What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, and ‘beautiful’? By applying empirical methods developed by social psychologists, we demonstrate that mathematicians' appraisals of proofs vary on four dimensions: aesthetics, intricacy, utility, and precision. We pay particular attention to mathematical beauty and show that, contrary to the classical view, beauty and simplicity are almost entirely unrelated in mathematics.

We investigated whether mathematicians typically agree about the qualities of mathematical proofs. Between-mathematician consensus in proof appraisals is an implicit assumption of many arguments made by philosophers of mathematics, but to our knowledge the issue has not previously been empirically investigated. We asked a group of mathematicians to assess a specific proof on four dimensions, using the framework identified by Inglis and Aberdein (2015). We found widespread disagreement between our participants about the aesthetics, intricacy, precision and utility of the (...) proof, suggesting that a priori assumptions about the consistency of mathematical proof appraisals are unreasonable. (shrink)

There has been little overt discussion of the experimental philosophy of logic or mathematics. So it may be tempting to assume that application of the methods of experimental philosophy to these areas is impractical or unavailing. This assumption is undercut by three trends in recent research: a renewed interest in historical antecedents of experimental philosophy in philosophical logic; a “practice turn” in the philosophies of mathematics and logic; and philosophical interest in a substantial body of work in adjacent disciplines, such (...) as the psychology of reasoning and mathematics education. This introduction offers a snapshot of each trend and addresses how they intersect with some of the standard criticisms of experimental philosophy. It also briefly summarizes the specific contribution of the other chapters of this book. (shrink)

This book explores the results of applying empirical methods to the philosophy of logic and mathematics. Much of the work that has earned experimental philosophy a prominent place in twenty-first century philosophy is concerned with ethics or epistemology. But, as this book shows, empirical methods are just as much at home in logic and the philosophy of mathematics. -/- Chapters demonstrate and discuss the applicability of a wide range of empirical methods including experiments, surveys, interviews, and data-mining. Distinct themes emerge (...) that reflect recent developments in the field, such as issues concerning the logic of conditionals and the role played by visual elements in some mathematical proofs. -/- Featuring leading figures from experimental philosophy and the fields of philosophy of logic and mathematics, this collection reveals that empirical work in these disciplines has been quietly thriving for some time and stresses the importance of collaboration between philosophers and researchers in mathematics education and mathematical cognition. (shrink)

Many of the methods commonly used to research mathematical practice, such as analyses of historical episodes or individual cases, are particularly well-suited to generating causal hypotheses, but less well-suited to testing causal hypotheses. In this paper we reflect on the contribution that the so-called hypothetico-deductive method, with a particular focus on experimental studies, can make to our understanding of mathematical practice. By way of illustration, we report an experiment that investigated how mathematicians attribute aesthetic properties to mathematical proofs. We demonstrate (...) that perceptions of the aesthetic properties of mathematical proofs are, in some cases at least, subject to social influence. Specifically, we show that mathematicians’ aesthetic judgements tend to conform to the judgements made by others. Pedagogical implications are discussed. (shrink)

COUNCIL FOR RESEARCH IN VALUES AND PHILOSOPHY MEMBERS S. Avineri, Jerusalem P. Balasubramaniam, Madras M. Bedna, Prague P....

As one approach to examining the way ethical decisions are made, we asked experts and novices to review a set of scenarios that depict some important ethical tensions in research. The method employed was “protocol analysis,” a talk-aloud technique pioneered by cognitive scientists for the analysis of expert performance. The participants were asked to verbalize their normally unexpressed thought processes as they responded to the scenarios, and to make recommendations for courses of action. We found that experts spent more time (...) working through the decision-making process than novices and also raised substantially more concerns than novices. Differences also exist among the three groups of experts. (shrink)

As one approach to examining the way ethical decisions are made, we asked experts and novices to review a set of scenarios that depict some important ethical tensions in research. The method employed was “protocol analysis,” a talk-aloud technique pioneered by cognitive scientists for the analysis of expert performance. The participants were asked to verbalize their normally unexpressed thought processes as they responded to the scenarios, and to make recommendations for courses of action. We found that experts spent more time (...) working through the decision-making process than novices and also raised substantially more concerns than novices. Differences also exist among the three groups of experts. (shrink)

_The Foundations of Knowing _ was first published in 1982. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. This collection of essays on the foundations of empirical knowledge brings together ten of Roderick M. Chisholm's most important papers in epistemology, three of them published for the first time, the others significantly revised and expanded for this edition. The essays in Part I constitute (...) a thoroughgoing defense of foundationalism—the doctrine that our justification for believing always rests upon a self-evident basis. In Part II, Chisholm applies foundationalist principles to various areas within the theory of knowledge, and in part III he presents a history of twentieth-century American epistemology. "Roderick M. Chisholm's work has been most influential both in the development of epistemology and in the widespread application of his analytic method. I am sure this publication featuring the unification of his views will be of great value to those working on the central issues of philosophy." Hector-Neri Castañeda, Indiana University Roderick Chisholm is Andrew W. Mellon Professor of the Humanities in the department of philosophy at Brown University. Among his books are _Perceiving: A Philosophical Study, Theory of Knowledge, Person and Object_,and _The First Person _. (shrink)

Cheng Man-ch’ing (1901–1975) is as responsible as anyone for the wide popularity of taijiquan in the West. While his stature as a master and teacher of taijiquan is legendary, he is less well-known as a philosopher. Yet Cheng wrote a number of philosophical commentaries on Chinese classics that shed light on his understanding of taijiquan. In this paper I propose that a consideration of Cheng’s philosophical reflections shows him to be a twentieth century Neo-Confucian who saw taijiquan as a key (...) component of the overall aim of moral self-cultivation. In transmitting taijiquan to his fellow Chinese and to the West, Cheng was attempting to convey traditional Chinese thought and action as expressed in Neo-Confucian moral ideals. For Cheng, taijiquan was more than a martial art or physical exercise; it was a way of life. (shrink)

In the Infamous Opening Sections from Part IX of Beyond Good and Evil, Nietzsche celebrates a strident kind of elitism and countenances, in however attenuated a form, the institution of slavery. “Every enhancement of the type ‘man,’” he writes, “has so far been the work of an aristocratic society—and it will be so again and again—a society that believes in the long ladder of an order of rank and difference in worth [Werthverschiedenheit] between man and man, and that needs slavery (...) [Sklaverei] in some sense or other” (257). In the section that follows, Nietzsche describes a “good and healthy aristocracy” as “accept[ing] with a good conscience the sacrifice of untold human beings who, for its sake [um ihretwillen] .. (shrink)

Are the characteristics and relationships among spatio-temporal entities "real" or are they simply conventional terms that note similarities among things in the world but lack any reality of their own? Or if they are real, what sort of reality do they have? Do we live in a world of causes and effects, or is this relation a useful contrivance for our convenience? What is the nature of this "I" that we invoke when referring to ourselves? Is it body? Mind? Both? (...) Neither? And once its nature is understood, what can be said of the choices it makes? Are they really ours, freely made by an independent will? Or is each choice determined more by the internal makeup of the "I" we happen to be and the social/environmental circumstances in which this "I" finds itself, rather than by any act of will? But if each of us "could not have chosen otherwise" than we have, are we no better than the machines we construct? Then again, maybe some of our more advanced machines should be considered conscious entities? Introduction to Metaphysics: The Fundamental Questions presents these and other intriguing questions, many of which have challenged philosophers from antiquity to the present in their efforts to speculate on the nature of what is real. Often filled with twists and turns, dark corners and hidden recesses, this journey of discovery is an exciting excursion into the depths of human understanding. As guides for this intellectual journey editor Andrew Schoedinger has chosen an impressive array of creative and thought-provoking philosophers: Peter Abelard, Aristotle, Renford Bambrough, George Berkeley, Joseph Butler, Rudolf Carnap, Roderick Chisholm, R.G. Collingwood, Arthur Danto, Donald Davidson, Rene Descartes, C.J. Ducasse, Alvin I. Goldman, Keith Gunderson, David Hume, John Locke, Alasdair MacIntyre, A.I. Melden, John Stuart Mill, D.F. Pears, Hilary Putnam, Anthony Quinton, Bertrand Russell, Michael Scriven, Sydney Shoemaker, P. F. Strawson, Richard Taylor, and others. This volume is a unique invitation to join a distinguished group of theorists as they tackle tough questions concerning the existence of universals, the nature of causation, understanding personal identity, the tangled web of free will, and the challenges posed by the advent of artificial intelligence. (shrink)

I offer a theory of advice. The theory has two parts: an account of the nature of advice, and an account of the quality of advice. In Sect. 2 I defend this definition: Advice: P advises R to X iff P communicates about X-ing to R in a manner that intentionally presents X-ing as worth reasoning to by R. In Sect. 4, I defend a tripartite account of the quality of advice: the standards relevant to whether advice is good concern (...) rational agency in general, the advisee’s particular situation, and the topic of the advice. These accounts of the nature and quality of advice are superior to extant alternatives on the basis of both descriptive adequacy and absurdity. (shrink)

Essentialists suppose that for every individual, if that individual exists at any possible world, then necessarily that individual exemplifies some non-trivial qualitative property essential to it, as such. Anti-essentialists deny this. One important argument leveled by some anti-essentialists against essentialism takes the form of a thought experiment, one originally introduced by Roderick Chisholm, sometimes referred to as Chisholm's Paradox (CP). In this essay, I defend essentialism against CP. I begin by presenting the argument and showing how it leads to (...) a contradiction of the essentialist thesis. I then consider one of the most popular solutions to CP to date, that given by Nathan Salmon. Next, I critique Salmon's proposal and show that it is an insufficient response on behalf of the essentialist. And finally, I propose a novel solution to the paradox and discuss why it is that many metaphysician in the past have found CP plausible, despite being fallacious. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Operating Through HatredAndrew G. Shuman“You’re not cutting my ***ing neck. The cancer is in my ***ing mouth.”While many patient encounters are memorable, Mr. K’s introduction to the head and [End Page 20] neck surgical oncology clinic is indelibly imprinted into the minds of all of the clinicians present on that certain autumn morning. This was, quite simply, a man who resonated hate. He was rude and disruptive. He insisted (...) on an expedited workup “without any waiting.” He questioned the ethnicity and nationality of his care providers. He told me, in no uncertain terms, that he did not appreciate my Jewish heritage—the swastika tattooed on his bicep underscored the point. He bragged about his recent incarceration for armed robbery. While my colleagues and I were tempted to simply refuse to assume his care, Mr. K had a bad problem—his recurrent tongue cancer required a major operation in order to offer him any hope for cure.Mr. K initially received an abbreviated course of radiation at an outside institution, which was limited by his non–compliance. While one might debate the wisdom of this decision in retrospect—in general, surgery is preferred for his type of tumor—the die was already cast. A heroic attempt at surgical salvage was now his only curative option. He previously sought care elsewhere... only to be fired by this original surgeon when Mr. K physically threatened him in the outpatient office during preoperative consultation. [It was the doctor’s fault for insulting him in the first place, Mr. K maintained... and no charges were filed.] We were, indeed, his last resort. Other than his recurrent cancer, Mr. K was robust; he was in his sixth decade, physically fit, and on the whole, fairly healthy. In the classic surgical lexicon, he was a reasonable surgical candidate. But was it reasonable to operate on such a person?I remember thinking, at the time, about our obligation to care for such an individual. Of course, being a medical professional carries with it many obligations, including a judicious assumption of personal risk. And, working in a tertiary care center begets the responsibility to assist referring clinicians in the management of difficult cases. Although professional obligations certainly have their limits, defining their bounds is decidedly more difficult. Paramount is creating an atmosphere of mutual trust and acceptance. Naturally, this was easier said than done in regard to Mr. K.Perhaps against our better judgment, we agreed to operate under the condition that he abide by strict behavioral ground rules, on our terms. We agreed upon the extent of the necessary operation (which indeed involved cutting his ***ing neck, much to his chagrin and reluctant acceptance). Mr. K promised to follow instructions for postoperative care. He assured us that he would not swear or yell (again). And, in the presence of hospital security, who reinforced our institutional policies regarding patient behavior, he guaranteed that he would not be verbally or physically violent or inappropriate, and would not make disparaging comments to other patients or staff. It seemed, at least, that we had an understanding.Needless to say, these rules were broken shortly after he awoke from surgery. I vividly remember being summoned from the OR when he threatened to murder his impressionable and terrified nurse a few days later, who would not acquiesce to his unreasonable demands. From that point onward, hospital security was deployed to his room regularly, and anything resembling a potential weapon was safeguarded. Any semblance of a mutual doctor–patient bond was shattered. At this point, everyone’s goal was simply to get Mr. K home.My visceral reactions to his behavior, while intense, were not unexpected, and fell in line with those of the entire team of clinicians caring for him. His antics brought his healthcare team together in collective unity (and condemnation). However, my surgical colleagues and I also felt somewhat guilty and responsible. While surgeons can choose to assume some degree of inherent personal danger in caring for a violent and angry patient, we also put the safety and soundness of the entire perioperative team in jeopardy, without necessarily seeking their input. But once we had decided to... (shrink)

In a series of papers, Stephen Kearns and Daniel Star defend the following general account of reasons: R: Necessarily, a fact F is a reason for an agent A to Φ iff F is evidence that an agent ought to Φ.In this paper, I argue that the reasons as evidence view will run afoul of a motivational constraint on moral reasons, and that this is a powerful reason to reject the reasons as evidence view. The motivational constraint is as follows: (...) M: For some consideration C to be a moral reason for an agent to Φ it must be possible for C to figure as part of the agent’s motivation for Φing without thereby undercutting (either partially or wholly) the positive moral evaluation of the agent in acting as she does.M presents a problem for Kearns and Star’s view because there will be cases where some consideration is evidence that an agent ought to Φ, but where if an agent was motivated by that consideration the agent’s action would thereby be worse from a moral perspective for that very reason. Further, I argue that this problem will likely arise on any moral theory that evaluates the motivation of an agent as a component of assessing the moral status of acts. (shrink)

A review‐article of Loren Baritz, City On a Hill, A History of Ideas and Myths in America, John Wiley and Sons C. Wright Mills, Sociology and Pragmatism, Paine‐Whitman Publishers Roderick M. Chisholm, Herbert Feigl, William K. Frankena, John Passmore, Manley Thompson, Philosophy, Prentice‐Hall Max Black, Philosophy in America, Cornell University Press.

Excerpt from A Guide to World-HistoryThe object of this book may best be indicated by explain ing briefly how the volume came to be written. As with the majority of people the author's acquaintance with history began at school. But, unlike the majority, he there contracted a taste for the subject which continued when his studies were no longer of a compulsory character. Naturally he was at first concerned with the more heroic and romantic aspects of the subject to be (...) found in our numerous drum-and-trumpet narratives. Gradually, however, he came to think that history might really have the scientific value so often attributed to it in the literature of the subject. Rightly interpreted could not history throw light on the present and into the avenues of the future The idea haunted him constantly, and he began reading up not only the most dry-as-dust chronicles, but also every book he could procure relating to the science or philosophy of history, as it is often called. After many years of almost unremitting study he believed he had garnered quite profitable ideas on general principles. But he still found himself baffled on such points as these.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

Sense-data, if they exist, could conceivably provide foundations for empirical knowledge. Those who are opposed to empirical foundationalism are therefore also prone to reject sense-data and arguments for their existence, e.g., Rorty, Bonjour; while foundationalists are prone to accept the existence of sense-data, e.g., Russell, Ayer, Broad, Price, Lewis. An exception to this is the position of Roderick Chisholm who accepts empirical foundationalism but rejects the existence of sense-data.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Self Between: From Freud to the New Social Psychology of FranceAndrew J. McKennaThe Self Between: From Freud to the New Social Psychology of France, by Eugene Webb; ix & 268 pp. Seattle: University of Washington Press, 1993, $35.00.That psychology and sociology are one science is the fundamental premise guiding Eugene Webb’s The Self Between, which he defines early on as “a self constituted dynamically and continuously by (...) the relationships it finds itself involved i n.” The “new social psychology of France” designated by his subtitle is mostly the one inspired by René Girard’s mimetic model of human behavior, to which four of Webb’s seven chapters are specifically devoted.Girard’s idea, which he learned from our literary masterpieces, is that human desire is mimetic, that it imitates other desires in its choice of objects and in pursuit of their possession. As desires converge on a single object, the locus of conflict will be between subjects rather within their individual psyches, a consequence that motivates Girard’s ongoing critique of Freudian psychoanalysis.But Freud’s theories are everywhere disputed in this book, which reports reliably on the devastating critiques advanced by François Roustang, Marie Balmary, and Mikkel Borch-Jacobsen. Roustang has convincingly (and entertainingly) uncovered Freud’s blindness to the pathologies of transference and discipleship investing the foundation of psychoanalysis. A pattern of rivalry for recognition and preeminence guides Freud’s career in a way that is reenacted around Lacan. Balmary, somewhat a Lacanian her self, has turned psychoanalytic theory against Freud to explore his own family secrets, while severely questioning the master’s bid for a universal theory pursued via self-analysis amidst a period of emotional upheaval. And Borch-Jacobsen has shown how th e dynamics of hypnosis that Freud rejected early on were brought back as transference, while arguing for his own part that mimetic identification with the other, rather than any primordial drives, is what brings the subject into being. These informat ive chapters help bring us up to date on significant debates that have developed since Lacan drew the French intellectual world, and so many Americans after it, into the orbit of psychoanalysis.But by far the bulk of Webb’s attention goes to Girard’s work and to that of [End Page 191] scholars and practitioners who have sought to extend it further in the social sciences. Principle among them is Jean-Michel Oughourlian, whose Puppet of Desire (translated by Webb in 1991) demonstrates how the mimetic model plays out in psychotherapy, notably in the workings of hypnotism and somnambulism, in cases of demonic possession, and in obsessional neurosis. In each case, the subject is unwitt ingly captive of another’s desire in a way that produces behavioral anomalies and disorders that are nonetheless available to lucid, jargon-free diagnosis. What is appealing here is the deployment of a rational explanation for irrational behavior, once we grasp the paradoxical rationale of desire; equally appealing prospects of actual healing are outlined here and at the end of the book, where possibilities of freedom and responsibility are resurrected from a technical vocabulary that smothers them.Girard’s idea of the self as relation, as interdividuality, rather than as a discreet unit, has social and political dimensions to which we only find tantalizing allusions in his works. They have been pursued with acumen by such writers as André Orléan, Paul Dumouchel and especially Jean-Pierre Dupuy, who figures importantly among those aligning systems theory with theories of social and economic organization. Like Borch-Jacobsen and Roustang, Dupuy restores due attention to concep tions of crowd behavior outlined at the end of the last century by Tarde and Le Bon, whose best insights Freud studiously discarded.This is richly interdisciplinary work, strongly suggesting that we variously redraw and erase lines defining academic fields. Occam’s razor flicks often and decisively in these pages, which restore needed balance to the effects of some wild er French imports. Webb brings no new ideas of his own to this capable synthesis, but his accurate report will help guide researchers toward major recent developments in France around and mostly beyond Freudian psychoanalysis... (shrink)

This paper investigates relationships between procedural-memory, declarative-memory, and working-memory skills and adult native English speakers’ novel sound-category learning. Participants completed a sound-categorization task that required integrating two dimensions: one native (vowel quality), one non-native (pitch). Similar information-integration category structures in the visual and auditory domains have been shown to be best learned implicitly (e.g., Maddox, Ing, & Lauritzen, 2006). Thus, we predicted that individuals with greater procedural-memory capacity would better learn sound categories, because procedural memory appears to support implicit learning (...) of new information and integration of dimensions. Seventy undergraduates were tested across two experiments. Procedural memory was assessed using a linguistic adaptation of the serial-reaction-time task (Misyak, Christiansen, & Tomblin, 2010a, 2010b). Declarative memory was assessed using the logical-memory subtest of the Wechsler Memory Scale-4th edition (WMS-IV; Wechsler, 2009). Working memory was assessed using an auditory version of the reading-span task (Kane et al., 2004). Experiment 1 revealed contributions of only declarative memory to dimensional integration, which might indicate not enough time or motivation to shift over to a procedural/integrative strategy. Experiment 2 gave twice the speech-sound training, distributed over two days, and also attempted to train at the category boundary. As predicted, effects of declarative memory were removed and effects of procedural memory emerged, but, unexpectedly, new effects of working memory surfaced. The results may be compatible with a multiple-systems account in which declarative and working memory facilitate transfer of control to the procedural system. (shrink)

Mathematical notation includes a vast array of signs. Most mathematical signs appear to be symbolic, in the sense that their meaning is arbitrarily related to their visual appearance. We explored the hypothesis that mathematical signs with iconic aspects—those which visually resemble in some way the concepts they represent—offer a cognitive advantage over those which are purely symbolic. An early formulation of this hypothesis was made by Christine Ladd in 1883 who suggested that symmetrical signs should be used to convey commutative (...) relations, because they visually resemble the mathematical concept they represent. Two controlled experiments provide the first empirical test of, and evidence for, Ladd's hypothesis. In Experiment 1 we find that participants are more likely to attribute commutativity to operations denoted by symmetric signs. In Experiment 2 we further show that using symmetric signs as notation for commutative operations can increase mathematical performance. (shrink)

In recent times developments in the natural sciences and in the sphere of environmental politics have compelled social scientists, and also some natural scientists, to rethink the relations that hitherto have been held, in Western thought generally and within particular disciplines, to characterize ‘nature’ on the one side and ‘culture’ on the other. This article considers the history of this conceptual boundary and looks at new conceptualizations of nature/culture, stimulated by developments both in biotechnology and in the ongoing controversies about (...) environmental degradation. It argues that while some of the contributions to reconfiguring, or abolishing, the nature/ culture division have been productive and stimulating of new ways of conceiving the world, there has nonetheless been an unfortunate tendency for social scientists to bring to bear inherited analytic dispositions on biotechnological and environmental matters. Instead of using these issues as means of challenging social scientific disciplinary dogmas and of engaging in constructive rapprochement with natural scientists, social scientists have in their analyses of such matters often merely asserted the hegemony of ‘culture’ over ‘nature’, and thus in effect the superiority of social scientific over natural scientific conceptualizations of the world. Far from overcoming the nature/culture boundary, social scientists have too often merely asserted the primacy of the sorts of subject matters and analytic techniques they feel comfortable with, rather than subjecting their practices to fully reflexive self-scrutiny. (shrink)

Historically people with learning difficulties1 have been either included in research without their consent or excluded from research that affects their treatment and care. Over the last 20 years, however, it has been recognised that to exclude the voice of people with learning difficulties in research that reflects their lived experiences challenges our notion of ethical practice. Cognitive ability has traditionally been one of the key factors in determining ability to consent. This paper identifies, through work with a group of (...) men with learning difficulties, the impact of different ways of presenting information to prospective participants on their ability to understand key issues in relation to participation in research and hence their ability to give informed consent2. (shrink)

Mathematicians often conduct aesthetic judgements to evaluate mathematical objects such as equations or proofs. But is there a consensus about which mathematical objects are beautiful? We used a comparative judgement technique to measure aesthetic intuitions among British mathematicians, Chinese mathematicians, and British mathematics undergraduates, with the aim of assessing whether judgements of mathematical beauty are influenced by cultural differences or levels of expertise. We found aesthetic agreement both within and across these demographic groups. We conclude that judgements of mathematical beauty (...) are not strongly influenced by cultural difference, levels of expertise, and types of mathematical objects. Our findings contrast with recent studies that found mathematicians often disagree with each other about mathematical beauty. (shrink)

A common description of a mathematical proof is as a logically structured sequence of assertions, beginning from accepted premises and proceeding by standard inference rules to a conclusion. Does this description match the language of proofs as mathematicians write them in their research articles? In this chapter, we use methods from corpus linguistics to look at the prevalence of imperatives and instructions in mathematical preprints from the arXiv repository. We find thirteen verbs that are used most often to form imperatives (...) in proofs, and that these show up significantly more often within proofs than in the surrounding mathematical writing. We also show that there are many more verbs used to form a diverse selection of instructions in proofs. These findings are at odds with the view of proofs as sequences of assertions. Instead, we argue in favour of the recipe model of proofs: that proofs are like recipes, giving instructions for mathematical actions to be carried out. (shrink)

Edited in hypertext by Andrew Chrucky. Reprinted with the permission of Professor David Rosenthal. Editor's Note: Due to the limitation of current hypertext, the following conventions have been used. In general, if an expression has some mark over it, that mark is placed as a prefix to the expression. All Greek characters are rendered by their names. Subscripts are placed in parentheses as concatenated suffixes: thus, e.g., HO is the chemical formula for water. Sellars' dot quotes are expressed by (...) bold periods. (shrink)

We examined a large set of conditional inference data compiled from several previous studies and asked three questions: How is normative performance related to intelligence? Does negative conclusion bias stem from Type 1 or Type 2 processing? Does implicit negation bias stem from Type 1 or Type 2 processing? Our analysis demonstrated that rejecting denial of the antecedent and affirmation of the consequent inferences was positively correlated with intelligence, while endorsing modus tollens inferences was not; that the occurrence of negative (...) conclusion bias was related to the extent of Type 2 processing; and that the occurrence of implicit negation bias was not related to the extent of Type 2 processing. We conclude that negative conclusion bias is, at least in part, a product of Type 2 processing, while implicit negation bias is not. (shrink)

The Scottish Mental Health Arts and Film Festival has seen hundreds of arts, public and community groups coproduce over 300 events to over 25,000 audience members. Integral to this arts-based approach, in contrast to social marketing or public education models, is the notion that mental health is an essentially contested concept whereby meanings are negotiated and debate encouraged. With emerging evidence that the festival is an ef ective way of engaging people intellectually and emotionally, we explore ethical issues, challenges and (...) paradoxes that have emerged as the festival has developed. Consideration is given to issues of power, purpose, opportunity costs, reach, impact, programming risks, and participation from those with experience of mental ill-health. Throughout, we explore practical implications for funding, managing, programming, marketing and evaluation of this and similar endeavours. (shrink)