To get to grips with what Shapiro does and can say about higher-order vagueness, it is first necessary to thoroughly review and evaluate his conception of (first-order) vagueness, a conception which is both rich and suggestive but, as it turns out, not so easy to stabilise. In Sections I–IV, his basic position on vagueness (see Shapiro [2003]) is outlined and assessed. As we go along, I offer some suggestions for improvement. In Sections V–VI, I review two key paradoxes of higher-order (...) vagueness, while in Section VII, I explore a possible line of response to such paradoxes given by Keefe [2000]. In Section VIII, I assess whether which Shapiro might adapt Keefe's response to combat both paradoxes. (shrink)

To get to grips with what Shapiro does and can say about higher-order vagueness, it is first necessary to thoroughly review and evaluate his conception of (first-order) vagueness, a conception which is both rich and suggestive but, as it turns out, not so easy to stabilise. In Sections I–IV, his basic position on vagueness (see Shapiro [2003]) is outlined and assessed. As we go along, I offer some suggestions for improvement. In Sections V–VI, I review two key paradoxes of higher-order (...) vagueness, while in Section VII, I explore a possible line of response to such paradoxes given by Keefe [2000]. In Section VIII, I assess whether which Shapiro might adapt Keefe's response to combat both paradoxes. (shrink)

It is generally supposed that borderline cases account for the tolerance of vague terms, yet cannot themselves be sharply bounded, leading to infinite levels of higher order vagueness. This higher order vagueness subverts any formal effort to make language precise. However, it is possible to show that tolerance must diminish at higher orders. The attempt to derive it from indiscriminability founders on a simple empirical test, and we learn instead that there is no limit to how small higher order tolerance (...) may become. That means there is no limit to how precisely we may draw the boundaries of borderline cases, thus forestalling any requirement for higher order vagueness. (shrink)

The PhD thesis advances a new approach to vagueness as dispersion, comparing it with the main philosophical theories of vagueness in the analytic tradition.

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.

Most words in natural language are vague, that is to say, they lack sharp boundaries and, hence, they have (actual or potential) borderline cases, where the word in question neither definitely applies nor definitely fails to apply. Vagueness gives rise to paradoxes, the best known of which is the sorites (concerned with how many grains of sand are needed to make a heap). Besides offering a solution to such paradoxes, a theory of vagueness should systematically describe how the truth conditions (...) of sentences with vague terms are determined; and it should also define the right logical principles for reasoning with such sentences. This article offers an introduction to the main theories of vagueness and to the problems they have to face. (shrink)

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

On the dominant view of vagueness, if it is vague whether Harry is bald, then all the specific facts about the distribution of hair on Harry's head, together with all the facts about Harry's comparison class, together with all the facts about our community-wide use of the word ‘bald’, fail to settle whether Harry is bald. On the dominant view, if it is vague whether Harry is bald, then nothing settles whether Harry is bald—it is unsettled, not merely epistemically, but (...) metaphysically, whether Harry is bald. Call this view vagueness-as-indeterminacy. Vagueness-as-indeterminacy entails the following proposition: that clear vagueness as to whether Harry is bald clearly does not entail that Harry is bald. I argue against this proposition, and thus against vagueness-as-indeterminacy. My argument consists of a defence of the following rival proposition: that it is vague whether clear vagueness as to whether Harry is bald entails that Harry is bald. The argument itself is short. Most of the paper is devoted to responding to various objections to the argument, as well as attempting to explain away the initial appeal of the proposition that clear vagueness as to whether Harry is bald clearly does not entail that Harry is bald. (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)

On two standard views of vagueness, vagueness as to whether Harry is bald entails that nobody knows whether Harry is bald—either because vagueness is a type of missing truth, and so there is nothing to know, or because vagueness is a type of ignorance, and so even though there is a truth of the matter, nobody can know what that truth is. Vagueness as to whether Harry is bald does entail that nobody clearly knows that Harry is bald and that (...) nobody clearly knows that Harry is not bald. But it does not entail that nobody knows that Harry is bald or that nobody knows that Harry is not bald. Hence, the two standard views of vagueness are mistaken. (shrink)

To get to grips with what Shapiro does and can say about higher-order vagueness, it is first necessary to thoroughly review and evaluate his conception of (first-order) vagueness, a conception which is both rich and suggestive but, as it turns out, not so easy to stabilise. In Sections I–IV, his basic position on vagueness (see Shapiro [2003]) is outlined and assessed. As we go along, I offer some suggestions for improvement. In Sections V–VI, I review two key paradoxes of higher-order (...) vagueness, while in Section VII, I explore a possible line of response to such paradoxes given by Keefe [2000]. In Section VIII, I assess whether which Shapiro might adapt Keefe’s response to combat both paradoxes. (shrink)

On the dominant view of vagueness, if it is vague whether Harry is bald, then it is unsettled, not merely epistemically, but metaphysically, whether Harry is bald. In other words, vagueness is a type of indeterminacy. On the standard alternative, vagueness is a type of ignorance: if it is vague whether Harry is bald, then, even though it is metaphysically settled whether Harry is bald, we cannot know whether Harry is bald. On my view, vagueness is neither a type of (...) indeterminacy nor a type of ignorance. Rather, it is sui generis. (shrink)

Scholars are divided as to whether reduction should be a central strategy for understanding the world. While reductive analysis is the standard mode of explanation in many areas of science and everyday life, many consider reductionism a sign of “intellectual naivete and backwardness.” In this paper I make three points about the proper status of anti-reductionism: First, reduction, is, in fact, a centrally important epistemic strategy. Second, reduction to physics is always possible for all causal properties. Third, there are, nevertheless, (...) reasons we want science to discover properties and explanations other than reductive physical ones. (shrink)

I aim to show how and why some definitions can be benignly circular. According to Lloyd Humberstone, a definition that is analytically circular need not be inferentially circular and so might serve to illuminate the application-conditions for a concept. I begin by tidying up some problems with Humberstone's account. I then show that circular definitions of a kind commonly thought to be benign have inferentially circular truth-conditions and so are malign by Humberstone's test. But his test is too demanding. The (...) inferences we actually use to establish the applicability of, e.g., colour concepts are designed to establish warranted assertability and not truth. Understood thus, dispositional analyses are not inferentially circular. (shrink)

Scholars are divided as to whether reduction should be a central strategy for understanding the world. While reductive analysis is the standard mode of explanation in many areas of science and everyday life, many scholars consider reductionism a sign of “intellectual naïveté and backwardness.” This article makes three points about the proper status of antireductionism: First, reduction is, in fact, a centrally important epistemic strategy. Second, reduction to physics is always possible for all causal properties. Third, there are, nevertheless, reasons (...) why we want science to discover properties and explanations other than reductive physical ones. (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)

There are some properties, like being bald, for which it is vague where the boundary between the things that have it and the things that do not lies. A number of arguments threaten to show that such properties can still be associated with determinate and knowable boundaries: not between the things that have it and those that don’t, but between the things such that it is borderline at some order whether they have it and the things for which it is (...) not. I argue that these arguments, if successful, turn on a contentious principle in the logic of determinacy: Brouwer’s Principle, that every truth is determinately not determinately false. Other paradoxes which do not appear to turn on this principle often tacitly make assumptions about assertion, knowledge and higher-order vagueness. In this paper I’ll show how one can avoid sharp higher-order boundaries by rejecting these assumptions. (shrink)

On the dominant view of vagueness, if it is vague whether Harry is bald, then it is unsettled, not merely epistemically, but metaphysically, whether Harry is bald. In other words, vagueness is a type of indeterminacy. On the standard alternative, vagueness is a type of ignorance: if it is vague whether Harry is bald, then, even though it is metaphysically settled whether Harry is bald, we cannot know whether Harry is bald. On my view, vagueness is neither a type of (...) indeterminacy nor a type of ignorance. Rather, it is sui generis. (shrink)