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.

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.

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.

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)

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)

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.

Timothy Williamson has fruitfully exploited formal resources to shed considerable light on the nature of knowledge. In the paper under examination, Williamson turns his attention to Gettier cases, showing how they can be motivated formally. At the same time, he disparages the kind of justification he thinks gives rise to these cases. He favors instead his own notion of justification for which Gettier cases cannot arise. We take issue both with his disparagement of the kind of justification that figures in (...) Gettier cases and the specifics of the formal motivation. (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)

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.

Are human beings purely material creatures, or is there something else to them, an immaterial part that does some (or all) of the thinking, and might even be able to outlive the death of the body? This book is about how a series of seventeenth-century philosophers tried to answer that question. It begins by looking at the views of Thomas Hobbes, who developed a thoroughly materialist account of the human mind, and later of God as well.

This paper uses neo-Fregean-style abstraction principles to develop the integers from the natural numbers (assuming Hume’s principle), the rational numbers from the integers, and the real numbers from the rationals. The first two are first-order abstractions that treat pairs of numbers: (DIF) INT(a,b)=INT(c,d) ≡ (a+d)=(b+c). (QUOT) Q(m,n)=Q(p,q) ≡ (n=0 & q=0) ∨ (n≠0 & q≠0 & m⋅q=n⋅p). The development of the real numbers is an adaption of the Dedekind program involving “cuts” of rational numbers. Let P be a property (of (...) rational numbers) and r a rational number. Say that r is an upper bound of P, written P≤r, if for any rational number s, if Ps then either s<r or s=r. In other words, P≤r if r is greater than or equal to any rational number that P applies to. Consider the Cut Abstraction Principle: (CP) ∀P∀Q(C(P)=C(Q) ≡ ∀r(P≤r ≡ Q≤r)). In other words, the cut of P is identical to the cut of Q if and only if P and Q share all of their upper bounds. The axioms of second-order real analysis can be derived from (CP), just as the axioms of second-order Peano arithmetic can be derived from Hume’s principle. The paper raises some of the philosophical issues connected with the neo-Fregean program, using the above abstraction principles as case studies. (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.

The traditional view in epistemology is that we must distinguish between being rational and being right (that is also, by the way, the traditional view about practical rationality). In his paper in this volume, Williamson proposes an alternative view according to which only beliefs that amount to knowledge are rational (and, thus, no false belief is rational). It is healthy to challenge tradition, in philosophy as much as elsewhere. But, in this instance, we think that tradition has it right. In (...) this paper we defend our version of the traditional view and argue against Williamson’s alternative. (shrink)

Draft for the Oxford Handbook of Margaret Cavendish (edited by Julie Crawford with Jacqueline Broad). -/- This chapter looks at Margaret Cavendish's treatment of the supernatural, beginning by asking how she distinguishes the natural from the supernatural, and then by examining her treatment of a series of alleged supernatural beings: fairies, ghosts, witches, the human supernatural soul, angels, and God. Throughout, it argues that Cavendish's approach to the supernatural is often similar to Thomas Hobbes's.

ABSTRACTExperts use their superior skills and understanding to mediate between evidence in some domain and non-experts. But how should we understand the proper relationship between experts and non-experts? In this paper, I present two ways of conceiving experts’ mediating role from the perspective of non-experts: the Authority View and the Advisor View. Jennifer Lackey has criticized the Authority View and defended the Advisor View. I defend an account of epistemic authority that avoids her criticisms while arguing the Advisor View lacks (...) the advantages she claims. Ultimately, I present a hybrid approach according to which whether we should treat experts as authorities or advisors varies depending upon the presence of certain epistemic and moral concerns. (shrink)

In this paper, I discuss how Nietzsche’s critique of nihilism concerns the complicity between Christian morality and modern atheism. I unpack in what sense Schopenhauer’s ascetic denial of the will signifies a return to nothingness, what he calls the nihil negativum. I argue that Nietzsche’s formulation of nihilism specifically targets Schopenhauer’s pessimism as the culmination of the Western metaphysical tradition, the crucial stage of its intellectual history in which the scientific pursuit of truth finally unveils the ascetic will to nothingness (...) that motivates it. I contend that Nietzsche’s critique of Schopenhauer anticipates current scholarly debates around the significance of the nihil negativum and offers a compelling objection against contemporary proponents of philosophical nihilism such as Eugene Thacker and Ray Brassier. (shrink)

Since virtually every mathematical theory can be interpreted in set theory, the latter is a foundation for mathematics. Whether set theory, as opposed to any of its rivals, is the right foundation for mathematics depends on what a foundation is for. One purpose is philosophical, to provide the metaphysical basis for mathematics. Another is epistemic, to provide the basis of all mathematical knowledge. Another is to serve mathematics, by lending insight into the various fields. Another is to provide an arena (...) for exploring relations and interactions between mathematical fields, their relative strengths, etc. Given the different goals, there is little point to determining a single foundation for all of mathematics. (shrink)

Second-language learners rarely arrive at native proficiency in a number of linguistic domains, including morphological and syntactic processing. Previous approaches to understanding the different outcomes of first- versus second-language learning have focused on cognitive and neural factors. In contrast, we explore the possibility that children and adults may rely on different linguistic units throughout the course of language learning, with specific focus on the granularity of those units. Following recent psycholinguistic evidence for the role of multiword chunks in online language (...) processing, we explore the hypothesis that children rely more heavily on multiword units in language learning than do adults learning a second language. To this end, we take an initial step toward using large-scale, corpus-based computational modeling as a tool for exploring the granularity of speakers' linguistic units. Employing a computational model of language learning, the Chunk-Based Learner, we compare the usefulness of chunk-based knowledge in accounting for the speech of second-language learners versus children and adults speaking their first language. Our findings suggest that while multiword units are likely to play a role in second-language learning, adults may learn less useful chunks, rely on them to a lesser extent, and arrive at them through different means than children learning a first language. (shrink)

To this circumstance is probably to be ascribed the little progress, which has hitherto been made in the PHILOSOPHY OF THE HUMAN MIND ; a, science, ...

cannot understand the language.”[1] This is not intended to cover (easily imaginable) cases of recording one's experiences in a personal code, for such a code, however obscure in fact, could in principle be deciphered. What Wittgenstein had in mind is a language conceived as necessarily comprehensible only to its single originator because the things which define its vocabulary are necessarily inaccessible to others.

An option for Business Ethics course offered in business schools or in philosophy departments, this text balances the perspectives of business and philosophy in the cases and readings. The focus of this text is on the benefits of good corporate conduct to the companies who practice good business ethics.

The essays collected in 'The Hegel Myths and Legends' serve the function of disabusing students and nonspecialists of these misconceptions by exposing these myths for what they are.

Merging of opinions results underwrite Bayesian rejoinders to complaints about the subjective nature of personal probability. Such results establish that sufficiently similar priors achieve consensus in the long run when fed the same increasing stream of evidence. Initial subjectivity, the line goes, is of mere transient significance, giving way to intersubjective agreement eventually. Here, we establish a merging result for sets of probability measures that are updated by Jeffrey conditioning. This generalizes a number of different merging results in the literature. (...) We also show that such sets converge to a shared, maximally informed opinion. Convergence to a maximally informed opinion is a (weak) Jeffrey conditioning analogue of Bayesian “convergence to the truth” for conditional probabilities. Finally, we demonstrate the philosophical significance of our study by detailing applications to the topics of dynamic coherence, imprecise probabilities, and probabilistic opinion pooling. (shrink)

Language was central to Hobbes's understanding of human beings and their mental abilities, and criticism of other philosophers' uses of language became a favorite critical tool for him. This paper connects Hobbes's theories about language to his criticisms of others' language, examining Hobbes's theories of propositions and truth, and how they relate to his claims that various sorts of proposition are absurd. It considers whether Hobbes in fact means anything more by 'absurd' than 'false'. And it pays particular attention to (...) Hobbes's categorization of causes of absurdity and of types of incoherent proposition, arguing that Hobbes's approach is only loosely related to later discussions of category mistakes. (shrink)

The answers to the questions in the title depend on the kind of pluralism one is talking about. We will focus here on our own views. The purpose of this article is to trace out some possible connections between these kinds of pluralism. We show how each of them might bear on the other, depending on how certain open questions are resolved.

In the _True Intellectual System_, Cudworth attacks types of atheist position—atomic atheism, hylozoic atheism, etc. He generally uses ancient examples to illustrate those types, but also criticizes some of his contemporaries. We can identify direct criticisms of contemporaries by finding quotations, paraphrases, and accounts of their views in the text. My primary question in this paper is, 'how much of the _True Intellectual System_ is directly about or aimed at Spinoza?' My ultimate answer, contrary to some prominent voices in the (...) existing literature, is 'not very much at all'. (shrink)

The is an old question over whether there is a substantial disagreement between advocates of different logics, as they simply attach different meanings to the crucial logical terminology. The purpose of this article is to revisit this old question in light a pluralism/relativism that regards the various logics as equally legitimate, in their own contexts. We thereby address the vexed notion of translation, as it occurs between mathematical theories. We articulate and defend a thesis that the notion of “same meaning” (...) is itself context-sensitive, depending on the purposes of a given conversation. (shrink)

The s, p, d and f blocks of the elements, as delimited by Charles Janet in 1928, can be represented as parallel slices of a regular tetrahedron. They also fit neatly on to the surface of a sphere. The reasons for this are discussed and the possible objections examined. An attempt is made to see whether there are philosophical implications of this unexpected geometrical regularity. A new tetrahedral design in transparent plastic is presented.

The purpose of this edited book is to provide new insight into the understanding of ethics as they relate to organization practice and managerial behavior in todays economy. It provides an overview and critique of ethics as it relates to key contemporary challenges and issues for organizations these include globalization, sustainability, consumerism, neo-liberalism, corporate collapses, leadership and corporate regulation. The book is organized around the core question: What are the ethics of organizing in todays institutional environment and what does this (...) mean for the practice of management and the organization of business? In responding to this question, the contributors examine ethics as it is deeply embedded in the everyday practice of management. Interdisciplinary contributions from sociology, philosophy, management, organization studies, and public administration provide unique perspectives, while case studies and examples drawn from practice illustrate the challenges and dilemmas faced in practice. Each chapter has a brief overview and introduction written by the editors which summarize the main points of each chapter in terms of their contributions to the overall aims of the book as well as drawing connections between the different chapters. (shrink)