This dissertation explores several illuminating points of intersection between the philosophy of perception and the philosophy of vagueness. Among other things, I argue: (i) that it is entirely unhelpful to theorize about perception or consciousness using Nagelian "what it's like" talk; (ii) that a popular recent account of perceptual phenomenology (representationalism) conflicts with our best theory of vagueness (supervaluationism); (iii) that there are no vague properties, for Evans-esque reasons; (iv) that it is impossible to insert "determinacy" (...) operators into representationalism in a truth-preserving manner; and (v) that strong versions of dualism are unable to accommodate the possibility of borderline consciousness. (shrink)

Some have argued that the vagueness exhibited by geographic names and descriptions such as ‘Albuquerque’, ‘the Outback’, or ‘Mount Everest’ is ultimately ontological: these terms are vague because they refer to vague objects, objects with fuzzy boundaries. I take the opposite stand and hold the view that geographic vagueness is exclusively semantic, or conceptual at large. There is no such thing as a vague mountain. Rather, there are many things where we conceive a mountain to be, each with (...) its precise boundary, and when we say ‘Everest’ we are just being vague as to which thing we are referring to. This paper defends this view against some plausible objections. (shrink)

Supervaluationism is a well known theory of vagueness. Subvaluationism is a less well known theory of vagueness. But these theories cannot be taken apart, for they are in a relation of duality that can be made precise. This paper provides an introduction to the subvaluationist theory of vagueness in connection to its dual, supervaluationism. A survey on the supervaluationist theory can be found in the Compass paper of Keefe (2008); our presentation of the theory in this paper (...) will be short to get rapidly into the logical issues. This paper is relatively self-contained. A modest background on propositional modal logic is, though not strictly necessary, advisable. The reader might find useful the Compass papers Kracht (2011) and Negri (2011) (though these papers cover issues of more complexity than what is demanded to follow this paper). (shrink)

My paper characterizes religious beliefs in terms of vagueness. I introduce my topic by providing a general overview of my main claims. In the subsequent section, I develop basic distinctions and terminology for handling the notion of religious tradition and capturing vagueness. In the following sections, I make the case for my claim that religious beliefs are vague by developing a general argument from the interconnection between the referential opacity of religious belief content and the long-term communitarian history (...) of the precisification of what such content means. I start from describing an empirical example in the third section, and then I move to settle the matter in a conceptually argumentative frame in the fourth one. My conclusions in the final section address a few of consequences relevant to debates about religious epistemology and religious diversity. (shrink)

You are morally permitted to save your friend at the expense of a few strangers, but not at the expense of very many. However, there seems no number of strangers that marks a precise upper bound here. Consequently, there are borderline cases of groups at the expense of which you are permitted to save your friend. This essay discusses the question of what explains ethical vagueness like this, arguing that there are interesting metaethical consequences of various explanations.

There are three main traditional accounts of vagueness : one takes it as a genuinely metaphysical phenomenon, one takes it as a phenomenon of ignorance, and one takes it as a linguistic or conceptual phenomenon. In this paper I first very briefly present these views, especially the epistemicist and supervaluationist strategies, and shortly point to some well-known problems that the views carry. I then examine a 'statistical epistemicist' account of vagueness that is designed to avoid precisely these problems (...) – it will be a view that provides an account of the phenomenon of vagueness as coming from our linguistic practices, while insisting that meaning supervenes on use, and that our use of vague terms does yield sharp and precise meanings, which we ignore, thus allowing bivalence to hold. (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)

Sample chapter from H. Asgeirsson, The Nature and Value of Vagueness in the Law (Hart Publishing, 2020), in which I present and partially defend a version of what has come to be called the communicative-content theory of law. Book abstract: Lawmaking is – paradigmatically – a type of speech act: people make law by saying things. It is natural to think, therefore, that the content of the law is determined by what lawmakers communicate. However, what they communicate is sometimes (...) vague and, even when it is clear, the content itself is sometimes vague. The monograph examines the nature and consequences of these two linguistic sources of indeterminacy in the law with the aim of providing plausible answers to three related questions: In virtue of what is the law vague? What might be good about vague law? How should courts resolve cases of vagueness? (shrink)

When the United States Supreme Court used the expression “with all deliberate speed” in the case Brown v. Board of Education, it did so presumably because of its vagueness. Many jurists, economists, linguists, and philosophers accordingly assume that vagueness can be strategically used to one’s advantage. Roy Sorensen has cast doubt on this assumption by strictly differentiating between vagueness and generality. Indeed, most arguments for the value of vagueness go through only when vagueness is confused (...) with generality. Sorensen claims that vagueness – correctly understood – has no function in law inter alia because judges lie systematically when confronted with borderline cases. I argue that both claims are wrong. First, judges do not need to resort to lying when adjudicating borderline cases, and even if they had to, this would not render vagueness useless. Secondly, vagueness has several important functions in law such as the reduction of decision costs and the delegation of power. Although many functions commonly attributed to the vagueness of legal expressions are in fact due to their generality or other semantic properties, vagueness has at least these two functions in law. (shrink)

The claim that all vagueness must be a feature of language or thought is the current orthodoxy. This is a claim about the “location” of vagueness. “Locating Vagueness” argues that this claim is false, largely by defending the possibility of borderline cases in the absence of language and thought. If the orthodoxy about the location of vagueness is false, then so too is any account of the “nature” of vagueness that implies that orthodoxy. So this (...) paper concludes that various accounts of the nature of vagueness are false. Among such accounts, so this paper argues, are the standard versions of supervaluationism and the standard versions of epistemicism. So I conclude that those accounts are false. Along the way, I present, and uncover ways to motivate, several heretical accounts of the nature of vagueness, including nonstandard versions of both supervaluationism and epistemicism. (shrink)

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

[Author's note: I am posting this dissertation since it may be of interest to some people working on vagueness and related topics. It does not represent my current views on the topic. I have never attempted to publish any of this work, though I hope some day to return to it.] -/- Philosophers have devoted a lot of attention to vagueness in recent years, but there is still no general consensus about how to resolve the Sorites paradox. Timothy (...) Williamson‘s epistemic view, which claims that our vague terms have unknown sharp boundaries, is the most popular and most controversial current account. No one has shown exactly what is wrong the epistemic view and no one has provided a satisfying alternative to it. These two projects – articulating what is wrong with the epistemic view, and providing a plausible alternative – are the primary goals of this dissertation. -/- Additionally, I survey ordinary intuitions that underlie Sorites paradoxes, and I note how these intuitions inform, and are informed by, a number of deeper philosophical debates in metaphysics, epistemology, philosophy of language, and ethics. In part, this serves as an explanation of why the Sorites paradox has remained so difficult to resolve. -/- The most common objection to the epistemic view – that it provides an unsatisfactory account of the connection between meaning and use – has not been successful in undermining the view. My own objection is a metaphysical, and not a semantic, objection: the epistemic view fails to provide the best explanation of what objects and properties exist. Instead, an eliminativist account of macro-level objects and properties, according to which there are no mountains and there is no property of being lavender-colored, is a better metaphysical account than one that claims that there are mountains and color properties that have sharp boundaries. -/- Of course, this eliminativist view is intuitively unappealing, and to show how statements in ordinary language can in some way be taken to be true, I introduce the normative choice account. According to this view, although non-normative facts about linguistic behavior and about the external world do not determine a precise reference for our terms, our choices may do so. I claim that this provides all that is needed for there to be semantic normativity. First, we are still guided in our choices to some extent by psychological tendencies, and second, there are resources in semantic deliberation to respond to aberrant uses of language. (shrink)

Vagueness, 'the quality or condition of being vague' (OED), has kept philosophers busy since ancient times. This article gives a concise account of vagueness.

This article discusses two arguments in favor of perdurance. The first is Sider’s argument from vagueness, “one of the most powerful” in favor of perdurantism. I make the observation that endurantists have principled grounds to claim that the argument is unsound, at least if endurance is formulated in locative rather than mereological terms. Having made this observation, I use it to emphasize a somewhat neglected difference between endurantists and perdurantists with respect to their views on material objects. These views, (...) in the case of endurantists, lead to a further, less than conclusive but nevertheless interesting argument against endurantism—the anti-fundamentality argument—which I discuss and tentatively endorse. That argument posits that endurantists must take location to be a fundamental relation, and that this has as a consequence the metaphysical possibility of some rather unwelcome scenarios. Perdurantists may avoid this consequence by denying that location is fundamental, perhaps by embracing supersubstantivalism. (shrink)

Composite materialism, as I will understand it, is the view that human persons are composite material objects. This paper develops and investigates an argument, The Vague Singulars Argument, for the falsity of composite materialism. We shall see that cogent or not, the Vague Singulars Argument has philosophically significant ramifications.

The topic of this paper is whether there is metaphysical vagueness. It is shown that it is important to distinguish between the general phenomenon of indeterminacy and the more narrow phenomenon of vagueness (the phenomenon that paradigmatically rears its head in sorites reasoning). Relatedly, it is important to distinguish between metaphysical indeterminacy and metaphysical vagueness. One can wish to allow metaphysical indeterminacy but rule out metaphysical vagueness. As is discussed in the paper, central argument against metaphysical (...) vagueness, like those of Gareth Evans and Mark Sainsbury, would if successful rule out metaphysical indeterminacy. One way to argue specifically against the possibility of metaphysical vagueness might be thought to be to argue for a specific theory of the nature of vagueness according to which vagueness is a semantic phenomenon. But it is shown that there are complications also pertaining to arguments with that structure. Toward the end of the paper, I discuss Trenton Merricks’ well-known argument against a semantic view on vagueness and for a metaphysical view. (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 (...) class='Hi'>vagueness is illustrated by the concept of “natural kind”, which is essential to realism/anti-realism debates. (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)

In ‘Something to Do with Vagueness ...’, Linda Burns defends an analogy between the informational and the borderline-case variety of vagueness. She argues that the latter is in fact less extraordinary and less disastrous than people in the tradition of Michael Dummett and Crispin Wright have told us. However, her account involves presuppositions that cannot be taken for granted. Here is to take a closer look at some of these presuppositions and argue hat they may—when left unguarded—undermine much (...) of Burns’ general account. (shrink)

A presentation of the Lewis-Sider argument from vagueness for unrestricted composition and possible responses.

This paper explores the interaction of well-motivated (if controversial) principles governing the probability conditionals, with accounts of what it is for a sentence to be indefinite. The conclusion can be played in a variety of ways. It could be regarded as a new reason to be suspicious of the intuitive data about the probability of conditionals; or, holding fixed the data, it could be used to give traction on the philosophical analysis of a contentious notion—indefiniteness. The paper outlines the various (...) options, and shows that ‘rejectionist’ theories of indefiniteness are incompatible with the results. Rejectionist theories include popular accounts such as supervaluationism, non-classical truth-value gap theories, and accounts of indeterminacy that centre on rejecting the law of excluded middle. An appendix compares the results obtained here with the ‘impossibility’ results descending from Lewis ( 1976 ). (shrink)

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..

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

It is common to think that what theory of linguistic vagueness is correct has implications for debates in philosophy of law. I disagree. I argue that the implications of particular theories of vagueness on substantive issues of legal theory and practice are less far-reaching than often thought. I focus on four putative implications discussed in the literature concerning (i) the value of vagueness in the law, (ii) the possibility and value of legal indeterminacy, (iii) the possibility (...) of the rule of law, and (iv) strong discretion. I conclude with some methodological remarks. Delineating questions about conventional meaning, the metaphysics/metasemantics of (legal) content determination, and norms of legal interpretation and judicial practice can motivate clearer answers and a more refined understanding of the space of overall theories of vagueness, interpretation, and law. (shrink)

In his essay ‘“Wang’s Paradox”’, Crispin Wright proposes a solution to the Sorites Paradox (in particular, the form of it he calls the ‘Paradox of Sharp Boundaries’) that involves adopting intuitionistic logic when reasoning with vague predicates. He does not give a semantic theory which accounts for the validity of intuitionistic logic (and the invalidity of stronger logics) in that area. The present essay tentatively makes good the deficiency. By applying a theorem of Tarski, it shows that intuitionistic logic is (...) the strongest logic that may be applied, given certain semantic assumptions about vague predicates. The essay ends with an inconclusive discussion of whether those semantic assumptions should be accepted. (shrink)

Gareth Evans has argued that the existence of vague objects is logically precluded: The assumption that it is indeterminate whether some object a is identical to some object b leads to contradiction. I argue in reply that, although this is true—I thus defend Evans's argument, as he presents it—the existence of vague objects is not thereby precluded. An 'Indefinitist' need only hold that it is not logically required that every identity statement must have a determinate truth-value, not that some such (...) statements might actually fail to have a determinate truth-value. That makes Indefinitism a cousin of mathematical Intuitionism. (shrink)

One of the hardest problems in philosophy, one that has been around for over two thousand years without generating any significant consensus on its solution, involves the concept of vagueness: a word or concept that doesn't have a perfectly precise meaning. There is an argument that seems to show that the word or concept simply must have a perfectly precise meaning, as violently counterintuitive as that is. Unfortunately, the argument is usually so compressed that it is difficult to (...) see why exactly the problem is so hard to solve. In this article I attempt to explain just why it is that the problem – the sorites paradox – is so intractable.Export citation. (shrink)

The Causal Exclusion Problem is raised in many domains, including in the metaphysics of macroscopic objects. If there is a complete explanation of macroscopic effects in terms of the microscopic entities that compose macroscopic objects, then the efficacy of the macroscopic will be threatened with exclusion. I argue that we can avoid the problem if we accept that macroscopic objects are ontically vague. Then, it is indeterminate which collection of microscopic entities compose them, and so information about microscopic entities is (...) insufficient to provide a complete explanation of certain properties of macroscopic objects. After outlining this solution, I consider several objections. (shrink)

This paper asks: Is the quantifier variantist committed to metaphysical vagueness? My investigation of this question goes via a study of vague existence. I’ll argue that the quantifier variantist is committed to vague existence and that the vague existence posited by the variantist requires a puzzling sort of metaphysical vagueness. Specifically, I distinguish between (what I call) positive and negative metaphysical vagueness. Positive metaphysical vagueness is (roughly) the claim that there is vagueness in the world; (...) negative metaphysical vagueness is (roughly) the claim that there is vagueness that is not in our language or thought. I’ll argue that the quantifier variantist’s commitment to vague existence comes with positive metaphysical vagueness -- even if it doesn't require negative metaphysical vagueness. (shrink)

The exploration of chemical periodicity over the past 250 years led to the development of the Periodic System of Elements and demonstrates the value of vague ideas that ignored early scientific anomalies and instead allowed for extended periods of normal science where new methodologies and concepts are developed. The basic chemical element provides this exploration with direction and explanation and has shown to be a central and historically adaptable concept for a theory of matter far from the reductionist frontier. This (...) is explored in the histories of Prout’s hypothesis, Döbereiner Triads, element inversions necessary when ordering chemical elements by atomic weights, and van den Broeck’s ad-hoc proposal to switch to nuclear charges instead. The development of more accurate methods to determine atomic weights, Rayleigh and Ramsey’s gas separation and analytical techniques, Moseley’s X-ray spectroscopy to identify chemical elements, and more recent accelerator-based cold fusion methods to create new elements at the end of the Periodic Table point to the importance of methodological development complementing conceptual advances. I propose to frame the crossover from physics to chemistry not as a loss of accuracy and precision but as an increased application of vague concepts such as similarity which permit classification. This approach provides epistemic flexibility to adapt to scientific anomalies and the continued growth of chemical compound space and rejects the Procrustean philosophy of reductionist physics. Furthermore, it establishes chemistry with its explanatory and operational autonomy epitomized by the periodic system of elements as a gateway to other experimental sciences. (shrink)

In his article “Issues of Pragmaticism” published in 1905, in The Monist, Charles S. Peirce complains that “Logicians have been at fault in giving Vagueness the go-by, so far as not even to analyze it.” That same year, occupying himself with the consequences of “Critical commonsensism,” he affirmed, “I have worked out the logic of vagueness with something like completeness,” a statement that causes the majority of the commentators on his work, including the editors of the Collected Papers (...) to ask where this logic is to be found. The fever for finding Peirce's manuscripts is fed by the hope of some researchers of discovering the logic of vagueness, a hope that has grown since Carolyn Eisele's publication of his mathematical works. Others - and I count myself among them - believe that in reality this is a matter of something already known. That is, they interpret the affirmation ending the paragraph of reproach addressed to logicians, “The present writer has done his best to work out the Stechiology, Critic, and Methodeutik of the subject,” as a tripartite semiotic of the vague, still limited, according to Peirce's older works, to symbols, that is, to the signs of natural language examined from the perspective of logic. (shrink)

Ted Sider’s Proportionality of Justice condition requires that any two moral agents instantiating nearly the same moral state be treated in nearly the same way. I provide a countermodel in supervaluation semantics to the proportionality of justice condition. It is possible that moral agents S and S' are in nearly the same moral state, S' is beyond all redemption and S is not. It is consistent with perfect justice then that moral agents that are not beyond redemption go determinately to (...) heaven and moral agents that are beyond all redemption go determinately to hell. I conclude that moral agents that are in nearly the same moral state may be treated in very unequal ways. (shrink)

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

John Burgess has recently argued that Timothy Williamson’s attempts to avoid the objection that his theory of vagueness is based on an untenable metaphysics of content are unsuccessful. Burgess’s arguments are important, and largely correct, but there is a mistake in the discussion of one of the key examples. In this note I provide some alternative examples and use them to repair the mistaken section of the argument.

In his fascinating and provocative paper, "Sharp Boundaries for Blobs," Roy Sorensen gives several arguments against the possibility of "vague objects," or objects with indeterminate boundaries.1 In what follows, I will examine the main argument given by Sorensen in his paper. This argument has a great deal of initial plausibility. Moreover, I happen to sympathize with its conclusion. Nevertheless, it seems to me that Sorensen's argument fails to establish that conclusion. The purpose of this paper is to show why. I (...) will argue that, upon careful examination, it can be seen that Sorensen's argument involves a fatal equivocation. Sorensen's argument is based on a kind of thought experiment. We are asked to consider, as a paradigm example of a vague object, a grey sphere (also known as "the blob") that fades into a white background. And we are asked to imagine a spherical cavity growing from the center of the blob, so that the growth of the cavity eventually destroys the blob. Sorensen's argument, which is explicitly spelled out in Section I of his paper, goes like this: 1. The blob must have a boundary. 2. If a spherical cavity grows from the center of the blob, the blob's outer boundary is completely unaffected as long as some of the blob remains. 3. As soon as nothing remains of the blob, the blob's boundary goes out of existence all at once. (shrink)

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

In the course of. his philosophic career, Charles Peirce made repeated attempts to construct mathematical definitions of the commonsense or experimental notion of 'continuity'. In what I will label his Final Definition of Continuity, however, Peirce abandoned the attempt to achieve mathe­matical definition and assigned the analysis of continuity to an otherwise unnamed extra-mathematical science. In this paper, I identify the Final Definition, attempt to define its terms, and suggest that it belongs to Peirce's emergent semiotics of vagueness. I (...) argue, further, that it marks the transformation of Peirce's synechism. Before the time of his Final Definition, Peirce adopted a theory of continuity as a foundational principle of metaphysics and assumed this principle might be formalized in a mathe­matics of continuity. After the Final Definition, Peirce abandoned his foundationalism in favor of what he called a critical common-sensism. This is the claim that philosophy (and with it, logic) derives its norms from the observation of actual cognitive practices and that continuity is a distinguishing mark of actual as opposed to merely possible or imagined practices. (shrink)

In this paper, we take the approach of the lexicon makers: We contemplate human language instead of trying to resist its forces. Basically, some sigmatoids seem to have been created to be free of boundaries: We fence them as we please when we apply them to our assertions, but they are quite vague in the lexicon. We here identify at least two types of such sigmatoids: The synthetisers and the specifiers. The former would originate from our capacity of isolating common (...) features of objects that, in principle, have no possible intersection. The latter would originate from our attempt of describing the 3D World by means of 2D entities. We conclude that the intrinsic vagueness of these sigmatoids is something not only acceptable, but either pleasant or necessary. (shrink)

A discussion on this so debatable and debated concept, Higher Order Vagueness. After going through the issues that make Higher Order Vagueness an object of scientific attention, we conclude that vagueness is undesirable in logical systems but desirable in language, and the Semiotics Universe splits into three other universes inside of the universe of the Computer Science Systems. We create a new way of addressing problems with sigmatoids, and define vagueness in an almost mathematical fashion.

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)

According to Russell, the notation in Principia Mathematica has been designed to avoid the vagueness endemic to our natural language. But what does Russell think vagueness is? My argument is an attempt to show that his views on vagueness evolved and that the final conception he adopts is not coherent. Three phases of his conception of vagueness are identified, the most significant being the view that he articulates on vagueness in his 1923 address to the (...) Jowett Society. My central thesis is that the 1912 conception of vagueness -- what I characterize as "semantic egalitarianism" -- seriously conflicts with the later paradoxical account of vagueness. (shrink)

This article argues that resolutions to the sorites paradox offered by epistemic and supervaluation theories fail to adequately account for vagueness. After explaining the paradox, I examine the epistemic theory defended by Timothy Williamson and discuss objections to his semantic argument for vague terms having precise boundaries. I then consider Rosanna Keefe's supervaluationist approach and explain why it fails to accommodate the problem of higher-order vagueness. I conclude by discussing how fuzzy logic may hold the key to resolving (...) the sorites paradox without positing indefensible borders to the correct application of vague terms. (shrink)

Stewart Shapiro’s book develops a contextualist approach to vagueness. It’s chock-full of ideas and arguments, laid out in wonderfully limpid prose. Anyone working on vagueness (or the other topics it touches on—see below) will want to read it. According to Shapiro, vague terms have borderline cases: there are objects to which the term neither determinately applies nor determinately does not apply. A term determinately applies in a context iff the term’s meaning and the non-linguistic facts determine that they (...) do. The non-linguistic facts include the “external” context: “comparison class, paradigm cases, contrasting cases, etc.” (33) But external-contextsensitivity is not what’s central to Shapiro’s contextualism. Even fixing external context, vague terms’ (anti-)extensions exhibit sensitivity to internal context: the decisions of competent speakers. According to Shapiro’s open texture thesis, for each borderline case, there is some circumstance in which a speaker, consistently with the term’s meaning and the non-linguistic facts, can judge it to fall into the term’s extension and some circumstance in which the speaker can judge it to fall into the term’s anti-extension: she can “go either way.” Moreover, borderline sentences are Euthyphronically judgment- dependent: a competent speaker’s judging a borderline to fall into a term’s (anti- )extension makes it so. For Shapiro, then, a sentence can be true but indeterminate: a case left unsettled by meaning and the non-linguistic facts (and thus indeterminate, or borderline) may be made true by a competent speaker’s judgment. Importantly, among the non-linguistic facts that constrain speakers’ judgments (at least in the cases Shapiro cares about) is a principle of tolerance: for all x and y, if x and y differ marginally in the relevant respect (henceforth, Mxy), then if one competently judges Bx, one cannot competently judge y in any other manner in the same (total) context.1 This does not require that one judge By: one might not consider the matter at all.. (shrink)

This article provides an intuitive semantic account of a new logic for comparisons (CL), in which atomic statements are assigned both a classical truth-value and a “how much” value or extension in the range [0, 1]. The truth-value of each comparison is determined by the extensions of its component sentences; the truth-value of each atomic depends on whether its extension matches a separate standard for its predicate; everything else is computed classically. CL is less radical than Casari’s comparative logics, in (...) that it does not allow for the formation of comparative statements out of truth-functional molecules. It is argued that CL provides a better analysis of predicate vagueness than classical logic, fuzzy logic or supervaluation theory. (shrink)

This paper explores what the epistemic account of vagueness means for theories of legal interpretation. The thesis of epistemicism is that vague statements are true or false even though it is impossible to know which. I argue that if epistemicism is accepted within the domain of the law, then the following three conditions must be satisfied: Interpretative reasoning within the law must adhere to the principle of bivalence and the law of excluded middle, interpretative reasoning within the law must (...) construe vague statements as an epistemic phenomenon, and epistemicism must be expanded to include normative considerations in order to account for legal theories that are consistent with the first two conditions. The first two conditions are internal to a particular theory of legal interpretation, while the third condition is external to a particular theory of legal interpretation. My conclusion shows that there are legal theories that are internally consistent with the fundamental features of epistemicism. However, within the domain of law—and specifically in the case of legal theories that are internally consistent with epistemicism—I show that vagueness cannot be explained simply by our ignorance of the meaning and use of vague expressions. Rather, epistemicism must also account for ignorance of the requisite normative considerations in legal theories with which it is otherwise consistent. (shrink)

Wether the chicken or the egg came first, is not only a mind-boggling but a substantial question. Its answer depends on the biological background theory one assumes. I review recent work on the topic (by Teichmann, Sorensen, Waller and Raatzsch) and resolve some of the disputes between these authors by borrowing from Aristotle the distinction between chicken-producing eggs. I then introduce the concept of a quasi-species to make explicit the vagueness involved in species-terms and prove 13 different priority-claims within (...) a Darwinian framework. (shrink)