Indeterminacy

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.

In seinem Buch "Free Agents" stellt der Neurowissenschaftler und Evolutionsgenetiker Kevin Mitchell ein evolutionäres Erklärungsmodell für den freien Willen vor. Aus philosophischer Sicht relevant ist das Buch vor allem, weil es ein zentrales Credo der aktuellen Freiheits-Debatte in Frage stellt, nämlich die Auffassung, ein naturwissenschaftlich vertretbares Freiheitsverständnis müsse mit dem Determinismus im Einklang stehen. Mitchell geht auf Distanz zum Kompatibilismus und nimmt mit naturwissenschaftlicher Argumentation für die libertarische Gegenposition Partei (auch wenn er selbst diesen Ausdruck nicht verwendet). Sein Buch ist (...) zweifellos das bisher umfassendste Werk dieser Art, und seine durchwegs nachvollziehbar aufgebaute Argumentation wird mit viel empirischer Evidenz aus Physik, Biochemie und Evolutionsbiologie unterlegt. Das zentrale Element seines Ansatzes ist die Qualifizierung lebender Organismen als Akteure. Alle Lebewesen sind gemäß Mitchell "autonomous entities, imbued with purpose and able to act on their own terms" (19). Rund die Hälfte seines Buches widmet Mitchell dem Thema, wie sich die Fähigkeiten der Lebewesen als Akteure im Laufe der Evolutionsgeschichte entwickelt und ausdifferenziert haben. Er zeigt Schritt für Schritt auf, wie aus der Sensorik und Bewegungssteuerung niedriger Organismen immer raffiniertere Formen der Verhaltenssteuerung mithilfe von Nervensystemen erwuchsen. Auf dieser Basis kommt er dann etwa in der Mitte seines Buches eingehend auf den Determinismus zu sprechen, und er weist diesen mit überzeugenden Argumenten einschließlich seiner kompatibilistischen Spielart zurück, und mit ihm zusammen gleich auch den Reduktionismus. Unbestimmtheit und Naturgesetzlichkeit schließen sich gemäß Mitchell keineswegs aus, und entscheidend ist für ihn, dass in komplexen Systemen die physikalischen Elementarvorgänge die Dynamik und Entwicklung des Gesamtsystems nicht vollständig determinieren: Sie sind nicht "causally comprehensive" (280). Unbestimmtheit scheint damit ein Element der Natur zu sein, welches Gesetzmäßigkeiten höherer Ordnung überhaupt erst möglich macht. Dies gilt sowohl für den auf Variation und Selektion beruhenden Evolutionsprozess als Ganzes, als auch für die durch ihn entstandene Fähigkeit tierischer Lebewesen zur zielgerichteten Steuerung ihres Verhaltens. Freies Handeln wird so gesehen zur am höchsten entwickelten Form der Fähigkeit, sich die wegen der Unbestimmtheit in der Natur vorhandenen Spielräume zu Nutze zu machen (harnessing indeterminacy). Die oft als naturgesetzlich unmöglich gebrandmarkte Vorstellung einer top-down wirkenden Akteurkausalität (agent causation) wird in Mitchells systembasiertem Erklärungsansatz zum naturwissenschaftlich erklärbaren Phänomen, und das gleiche gilt dementsprechend auch für die Freiheit nach libertarischem Verständnis. Wichtig zu erwähnen ist schließlich noch, dass Mitchell darunter keineswegs eine unbedingte Freiheit versteht, nicht "some nebulous, spooky, mystical property granted to us by the gods", sondern schlicht und einfach "an evolved biological function that depends on the proper functioning of a distributed set of neural resources" (282), welche uns die Fähigkeit zur bewussten und rationalen Kontrolle über unsere Handlungen verleiht - nicht mehr, aber auch nicht weniger. Bis jetzt hat Mitchells Buch vor allem im Leserkreis naturwissenschaftlicher Sachbuchliteratur Anklang gefunden. Darüber hinaus ist es aber schlichtweg allen zu empfehlen, die am Thema Willensfreiheit interessiert sind, und fast noch mehr denjenigen, die von diesem Thema genug haben in der Meinung, dazu ließe sich ohnehin nichts Neues mehr sagen. Vor allem ist aber zu hoffen, dass das Buch auch seinen Weg in das philosophische Seminar an Hochschulen findet, wo es den Schriften Daniel Dennetts, des wohl berühmtesten Kompatibilisten, gegenübergestellt werden sollte, denn der Vergleich ist interessant, weil dessen evolutionsbasierter Naturalismus abgesehen von den fundamentalen Differenzen bezüglich Determinismus und Reduktionismus demjenigen Mitchells gar nicht so unähnlich ist. (shrink)

A constant of Frege’s writing is his rejection of indeterminate predicates as found in natural language. This paper follows Frege’s remarks on vagueness from the early "Begriffsschrift” to his mature works, drawing brief parallels with the main contemporary theories of vagueness. I critically examine Frege’s arguments for the inconsistency of natural language and argue that the inability to accommodate vagueness in his mature ontology is mainly due to heuristic rules of thumb which Frege took as essential, not to a deep (...) problem in his fundamental apparatus. (shrink)

Many accept David Lewis's (1983) claim that, among the candidate meanings for our predicates, some are more natural than others -- they do better or worse at ``carving nature at its joints''. Call this claim predicate naturalism. Disagreement remains over whether the notion of naturalness extends ``beyond the predicate'' (à la Sider, 2011). Are the candidate meanings of logical vocabulary also more or less natural? Call this claim logical naturalism. -/- One motivation for predicate naturalism comes from its supposed ability (...) to help rebut various radical indeterminacy arguments associated with Hilary Putnam (1977, 1980, 1981). It does so in combination with a popular meta-semantic theory called reference magnetism. I argue that the same threats of Putnam-style radical indeterminacy rearise for proponents of predicate naturalism -- threats which logical naturalism helps rebuts. So, if we accept predicate naturalism because it helps fend off threats of indeterminacy, we should also accept logical naturalism. (shrink)

A popular and enduring approach to the liar paradox takes the concept of truth to be inconsistent. Very roughly, truth is an inconsistent concept if the central principles of this concept (taken together) entail a contradiction, where one of these central principles is Tarski's T-schema for truth: a sentence S is true if and only if p, (where S says that p). This article targets a version of Inconsistentism which: retains classical logic and bivalence; takes the truth-predicate “is true” to (...) pick out a property (and determine a non-empty extension relative to a given world); and holds that liar sentences exhibit a certain kind of indeterminacy in truth-value. Call such a view Modest Inconsistentism since it is somewhat more conservative in its outlook than various other forms of Inconsistentism. Such a modest view has its attractions: we retain the thesis that the liar sentence is meaningful; we get to respect the claims that there are truths and that there is a property of truth; we get to keep classical logic and bivalence; and, prima facie, no strengthened liar paradox is in the offing. The main aim in this paper is to show that Modest Inconsistentism, despite its initial attractions, is in deep trouble—because it does, after all, give rise to a strengthened liar paradox. We shall also see that there are related kinds of theory which are also subject to the same worry. (shrink)

I develop an expressivist account of verbal disagreements as practical disagreements over how to use words rather than factual disagreements over what words actually mean. This account enjoys several advantages over others in the literature: it can be implemented in a neo-Stalnakerian possible worlds framework; it accounts for cases where speakers are undecided on how exactly to interpret an expression; it avoids appeals to fraught notions like subject matter, charitable interpretation, and joint-carving; and it naturally extends to an analysis of (...) metalinguistic negotiations. (shrink)

The debate over the meanings of indexical expressions has relied heavily on the method of counterexamples. This paper challenges that method by showing that purported counterexamples can often be explained away by appeal to perspective shifts. For these counterexamples to establish anything about indexical reference, we must identify the conditions under which theorists can legitimately appeal to perspective shifts. Some tests for semantic content are considered and it is argued that none of them can tell us when appeal to perspective (...) shift is admissible. The paper then considers how we should proceed if we become convinced that there is no way to identify the content of indexical expressions, offering reasons in favour of a nihilist conception of character over an epistemicist or pluralist conception. (shrink)

In philosophy, as in any other theoretical endeavor, it is not rare to find conflicting but equally well grounded positions. Besides defending one of the positions and criticizing the other, philosophers can opt for pursuing other, more sophisticated, approaches aimed at incorporating the insights, intuitions, and arguments from both sides of the debate into a unified theory: Dialetheism, Analetheism, Gradualism, Pluralism and Relativism. The purpose of this article is to present each strategy's basic argumentative structure, relative strengths, and challenges, trying (...) to determine in which situations one is more appropriate than the others. Despite substantial differences between them, all four options have deep structural similarities; and which option is better for which dilemma or paradox will depend ultimately on a combination of epistemological, linguistic, and metaphysical factors. (shrink)

What determines the meaning of a context-sensitive expression in a context? It is standardly assumed that, for a given expression type, there will be a unitary answer to this question; most of the literature on the subject involves arguments designed to show that one particular metasemantic proposal is superior to a specific set of alternatives. The task of the present essay will be to explore whether this is a warranted assumption, or whether the quest for the one true metasemantics might (...) be a Quixotic one. We argue that there are good reasons—much better than are commonly appreciated—for thinking the latter, but that there nevertheless remains significant scope for metasemantic theorizing. We conclude by outlining our preferred option, metasemantic pluralism. (shrink)

This book launches a sustained defense of a radical interpretation of the doctrine of the open future. Patrick Todd argues that all claims about undetermined aspects of the future are simply false.

The liar paradox is a famous and ancient paradox related to logic and philosophy. It shows it is perfectly possible to construct sentences that are correct grammatically and semantically but that cannot be true or false in the traditional sense. In this paper the authors show four approaches to interpreting paradoxes that illustrate the influence of: the levels of language, their belonging to indeterminate compatible propositions or indeterminate propositions, being based on universal antinomy and the theory of dialetheism.

Truth pluralism offers the latest extension in the tradition of substantive theorizing about truth. While various forms of this thesis are available, most frameworks commit to domain reliance. According to domain reliance, various ways of being true, such as coherence and correspondence, are tied to discourse domains rather than individual sentences. From this follows that the truth of different types of sentences is accounted for by their domain membership. For example, sentences addressing ethical matters are true if they cohere and (...) those addressing extensional states of affairs if they correspond. By tying distinct truth-grounding properties to domains rather than individual sentences, truth pluralists avoid certain issues with definitional ambiguity and indeterminacy. I argue that contrary to the ideal situation, domains fail to provide the sought-after benefits of achieving definitional unambiguity and determinacy in the standard domain reliant pluralist frameworks. The reason is that, when combined with the inherently ambiguous nature of certain truth-relevant terms of sentences, fringe cases emerge, causing some of them to count as members of multiple domains. Consequently, some sentences end up being both true and false in the standard domain reliant pluralist frameworks, thus conflicting with both standard laws of non-contradiction and identity. Finally, I argue that truth pluralists should pay closer attention to the hitherto neglected question of inherent natural language ambiguity. (shrink)

A number of authors have defended permissivism by appealing to rational supererogation, the thought that some doxastic states might be rationally permissible even though there are other, more rational beliefs available. If this is correct, then there are situations that allow for multiple rational doxastic responses, even if some of those responses are rationally suboptimal. In this paper, I will argue that this is the wrong approach to defending permissivism—there are no doxastic states that are rationally supererogatory. By the lights (...) of contemporary linguistics, ‘rational’ is an absolute gradable adjective, and as such, can only be applied to things that satisfy the top of the scale of rationality. For this reason, it is not possible to believe what is rational while also failing to believe what is rationally optimal. (shrink)

Roads to Reference: An Essay on Reference Fixing in Natural Language by Mario Gómez-Torrente provides an ample attack against certain more recent variants of descriptivism in the theory of reference. The book discusses a wide variety of expressions, but the focus of this short note is on proper names and natural kind terms. In the case of proper names, indeterminacy plays an important role in Gómez-Torrente’s critical argument. Some questions related to it are raised. As to natural kind terms, the (...) differences between ordinary kind terms and scientific kind terms are discussed, and the somewhat ignored relevance of reference borrowing for natural kind terms is emphasized. (shrink)

A middle fact is a true proposition about what would have happened had A been true (where A is in fact false), whose truth isn't entailed by any non-counterfactual facts. I argue that there are no middle facts; if there were, we wouldn't know them, and our ignorance of them would result in ignorance about whether regret is fitting in cases where we clearly know it is. But there's a problem. Consider an unflipped fair coin which is such that no (...) non-counterfactual fact determines that it would have landed heads had it been flipped (or tails had it been flipped). If there are no middle facts, it's not true that it would have landed heads had it been flipped nor that it would have landed tails had it been flipped. Yet each counterfactual is still possibly true for all we know. I argue that we can resolve this tension in the anti-middle fact position, further strengthening the case against middle facts. (shrink)

I am a friend of supervaluationism. A statement lacks a definite truth value if, and only if, it comes out true on some admissible ways of precisifying the semantics of the relevant vocabulary and false on others. In this paper, I focus on the special case of identity statements. I take it that such statements, too, may occasionally suffer a truth-value gap, including philosophically significant instances. Yet there is a potentially devastating objection that can be raised against the supervaluationist treatment (...) of such cases—in fact two objections. Luckily, both can be resisted. But seeing how requires that we take a closer look at the ontological presuppositions of supervaluationism, allowing for more leeway than is usually supposed. (shrink)

The paper aims to rectify the reception of Heidegger’s so-called “hermeneutic violence,” by addressing the under-investigated issue of its actual target and rationale. Since the publication of Kant and the Problem of Metaphysics, some of Heidegger’s contemporary readers, such as Cassirer, as well as more recent commentators, accused Heidegger of doing violence to Kant’s and other philosophers’ texts. I show how the rationale of Heidegger’s self-acknowledged violence becomes tenable in light of his personal notes on his Kant book, and of (...) several hermeneutic tenets from Being and Time. The violence at stake turns out to be a genuine method, involving the appropriation (Zueignen) and the elaboration (Ausarbeiten) of an interpreted text. Its target, I argue, is not the text itself, as it was often assumed, but its reception by a community or tradition. Thus, that violence may well instill interpretive conflict, yet its purpose is to salvage a text from a conventional and ossified reception, namely, from what Heidegger regards as the authoritarianism of idle talk (Gerede) in a philosophical milieu. (shrink)

Miriam Schoenfield argues that moral realism and moral vagueness imply ontic vagueness. In particular, she argues that neither shifty nor rigid semantic accounts of vagueness can provide a satisfactory explanation of moral vagueness for moral realists. This paper constitutes a response. I argue that Schoenfield's argument against the shifty semantic account presupposes that moral indeterminacies can, in fact, be resolved determinately by crunching through linguistic data. I provide different reasons for rejecting this assumption. Furthermore, I argue that Schoenfield's rejection of (...) the rigid semantic account is based on a presupposition that ultimately implies the very same claim that is under dispute: the vagueness of moral predicates in imperfect languages persists in the perfect language, as well. (shrink)

People often speak loosely, uttering sentences that are plainly false on their most strict interpretation. In understanding such speakers, we face a problem of underdetermination: there is often no unique interpretation that captures what they meant. Focusing on the case of incomplete definite descriptions, this paper suggests that speakers often mean bundles of propositions. When a speaker means a bundle, their audience can know what they mean by deriving any one of its members. Rather than posing a problem for the (...) interpretation of loose talk, the underdetermination of a uniquely correct interpretation allows for various ways in which the audience can grasp the speaker’s meaning. (shrink)

Jamie Tappenden was one of the first authors to entertain the possibility of a common treatment for the Liar and the Sorites paradoxes. In order to deal with these two paradoxes he proposed using the Strong Kleene semantic scheme. This strategy left unexplained our tendency to regard as true certain sentences which, according to this semantic scheme, should lack truth value. Tappenden tried to solve this problem by using a new speech act, articulation. Unlike assertion, which implies truth, articulation only (...) implies non-falsity. In this paper I argue that Tappenden’s strategy cannot be successfully applied to truth and the Liar. (shrink)

Quine (1960, Word and object. Cambridge, Mass.:MIT Press, ch. 2) claims that there are a variety of equally good schemes for translating or interpreting ordinary talk. ‘Rabbit’ might be taken to divide its reference over rabbits, over temporal slices of rabbits, or undetached parts of rabbits, without significantly affecting which sentences get classified as true and which as false. This is the basis of his famous ‘argument from below’ to the conclusion that there can be no fact of the matter (...) as to how reference is to be divided. Putative counterexamples to Quine’s claim have been put forward in the past (see especially Evans 1975; 1975, Journal of Philosophy, LXXII(13), 343–362. Reprinted in McDowell (Ed.), Gareth Evans: Collected papers. Oxford: Clarendon Press.), and various patches have been suggested (e.g. Wright (1997, The indeterminacy of translation. In C. Wright & B. Hale (Eds.), A companion to the philosophy of language (pp. 397–426). Oxford: Blackwell)). One lacuna in this literature is that one does not find any detailed presentation of what exactly these interpretations are supposed to be. Drawing on contemporary literature on persistence, the present paper sets out detailed semantic treatments for fragments of English, whereby predicates such as ‘rabbit’ divide their reference over four-dimensional continuants (Quine’s rabbits), instantaneous temporal slices of those continuants (Quine’s rabbit-slices) and the simple elements which compose those slices (undetached rabbit parts) respectively. Once we have the systematic interpretations on the table, we can get to work evaluating them. (shrink)

The paper considers the Quinean heritage of the argument for the indeterminacy of translation. Beyond analyzing Quine’s notion of stimulus meaning, the paper discusses two Kripkean argument’s against the Quinean claim that dispositions can provide the basis for an account of meaning: the Normativity Argument and the Finiteness Argument. An analogy between Kripke’s arguments and Hume’s argument for epistemological skepticism about the external world will be drawn. The paper shows that the answer to Kripke’s rule-following skepticism is analogous to the (...) answer to Humean skepticism: our use of concepts is more basic than, and presupposed by, the statement of the skeptical problem itself. (shrink)

Alan Bullock demonstrates the continuity of mankind's thought and concerns from the historical past, through the troubled and often confusing present into the almost invisible future. This continuum offers us a basis for achieving understanding and perspective, for relating past, present and future. Without seeing this relationship, the moment of our lifetime must seem isolated and meaningless. Co-pubished with the Aspen Institute.

While philosophers feel relatively comfortable about talking of the present and the past, some of them feel uncomfortable about talking in just the same way of future events. They feel that, in general, discourse about the future differs significantly from discourse about the past and present, and that these differences reflect a logical asymmetry between the past and future beyond the merely defining fact that the future succeeds, and the past precedes, the present time. The problem is: how can we (...) talk about events which have not yet happened, or at any rate are not yet bound to happen, or whose participants do not yet exist? The effect of these worries has led them to claim to recognise restrictions on our talk about the future which do not govern talk about the past and present. The most famous of these views is Aristotle's. According to one familiar interpretation, he holds that a statement about a future event which is not yet settled, a contingent event in the future, is neither true nor false, even though the statement that the event either will or will not happen is necessarily true. Proponents of this view felt that if a future-tensed statement were already true then the fact that it stated would already be settled. I do not propose to discuss this well-known and muchdiscussed doctrine of Aristotle's, but I do want to consider some allied views which have been aired recently, and to look at their philosophical significance. Before I look at these, however, it will be convenient to recall three of the main reasons why the Aristotelian doctrine is unpopular. In the first place it is paradoxical to accept that a statement of the form p v ∼ p is true while claiming that neither of its disjuncts is true. Then there are misgivings about the notion of truth involved: many feel that truth is essentially an attribute of timeless propositions and that it is nonsense to talk of a statement's becoming true as you would of Aristotle's views if the event described became inevitable. There is also the difficulty of accounting for the meaning of a future-tensed sentence which may express a statement that is neither true nor false simply because what it states is not yet settled. It could not be said of the sentence expressing such a statement that you know what it means if you know what it is for the sentence to express a true statement. I know the meaning of the present-tensed sentence ‘A sea-battle is now being waged’ if I know that it can normally be used to make a true statement precisely in the event of there being a sea-battle being waged at present. But I do not know the meaning of the future-tensed sentence ‘A sea-battle will be waged tomorrow’ simply by knowing that the sentence expresses a true statement if it is already settled that there is going to be a battle: the statement doesn't mean that the battle is already settled, otherwise it would not lack a truth-value when the matter was still open – it would be false. (shrink)

Legal indeterminacy refers to the lack of determinate knowledge, of what a legal rule means and of how judges should apply it. Where law is indeterminate, no theory, rule, or principle constrains a judge to interpret or apply a law in a particular way. Consequently a case could have several different answers, yet all of them equally valid. The notion that judges make rather than find law implies to many observers consequences such as unequal or arbitrary treatment of individuals. Drawing (...) on an interdisciplinary body of scholarship, I confront the phenomenon of legal indeterminacy with two questions: How is justice possible when aspects of the legal regime seem arbitrary, inconsistent, and subjective? And how should a society deal with indeterminacy? Chapter 1 provides an extended example of the phenomenon of indeterminacy, namely in the legal regulation of speech. Chapter 2 shows that various counter arguments, including several prominent theories of determinacy, do not preclude or otherwise defeat the thesis of indeterminacy. Chapter 3, drawing on pragmatism, develops a theory of "enlightened localism," a form of relativism that can explain why indeterminacy in social norms is not often a problem in the day to day functioning, or even legitimation, of modern polities. The meaning and application of norms often need not be consistent over time or between cases; validity can only be relative. Such relativism presupposes a non-absolute objectivity, where we can give decisions objective grounds for the most part, but not grounds valid semper, ubique, et omnibus. Weakly objective grounds are locally rather than universally applicable. Chapter 4 shows that although such a theory invokes no ultimate foundation for itself, it is expressly not postmodern. Chapter 5 develops enlightened localism as a theory of a democratic legal order under conditions of indeterminacy. Chapter 6 examines indeterminacy in legal community, and chapter 7, how courts of law can respond to that problem. Chapter 8 analyzes indeterminacy in legal rules, and chapter 9, how a micro-sociological methodology can approach the phenomenon empirically. Chapter 10 investigates indeterminacy in normative criticism, and chapter 11, how social critique might deal with indeterminacy. (shrink)

According to W. V. O. Quine translation is indeterminate. The thesis has attracted a good deal of attention and criticism. In spite of this fact, however, there seems to be little understanding of the nature of the thesis itself and Quine's reasons for it, at least on the part of those commentators and critics who have committed themselves in print. Thus, in my study of Quine I am primarily concerned with answering the following three questions: Exactly what does the indeterminacy (...) thesis amount to, i.e. just what is being claimed? What are Quine's reasons/arguments for the thesis? What is the role of the thesis in Quine's philosophy, i.e. how does it relate to other doctrines embraced by Quine? ;I give what I take to be the real grounds for the indeterminacy thesis and then I examine this rationally reconstructed argument from the perspective of its relationships with and impact on other Quinean doctrines, e.g. the rejection of the notion of analyticity, underdetermination, holism, etc. This rationally reconstructed argument is found to turn on two fundamental theses which pervade Quine's thought: individual sentences do not have their own objective evidence, i.e. an indeterminacy thesis with respect to the allocation of objective evidence to individual sentences, and cognitive meaning is objective evidence, i.e. a version of the verificationist theory of cognitive meaning. ;I then examine the thesis of referential inscrutability and present an argument for it. This argument depends upon what I call 'the indeterminacy of truth' which will be the fourth identifiable indeterminacy thesis in Quine's thought. And the indeterminacy of truth is itself shown to be a consequence of the thesis of translational indeterminacy. ;Finally, I consider the question of whether Quine can sharply contrast physics with linguistics/translation or, more generally, whether he can sharply contrast truth in general with truth in translation. (shrink)

Quine's philosophy, early and late, proceeds from the natural standpoint, that is the explicit acceptance of science. This paper attempts to explain what this means and how it fits with his early criticism of reductive empiricism. A kind of horizontal reductionism remains, it is argued, which aims to explain the import of his thesis of the indeterminacy of translation. In the second part of this paper an argument is developed to cast doubt on the significance of this thesis. Because of (...) the possibility of languages containing grue-like predicates, the very idea of determinacy loses all significance. The natural standpoint cannot rescue determinacy and thus cannot provide support for indeterminacy. (shrink)

This paper is a survey of how economists and philosophers approach the issue of comparisons. More precisely, it is about what formal representation is appropriate whenever our ability to compare things breaks down. We restrict our attention to failures that arise with ordinal comparisons. We consider a number of formal approaches to this problem including one based on the idea of parity. We also consider the claim that the failure to compare things is a consequence of vagueness. We contrast two (...) theories of vagueness; fuzzy set theory and supervaluation theory. Some applications of these theories are described. (shrink)