As introduction to the special issue on the semantics of cardinals, we offer some background on the relevant literature, and an overview of the contributions to this volume. Most of these papers were presented in earlier form at an interdisciplinary workshop on the topic at The Ohio State University, and the contributions to this issue reflect that interdisciplinary character: the authors represent both fields in the title of this journal.

The purpose of this article is to explore the extent to which mathematics is subject to open texture and the extent to which mathematics resists open texture. The resistance is tied to the importance of proof and, in particular, rigor, in mathematics.

Supported decision-making has been promoted at a policy level and within international human rights treaties as a way of ensuring that people with disabilities enjoy the right to legal capacity on an equal basis with others. However, little is known about the practical issues associated with implementing supported decision-making, particularly in the context of dementia. This study aimed to understand the experiences of people with dementia and their family members with respect to decision-making and their views on supported decision-making. Thirty-six (...) interviews were undertaken with fifty-seven participants across three states in Australia. Interpretative Phenomenological Analysis was used as the methodological approach, with relational autonomy as a theoretical perspective. We identified two overarching themes relating to participants’ experiences with decision-making: “the person in relationship over time” and “maintaining involvement.” Participant views on the practical issues associated with supported decision-making are addressed under the themes of “facilitating decision-making,” “supported decision-making arrangements,” “constraints on decision-making,” and “safeguarding decision-making.” While participants endorsed the principles of supported decision-making as part of their overarching strategy of “maintaining involvement” in decision-making, they recognized that progressive cognitive impairment meant that there was an inevitable transition toward greater involvement of, and reliance upon, others in decision-making. Social and contextual “constraints on decision-making” also impacted on the ability of people with dementia to maintain involvement. These themes inform our proposal for a “spectrum approach” to decision-making involvement among people living with dementia, along with recommendations for policy and practice to assist in the implementation of supported decision-making within this population. (shrink)

Supported decision-making has been promoted at a policy level and within international human rights treaties as a way of ensuring that people with disabilities enjoy the right to legal capacity on an equal basis with others. However, little is known about the practical issues associated with implementing supported decision-making, particularly in the context of dementia. This study aimed to understand the experiences of people with dementia and their family members with respect to decision-making and their views on supported decision-making. Thirty-six (...) interviews were undertaken with fifty-seven participants across three states in Australia. Interpretative Phenomenological Analysis was used as the methodological approach, with relational autonomy as a theoretical perspective. We identified two overarching themes relating to participants’ experiences with decision-making: “the person in relationship over time” and “maintaining involvement.” Participant views on the practical issues associated with supported decision-making are addressed under the themes of “facilitating decision-making,” “supported decision-making arrangements,” “constraints on decision-making,” and “safeguarding decision-making.” While participants endorsed the principles of supported decision-making as part of their overarching strategy of “maintaining involvement” in decision-making, they recognized that progressive cognitive impairment meant that there was an inevitable transition toward greater involvement of, and reliance upon, others in decision-making. Social and contextual “constraints on decision-making” also impacted on the ability of people with dementia to maintain involvement. These themes inform our proposal for a “spectrum approach” to decision-making involvement among people living with dementia, along with recommendations for policy and practice to assist in the implementation of supported decision-making within this population. (shrink)

This book returns the reader to an agenda for addressing equity in schools, emphasizing the need to reexamine past reform efforts and the work ahead for educational leaders in reshaping schools and schooling.

Presents a plethora of approaches to developing human potential in areas not conventionally addressed. Organized in two parts, this international collection of essays provides viable educational alternatives to those currently holding sway in an era of high-stakes accountability.

Some authors have claimed that ante rem structuralism has problems with structures that have indiscernible places. In response, I argue that there is no requirement that mathematical objects be individuated in a non-trivial way. Metaphysical principles and intuitions to the contrary do not stand up to ordinary mathematical practice, which presupposes an identity relation that, in a sense, cannot be defined. In complex analysis, the two square roots of –1 are indiscernible: anything true of one of them is true of (...) the other. I suggest that ‘i’ functions like a parameter in natural deduction systems. I gave an early version of this paper at a workshop on structuralism in mathematics and science, held in the Autumn of 2006, at Bristol University. Thanks to the organizers, particularly Hannes Leitgeb, James Ladyman, and Øystein Linnebo, to my commentator Richard Pettigrew, and to the audience there. The paper also benefited considerably from a preliminary session at the Arché Research Centre at the University of St Andrews. I am indebted to my colleagues Craige Roberts, for help with the linguistics literature, and Ben Caplan and Gabriel Uzquiano, for help with the metaphysics. Thanks also to Hannes Leitgeb and Jeffrey Ketland for reading an earlier version of the manuscript and making helpful suggestions. I also benefited from conversations with Richard Heck, John Mayberry, Kevin Scharp, and Jason Stanley. CiteULike Connotea Del.icio.us What's this? (shrink)

In lieu of an abstract, here is a brief excerpt of the content:70 HUME'S LETTER TO STEWART A Note on a Paper by D. C. Stove In a recent paper, D. C. Stove raises an historical problem. There exists a letter, written in 1754 by Hume to John Stewart, then Professor of Natural Philosophy at Edinburgh, in which the following words occur:. „. J never asserted so absurd a Proposition, as that any thing might arise without a Cause: (...) I only maintained, that our Certainty of the Falsehood of that Proposition proceeded neither from Intuition nor Demonstration; but from another Source. Some commentators, most notably Norman Kemp-Smith, take this as telling strongly in favour of a non-sceptical reading of Hume. Stove undertakes to show beyond reasonable doubt that the claim made in the letter is in blatant contradiction with central theses of Hume's published philosophy, so that it has to be regarded as useless as evidence for the interpretation of the latter. There is a mystery as to how Hume came to say something so clearly false about what he himself had written; Stove offers certain conjectures, none of which he finds wholly satisfactory. As the conclusion of the first, exegetical, part of his article, Stove advances the thesis that Hume held the falsity of the Causal Principle to be possible in at least three senses of "possible". These senses he specifies accurately, but doesn't wish to rest anything on the detail of his specification of the third; it is important only that it be stronger than either of the preceding two. This done, he takes a look at the letter to Stewart, and says, with reference to the first part of the 71 passage quoted above: That something might begin to exist without a cause, is evidently equivalent to the proposition that it is possib Ie for something to begin to exist without a cause. That, in turn, is evidently equivalent to the proposition that the falsity of the Causal Principle is possible. (Stove's o underlining). It follows that what Hume says in the letter is simply false. It could be true only if the "might" referred to some sense of possibility even weaker than the weakest of Stove's three senses. But since that is mere self-consistency, there is no such sense. Now the argument to the contradiction relies on reading "might" as "it is possible", in some sense of those words. Stove says, as we have seen, that they are "evidently equivalent", but the equivalence is certainly not evident, and it may well be asked whether it exists at all. After all, there are English constructions with "might" which don't have modal force: "Do you think something might have happened to them without our knowing about it?" The hearer is not, of course, being asked whether it- is possible that something should have happened without their knowledge; he is being asked for his opinion on whether something actually has so happened. "Most unlikely", would be a perfectly natural and acceptable response. Again : "ïou stay here, to take care of any problem that might arise before we get back". Obviously it is not intended that the hearer should start taking precautions against all possibilities, only that he should cope with whatever actually arises, if anything. 72 This is quite normal modern usage, and I know no reason to think that it wasn't also norT.il usage in the 18th Century. Admittedly, it isn't modern philocophers ' usage - we would be very careful, in writing or; logical matters, not to use the word "might" unless it was definitely the modal proposition that we had in mind, but earlier times haven't always been so professional about their vocabulary. Certainly, if Hume, in the letter to Stewart, was denying that he had ever asserted the possibility of the falsehood of the Causal Principle it would be, as Stove shows, extremely hard to see what he could have been thinking of. But if what he meant could have been as well expressed by "I never asserted... that anything arises without a cause" then most of Stove's problems are over, for there is no 3 conflict with any of the theses (1) - (3) which he... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:70 HUME'S LETTER TO STEWART A Note on a Paper by D. C. Stove In a recent paper, D. C. Stove raises an historical problem. There exists a letter, written in 1754 by Hume to John Stewart, then Professor of Natural Philosophy at Edinburgh, in which the following words occur:. „. J never asserted so absurd a Proposition, as that any thing might arise without a Cause: (...) I only maintained, that our Certainty of the Falsehood of that Proposition proceeded neither from Intuition nor Demonstration; but from another Source. Some commentators, most notably Norman Kemp-Smith, take this as telling strongly in favour of a non-sceptical reading of Hume. Stove undertakes to show beyond reasonable doubt that the claim made in the letter is in blatant contradiction with central theses of Hume's published philosophy, so that it has to be regarded as useless as evidence for the interpretation of the latter. There is a mystery as to how Hume came to say something so clearly false about what he himself had written; Stove offers certain conjectures, none of which he finds wholly satisfactory. As the conclusion of the first, exegetical, part of his article, Stove advances the thesis that Hume held the falsity of the Causal Principle to be possible in at least three senses of "possible". These senses he specifies accurately, but doesn't wish to rest anything on the detail of his specification of the third; it is important only that it be stronger than either of the preceding two. This done, he takes a look at the letter to Stewart, and says, with reference to the first part of the 71 passage quoted above: That something might begin to exist without a cause, is evidently equivalent to the proposition that it is possib Ie for something to begin to exist without a cause. That, in turn, is evidently equivalent to the proposition that the falsity of the Causal Principle is possible. (Stove's o underlining). It follows that what Hume says in the letter is simply false. It could be true only if the "might" referred to some sense of possibility even weaker than the weakest of Stove's three senses. But since that is mere self-consistency, there is no such sense. Now the argument to the contradiction relies on reading "might" as "it is possible", in some sense of those words. Stove says, as we have seen, that they are "evidently equivalent", but the equivalence is certainly not evident, and it may well be asked whether it exists at all. After all, there are English constructions with "might" which don't have modal force: "Do you think something might have happened to them without our knowing about it?" The hearer is not, of course, being asked whether it- is possible that something should have happened without their knowledge; he is being asked for his opinion on whether something actually has so happened. "Most unlikely", would be a perfectly natural and acceptable response. Again : "ïou stay here, to take care of any problem that might arise before we get back". Obviously it is not intended that the hearer should start taking precautions against all possibilities, only that he should cope with whatever actually arises, if anything. 72 This is quite normal modern usage, and I know no reason to think that it wasn't also norT.il usage in the 18th Century. Admittedly, it isn't modern philocophers ' usage - we would be very careful, in writing or; logical matters, not to use the word "might" unless it was definitely the modal proposition that we had in mind, but earlier times haven't always been so professional about their vocabulary. Certainly, if Hume, in the letter to Stewart, was denying that he had ever asserted the possibility of the falsehood of the Causal Principle it would be, as Stove shows, extremely hard to see what he could have been thinking of. But if what he meant could have been as well expressed by "I never asserted... that anything arises without a cause" then most of Stove's problems are over, for there is no 3 conflict with any of the theses (1) - (3) which he... (shrink)

Just about every theorist holds that vague terms are context-sensitive to some extent. What counts as ?tall?, ?rich?, and ?bald? depends on the ambient comparison class, paradigm cases, and/or the like. To take a stock example, a given person might be tall with respect to European entrepreneurs and downright short with respect to professional basketball players. It is also generally agreed that vagueness remains even after comparison class, paradigm cases, etc. are fixed, and so this context sensitivity does not solve (...) the problems with vague terms. In this paper, I briefly sketch the main features of my broadly contextualist account of vagueness, that of the late Ruth Manor, and that of Agustín Rayo, showing how the three accounts relate to, and reinforce, each other, noting a seeming difference. A key item used to articulate my own view is David Lewis's notion of conversational score. This is used to track which borderline cases have been called in the course of a conversation. Manor alludes to Lewis's notion of accommodation, a key aspect of the kinematics of conversation, and Rayo invokes Stalnaker's notion of common ground. I'll show how the conversational score could be employed to develop and extend their views, showing how vague terms, as they construe them, are (or can be) deployed in conversation, consistent with both the underlying indeterminacy of the terms and normal communicative goals. To help develop all three views further, I invoke Craige Roberts's notion of Retrievability, a tool developed to show how definites, such as definite descriptions, singular pronouns, and proper names, are deployed in conversation, in a Lewis-style scorekeeping framework. This, I think, is exactly the right way to understand conversations in what Manor calls non-sorities situations and, to invoke my own view, in sorites situations as well. (shrink)

A review of Robert. B. Stewart's edited volume concerning a discussion between William Dembski and Michael Ruse. Further contributions are included from William Lane Craig and others.

The counterfactual mental state of negligent criminal activity invites skepticism from those who see mental states as essential to responsibility. Here, I offer a revision of the mental state of criminal negligence, one where the mental state at issue is actual and not merely counterfactual. This revision dissolves the worry raised by the skeptic and helps to explain negligence’s comparatively reduced culpability.

In On What Matters, Derek Parfit enters the debate between actualists and possibilists. This debate concerns mere possibilia, possible but non-actual things such as golden mountains and talking donkeys. Roughly, possibilism says that there are such things, and actualism says that there are not. Parfit not only argues for possibilism but also argues that some self-proclaimed actualists are, in fact, unwitting possibilists. -/- I argue that although Parfit’s arguments do not fully succeed, they do highlight a tension within the frameworks (...) of many actualists. Many actualists conscript abstract objects into the role of "possible worlds" to avoid quantifying over mere possibilia. But, in doing so, actualists must quantify over mere possibilia anyway. When we alleviate this tension, a Parfit-friendly form of actualism arguably remains. This form of actualism says that while everything that exists is actual, it is also true in some sense that there are mere possibilia. (shrink)

The use of computers and the role of women in radio astronomy and X-ray crystallography research at the Cavendish Laboratory between 1949 and 1975 have been investigated. We recorded examples of when computers were used, what they were used for and who used them from hundreds of papers published during these years. The use of the EDSAC, EDSAC 2 and TITAN computers was found to increase considerably over this time-scale and they were used for a diverse range of applications. The (...) majority of references to computer operators and programmers referred to women, 57% for astronomy and 62% for crystallography, in contrast to a very small proportion, 4% and 13% respectively, of female authors of papers. (shrink)

Guthrie contends that religion can best be understood as systematic anthropomorphism - the attribution of human characteristics to nonhuman things and events. Religion, he says, consists of seeing the world as human like. He offers a fascinating array of examples to show how this strategy pervades secular life and how it characterizes religious experience.

Various strands of religious thought distinguish veneration from worship. According to these traditions, believers ought to worship God alone. To worship anything else, they say, is idolatry. And yet many of these same believers also claim to venerate—but not worship—saints, angels, images, relics, tombs, and even each other. But what's the difference? Tim Bayne and Yujin Nagasawa (2006: 302) are correct that “it seems to be extremely difficult to distinguish veneration from worship.” Many have argued throughout history that veneration collapses (...) into worship and that those who venerate saints or icons are guilty of idolatry. In this essay, we distinguish worship from veneration in two stages. First, we give a formal account of their difference. Drawing from St. John of Damascus (c. 675-749 AD), we argue that worship is a determinate of the determinable veneration. Second, we give more substantive accounts of both that explain their differences and similarities. Drawing again from St John, we argue that acts of veneration and worship signify subordination. Their difference, however, lies in the fact that worship alone requires absolute subordination. (shrink)

It describes and explains the patient-centered model examining and evaluating qualitative and quantitative research. It comprehensively covers the evolution and the six interactive components of the patient-centered clinical method, taking the reader through the relationships between the patient and doctor and the patient and clinician. All the editors are professors in the Department of Family Medicine at the University of Western Ontario, London, Canada.

A framework for pragmatic analysis is proposed which treats discourse as a game, with context as a scoreboard organized around the questions under discussion by the interlocutors. The framework is intended to be coordinated with a dynamic compositional semantics. Accordingly, the context of utterance is modeled as a tuple of different types of information, and the questions therein — modeled, as is usual in formal semantics, as alternative sets of propositions — constrain the felicitous flow of discourse. A requirement of (...) Relevance is satisfied by an utterance (whether an assertion, a question or a suggestion) iff it addresses the question under discussion. Finally, it is argued that the prosodic focus of an utterance canonically serves to reflect the question under discussion (at least in English), placing additional constraints on felicity in context. (shrink)

We can enrich the explanation of how we should treat kid wrongdoers by recognizing that it matters who does the blaming and punishing. That we should think about who does the blaming and punishing is perhaps unsurprising, but it is nonetheless often underappreciated. Here, I offer two lessons about blame and punishment by thinking about who judges kids. First, the right account of moral and legal responsibility should allow that kids may rightly blame each other, and I argue that we (...) can best accommodate this by relativizing the threshold of competence needed for responsibility. Second, although each kid is an individual and, as a result, the implications of immaturity vary signifi- cantly from kid to kid, we should give kids a break as kids, that is, based on our categorizing them as kids. That we should and do categorize in that way reflects the nature of the criminal justice system as an institution and the nature of us as social beings. (shrink)

The standard philosophical project of analysing the concept of knowledge has radical defects in its arbitrary restriction of the subject matter, and its risky theoretical presuppositions. Edward Craig suggests a more illuminating approach, akin to the `state of nature' method found in political theory, which builds up the concept from a hypothesis about the social function of knowledge and the needs it fulfils. Light is thrown on much that philosophers have written about knowledge, about its analysis and the obstacles (...) to its analysis, and on the debate over scepticism. It becomes apparent why many languages not only have such constructions as `knows whether' and `knows that', but also have equivalents of `knows how to' and `know' followed by a direct object. Thus the inquiry is both broadened in scope and made theoretically less fragile. (shrink)

Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.

How can we talk meaningfully about the past if it does not exist to be talked about? What gives time its direction? Is time travel possible? This defence of presentism - the view that only the present exists - makes an original contribution to a fast growing and exciting debate.

This paper attempts to show how Adorno’s thought can illuminate our reflections on the future of work. It does so by situating Adorno’s conception of genuine activity in relation to his negativist critical epistemology and his subtle account of the distinction between true and false needs. What emerges is an understanding of work that can guide our aspirations for the future of work, and one we illustrate via discussions of creative work and care work. These are types of work which (...) cater to persistent human needs, albeit ones that are distorted under present social conditions. Adorno’s thought helps us to understand why this is the case. (shrink)

Many want to know what bitcoin is and how it works. But bitcoin is as complex as it is controversial, and relatively few have the technical background to understand it. In this paper, I offer an accessible on-ramp for understanding bitcoin in the form of a model. My model reveals both what bitcoin is and how it works. More specifically, it reveals that bitcoin is a fictional substance in a massively coauthored story on a network that automates and distributes jobs (...) normally entrusted to centralized publishing institutions. My model therefore falsifies a popular view according to which each bitcoin is a chunk of code. (shrink)

Stewart Shapiro's aim in Vagueness in Context is to develop both a philosophical and a formal, model-theoretic account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases. A person can be tall with respect to male accountants and not tall with respect to professional basketball players. The main (...) feature of Shapiro's account is that the extensions of vague terms also vary in the course of a conversation, even after the external contextual features, such as the comparison class, are fixed. A central thesis is that in some cases, a competent speaker of the language can go either way in the borderline area of a vague predicate without sinning against the meaning of the words and the non-linguistic facts. Shapiro calls this open texture, borrowing the term from Friedrich Waismann.The formal model theory has a similar structure to the supervaluationist approach, employing the notion of a sharpening of a base interpretation. In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity. The ultimate goal of the technical aspects of the work is to delimit a plausible notion of logical consequence, and to explore what happens with the sorites paradox.Later chapters deal with what passes for higher-order vagueness - vagueness in the notions of 'determinacy' and 'borderline' - and with vague singular terms, or objects. In each case, the philosophical picture is developed by extending and modifying the original account. This is followed with modifications to the model theory and the central meta-theorems.As Shapiro sees it, vagueness is a linguistic phenomenon, due to the kinds of languages that humans speak. But vagueness is also due to the world we find ourselves in, as we try to communicate features of it to each other. Vagueness is also due to the kinds of beings we are. There is no need to blame the phenomenon on any one of those aspects. (shrink)

How can we talk meaningfully about the past if it does not exist to be talked about? What gives time its direction? Is time travel possible? This defence of presentism - the view that only the present exists - makes an original contribution to a fast growing and exciting debate.

Many contemporary theorists charge that naïve realists are incapable of accounting for illusions. Various sophisticated proposals have been ventured to meet this charge. Here, we take a different approach and dispute whether the naïve realist owes any distinctive account of illusion. To this end, we begin with a simple, naïve account of veridical perception. We then examine the case that this account cannot be extended to illusions. By reconstructing an explicit version of this argument, we show that it depends critically (...) on the contention that perceptual experience is diaphanous, or more minimally and precisely, that there can be no difference in phenomenal properties between two experiences without a difference in the scenes presented in those experiences. Finding no good reason to accept this claim, we develop and defend a simple, naïve account of both veridical perception and illusion, here dubbed Simple, Austere Naïve Realism. (shrink)

The dominant response to this problem of the criterion focuses on the alleged requirement that we need to know a belief source is reliable in order for us to acquire knowledge by that source. Let us call this requirement, “The KR principle”.

Justification for psychiatric paternalism is most easily established where mental illness renders the person mentally incompetent, depriving him of the capacity for rational agency and for autonomy, hence undermining the basis for liberal rights against paternalism. But some philosophers, and no doubt some doctors, have been deeply concerned by the inadequacy of the concept of mental incompetence to encapsulate some apparently appealing cases for psychiatric paternalism. We ought to view mental incompetence as just one subset of a broader justification for (...) psychiatric paternalism. The very basis of liberal limitations on psychiatric paternalism, whether described in terms of rights to autonomy or as respect for differences in values and lifestyles, presupposes a sense of moral persistence, and hence some sufficiently persistent self. Paternalistic intervention is warranted when we are unable to govern our lives in a manner consistent with the goals and values that comprise that ‘self’. One way that can occur is when we lack the mental capacities required for autonomy, such that we are unable to interpret and interact with our environment in order to meaningfully pursue our goals, i.e. mental incompetence. But it can also occur when we are subject to impositions that alter our goals without altering our capacity to pursue them — i.e. when it is our ‘self’ that is impaired rather than our competence. (shrink)

In order to determine whether a particular course of conduct is ethically permissible it is important to have a concept of what it means to be harmed. The dominant theory of harm is the counterfactual account, most famously proposed by Joel Feinberg. This determines whether harm is caused by comparing what actually happened in a given situation with the ‘counterfacts’ i.e. what would have occurred had the putatively harmful conduct not taken place. If a person's interests are worse off than (...) they otherwise would have been, then a person will be harmed. This definition has recently faced challenges from bioethicists such as John Harris, Guy Kahane and Julian Savulescu who, believing it to be severely flawed, have proposed their own alternative theories of the concept. In this article I will demonstrate that the shortcomings Harris, Kahane and Savulescu believe are present in Feinberg's theory are illusory and that it is their own accounts of harm that are fraught with logical errors. I maintain that the arguments presented to refute Feinberg's theory not only fail to achieve this goal and can be accommodated within the counterfactual account but that they actually undermine the theories presented by their respective authors. The final conclusion will be that these challenges are misconceived and fail to displace the counterfactual theory. (shrink)

In the early twentieth century an apparently obscure philosophical debate took place between F. H. Bradley and Bertrand Russell. The historical outcome was momentous: the demise of the movement known as British Idealism, and its eventual replacement by the various forms of analytic philosophy. Since then, a conception of this debate and its rights and wrongs has become entrenched in English-language philosophy. Stewart Candlish examines afresh the events of this formative period in twentieth-century thought and comes to some surprising (...) conclusions. (shrink)

Stewart Shapiro's aim in Vagueness in Context is to develop both a philosophical and a formal, model-theoretic account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases. A person can be tall with respect to male accountants and not tall with respect to professionalbasketball players. The main feature (...) of Shapiro's account is that the extensions of vague terms also vary in the course of a conversation, even after the external contextual features, such as the comparison class, are fixed. A central thesis is that in some cases, a competent speaker ofthe language can go either way in the borderline area of a vague predicate without sinning against the meaning of the words and the non-linguistic facts. Shapiro calls this open texture, borrowing the term from Friedrich Waismann.The formal model theory has a similar structure to the supervaluationist approach, employing the notion of a sharpening of a base interpretation. In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity. The ultimate goal of the technical aspects of the work is to delimit a plausible notion of logical consequence, and to explore what happens with the sorites paradox.Later chapters deal with what passes for higher-order vagueness - vagueness in the notions of 'determinacy' and 'borderline' - and with vague singular terms, or objects. In each case, the philosophical picture is developed by extending and modifying the original account. This is followed with modifications to the model theory and the central meta-theorems.As Shapiro sees it, vagueness is a linguistic phenomenon, due to the kinds of languages that humans speak. But vagueness is also due to the world we find ourselves in, as we try to communicate features of it to each other. Vagueness is also due to the kinds of beings we are. There is no need to blame the phenomenon on any one of those aspects. (shrink)