This paper considers Joseph Margolis’ aesthetics as an insightful way to draw a critical balance on the whole venture of defining art, with a crucial reference to Wittgenstein’s legacy. The point of departure is Margolis’ claim that the whole definition debate began with a misinterpretation of Wittgenstein’s teaching, whose meaning would not consist in denying any definition of art, but rather in refuting the possibility of giving one only, clear and distinct as well as context-independent definition of (...) it. The chapter moves on to reconsider Margolis’ first definition of works of art as physically embodied and culturally emergent entities by focusing both on its significance within the analytic debate and on those features leading him beyond the question “What is art?”, towards a philosophy of culture and philosophical anthropology. To understand art, we need to address the question of the relation between a cultural form of life and the nature of persons or selves taking part in it. Hence, we are compelled to broaden the margins of the definition and the question arises of whether it is still worthwhile to speak of a philosophical definition of art beyond the everyday usage of the term “definition”. (shrink)

According to an influential view, asserting a proposition involves undertaking some “commitment” to the truth of that proposition. But accounts of what it is for someone to be committed to the truth of a proposition are often vague or imprecise, and are rarely put to work to define assertion. This paper aims to fill this gap. It offers a precise characterisation of assertoric commitment, and shows how it can be applied to define assertion. On the proposed view, acquiring commitment is (...) not sufficient for asserting. To assert, commitment must be acquired by explicitly presenting a proposition as true. (shrink)

The account of vagueness Bertrand Russell provided in his 1923 paper, entitled simply “Vagueness” (see Russell [1923]1997), has been thought by some to be inconsistent. One main objection, raised by Timothy Williamson (1994), is that Russell’s attempt early in the paper to distinguish vagueness from generality is at odds with the definition of vagueness he presents later in the same paper. It is as if, as Williamson puts it, Russell “backslides” from his previous distinction (1994, (...) 60), resulting in a conflation of generality and vagueness that is at best problematic for a rigorous account of the phenomenon of vagueness. In this paper, I will defend Russell from this particular objection. While his 1923 paper may not be as clear at various points as one might hope, I do believe it is possible to construct a single theory of vagueness that can be applied equally well to his earlier and later discussions. Thus, Russell’s view is not ultimately inconsistent. In this paper, I will first present the interpretation of Russell’s concept of vagueness that falls prey to the charge of conflating vagueness and generality. Once the problem is clear, I will present an alternative interpretation, one that arises from certain reflections on G. W. Leibniz’s theory of perception. This Leibnizian interpretation of Russell, I will argue, resolves the apparent contradiction in Russell’s account of vagueness. (shrink)

I present the strict definition of intended effects and pose two questions for its critics: Apart from rationalizing moral intuitions about the craniotomy and other controversial cases, why classify an effect as intended if it does not explain the action? What definition of intended effects can people use to guide their actions? These questions show that broad definitions of intended effects have no basis in action theory and are too vague to guide people’s actions. I suggest that broad (...) definitions seem plausible because people confuse what someone intends and what someone is responsible for causing. (shrink)

There has recently been a growing interest in the topic of vagueness and indeterminacy in contemporary metaphysics, with two views taking center stage. The semantic view holds that indeterminacy is due to vagueness in the extension of concepts, while the ontological view holds that indeterminacy is due to the vagueness of certain objects. There has, however, been little research on discussions of vagueness and indeterminacy in early-modern philosophy despite the relevance of vagueness and indeterminacy for (...) issues such as real and nominal definitions, clear and distinct ideas, and the principle of complete determination. In this paper, I survey discussions of vagueness in Locke, Leibniz, and Kant and point to ways in which the problem of vagueness and indeterminacy touches on broader issues in their respective philosophies. Although Locke, Leibniz, and Kant all suggest that vagueness is a semantic phenomenon, Kant also appears to countenance an ontological view according to which objects as appearances may sometimes be indeterminate. (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)

The contemporary Platonists in the philosophy of mathematics argue that mathematical objects exist. One of the arguments by which they support this standpoint is the so-called Enhanced Indispensability Argument (EIA). This paper aims at pointing out the difficulties inherent to the EIA. The first is contained in the vague formulation of the Argument, which is the reason why not even an approximate scope of the set objects whose existence is stated by the Argument can be established. The second problem is (...) reflected in the vagueness of the very term indispensability, which is essential to the Argument. The paper will remind of a recent definition of the concept of indispensability of a mathematical object, reveal its deficiency and propose an improvement of this definition. Following this, we will deal with one of the consequences of the arbitrary employment of the concept of indispensability of a mathematical theory. We will propose a definition of this concept as well, in accordance with the common intuition about it. Eventually, on the basis of these two definitions, the paper will describe the relation between these two concepts, in the attempt to clarify the conceptual apparatus of the EIA. (shrink)

In this special issue, our objective is to clarify what biosemioticians may mean insofar as they claim that living systems are capable of making choices or that biosemiotic interpretations are partially indeterminate. A number of different senses of the term “chance” are discussed as we move toward a consensus. We find that biosemiosic chance may arise out of conditions involving quantum indeterminacy, randomness, deterministic chaos, or unpredictability, but biosemiosic chance is mainly due to the fact that living entities invest their (...) environments with different meanings and values, which are not inherent in the material aspects. Accordingly, interpretive responses are in part self-determined. A self-determined interpretation may be thought of as a process in which localized biases constrain the probabilities of the outcomes of the interactions between an agent and its environment. The agent’s internal formal constraints that are defined by similarity and proximity are relative and, as such, vague, and thus interpretation may be somewhat underdetermined and involve an element of chance. (shrink)

According to the dominant approach in the theory of vagueness, the nature of the vagueness of an expression ‘F’ consists in its presenting borderline cases in an appropriately ordered series: objects which are neither definitely F nor definitely not F (where the notion of definiteness can be semantic, ontic, epistemic, psychological or primitive). In view of the various problems faced by theories of vagueness adopting the dominant approach, the thesis proposes to reconsider the naive theory of (...) class='Hi'>vagueness, according to which the nature of the vagueness of an expression consists in its not drawing boundaries between any neighbouring objects in an appropriately ordered series. It is argued that expressions and concepts which do present this feature play an essential role in our cognitive and practical life, allowing us to conceptualize---in a way which would otherwise be impossible---the typically coarse-grained distinctions we encounter in reality. Despite its strong initial plausibility and ability to explain many phenomena of vagueness, the naive theory is widely rejected because thought to be shown inconsistent by the sorites paradox. In reply, it is first argued that accounts of vagueness based on the dominant approach are themselves subject to higher-order sorites paradoxes. The paradox is then solved on behalf of the naive theory by rejecting the unrestricted transitivity of the consequence relation on a vague language; a family of logics apt for reasoning with vague expressions is proposed and studied (using models with partially ordered values). The characteristic philosophical and logical consequences of this novel solution are developed and defended in detail. In particular, it is shown how the analysis of what happens in the attempt of surveying a sorites series and deciding each case allows the naive theory to recover a "thin" notion of a borderline case. (shrink)

"The purpose of this book is to examine and explicate a definition given in Philosophical Investigations. The definition of the meaning of a word is that "the meaning of a word is its use in the language." Hallet understands this as a definition in the strict sense of the word. In Chapter I, the author look to the Tractatus for its treatment of the picture theory of meaning and the Bedeutung/Sinn distinction. The conclusion which he pulls from (...) the early work is that, for Wittgenstein, meaning was already in a proposition by way of the meaning of names. Yet, only in the use or application, i.e. in a proposition with sense is meaning revealed. Although the Tractatus is far from saying that meaning is use, certain guiding themes are elaborated and carried into later works; namely, the search for meaning, the impossibility of meaning outside use, and meaning as revealed by use. Chapter II, III, and especially IV bear the brunt of establishing Hallet's thesis that Wittgenstein presented a significant and sound definition. He begins by showing what Wittgenstein proved meaning not to be: meaning is not images, objects, mental referents, nor feelings. All of these theories have convincing confirmation in certain respects, yet analysis, i.e. observation of the actual working of language, shows each to be too narrow. In making his transition to the true definition, the author shows Wittgenstein elaborating theses that meaning is to be found in the system or context of language. These are elaborated only to be cast aside as were the previous suggestions. The pattern elicited from these examinations is that meaning is use and, hence, defined as such. To explicate the definition, Hallett presents and examines seven characteristics of use: complexity, regularity and utility, abstraction, openness, vagueness, variety, and family resemblances. The book concludes with a consideration of the major objections to Wittgenstein's definition."-The Review of Metaphysics. (shrink)

This paper aims to uncover where the disagreement between illusionism and anti-illusionism about phenomenal consciousness lies fundamentally. While illusionists claim that phenomenal consciousness does not exist, many philosophers of mind regard illusionism as ridiculous, stating that the existence of phenomenal consciousness cannot be reasonably doubted. The question is, why does such a radical disagreement occur? To address this question, I list various characterisations of the term “phenomenal consciousness”: (1) the what-it-is-like locution, (2) inner ostension, (3) thought experiments such as philosophical (...) zombies, inverted qualia and Mary’s room, (4) scientific knowledge about secondary properties, (5) theoretical properties such as being ineffable and being intrinsic, and (6) appearance/reality collapse. Then I examine whether each characterization provides (i) a dubitable sense of phenomenal consciousness in which the existence of phenomenal consciousness can be reasonably doubted, (ii) an indubitable sense in which its existence cannot be reasonably doubted, or (iii) a gray sense in which it is controversial whether its existence can be reasonably doubted. By doing so, I show that there is no single sense of phenomenal consciousness in which illusionists and anti-illusionists disagree whether the existence of phenomenal consciousness can be reasonably doubted. I conclude that the disagreement between illusionists and anti-illusionists is fundamentally terminological: while illusionists adopt a dubitable sense of phenomenal consciousness, anti-illusionists adopt an indubitable sense of phenomenal consciousness. Because of the extreme vagueness and ambiguity of the term “phenomenal consciousness”, illusionists and anti-illusionists fail to see that they talk about different senses of phenomenal consciousness. (shrink)

Los dos grandes problemas del enfoque supervaluacionista para la vaguedad son determinar cuáles son las precisificaciones admisibles y la vaguedad de orden superior ilimitado. Apelando al uso de los términos vagos por la comunidad lingüística competente puede dividirse de forma tajante la extension de un término precisando en qué casos se aplica definidamente, en cuáles se aplica indefinidamente y en cuales es indeterminado si se aplica. Esto produce dos órdenes de vaguedad, con lo que se bloquean los argumentos sorites. Finalmente (...) se indaga qué semántica resulta más adecuada para una vaguedad de segundo orden. La vaguedad se basa en una indeterminación determinada en la aplicación de ciertos términos por parte de los hablantes nativos. The two main problems for the supevaluationationist approach to vagueness are deciding which precifications are admissible and unlimited higher-order vagueness. Resorting to the use of vague terms by the competent linguistic community the extension of a term can be sharply divided, making precise in which cases it applies definitely, when it applies indefinitely and when it is undetermined whether it applies. This produces two orders of vagueness, and as a result sorties arguments are blocked. Finally, it is enquired what semantic fits better to second order vagueness. Vagueness is based on a determined indeteminacy concerning the application of certain terms by native speakers. (shrink)

This dissertation explores several accounts of the intuitions speakers have concerning the truth values of utterances of sentences containing vague nouns and adjectives. While some semanticists have attempted to account for these intuitions with multi-valued logics and supervaluation theories of truth, I focus on how utterances of vague sentences affect hearers' beliefs. ;Following a critique of the major semantical accounts of vagueness, I propose a formal theory of how beliefs are revised following utterances of sentences of the form X (...) is A, X is A and B, and X is A and not A, where A and B are vague scalar adjectives. Formally, a hearer's beliefs are represented as a set of weighted sentences, and the information conveyed by a speaker's utterance is represented as a set of weighted conditionals. When a speaker utters a sentence, a function on these sets yields the hearer's revised beliefs. I derive from this theory a criterion for proper assertability: a sentence is properly assertable in a given context if the maximum information loss that could obtain between competent discourse participants is less than some threshold. I argue that this criterion often predicts the truth-value judgements competent speakers make which violate the basic rules of logic. I extend these theories to utterances of sentences containing vague non-scalar nouns. ;In the second half of the dissertation, I propose two semantic accounts of vagueness. One incorporates the assertability criterion into its definition of truth. The other is independent of it. The former accounts for a large set of intuitions concerning the truth values of utterances of vague sentences. The latter accounts for only a subset of those intuitions, leaving the rest to be explained independently by the theory of proper assertability. ;I conclude with brief discussions of the Sorites Paradox and the experimental data obtained by Tversky and Kahneman which purport to demonstrate people's poor intuitions concerning the probabilities of conjunctions. (shrink)

In VAGUENESS AND DEGREES OF TRUTH, Nicholas Smith develops a new theory of vagueness: fuzzy plurivaluationism. -/- A predicate is said to be VAGUE if there is no sharply defined boundary between the things to which it applies and the things to which it does not apply. For example, 'heavy' is vague in a way that 'weighs over 20 kilograms' is not. A great many predicates -- both in everyday talk, and in a wide array of theoretical vocabularies, (...) from law to psychology to engineering -- are vague. -/- Smith argues, based on a detailed account of the defining features of vagueness, that an accurate theory of vagueness must involve the idea that truth comes in degrees. The core idea of degrees of truth is that while some sentences are true and some are false, others possess intermediate truth values: they are truer than the false sentences, but not as true as the true ones. Degree-theoretic treatments of vagueness have been proposed in the past, but all have encountered significant objections. In light of these, Smith develops a new type of degree theory. Its innovations include a definition of logical consequence that allows the derivation of a classical consequence relation from the degree-theoretic semantics, a unified account of degrees of belief and their relationships with degrees of truth and subjective probabilities, and the incorporation of semantic indeterminacy -- the view that vague statements need not have unique meanings -- into the degree-theoretic framework. -/- As well as being essential reading for those working on vagueness, Smith's book provides an excellent entry-point for newcomers to the area -- both from elsewhere in philosophy, and from computer science, logic and engineering. It contains a thorough introduction to existing theories of vagueness and to the requisite logical background. (shrink)

The purpose of this book is to examine and explicate a definition given in Philosophical Investigations. The definition of the meaning of a word is that "the meaning of a word is its use in the language." Hallett understands this as a definition in the strict sense of the word. In Chapter I, the author looks to the Tractatus for its treatment of the picture theory of meaning and the Bedeutung/sinn distinction. The conclusion which he pulls from (...) the early work is that, for Wittgenstein, meaning was already in a proposition by way of the meaning of names. Yet, only in the use or application, i.e., in a proposition with sense is meaning revealed. Although the Tractatus is far from saying that meaning is use, certain guiding themes are elaborated and carried into later works; namely, the search for meaning, the impossibility of meaning outside use, and meaning as revealed by use. Chapter II, III, and especially IV bear the brunt of establishing Hallett’s thesis that Wittgenstein presented a significant and sound definition. He begins by showing what Wittgenstein proved meaning not to be: meaning is not images, objects, mental referents, nor feelings. All of these theories have convincing confirmation in certain respects, yet analysis, i.e., observation of the actual working of language, shows each to be too narrow. In making his transition to the true definition, the author shows Wittgenstein elaborating the theses that meaning is to be found in the system or context of language. These are elaborated only to be cast aside as were the previous suggestions. The pattern elicited from these examinations is that meaning is use and, hence, defined as such. To explicate the definition, Hallett presents and examines seven characteristics of use: complexity, regularity and utility, abstraction, openness, vagueness, variety, and family resemblances. The book concludes with a consideration of the major objections to Wittgenstein’s definition. There are too many objections presented to be handled justly. For the most part, the argument is superficial, usually presuming a familiarity with the issue, and with but an indication of how the objection could be handled. The strength of the book is that it gives an organization to Wittgenstein’s later thinking, especially by way of the above-mentioned seven characteristics. In identifying and elucidating them, Hallett does Wittgenstein students a great service. Its chief weakness, although pale in regard to the overall worth, is that the main thesis is not firmly established. To say that a precise and complete definition is given is contrary to what is maintained throughout the Investigations, and perhaps a serious misreading of the German word, erklaren, as the precise English phrase, "to define." There are extensive notes and an adequate index.—W. A. F. (shrink)

This paper presents and defends a definition of vagueness, compares it favourably with alternative definitions, and draws out some consequences of accepting this definition for the project of offering a substantive theory of vagueness. The definition is roughly this: a predicate 'F' is vague just in case for any objects a and b, if a and b are very close in respects relevant to the possession of F, then 'Fa' and 'Fb' are very close in (...) respect of truth. The definition is extended to cover vagueness of many-place predicates, of properties and relations, and of objects. Some of the most important advantages of the definition are that it captures the intuitions which motivate the thought that vague predicates are tolerant, without leading to contradiction, and that it yields a clear understanding of the relationships between higher-order vagueness, sorites susceptibility, blurred boundaries, and borderline cases. The most notable consequence of the definition is that the correct theory of vagueness must countenance degrees of truth. (shrink)

Richard Wollheim threatened George Dickie's institutional definition of art with a dilemma which entailed that the theory is either redundant or incomprehensible and useless. This article modifies the definition to avoid such criticism. First, it shows that the definition's concept of the artworld is not vague when understood as a conventional system of beliefs and practices. Then, based on Gaut's cluster theory, it provides an account of reasons artworld members have to confer the status of a candidate (...) for appreciation. An authorised member of an artworld has a good reason to confer the status on an object if it satisfies a subset of criteria respected as sufficient within this artworld. The first horn of the dilemma is averted because explaining the reasons behind conferral cannot eliminate references to the institution, and the second loses its sharpness, as accepting partial arbitrariness of the conferral does not deprive the theory of its explanatory power. (shrink)

The purpose of this book is to examine and explicate a definition given in Philosophical Investigations. The definition of the meaning of a word is that "the meaning of a word is its use in the language." Hallett understands this as a definition in the strict sense of the word. In Chapter I, the author looks to the Tractatus for its treatment of the picture theory of meaning and the Bedeutung/sinn distinction. The conclusion which he pulls from (...) the early work is that, for Wittgenstein, meaning was already in a proposition by way of the meaning of names. Yet, only in the use or application, i.e., in a proposition with sense is meaning revealed. Although the Tractatus is far from saying that meaning is use, certain guiding themes are elaborated and carried into later works; namely, the search for meaning, the impossibility of meaning outside use, and meaning as revealed by use. Chapter II, III, and especially IV bear the brunt of establishing Hallett’s thesis that Wittgenstein presented a significant and sound definition. He begins by showing what Wittgenstein proved meaning not to be: meaning is not images, objects, mental referents, nor feelings. All of these theories have convincing confirmation in certain respects, yet analysis, i.e., observation of the actual working of language, shows each to be too narrow. In making his transition to the true definition, the author shows Wittgenstein elaborating the theses that meaning is to be found in the system or context of language. These are elaborated only to be cast aside as were the previous suggestions. The pattern elicited from these examinations is that meaning is use and, hence, defined as such. To explicate the definition, Hallett presents and examines seven characteristics of use: complexity, regularity and utility, abstraction, openness, vagueness, variety, and family resemblances. The book concludes with a consideration of the major objections to Wittgenstein’s definition. There are too many objections presented to be handled justly. For the most part, the argument is superficial, usually presuming a familiarity with the issue, and with but an indication of how the objection could be handled. The strength of the book is that it gives an organization to Wittgenstein’s later thinking, especially by way of the above-mentioned seven characteristics. In identifying and elucidating them, Hallett does Wittgenstein students a great service. Its chief weakness, although pale in regard to the overall worth, is that the main thesis is not firmly established. To say that a precise and complete definition is given is contrary to what is maintained throughout the Investigations, and perhaps a serious misreading of the German word, erklaren, as the precise English phrase, "to define." There are extensive notes and an adequate index.—W. A. F. (shrink)

Systems medicine, which is based on computational modelling of biological systems, is emerging as an increasingly prominent part of the personalized medicine movement. It is often promoted as ‘P4 medicine’. In this article, we test promises made by some of its proponents that systems medicine will be able to develop a scientific, quantitative metric for wellness that will eliminate the purported vagueness, ambiguity, and incompleteness—that is, normativity—of previous health definitions. We do so by examining the most concrete and relevant (...) evidence for such a metric available: a patent that describes a systems medicine method for assessing health and disease. We find that although systems medicine is promoted as heralding an era of transformative scientific objectivity, its definition of health seems at present still normatively based. As such, we argue that it will be open to influence from various stakeholders and that its purported objectivity may conceal important scientific, philosophical, and political issues. We also argue that this is an example of a general trend within biomedicine to create overly hopeful visions and expectations for the future. (shrink)

Two principal sources of imprecision in legal drafting (vagueness and ambiguity) are identified and illustrated. Virtually all of the ambiguity imprecision encountered in legal discourse is ambiguity in the language used to express logical structure, and virtually all of the imprecision resulting is inadvertent. On the other hand, the imprecision encountered in legal writing that results from vagueness is frequently, if not most often, included there deliberately; the drafter has considered it and decided that the vague language best (...) accomplishes the purpose at hand. This paper focuses on the use of some defined terminology for minimizing inadvertent ambiguity in the logical structure of legal discourse, where desired by the drafter. The current set of signaled structural definitions that are included in the A-Hohfeld language are first set forth and their use is illustrated in an extensive example from the treaty establishing the European Economic Community. The use of definitions in legal writing is widespread, butaddressed almost exclusively to controlling the vagueness of substantive legal terms; they are seldom used for structural purposes. Furthermore, their use in American legislative drafting is unsignaled. Here, attention is devoted to the relatively-neglected domain in legal discourse of imprecisely expressed logical structure, and the remedy offered, where desired by the drafter, is a set of signaled structuraldefinitions for use in controlling such imprecision. (shrink)

The purpose of the present project is to show the manner in which Early Heidegger's notion authenticity is vague. We cannot, given the rest of Heidegger's ontology of Dasein in Being and Time, tell what counts as a case of authentic, rather than inauthentic existence. The first half of the present work is devoted to carefully explaining some relevant, general features of Dasein's ontology, followed by an explanation of the structures associated with authenticity. In the third chapter I defend Heidegger's (...) account of authenticity and, in the process, my own interpretation of his account. In the final chapter I argue in favor of my main claim that Heidegger's notion of authenticity is vague in nature and that a case of a particular, authentic Dasein cannot be definitively derived. (shrink)

The problem of the time of a killing concerns exactly when and where to locate our actions. It is a problem for many of our actions beyond killing, and there are versions of the problem that can be raised no matter where your theory locates actions in particular. To answer the problem, I claim that we should be guided to the referent of ‘the killing’ by examining the definition of ‘to kill.’ Once we have the correct definition, we (...) can see that there are several candidate events that might be the referent of ‘the killing,’ but that the definition does not determine which of them is the referent. So, I argue that it is indeterminate or vague which event is ‘the killing.’ This solution is general across many action verbs, appeals to a minimally controversial type of vagueness, avoids the unintuitive results of views that determinately locate killings, and is compatible with different views about the location of actions. In the concluding section, I show how appealing to vagueness is distinct from and superior to appealing to ambiguity. (shrink)

In this paper we advance a new solution to Quinn’s puzzle of the self-torturer. The solution falls directly out of an application of the principle of instrumental reasoning to what we call “vague projects”, i.e., projects whose completion does not occur at any particular or definite point or moment. The resulting treatment of the puzzle extends our understanding of instrumental rationality to projects and ends that cannot be accommodated by orthodox theories of rational choice.

Discussions of higher-order vagueness rarely define what it is for a term to have nth-order vagueness for n>2. This paper provides a rigorous definition in a framework analogous to possible worlds semantics; it is neutral between epistemic and supervaluationist accounts of vagueness. The definition is shown to have various desirable properties. But under natural assumptions it is also shown that 2nd-order vagueness implies vagueness of all orders, and that a conjunction can have 2nd-order (...) vagueness even if its conjuncts do not. Relations between the definition and other proposals are explored; reasons are given for preferring the present proposal. (shrink)

How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality interact? This paper proposes a model-theoretic framework for investigating the logic and semantics of that interaction. The framework is put forward in an ecumenical spirit: it is intended to be applicable to all theories of vagueness that express vagueness using a definiteness (or: determinacy) operator. We (...) will show how epistemicists, supervaluationists, and theorists of metaphysical vagueness like Barnes and Williams (2010) can interpret the framework.  We will also present a complete axiomatization of the logic we recommend to both epistemicists and local supervaluationists. . (shrink)

This paper deals with the truth-Conditions and the logic for vague languages. The use of supervaluations and of classical logic is defended; and other approaches are criticized. The truth-Conditions are extended to a language that contains a definitely-Operator and that is subject to higher order vagueness.

Most descriptions of higher-order vagueness in terms of traditional modal logic generate so-called higher-order vagueness paradoxes. The one that doesn't is problematic otherwise. Consequently, the present trend is toward more complex, non-standard theories. However, there is no need for this.In this paper I introduce a theory of higher-order vagueness that is paradox-free and can be expressed in the first-order extension of a normal modal system that is complete with respect to single-domain Kripke-frame semantics. This is the system (...) QS4M+BF+FIN. It corresponds to the class of transitive, reflexive and final frames. With borderlineness defined logically as usual, it then follows that something is borderline precisely when it is higher-order borderline, and that a predicate is vague precisely when it is higher-order vague.Like Williamson's, the theory proposed here has no clear borderline cases in Sorites sequences. I argue that objections that there must be clear borderline cases ensue from the confusion of two notions of borderlineness—one associated with genuine higher-order vagueness, the other employed to sort objects into categories—and that the higher-order vagueness paradoxes result from superimposing the second notion onto the first. Lastly, I address some further potential objections. (shrink)

The long ongoing and partly heated debate on the concept of disease has not led to any consensus on the status of this apparently essential concept for modern health care. The arguments range from claims that the disease concept is vague, slippery, elusive, or complex, and to statements that the concept is indefinable and unnecessary. The unsettled status of the concept of disease is challenging not only to health care where diagnosing, treating, and curing disease are core aims, but also (...) to the branch of philosophy that tries to clarify concepts. This article discusses three claims about the concept of disease: that it is vague, complex, and that it is indefinable. It investigates (a) what is meant by these claims (b) what their implications are, and (c) whether the claims are sound or not. It is argued that some of the arguments are flawed and miss important points about concept analysis. This does not mean, however, that disease is a clear concept with a crisp definition. It only rules out speculative claims that disease necessarily is vague, complex, and indefinable. It appears at least as hard to show that disease is indefinable as it is to define it. (shrink)

In psychiatry there is no sharp boundary between the normal and the pathological. Although clear cases abound, it is often indeterminate whether a particular condition does or does not qualify as a mental disorder. For example, definitions of ‘subthreshold disorders’ and of the ‘prodromal stages’ of diseases are notoriously contentious. Philosophers and linguists call concepts that lack sharp boundaries, and thus admit of borderline cases, ‘vague’. This overview chapter reviews current debates about demarcation in psychiatry against the backdrop of key (...) issues within the philosophical discussion of vagueness: Are there various kinds of vagueness? Is all vagueness representational? How does vagueness relate to epistemic uncertainty? What is the value of vagueness? Given the immense social, moral, and legal importance of demarcating the normal from the pathological in psychiatry, what are the pros and cons of gradualist approaches to mental disorders, that is, of construing boundaries as matters of degree? (shrink)

Consider an object or property a and the predicate F. Then a is vague if there are questions of the form: Is a F? that have no yes-or-no answers. In brief, vague properties and kinds have borderline instances and composite objects have borderline constituents. I'll use the expression "borderline cases" as a covering term for both. ;Having borderline cases is compatible with precision so long as every case is either borderline F, determinately F or determinately not F. Thus, in addition (...) to borderline cases, vagueness requires "fuzzy borders". A has fuzzy borders if there is no sharp line between a's borderline cases, a's determinate cases and a's determinate non-cases. To illustrate, loudness is vague because in a continuum of gradually increasing volume, there is no fact about where the last definite loud noise is and where the first borderline noise is. ;Actual borderline cases are not required for vagueness. Suppose actual noises are either ear-shatteringly loud or silent. Even so, loudness is vague since it could have borderline instances. Just so for objects. Suppose a table is cleanly bounded such that there is a sharp break between the table and its surroundings. Still, that table is vague since there are worlds at which it is indeterminate whether some wood molecule a is, or is not, part of that table. ;There are three views about which things can be vague. On the linguistic view, vagueness is solely a feature of expressions. On the nihilistic view, nothing is vague because vagueness is incoherent. Pitted against these views is the ontological conception of vagueness according to which borderline instances and constituents arise due to genuine indeterminacy in nature. ;My dissertation defends the ontological conception. I argue against the adequacy of the theory's rivals, disarm a damaging objection and demonstrate the causal superiority of vague events. Anyone familiar with the literature on vagueness will notice that only a subset of issues are discussed. What I offer is preliminary--I hope only to make the theory of ontological vagueness attractive enough to merit future work. (shrink)

Touching your mother's foot is incest because all the rest is a matter of degree (or so said Diogenes). That's just one expression of the puzzle of vagueness. Here's another: the passage of one second cannot mark the transition from being a pupa to being a butterfly--if something is a pupa at one time then in all close instants it remains a pupa; alas, it follows from this, via trivial logic, that there are no butterflies. Or again: it's vague (...) where the Highlands of Scotland begin and end, so, a small step in the direction of London cannot mark the boundary between the Lowlands and the Highlands. But then it follows, via trivial logic, that one is unable to leave the Highlands (even when in London). What's driving these paradoxical arguments seems to be the very vagueness of the terms involved: such terms as 'incest', 'butterfly', 'pupa', 'The Highlands' are all vague and such vagueness seems to make them tolerant to marginal change. The puzzles of vagueness are not only deep (in that they admit of no uncontroversial and entirely satisfactory solution), they are also broad, for vague language is everywhere. In this course, you will be introduced to the various puzzles of vagueness and whether and how we might best address them. We will tackle such as questions as: Does the possibility of vagueness entail that there simply cannot be a logic of natural language? Does it entail that language is governed by inconsistent rules? Or does vagueness require some special or deviant logic? Is vagueness a special species of ignorance? Is the world, in some sense, vague? Is there an uncontroversial definition of vagueness or can we only isolate the phenomenon from within some substantive and controversial conception? What is higher-order vagueness and why is it considered to be such a puzzling phenomenon? Must the truth about vagueness be so strange? In what exact way are vague expressions tolerant? (shrink)

Development of decision-support and intelligent agent systems necessitates mathematical descriptions of uncertainty and fuzziness in order to model vagueness. This paper seeks to present an outline of Peirce’s triadic logic as a practical new way to model vagueness in the context of artificial intelligence. Charles Sanders Peirce was an American scientist–philosopher and a great logician whose triadic logic is a culmination of the study of semiotics and the mathematical study of anti-Cantorean model of continuity and infinitesimals. After presenting (...) Peircean semiotics within AI perspective, a mathematical formulation of a Peircean triadic set is given in relationship with classical and fuzzy sets. Using basic logical operators, all possible respective implication operators, bi-equivalence operators, valid rules of inference, and associative, distributive and commutative logical properties are derived and verified through the truth function approach. In order to suggest practical directions, aggregation operators for Peirce’s triadic logic have been formulated. A mathematical formulation of a medical diagnostic problem and ER diagram of a library management system using Peirce’s triadic relation show potential for further applications of the proposed triadic set and triadic logic. Alongside, a classical AI game—The Wumpus World—is implemented to show practical efficacy in comparison with binary implementation. Besides giving some preliminary formulations for trichotomous set theory and definition of finite automaton, development of hybrid architectures for intelligent agents and evolutionary computations are discussed as potential practical avenues for Peirce’s triadic logic. (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)

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)

David Lewis (1986) criticizes moderate views of composition on the grounds that a restriction on composition must be vague, and vague composition leads, via a precisificational theory of vagueness, to an absurd vagueness of existence. I show how to resist this argument. Unlike the usual resistance, however, I do not jettison precisificational views of vagueness. Instead, I blur the connection between composition and existence that Lewis assumes. On the resulting view, in troublesome cases of vague composition, there (...) is an object, which definitely exists, about which it is vague whether the relevant borderline parts compose it. (shrink)

Ben-Yami presents Wittgenstein’s explicit criticism of the Platonic identification of an explanation with a definition and the alternative forms of explanation he employed. He then discusses a few predecessors of Wittgenstein’s criticisms and the Fregean background against which he wrote. Next, the idea of family resemblance is introduced, and objections answered. Wittgenstein’s endorsement of vagueness and the indeterminacy of sense are presented, as well as the open texture of concepts. Common misunderstandings are addressed along the way. Wittgenstein’s ideas, (...) as is then shown, have far-reaching implications for knowledge of meaning and the nature of logic, and with them to the nature of the philosophical project and its possible achievements. (shrink)

The nature of vagueness is investigated via a preliminary definition and a discussion of the classical sorites paradox ; this is carried further by asking for the origins of vagueness and a critique of several attempts to remove it from language. It is shown that such attempts are ill motivated and doomed for failure since vagueness is not just a matter of ignorance but firmly grounded in epistemic and metaphysical facts. Finally, the philosophical interest of real (...) vagueness is illustrated by the concept of “natural kind”, which is essential to realism/anti-realism debates. (shrink)

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

In psychiatry there is no sharp boundary between the normal and the pathological. Although clear cases abound, it is often indeterminate whether a particular condition does or does not qualify as a mental disorder. For example, definitions of ‘subthreshold disorders’ and of the ‘prodromal stages’ of diseases are notoriously contentious. -/- Philosophers and linguists call concepts that lack sharp boundaries, and thus admit of borderline cases, ‘vague’. Although blurred boundaries between the normal and the pathological are a recurrent theme in (...) many publications concerned with the classification of mental disorders, systematic approaches that take into account philosophical reflections on vagueness are rare. This book provides interdisciplinary discussions about vagueness in psychiatry by bringing together scholars from psychiatry, psychology, philosophy, history, and law. It draws together various lines of inquiry into the nature of gradations between mental health and disease and discusses the individual and societal consequences of dealing with blurred boundaries in medical practice, forensic psychiatry, and beyond. -/- Part I starts with an overview chapter that helps readers to navigate through the philosophy of vagueness and through the various debates surrounding demarcation problems in the classification and diagnosis of mental illness. Part II encompasses historical and recent philosophical positions on gradualist approaches to health and disease. Part III approaches the vagueness of present psychiatric classification systems, and the debates concerning their revisions by scrutinizing controversial categories, such as posttraumatic stress disorder, and the difficulties of day-to-day diagnostic and therapeutic practice. Part IV finally focuses on social, moral, and legal implications that arise when being mentally ill is a matter of degree. (shrink)

The long ongoing and partly heated debate on the concept of disease has not led to any consensus on the status of this apparently essential concept for modern health care. The arguments range from claims that the disease concept is vague, slippery, elusive, or complex, and to statements that the concept is indefinable and unnecessary. The unsettled status of the concept of disease is challenging not only to health care where diagnosing, treating, and curing disease are core aims, but also (...) to the branch of philosophy that tries to clarify concepts. This article discusses three claims about the concept of disease: that it is vague, complex, and that it is indefinable. It investigates what is meant by these claims, what their implications are, and whether the claims are sound or not. It is argued that some of the arguments are flawed and miss important points about concept analysis. This does not mean, however, that disease is a clear concept with a crisp definition. It only rules out speculative claims that disease necessarily is vague, complex, and indefinable. It appears at least as hard to show that disease is indefinable as it is to define it. (shrink)