moral principles to different business contexts and situations are likely to prove more accurate and useful. (shrink)

The purpose of this essay is to shed some light on a certain type of sentence, which I call a borderline contradiction. A borderline contradiction is a sentence of the form F a ∧ ¬F a, for some vague predicate F and some borderline case a of F , or a sentence equivalent to such a sentence. For example, if Jackie is a borderline case of ‘rich’, then ‘Jackie is rich and Jackie isn’t rich’ is a borderline contradiction. Many theories (...) of vague language have entailments about borderline contradictions; correctly describing the behavior of borderline contradictions is one of the many tasks facing anyone offering a theory of vague language. Here, I first briefly review claims made by various theorists about these borderline contradictions, attempting to draw out some predictions about the behavior of ordinary speakers. Second, I present an experiment intended to gather relevant data about the behavior of ordinary speakers. Finally, I discuss the experimental results in light of several different theories of vagueness, to see what explanations are available. My conclusions are necessarily tentative; I do not attempt to use the present experiment to demonstrate that any single theory is incontrovertibly true. Rather, I try to sketch the auxiliary hypotheses that would need to be conjoined to several extant theories of vague language to predict the present result, and offer some considerations regarding the plausibility of these various hypotheses. In the end, I conclude that two of the theories I consider are better-positioned to account for the observed data than are the others. But the field of logically-informed research on people’s actual responses to vague predicates is young; surely as more data come in we will learn a great deal more about which (if any) of these theories best accounts for the behavior of ordinary speakers. (shrink)

We argue that standard definitions of ‘vagueness’ prejudice the question of how best to deal with the phenomenon of vagueness. In particular, the usual understanding of ‘vagueness’ in terms of borderline cases, where the latter are thought of as truth-value gaps, begs the question against the subvaluational approach. According to this latter approach, borderline cases are inconsistent (i.e., glutty not gappy). We suggest that a definition of ‘vagueness’ should be general enough to accommodate any genuine contender in the debate over (...) how to best deal with the sorites paradox. Moreover, a definition of ‘vagueness’ must be able to accommodate the variety of forms sorites arguments can take. These include numerical, total-ordered sorites arguments, discrete versions, continuous versions, as well as others without any obvious metric structure at all. After considering the shortcomings of various definitions of ‘vagueness’, we propose a very general non-question-begging definition. (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)

Epistemicists claim that vague predicates have precise but unknow- able cutoffs. I argue against against the standard, Williamsonian, answer, that appeals to metalinguistic safety: we can know that p even if our true belief that p is metalinguistically lucky. I then propose that epistemicists should be diagonalized epistemicists and show how this alternative formulation of the view avoids the chal- lenge. However, in an M. Night Shyamalan-style twist, I then argue we should not be diagonalized epistemicists either.

Critiques John Martin Fischer's bootstrapping model of divine foreknowledge. Invited contribution to a special journal issue on John Martin Fischer's _Our Fate: Essays on God and Free Will_ (Oxford, 2016).

The present PhD dissertation aims to examine the relation between modality and change in Aristotle’s metaphysics. -/- On the one hand, Aristotle supports his modal realism (i.e., worldly objects have modal properties - potentialities and essences - that ground the ascriptions of possibility and necessity) by arguing that the rejection of modal realism makes change inexplicable, or, worse, banishes it from the realm of reality. On the other hand, the Stagirite analyses processes by means of modal notions (‘change is the (...) actuality of what is virtual insofar as it is virtual’). In other words: to grasp what change is, one has to resort to the modal idiom of potentialities, while the fact that there is change is indicative of the fact that nature is full of modal properties. -/- Aristotle’s modal and kinetic realism finds a negative in the figure of the Megaric Diodorus Kronus. The polemical situation of Greek philosophy has indeed the dialectical advantage of not opposing the Aristotelian position to a sui generis straw man. Both in its reduction of modal judgements to temporal quantifications and in its dissolution of the reality of the state-of-being-in-motion in favour of a cinematographic view of processes, the philosophical figure of reductionist antirealism embodied by Diodorus constitutes an alternative that takes the opposite view of Aristotle’s realism. -/- The present study is structured as a discussion between these two positions. In the face of Diodorus’ antirealist challenges, Aristotle articulates modal and kinetic considerations: the answers he gives to Diodorus’ puzzles thus provide valuable insight into his metaphysics. Moreover, the examination of Aristotle’s and Diodorus’ metaphysics, because of their insight and originality, will not fail to interest the philosopher concerned with the metaphysical foundations of modern physics, insofar as the entanglement between modalities and processes is nowadays at the core of mechanics (phase spaces, path integrals, etc.). (shrink)

The purpose of this introduction is to give a rough overview of the discussion of the formalization of arguments, focusing on deductive arguments. The discussion is structured around four important junctions: i) the notion of support, which captures the relation between the conclusion and premises of an argument, ii) the choice of a formal language into which the argument is translated in order to make it amenable to evaluation via formal methods, iii) the question of quality criteria for such formalizations, (...) and finally iv) the choice of the underlying logic. This introductory discussion is supplemented by a brief description of the genesis of the special issue, acknowledgements, and summaries of each article. (shrink)