SummaryThe germs of future development, contained in Aristotle's logical works, are indicated, and their influence on the later evolution of logic is explained.The history of symbolic logic since Boole's Mathematical analysis and De Morgan's Formal logic, both of which were published in 1847, is divided into four approximately subsequent phases, viz.:1. algebra of logic; this phase is characterized by Boole's work;2. logical foundation of mathematics; this phase is characterized by Frege's, Peano's and Russell's work, by the discovery of the antonomies (...) of logic and set theory, by the Couturat‐Poincaré debate and by the rise of Brouwer's intuitionism;3. intuitive metamathematics, concentrating in Hilbert's attempts towards a consistency proof for classical analysis; the discovery of Gödel's theorem necessitated a change of policy;4. axiomatic methodology, deriving from Hilbert's metamathematics and culminating so far in Tarski's semantics. — E. W. B. (shrink)

Is the restricted, consistent, version of the T-scheme sufficient for an ‘implicit definition’ of truth? In a sense, the answer is yes (Haack 1978 , Quine 1953 ). Section 4 of Ketland 1999 mentions this but gives a result saying that the T-scheme does not implicitly define truth in the stronger sense relevant for Beth’s Definability Theorem. This insinuates that the T-scheme fares worse than the compositional truth theory as an implicit definition. However, the insinuation is mistaken. For, as (...) Bays rightly points out, the result given extends to the compositional truth theory also. So, as regards implicit definability, both kinds of truth theory are equivalent. Some further discussion of this topic is mentioned (Gupta 2008 , Ketland 2003 , McGee 1991 ), all in agreement with Bays’s analysis. (shrink)

In 1999, Jeffrey Ketland published a paper which posed a series of technical problems for deflationary theories of truth. Ketland argued that deflationism is incompatible with standard mathematical formalizations of truth, and he claimed that alternate deflationary formalizations are unable to explain some central uses of the truth predicate in mathematics. He also used Beth’s definability theorem to argue that, contrary to deflationists’ claims, the T-schema cannot provide an ‘implicit definition’ of truth. In this article, I want to challenge (...) this final argument. Whatever other faults deflationism may have, the T-schema does provide an implicit definition of the truth predicate. Or so, at any rate, I shall argue. (shrink)

König, D. [1926. ‘Sur les correspondances multivoques des ensembles’, Fundamenta Mathematica, 8, 114–34] includes a result subsequently called König's Infinity Lemma. Konig, D. [1927. ‘Über eine Schlussweise aus dem Endlichen ins Unendliche’, Acta Litterarum ac Scientiarum, Szeged, 3, 121–30] includes a graph theoretic formulation: an infinite, locally finite and connected graph includes an infinite path. Contemporary applications of the infinity lemma in logic frequently refer to a consequence of the infinity lemma: an infinite, locally finite tree with a root has (...) a infinite branch. This tree lemma can be traced to [Beth, E. W. 1955. ‘Semantic entailment and formal derivability’, Mededelingen der Kon. Ned. Akad. v. Wet., new series 18, 13, 309–42]. It is argued that Beth independently discovered the tree lemma in the early 1950s and that it was later recognized among logicians that Beth's result was a consequence of the infinity lemma. The equivalence of these lemmas is an easy consequence of a well known result in graph theory: every connected, locally finite graph has among its partial subgraphs a spanning tree. (shrink)

This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows (...) for the first book-length treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line. In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle and orthogonal polynomials on the real line, Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC. (shrink)

Reduced Environmental Stimulation Therapy (REST) alters the balance of sensory input to the nervous system by systematically attenuating sensory signals from visual, auditory, thermal, tactile, vestibular, and proprioceptive channels. Previous research from our group has shown that REST via floatation acutely reduces anxiety and blood pressure while simultaneously heightening interoceptive awareness in clinically anxious populations. Anorexia nervosa (AN) is an eating disorder characterized by elevated anxiety, distorted body representation, and abnormal interoception, raising the question of whether REST might positively impact (...) these symptoms. However, this approach has never been studied in eating disorders and it is unknown whether exposure to REST might worsen AN symptoms. To examine these possibilities we conducted an open-label study to investigate the safety and tolerability of REST in AN. We also explored the impact of REST on affective symptoms, body image disturbance, and interoception. Twenty-one partially weight-restored AN outpatients completed a protocol involving four sequential sessions of REST: reclining in a zero-gravity chair, floating in an open pool, and two sessions of floating in an enclosed pool. All sessions were 90 minutes, approximately one week apart. We measured orthostatic blood pressure before and immediately after each session (primary outcome), in addition to collecting blood pressure readings every 10 minutes during the session using a wireless waterproof system as a secondary outcome measure. Each participant's affective state, awareness of interoceptive sensations, and body image was assessed before and after every session (exploratory outcomes). There was no evidence of orthostatic hypotension following floating, and no adverse events (primary outcome). Secondary analyses revealed that REST induced statistically significant reductions in blood pressure, anxiety and negative affect, heightened awareness of cardiorespiratory but not gastrointestinal sensations, and reduced body image dissatisfaction. The findings from this initial trial suggest that individuals with AN can safely tolerate the physical effects of REST via floatation. Future randomized controlled trials will need to investigate whether these initial observations of improved anxiety, interoception, and body image disturbance can be effectively extended to acutely ill AN populations. (shrink)

According to accounts of the Passion, Christ cries out from the cross, “My God, my God, why have you forsaken me?” The cry, I argue, manifests that Christ lacks a belief that God is with him. Given the standard view of faith—belief that p is required for faith that p—it would follow that Christ lost his faith that God is with him just before he died. In this paper, I challenge the standard view by looking at the cognitive requirement of (...) faith. Although faith that p requires some positive cognitive orientation toward p, that orientation need not be belief. I show that reliance is an alternative stance that fulfills the cognitive requirement of faith. Reliance aims at providing sensible guidance for action that is in accord with one’s values/ends. Thinking of the cognitive component of Christ’s faith in terms of reliance makes sense of the doubt manifested in his cry. (shrink)

The year is 1901. Two minor celebrities from opposite corners of the globe share an evening meal in Chicago. Both are politically left-leaning, both are evolutionists of a sort, both are concerned with the plight of the poor in the face of the escalation of the Industrial Revolution. The Russian man has been giving a series of lectures to the people of Chicago; he is staying at the American woman's settlement house-Hull House. They are Jane Addams, Chicago's activist social worker (...) and Petr Kropotkin, Russian nobleman by birth, anarchist in politics, and naturalist by inclination. Each awaits publication of their first full-length book concerning politics and moral development: Democracy and Social Ethics (1902) on .. (shrink)

_Wittgenstein's Art of Investigation_ is one of the first to focus on and provide an original and detailed analysis of Wittgenstein's grammatical investigations. Beth Sarkey offers us new insight into the historical context and influences on method which will help students understand the intricacies and depth of his work.

_Wittgenstein's Art of Investigation_ is one of the first to focus on and provide an original and detailed analysis of Wittgenstein's grammatical investigations. Beth Sarkey offers us new insight into the historical context and influences on method which will help students understand the intricacies and depth of his work.

This article examines literature from cultural anthropology for insights into ethics. It particularly addresses the moral issue of justly understanding those people different from oneself. Clifford Geertz, pragmatist as well as anthropologist, draws upon the rhetorical theory of Kenneth Burke in his 1988 book Works and Lives. Just this sort of cross-disciplinary borrowing offers resources for understanding what were once religiously-based ethics in a humanistic context. The rhetorical style of various cultural anthropologists serves to inform the rhetorical forms of appeal (...) of theistic and non- theistic ethics. (shrink)

This chapter first distinguishes between originality and creativity. True originality is rare, whether in art, science, or LEGO, because to be truly original means to have done something that no one has ever done before, and that no one could have anticipated. Most LEGO creations will not meet that condition, for with the exception of serious hobbyists who undertake massive builds, most players who make original creations are making creations that are commonplace. Painting or remolding or placing stickers on the (...) bricks counts against the spirit of LEGO creation. The chapter then discusses The LEGO Movie embodies the paradox that presents three conflicting models of creative LEGO play, illustrated by the Master Builders, Finn's father, and Emmet. The movie's creators were deliberately playing around with conflicting popular conceptions of creativity: creativity as madness, creativity as thinking outside the box, and creativity as vision. (shrink)

Baruch Spinoza was born in Amsterdam during a period of unprecedented scientific, artistic, and intellectual discovery. Upon its release, Spinoza’s Ethics was banned; today it is the quintessential example of philosophical method. Although acknowledged as difficult, the book is widely taught in philosophy, literature, history, and politics. This introduction is designed to be read side by side with Spinoza's work. As a guide to the style, vocabulary, and arguments of the Ethics, it offers a range of interpretive possibilities to prepare (...) students to become conversant with Spinoza's philosophical method and his challenge to conventional thinking. (shrink)

Intellectual historian Andrew Jewett sets an enormous task for himself: to trace the history and context of science and values relations over the course of some hundred-odd years of U.S. history. He does this to further an argument that science was once explicitly connected to the study of human values, and that the story that explains how science became value neutral is a contingent one. It could have happened differently, he argues, and it should have. Furthermore, because that history is (...) contingent, we are free to still change our academic habits and to allow the social sciences to be sciences alongside the natural and physical sciences. The reason this would be worth doing, according to Jewett, is.. (shrink)

There is increasing interest in artifacts among philosophers. The leading edge is the metaphysics of artifacts and artifact kinds. However, an important question has been neglected. What is the ontological status of the category ‘artifact’ itself? Dan Sperber (2007) argues against its theoretical integrity for the purposes of naturalistic social sciences. In Section 2, I lay out Sperber’s argument, which is based on the observed continuum between natural objects and artifacts. I also review the implicit support for this continuum argument (...) in the philosophical literature on artifacts. In Section 3, I diagnose the fatal weakness affecting continuum-based arguments about categories. They fail to take into account recent thinking about classification in philosophy of science, which has been forced to accommodate continua in biology. In Section 4, I focus specifically on the species problem in philosophy of biology, and on pluralism about species concepts as a response to it. I then identify an analogous artifact problem, and argue that pluralism about artifact concepts is an appropriate and defensible response here as well. Finally, in Section 5, I show that just as species pluralism leads to skepticism about the species category, so artifact pluralism leads to skepticism about the artifact category. I thus arrive at Sperber’s conclusion by an alternate route that does not run afoul of the weakness affecting continuum-based arguments about categories. (shrink)

That women tend to see harassment where men see harmless fun or normal gendered interaction is one of the more robust findings in sexual harassment research. Using in-depth interviews with employed men and women, this article argues that these differences may be partially explained by the performative requirements of masculinity. The ambiguous practice of “girl watching” is centered, and the production of its meaning analyzed. The data suggest that men's refusal to see their behavior as harassing may be partially explained (...) through the objectification and attenuated empathy that the production of masculine identities may require. Thus, some forms of harassment and their interpretations may more accurately be seen as acts of ignoring than states of ignorance. Implications for anti-sexual harassment policies and training are explored. (shrink)

Tool use rivals language as an important domain of cognitive phenomena, and so as a source of insight into the nature of cognition in general. But the favoured current definition of tool use is inadequate because it does not carve the phenomena of interest at the joints. Heidegger's notion of equipment provides a more adequate theoretical framework. But Heidegger's account leads directly to a non-individualist view of the nature of cognition. Thus non-individualism is supported by concrete considerations about the nature (...) of tools and tool use. (shrink)

ABSTRACT Land is essential to actually built utopias. Literature regarding built utopias pays next to no attention to the land under them or how it was obtained. Currently Canada's national conversation increasingly pivots around colonization by Europeans and the still unresolved takeover of lands of long-resident Indigenous peoples. The article's objective is to explore a present-centered approach to studying built utopias for its potential to explain how a Eurocentric conception of utopia was invested in the land. The approach draws on (...) James Holstun's 1987 study of Puritan utopias to analyze the circumstances utopists encountered contemporaneously with building and maintaining settlements. The test case of 7,000 Mennonite biblical pacifists left detailed information about how actualized utopia works. The expectation is that research from many such past concrete experiences could astutely and practically inform the next inevitably land-related utopian vision, which, it seems, will be ecologically inspired. (shrink)

This book is a study of Wittgenstein's descriptive, improvisational, and performative art of philosophical investigation. In addition to clarifying the nature of Wittgenstein's grammatical investigations, this study highlights several neglected aspects of his work: its humour and playfulness, its collaborative nature, and its emphasis on the imagination. These aspects often become distorted under the pressure of theory and argumentation, resulting in interpretations that equate grammatical investigation with confession, therapy, or a common sense view of the world. After presenting Wittgenstein's art (...) of investigation in part one, this study challenges these dominant and influential interpretations in part two. The volume examines Wittgenstein's mottos, forewords, and dedications. It looks at the art of his philosophical and grammatical investigations, linking it to drama and improvisation. The book discusses the complexity and subtlety of Wittgenstein's response to Augustine in the opening of the Investigations, and Wittgenstein's response to Moore's defence of common sense in On Certainty. The book also examines three kinds of therapeutic readings: those that compare Wittgenstein's philosophy to psychoanalysis, those that compare his philosophy to therapy generally, and those that describe philosophy itself as an illness or as the cause of illness. (shrink)

In the last decade, reading research has seen a paradigmatic shift. A new wave of computational models of orthographic processing that offer various forms of noisy position or context-sensitive coding have revolutionized the field of visual word recognition. The influx of such models stems mainly from consistent findings, coming mostly from European languages, regarding an apparent insensitivity of skilled readers to letter order. Underlying the current revolution is the theoretical assumption that the insensitivity of readers to letter order reflects the (...) special way in which the human brain encodes the position of letters in printed words. The present article discusses the theoretical shortcomings and misconceptions of this approach to visual word recognition. A systematic review of data obtained from a variety of languages demonstrates that letter-order insensitivity is neither a general property of the cognitive system nor a property of the brain in encoding letters. Rather, it is a variant and idiosyncratic characteristic of some languages, mostly European, reflecting a strategy of optimizing encoding resources, given the specific structure of words. Since the main goal of reading research is to develop theories that describe the fundamental and invariant phenomena of reading across orthographies, an alternative approach to model visual word recognition is offered. The dimensions of a possible universal model of reading, which outlines the common cognitive operations involved in orthographic processing in all writing systems, are discussed. (shrink)

This article examines, by way of a case study, a community where groundwater has been highly contaminated with nitrate and how that situation brings together matters of public policy, environmental justice, and emerging technology. The Mountain View community lies in an unincorporated area of Bernalillo County, New Mexico; the neighborhood is 77% Hispanic and is a pocket of poverty whose residents are considered at risk for environmental injustice. Groundwater nitrate contamination was discovered in the 1960s, but residents were merely encouraged (...) to dig deeper wells, until 1984 when most residents were put on nearby municipal water after a child was poisoned and hospitalized with methemoglobinemia, known as blue baby syndrome. In situ biodenitrification is an emerging technology that has been shown to completely remediate groundwater nitrate contamination after the injection of a food source for naturally occurring denitrifying bacteria; this technology is being considered for use in Mountain View. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Christian Ethics: A Very Short Introduction, and: Christian Ethics: A Brief History, and: Behaving in Public: How to Do Christian EthicsBeth K. HaileChristian Ethics: A Very Short Introduction D. Stephen Long Oxford: Oxford University Press, 2010. 144 pp. $11.95Christian Ethics: A Brief History Michael Banner West Sussex, UK: Wiley-Blackwell, 2009. 160 pp. $24.95Behaving in Public: How to Do Christian Ethics Nigel Biggar Grand Rapids, Mich.: Eerdmans, 2011. 142 (...) pp. $16.00In calling ethics “Christian,” the question of distinctiveness, or the normative force of theological claims, inevitably arises. Three new books explore what Christian ethics looks like if it is to take seriously its theological basis for engaging the world.Stephen D. Long, professor of systematic theology at Marquette University, attends to the difficulties in predicating “Christian” of “ethics,” yet he is concerned more with explaining how Christianity can be ethical rather than vice versa. His Christian Ethics: A Very Short Introduction opens with a quote from Christopher Hitchens and later dedicates almost an entire chapter to analyzing the failures of Christian ethics. From the Crusades to colonialism, the Galileo affair to slavery, Long provocatively asks whether modern ethics emerges as a result of the failure of Christian moral claims. While not sidestepping the difficulties in Christian history, Long is careful to note how this history is often distorted to serve the goals of contemporary secular politics, goals which he points out have resulted in the bloody failures of the twentieth century. Perhaps a renewed interest in Christian ethics, Long notes, is a result of the failures of secularism.Long manages to cover a surprising breadth of material in his brief book, from a sweeping historical overview of Christian theology to a final chapter on [End Page 195] the practical matters of sex, money, and political power. Long also summarizes some important theological differences among Christians that lead to practical disagreements about the nature of Christian ethics. His overview of the Catholic-Lutheran convergence on matters of faith and works is particularly helpful in establishing the theological basis for an ecumenical Christian ethics. This historical survey serves to illustrate that ethics is both an integral part of and a contradiction to Christianity. Still, argues Long, while Christianity may claim to be more than ethical, it may never claim to be less.While commendable in breadth, the genre of the “very short introduction” precludes depth and must necessarily omit important information. In his summary of Catholic ethics, for example, Long addresses nominalism and probabilism but omits the Catholic social tradition, a particularly glaring omission given his topic. In the end, the target audience is the educated and curious layperson, more suitable for a church group than a classroom, though this is reflective of the nature of “the very short introduction” series and does not indicate any limitation in Long’s skill as a scholar.In the spirit of brevity, Michael Banner, Fellow of Trinity College in Cambridge, offers Christian Ethics: A Brief History, which, like any brief history, paints with broad and admittedly selective strokes. The aim of this work is not to evaluate the normative value of Christian claims but rather to establish the ethical implications of Christian belief. Unlike Long, who directly addresses the ethical failures of the church, Banner is more apologetic. In clarifying the difficulties of writing a text such as this one, he observes that Christian history has not been guided by texts as much as by action. In this vein, Banner begins not chronologically but with the Rule of St. Benedict and its call to live in a relationship with God and neighbor characterized by love.Banner grounds the theoretical dimension of Christian ethics in this emphasis on practice. Given the way of life Christians are called to, what are its limitations and possibilities? Banner turns to Augustine’s notion of the weakness of the will and the human creature’s need for grace, which he then places in creative tension with Aquinas’s emphasis on the harmony between faith and reason. In somewhat breathtaking conciseness, Banner describes how the Scholastic emphasis on natural law, casuistry, and the categorizing of sins led to what he calls... (shrink)

In “Performance Philosophy — Staging a New Field,” Laura Cull approaches performance as a source of philosophical insight and philosophy as a species of performance. This calls for a radical transformation of philosophy and its practices. What form might this take? Wittgenstein’s later philosophy provides one example. The language games presented in the opening remarks of the Philosophical Investigations are meant to be played out. They involve improvisation based on general scenes, stock characters, and linguistic play. When enacted, they are (...) slapstick. As such, they offer a method of philosophical investigation in which clarity and insight are inherent in the performance itself. Wittgenstein’s language games were directly influenced by the subversive practices of Austrian commedia dell’arte and slapstick. By their very nature, they challenge the pretensions of philosophical explanation and theory. Unlike attempts to compare Wittgenstein’s philosophy to theatre, enacting language games is a form of philosophical performance. Andrew Lugg notes that recent attempts to compare Wittgenstein’s philosophy to theatre problematize the opening remarks of the Investigations. However, enacting language games as a form of philosophical performance makes what is hidden, in all of its simplicity and familiarity, obvious, striking, and engaging. (shrink)

The concept of übersichtliche Darstellung is of fundamental significance for Wittgenstein . Hacker translates übersichtliche Darstellung as ‘surveyable representation’ and equates it with the tabulation of grammar. He asks what surveyability means, whether examples can be found in Wittgenstein’s work, and why this method characterizes the form of account he gives. Ultimately, however, Hacker is unable to answer these questions and he attributes this failure to Wittgenstein. This paper argues that it is Hacker’s interpretation that fails, and presents an alternate (...) understanding of übersichtliche Darstellung ; one that enables us to answer Hacker’s questions in a manner consistent with Wittgenstein’s philosophical practices. Normal 0 false false false EN-US X-NONE X-NONE. (shrink)

Much of the work coming out of Women’s Studies spaces narrowly defines what it means to be a woman. Antagonizing White Feminism pushes back against this exclusive discourse by invoking intersectionality and centering the experiences of Trans Women, Femmes, Women of Color, Queer Women, and Gender Variant and Gender Non- Conforming people.