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

This discusses the kind of paradox that has since become known as "the forced march sorites", here called "the transition question". The question is whether this is really a new kind of paradox, or the familiar sorites in unfamiliar garb. The author argues that resources adequate to deal with ordinary sorites are sufficient to deal with the transition question, and tentatively proposes an affirmative answer.

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)

The use of vague language in law has important implications for legal theory. Legal philosophers have occasionally grappled with those implications, but they have not come to grips with the characteristic phenomenon of vagueness: the sorites paradox. I discuss the paradox, and claim that it poses problems for some legal theorists (David Lyons, Hans Kelsen, and, especially, Ronald Dworkin). I propose that a good account of vagueness will have three consequences for legal theory: (i) Theories that deny that vagueness in (...) formulations of the law leads to discretion in adjudication (including Dworkin's) cannot accommodate “higher-order” vagueness, (ii) A legal theory should accept that the law is partly indeterminate when it can be stated in vague language, (iii) However, the traditional formulation of the indeterminacy claim, that a vague statement is “neither true nor false” in a borderline case, is misconceived and should be abandoned. (shrink)

This anthology of the very latest research on truth features the work of recognized luminaries in the field, put together following a rigorous refereeing process. Along with an introduction outlining the central issues in the field, it provides a unique and unrivaled view of contemporary work on the nature of truth, with papers selected from key conferences in 2011 such as Truth Be Told, Truth at Work, Paradoxes of Truth and Denotation and Axiomatic Theories of Truth. Studying the nature of (...) the concept of ‘truth’ has always been a core role of philosophy, but recent years have been a boom time in the topic. With a wealth of recent conferences examining the subject from various angles, this collection of essays recognizes the pressing need for a volume that brings scholars up to date on the arguments. Offering academics and graduate students alike a much-needed repository of today’s cutting-edge work in this vital topic of philosophy, the volume is required reading for anyone needing to keep abreast of developments, and is certain to act as a catalyst for further innovation and research. (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)

Gareth Evans proved that if two objects are indeterminately equal then they are different in reality. He insisted that this contradicts the assumption that there can be vague objects. However we show the consistency between Evans's proof and the existence of vague objects within classical logic. We formalize Evans's proof in a set theory without the axiom of extensionality, and we define a set to be vague if it violates extensionality with respect to some other set. There exist models of (...) set theory where the axiom of extensionality does not hold, so this shows that there can be vague objects. (shrink)

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

The basic philosophical controversy regarding ordinary objects is: Do tables and chairs, sticks and stones, exist? This paper aims to do two things: first, to explain why how this can be a controversy at all, and second, to explain why this controversy has arisen so late in the history of philosophy. Section 1 begins by discussing why the 'obvious' sensory evidence in favor of ordinary objects is not taken to be decisive. It goes on to review the standard arguments against (...) the existence of ordinary objects – including those based on problems with causal redundancy, parsimony, co-location, sorites arguments, and the special composition question. Section 2 goes on to address what it is about the contemporary approach to metaphysics that invites and sustains this kind of controversy, and helps make evident why debates about ordinary objects lead so readily to debates in metametaphysics about the nature of metaphysics itself. (shrink)

In the Transcendental Ideal Kant discusses the principle of complete determination: for every object and every predicate A, the object is either determinately A or not-A. He claims this principle is synthetic, but it appears to follow from the principle of excluded middle, which is analytic. He also makes a puzzling claim in support of its syntheticity: that it represents individual objects as deriving their possibility from the whole of possibility. This raises a puzzle about why Kant regarded it as (...) synthetic, and what his explanatory claim means. I argue that the principle of complete determination does not follow from the principle of excluded middle because the externally negated or ?negative? judgement ?Not (S is P)? does not entail the internally negated or ?infinite? judgement ?S is not-P.? Kant's puzzling explanatory claim means that empirical objects are determined by the content of the totality of experience. This entails that empirical objects are completely determinate if and only if the totality of experience has a completely determinate content. I argue that it is not a priori whether experience has such a completely determinate content and thus not analytic that objects obey the principle of complete determination. (shrink)

Semantic indeterminacy is the ether of philosophy of language. It fills the interstices of our intentions and pervades accounts of presupposition, tense, fiction, translation, and especially, vagueness. Yet semantic indeterminacy is as impossible as ectoplasm. Indeed, more so! The demonstration need only borrow a few assumptions used elsewhere in widely accepted impossibility results. Since an impossibility is never a necessary condition for anything actual, semantic indeterminacy must be superfluous. Language is no more explained by semantic indeterminacy than calculus is explained (...) by (pre-Robinsonian) infinitesimals. (shrink)

Several philosophers have recently developed accounts of relative truth. Given that logical consequence is often characterized in terms of truth preservation, notions of truth are often associated with corresponding notions of logical consequence. Accordingly, in his Assessment Sensitivity: Relative Truth and Its Applications, John MacFarlane provides two different definitions of logical consequence that incorapte assessment context-sensitive truth. One motivation for adopting an assessment context-sensitive account of truth for judgements about taste is to explain how conflicting taste claims can be true (...) relative to different contexts of assessment. However, in the midst of dialogues in which conflicting taste claims are made, it is also possible for the participants in the dialogue to make conflicting claims about what inferences are and are not logically valid. This paper accomplishes two objectives. First, I argue that MacFarlane’s notions of logical consequence do not adequately account for important features of some dialogues in which conflicting logical claims are made. In particular, I argue that MacFarlane’s accounts of logical consequence do not explain how logical claims made about inferences in taste-discourse could be assessment context-sensitive. Second, I propose a consequence relation that can be incorporated into an assessment context-sensitive account of logical claims made about inferences in taste discourse. (shrink)

Various arguments have recently been put forward to support the existence of vague or fuzzy objects. Nevertheless, the only possibly compelling argument would support, not the existence of vague objects, but indeterminately existing objects. I argue for the non‐existence of any vague entities—either particulars or properties ‐ in the mind‐independent world. Even so, many philosophers have claimed that to reduce vagueness to semantics is of no avail, since linguistic vagueness betrays semantic incoherence and this is no less a problem than (...) is ontological incoherence. After spelling out why there are fewer essentially vague concepts than usually thought. I claim that only the linguistic competence of the whole speaking community for each word can draw the sharp boundaries for its concept, even if these are unknowable in practice and still leave a precise range of indetermination. This could explain both the existence of boundaries and our non‐removable ignorance of them, fulfilling the intuitions of the epistemic theory of vagueness with the supervaluationist's indeterminacy. (shrink)

Various arguments have recently been put forward to support the existence of vague or fuzzy objects. Nevertheless, the only possibly compelling argument would support, not the existence of vague objects, but indeterminately existing objects. I argue for the non‐existence of any vague entities—either particulars or properties ‐ in the mind‐independent world. Even so, many philosophers have claimed that to reduce vagueness to semantics is of no avail, since linguistic vagueness betrays semantic incoherence and this is no less a problem than (...) is ontological incoherence. After spelling out why there are fewer essentially vague concepts than usually thought. I claim that only the linguistic competence of the whole speaking community for each word can draw the sharp boundaries for its concept, even if these are unknowable in practice and still leave a precise range of indetermination. This could explain both the existence of boundaries and our non‐removable ignorance of them, fulfilling the intuitions of the epistemic theory of vagueness with the supervaluationist's indeterminacy. (shrink)

The recent development and exploration of mixed metainferential logics is a breakthrough in our understanding of nontransitive and nonreflexive logics. Moreover, this exploration poses a new challenge to theorists like me, who have appealed to similarities to classical logic in defending the logic ST, since some mixed metainferential logics seem to bear even more similarities to classical logic than ST does. There is a whole ST-based hierarchy, of which ST itself is only the first step, that seems to become more (...) and more classical at each level. I think this seeming is misleading: for certain purposes, anyhow, metainferential hierarchies give us no reason to move on from ST. ST is indeed only the first step on a grand metainferential adventure; but one step is enough. This paper aims to explain and defend that claim. Along the way, I take the opportunity also to develop some formal tools and results for thinking about metainferential logics more generally. (shrink)

The recent development and exploration of mixed metainferential logics is a breakthrough in our understanding of nontransitive and nonreflexive logics. Moreover, this exploration poses a new challenge to theorists like me, who have appealed to similarities to classical logic in defending the logic ST, since some mixed metainferential logics seem to bear even more similarities to classical logic than ST does. There is a whole ST-based hierarchy, of which ST itself is only the first step, that seems to become more (...) and more classical at each level. I think this seeming is misleading: for certain purposes, anyhow, metainferential hierarchies give us no reason to move on from ST. ST is indeed only the first step on a grand metainferential adventure; but one step is enough. This paper aims to explain and defend that claim. Along the way, I take the opportunity also to develop some formal tools and results for thinking about metainferential logics more generally. (shrink)

It is generally agreed that vague predicates like ‘red’, ‘rich’, ‘tall’, and ‘bald’, have borderline cases of application. For instance, a cloth patch whose color lies midway between a definite red and a definite orange is a borderline case for ‘red’, and an American man five feet eleven inches in height is (arguably) a borderline case for ‘tall’. The proper analysis of borderline cases is a matter of dispute, but most theorists of vagueness agree at least in the thought that (...) borderline cases for vague predicate ‘ ’ are items whose satisfaction of ‘ ’ is in some sense unclear or problematic: it is unclear whether or not the patch is red, unclear whether or not the man is tall.1 For example, Lynda Burns cites a widespread view as holding that borderline cases “are not definitely within the positive or negative extension of the predicate. … Border- line cases are seen as falling within a gap between the cases of definite application of the predicate and cases of definite application of its negation” (1995, 30). Michael Tye writes that the “concept of a border- line case is the concept of a case that is neither definitely in nor defi- nitely out” (1994b, 18). (shrink)

In 1978, Gareth Evans published a short and somewhat cryptic article purporting to establish that there are no vague objects. This paper is a commentary on this. Prima facie, the claim that there are no vague objects is clearly false. Mt Everest, for example, has no precise boundaries. And if this is so, there must be something wrong with Evans' argument. In the paper, I discuss what this is, giving a model of vague objects in the process.

In the paper Evans’s argument concerning indeterminate identity statements is presented and discussed. Evans’s paper in which he formulated his argument is one of the most frequently discussed papers concerning identity. There are serious doubts concerning what Evans wanted to prove by his argument. Theorists have proposed two competing and incompatible interpretations. According to some, Evans purposefully constructed an invalid argument in order to demonstrate that the vague objects view cannot diagnose the fallacy and is therefore untenable. According to others, (...) Evans wanted to formulate a (valid) argument to the effect that there cannot be vague identity statements whose vagueness is due solely to the existence of vague objects. As it has been argued, if it is the former interpretation which is correct, than the argument really is invalid, but it is doubtful whether it achieves its aim. It might be claimed that “the vague objects view” it refutes is not the view that most vague objects theorists hold. The main part of the paper is devoted to the second interpretation and the discussions concerning the validity of the argument on this interpretation. It appears that the vague objects theorist is in a position to object to the validity of every single step of the proof. (shrink)

Epistemicism is the view that seemingly vague predicates are not in fact vague. Consequently, there must be a sharp boundary between a man who is bald and one who is not bald. Although such a view is often met with incredulity, my aim is to provide a defense of epistemicism in this essay. My defense, however, is backhanded: I argue that the formal commitments of epistemicism are the result of good practical reasoning, not metaphysical necessity. To get to that conclusion, (...) I spend most of the essay arguing that using a formal system like classical logic to manage seemingly vague situations requires practical principles to mediate between the formalism and what it aims to represent. (shrink)

In this paper I develop a semantic theory of vagueness that is immune to worries regarding the use of precise mathematical tools. I call this view semantic quietism. This view has the advantage of being clearly compatible with the phenomenon of vagueness. The cost is that it cannot capture every robust semantic fact.

It is notoriously difficult to model the range of application of vague predicates relative to a suitable sorites series. In this paper I offer some critical remarks against an interesting view that has received little attention in the literature. According to it, the sharp cut-offs we find in our semantic models are just artifacts of the theory, and, as such, they are harmless. At the end I discuss a contextualist view that, at a cost, may be able to get around (...) the problems related to sharp cut-offs incurred in by other theories of vagueness. Es sumamente difícil modelar el rango de aplicación de predicados vagos relativo a una serie sorites apropiada. En este artículo ofrezco algunos comentarios críticos en contra de una postura interesante que ha recibido poca atención en la literatura. De acuerdo con ella, los cortes precisos que encontramos en modelos semánticos son simplemente artefactos de la teoría, y, como tales, son inofensivos. Al final del artículo discuto una postura contextualista que, no sin sacrificios, podría ser capaz de evadir los problemas relacionados con cortes precisos que otras teorías de la vaguedad poseen. (shrink)

The principle of Summation, which is a technically sharpened version of the familiar claim that a whole is a sum of its parts, is presented by Peter van Inwagen as a trivial truth. I argue to the contrary, that it is incompatible with the natural assumption that a whole may gain or lose parts non-instantaneously. For, as I show, the latter assumption implies that something can be determinately a whole without being determinately a sum of parts, and this, in turn, (...) indicates the falsity of Summation. I point out that the tension between Summation and the possibility of non-instantaneous gain or loss of parts compels us to rethink the relations between the concepts of whole and sum, and may have far reaching consequences for the mereology of physical objects. (shrink)

Three-valued logics are standardly used to formalize gappy languages, i.e., interpreted languages in which sentences can be true, false or neither. A three-valued logic that assigns the same truth value to all gappy sentences is, in our view, insufficient to capture important semantic differences between them. In this paper we will argue that there are two different kinds of pathologies that should be treated separately and we defend the usefulness of a four-valued logic to represent adequately these two types of (...) gappy sentences. Our purpose is to begin the formal exploration of the four-valued logics that could be used to represent the phenomena in question and to show that these phenomena are present in natural language, at least according to some semantic theories of natural language. (shrink)

This paper motivates and explores an expressivist theory of vagueness, modelled on Allan Gibbard’s normative expressivism. It shows how Chris Kennedy’s semantics for gradable adjectives can be adjusted to fit into a theory on Gibbardian lines, where assertions constrain not just possible worlds but plans for action. Vagueness, on this account, is literally indecision about where to draw lines. It is argued that the distinctive phenomena of vagueness, such as the intuition of tolerance, can be explained in terms of practical (...) constraints on plans, and that the expressivist view captures what is right about several contending theories of vagueness. (shrink)

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

A person with one dollar is poor. If a person with n dollars is poor, then so is a person with n + 1 dollars. Therefore, a person with a billion dollars is poor. True premises, valid reasoning, a false a conclusion. This is an instance of the Sorites-paradox. (There are infinitely many such paradoxes. A man with an IQ of 1 is unintelligent. If a man with an IQ of n is unintelligent, so is a man with an IQ (...) of n+1. Therefore a man with an IQ of 200 is unintelligent.) Most attempts to solve this paradox reject some law of classical logic, usually the law of bivalence. I show that this paradox can be solved while holding on to all the laws of classical logic. Given any predicate that generates a Sorites-paradox, significant use of that predicate is actually elliptical for a relational statement: a significant token of "Bob is poor" means that Bob is poor compared to x, for some value of x. Once a value of x is supplied, a definite cutoff line between having and not having the paradox-generating predicate is supplied. This neutralizes the inductive step in the associated Sorites argument, and the would-be paradox is avoided. (shrink)

The sorites paradox is the name given to a class of paradoxical arguments, also known as little by little arguments, which arise as a result of the indeterminacy surrounding limits of application of the predicates involved. For example, the concept of a heap appears to lack sharp boundaries and, as a consequence of the subsequent indeterminacy surrounding the extension of the predicate ‘is a heap’, no one grain of wheat can be identified as making the difference between being a heap (...) and not being a heap. Given then that one grain of wheat does not make a heap, it would seem to follow that two do not, thus three do not, and so on. In the end it would appear that no amount of wheat can make a heap. We are faced with paradox since from apparently true premises by seemingly uncontroversial reasoning we arrive at an apparently false conclusion. (shrink)

. According to Horgans transvaluationist approach, the robustness that characterizes vague terms is inherently incoherent. He analyzes that robustness into two conceptual poles, individualistic and collectivistic, and ascribes the incoherence to the former. However, he claims vague terms remain useful nonetheless, because the collectivistic pole can be realized with a suitable non-classical logic and can quarantine the incoherence arising out of the individualistic pole. I argue, on the contrary, that the nonclassical logic fails to resolve the difficulty and that the (...) incoherence afflicts Horgans collectivistic pole as well, consequently invalidating the entire transvaluationist approach. An alternative, coherent conception of robustness is suggested. (shrink)

Vague existence can seem like the worst kind of vagueness in the world, or seem to be an entirely unintelligible notion. This bad reputation is based upon the rumour that if there is vague existence then there are non-existent objects. But the rumour is false: the modest brand of vague existence entailed by certain metaphysical theories of composition does not deserve its bad reputation.

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

PurposeGraham Priest has recently argued that the distinctive trait of classical mathematics is that the conditional of its underlying logic—that is, classical logic—is extensional. In this article, I aim to present an alternate explanation of the specificity of classical mathematics.MethodI examine Priest's argument for his claim and show its shortcomings. Then I deploy a model-theoretic presentation of logics that allows comparing them, and the mathematics based on them, more fine-grainedly.ResultsSuch a model-theoretic presentation of logics suggests that the specific character of (...) classical logic consists in the structure that it confers to its truth values and in the structure of the evaluation indices of its formulas, and that this trait is useful to explain the specific character of the logics and the mathematics based on them.ConclusionThe extensionality of the conditional in classical logic is a by-product of other structural features of a logic, which are more likely to be what gives a kind of mathematics based on it its specific character. (shrink)

The main thesis of this paper is that we sometimes are disposed to accept false and even jointly inconsistent claims by virtue of our semantic competence, and that this comes to light in the sorites and liar paradoxes. Among the subsidiary theses are that this is an important source of indeterminacy in truth conditions, that we must revise basic assumptions about semantic competence, and that classical logic and bivalence can be upheld in the face of the sorites paradox.

I will here present a number of problems concerning the idea that there is ontological vagueness, and the related claim that appeal to this idea can help solve some vagueness-related problems. A theme underlying the discussion will be the distinction between vagueness specifically and indeterminacy more generally (and, relatedly, the distinction between ontological vagueness and ontological indeterminacy). Even if the world is somehow ontologically indeterminate it by no means follows that it is, properly speaking, ontologically vague.1..

It might be thought that vagueness precludes the possibility of classical conceptual analysis and, thus, that the classical or definitional view of the nature of complex concepts is incorrect. The present paper argues that classical analysis can be had for concepts expressed by vague language since (1) all of the general theories of vagueness are compatible with the thesis that all complex concepts have classical analyses and also that (2) the meaning of vague expressions can be analyzed by having the (...) degree of vagueness of a given analysandum be mapped onto the vagueness of an analysans. (shrink)

In a recent paper, Barrio, Tajer and Rosenblatt establish a correspondence between metainferences holding in the strict-tolerant logic of transparent truth ST+ and inferences holding in the logic of paradox LP+. They argue that LP+ is ST+’s external logic and they question whether ST+’s solution to the semantic paradoxes is fundamentally different from LP+’s. Here we establish that by parity of reasoning, ST+ can be related to LP+’s dual logic K3+. We clarify the distinction between internal and external logic and (...) argue that while ST+’s nonclassicality can be granted, its self-dual character does not tie it to LP+ more closely than to K3+. (shrink)

Intuitively, vagueness involves some sort of indeterminacy: if Plato is a borderline case of baldness, then there is no fact of the matter about whether or not he’s bald—he’s neither bald nor not bald. The leading formal treatments of such indeterminacy—three valued logic, supervaluationism, etc.—either fail to validate the classical theorems, or require that various classically valid inference rules be restricted. Here we show how a fully classical, yet indeterminist account of vagueness can be given within natural semantics, an alternative (...) semantics for classical proof theory. The key features of the account are: there is a single notion of truth—definite truth—and a single notion of validity; sentences can be true, false, or undetermined; all classical theorems and all classical inference rule are valid; the sorites argument is unsound; ‘definitely’ is treated as a meta-language predicate; higher-order vagueness is handled via semantic ascent. (shrink)

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

In this article, I survey some of the major arguments against metaphysical indeterminacy and vagueness and outline potential responses.

A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of this paper is (...) to show that a large class of non-classical logics are strong enough to formulate their own model theory in a corresponding non-classical set theory. Specifically I show that adequate definitions of validity can be given for the propositional calculus in such a way that the metatheory proves, in the specified logic, that every theorem of the propositional fragment of that logic is validated. It is shown that in some cases it may fail to be a classical matter whether a given sentence is valid or not. One surprising conclusion for non-classical accounts of vagueness is drawn: there can be no axiomatic, and therefore precise, system which is determinately sound and complete. (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)