Quantum Non-Locality and Relativity is recognized as the premier philosophical study of Bell's Theorem and its implication for the relativistic account of space and time. Previous editions have been praised for the remarkable clarity of Maudlin's descriptions of both Bell's theorem and his examination of the potential conflict between the theorem and relativity. The third edition of this text has been carefully updated to reflect significant developments, including a new chapter covering important recent work in the foundations of physics. Foremost (...) among these is Roderich Tumiulka's explicit, relativistic theory that can reproduce the quantum mechanical violation of Bell's inequality. The "Free Will Theorem" of John Conway and Simon Kochen is also discussed, as is the status of locality in the Many Worlds interpretation of quantum theory. The book has also been updated to reflect recent results in information theory. The book introduces philosophers to the relevant physics and demonstrates how philosophical analysis can help to resolve some of the problems, and requires no technical background in Physics. All of the physics is presented from first principles, and as much as possible is presented pictorially"--Provided by publisher. (shrink)

This research compares and analyzes the verbal commentary of televised coverage of two women's and men's athletic events: the “final four” of the women's and men's 1989 National Collegiate Athletic Association basketball tournaments and the women's and men's singles, women's and men's doubles, and the mixed-doubles matches of the 1989 U.S. Open tennis tournament. Although we found less overtly sexist commentary than has been observed in past research, we did find two categories of difference: gender marking and a “hierarchy of (...) naming” by gender and, to a certain extent, by race. These differences are described and analyzed in light of feminist analyses of gendered language. It is concluded that televised sports commentary contributes to the construction of gender and racial hierarchies by marking women's sports and women athletes as “other,” by infantilizing women athletes, and by framing the accomplishments of women athletes ambivalently. (shrink)

Some machine learning models, in particular deep neural networks, are not very well understood; nevertheless, they are frequently used in science. Does this lack of understanding pose a problem for using DNNs to understand empirical phenomena? Emily Sullivan has recently argued that understanding with DNNs is not limited by our lack of understanding of DNNs themselves. In the present paper, we will argue, contra Sullivan, that our current lack of understanding of DNNs does limit our ability to understand with DNNs. (...) Sullivan’s claim hinges on which notion of understanding is at play. If we employ a weak notion of understanding, then her claim is tenable, but rather weak. If, however, we employ a strong notion of understanding, particularly explanatory understanding, then her claim is not tenable. (shrink)

Tim Mulgan presents a penetrating examination of consequentialism: the theory that human behavior must be judged in terms of the goodness or badness of its consequences. The problem with consequentialism is that it seems unreasonably demanding, leaving us no room for our own aims and interests. In response, Mulgan offers his own, more practical version of consequentialism--one that will surely appeal to philosophers and laypersons alike.

While provisions of youth sports concussion laws are very similar, little is known as to how they are being implemented, factors that promote or impede implementation, or the level of compliance in each jurisdiction. We aimed to describe state experiences with implementation in order to inform ongoing efforts to reduce the harm of sports-related traumatic brain injury and to guide future evaluations of the laws’ impacts and the development of future public health laws. We conducted key-informant interviews in 35 states (...) with recently enacted concussion legislation. States varied considerably in their readiness and capacity for implementation. Factors facilitating implementation included existing partnerships, procedures, and resources; centralized implementation authority; prior related efforts; and involvement in the policymaking process by those now charged with implementation. Inhibitors included ambiguous statutory language, unclear delegation of authority, and compliance difficulties. Ongoing challenges persist, including primary prevention; determining which providers are qualified to make return-to-play assessments and contents of those assessments; compliance difficulties in rural and under-served areas; and unclear responsibility for enforcement. Despite the similarity of youth sports concussion laws, early evidence suggests there is considerable variation in their implementation. These findings are critical for ongoing empirical investigations to accurately evaluate the laws’ provisions and to identify successful legal approaches to protecting young athletes. (shrink)

Over the past decade, a flurry of media stories devoted to sports-related concussions have drawn attention to the previously “silent epidemic” of traumatic brain injury in athletes. From 2001 to 2009, the annual number of sports-related TBI emergency department visits in individuals age 19 and under climbed from 153,375 to 248,414, an increase of increase of 62 percent. Multiple head injuries place youth athletes at risk for serious health conditions, including cerebral swelling, brain herniation, and even death — postconcussive conditions (...) that have collectively been referred to as “second impact syndrome.” Studies have shown that children and teens — and girls, in particular — are more likely to sustain a concussion and have a longer recovery time than adults. Recent research also suggests that even subconcussive hits in children and adolescents may result in longer-term health effects such as decreased cognitive functioning, increased rates of depression, memory problems, and mild cognitive impairment. (shrink)

This paper argues that a notion of statistical explanation, based on Salmon’s statistical relevance model, can help us better understand deep neural networks. It is proved that homogeneous partitions, the core notion of Salmon’s model, are equivalent to minimal sufficient statistics, an important notion from statistical inference. This establishes a link to deep neural networks via the so-called Information Bottleneck method, an information-theoretic framework, according to which deep neural networks implicitly solve an optimization problem that generalizes minimal sufficient statistics. The (...) resulting notion of statistical explanation is general, mathematical, and subcausal. (shrink)

Certainly I am in no way opposed to philosophy, or metaphysics in the sense that Wm. James defined it as a particularly intense effort to think clearly. Indeed, Klein would like to say that what I am talking about is nothing but metaphysics. But the kind of philosophy/metaphysics that is needed here is of a particular kind: a kind that does not separate philosophy/metaphysics and physics into two disjoint realms. It is of the kind that seeks to construct useful testable (...) physical theories that are adequately connected to what we can know. (shrink)

In recent years there has been an increase in the number of calls for moral education to receive greater public attention. In our pluralist society, however, it is difficult to find agreement on what exactly moral education requires. Philosophical Discussion in Moral Education develops a detailed philosophical defence of the claim that teachers should engage students in ethical discussions to promote moral competence and strengthen moral character. Paying particular attention to the teacher's role, this book highlights the justification for, and (...) methods of, creating a classroom community of ethical inquiry. (shrink)

Tim Button explores the relationship between words and world; between semantics and scepticism. -/- A certain kind of philosopher – the external realist – worries that appearances might be radically deceptive. For example, she allows that we might all be brains in vats, stimulated by an infernal machine. But anyone who entertains the possibility of radical deception must also entertain a further worry: that all of our thoughts are totally contentless. That worry is just incoherent. -/- We cannot, then, be (...) external realists, who worry about the possibility of radical deception. Equally, however, we cannot be internal realists, who reject all possibility of deception. We must position ourselves somewhere between internal realism and external realism, but we cannot hope to say exactly where. We must be realists, for what that is worth, and realists within limits. -/- In establishing these claims, The Limits of Realism critically explores and develops several themes from Hilary Putnam’s work: the model-theoretic arguments; the connection between truth and justification; the brain-in-vat argument; semantic externalism; and conceptual relativity. The book establishes the continued significance of these topics for all philosophers interested in mind, logic, language, or the possibility of metaphysics. (shrink)

Written by specialist practitioners with vast teaching experience, this is a unique, timely and accessible text that reinforces a contemporary focus on professionalism in medical practice.

This book is hoped to be only the beginning of explorations of the ancient Egyptian notion of upholding Order (Ma'at) through violence. Because of the scope of the topic, this study is limited to the most extreme measure of violence perpetrated in the service of Order: sanctioned killing. This study explores texts that affirm the proper occasions for such killings, and the religious framework behind these actions."--Publisher's website.

In June 2021, Missouri passed the “Second Amendment Preservation Act” (SAPA). Though SAPA passed easily and had gubernatorial support, many Missouri law enforcement agencies, including the Missouri Sheriff’s Association, oppose it. Missing from this policy conversation, and deserving of analysis, is the voice of Missouri citizens. Using qualitative interview data and survey data, we explored what if anything Missouri gun owners knew about SAPA and what they perceived its effects would be on gun-related murders, suicides, gun thefts, and mass shootings. (...) Most Missouri gun owners had not heard about SAPA and were ambivalent about its potential effect on gun safety outcomes. Our findings also indicate that respondents’ attitudes toward SAPA and the impact of such policy on safety is driven by gun ownership (i.e., primary versus living in a household with firearms), partisan identification, and attitudes toward government firearm regulation. (shrink)

The pull to coordinate with other individuals is fundamental, serving as the basis for our social connectedness to others. Discussed is a dynamical and ecological perspective to joint action, an approach that embeds the individual’s mind in a body and the body in a niche, a physical and social environment. Research on uninstructed coordination of simple incidental rhythmic movement, along with research on goal‐directed, embodied cooperation, is reviewed. Finally, recent research is discussed that extends the coordination and cooperation studies, examining (...) how synchronizing with another, and how emergent social units of perceiving and acting are reflected in people’s feelings of connection to others. (shrink)

Tim Bayne draws on philosophy, psychology, and neuroscience in defence of the claim that consciousness is unified. He develops an account of what it means to say that consciousness is unified, and then applies this account to a variety of cases - drawn from both normal and pathological forms of experience - in which the unity of consciousness is said to break down. He goes on to explore the implications of the unity of consciousness for theories of consciousness, for the (...) sense of embodiment, and for accounts of the self. The Unity of Consciousness draws on a wide range of findings within philosophy and the sciences of the mind to construct an account of the unity of consciousness that is both conceptually sophisticated and scientifically informed. (shrink)

In this article, I address concerns that the ontological priority claims definitive of ontic structural realism are as they stand unclear, and I do so by placing these claims on a more rigorous formal footing than they typically have been hitherto. I first of all argue that Kit Fine’s analysis of ontological dependence furnishes us with an ontological priority relation that is particularly apt for structuralism. With that in place, and with reference to two case studies prominent within the structuralist (...) literature, I consider whether any of structuralism’s distinctive priority claims may be regarded as warranted. The discussion as a whole has largely negative implications for the radical structuralism of French and Ladyman (including their ‘eliminativist’ interpretation of it), largely positive implications for the moderate structuralism primarily advocated by Esfeld and Lam, and some broad lessons for contemporary fundamentalist metaphysics as a whole. 1 Introduction2 The Right Priority Relation for Structuralism: Supervenience or Dependence?3 Introducing Ontological Dependence4 Fine’s System5 The Priority of Structure 1: Entangled Quantum Particles6 The Priority of Structure 2: The Group-Theoretic Conception of Elementary Particles7 Concluding Remarks. (shrink)

Essential Philosophy of Psychiatry is a concise introduction to the growing field of philosophy of psychiatry. Divided into three main aspects of psychiatric clinical judgement, values, meanings and facts, it examines the key debates about mental health care, and the philosophical ideas and tools needed to assess those debates, in six chapters. In addition to outlining the state of play, Essential Philosophy of Psychiatry presents a coherent and unified approach across the different debates, characterized by a rejection of reductionism and (...) an emphasis on the ineliminability of uncodified skilled judgement. The first part, Values, outlines the debate about whether diagnosis of mental illness is essentially value-laden and argues that the prospects for reducing illness or disease to plainly factual matters are poor. It also explains the important role of skilled contextual judgement, rather than a principles-based deduction, in ethical judgement. The second part, Meanings, examines the central role of understanding and a shared first person perspective, both against attempts to reduce meaning to basic information-processing mechanisms and to explain away the difficulties of understanding psychopathology in recent models of delusion. The third part, Facts, shows the importance of uncodified clinical judgements, both in assessing the validity of psychiatric taxonomy and in the application of Evidence Based Medicine. Despite advances in the codifaction of practice and operationalism of diagnosis, an element of judgement remains in the assessment both of what, at one level, is good evidence for diagnosis and treatment and what, at a higher level, is good evidence for the validity of classification overall. (shrink)

Ontic structural realism is a thesis of fundamentality metaphysics: the thesis that structure, not objects, has fundamental status. Claimed as the metaphysic most befitting of modern physics, OSR first emerged as an entreaty to eliminate objects from the metaphysics of fundamental physics. Such elimination was urged by Steven French and James Ladyman on the grounds that only it could resolve the ‘underdetermination of metaphysics by physics’ that they claimed reduced any putative objectual commitment to a merely ‘ersatz’ form of realism. (...) Few, however, have joined French and Ladyman either in acknowledging that such underdetermination exists or in attributing to it such drastic consequences. However, an alternative view that physics does sanction objects, albeit merely as ontologically secondary entities, represents a different and seemingly less extreme route to the same conclusion regarding the fundamentality of structure. But since what it means to be ‘ontologically prior’ is itself a vexed philosophical question, a stance must be taken as to how we are to understand priority before its prospects may be evaluated. In an earlier paper, I outlined how Fine’s notion of ontological dependence might be utilized to defend the priority-based approach to structuralism. Since then, however, I have become convinced that that ontological dependence is not a relation of priority after all. As a result, the arguments outlined in that paper stand in need of reassessment. In this work, I consider the prospects for priority-based structuralism when expressed in the idiom of determination. My conclusion will be that it has yet to be vindicated by our best physical theories, owing to the failure of symmetry structures to determine the world’s inventory of fundamental kinds. Nevertheless, the same symmetry considerations point towards there being renewed prospects for eliminativism—an eliminativism, moreover, of more naturalistic appeal than that hitherto associated with OSR. 1Introduction 2Structuralist Strategies 3Defining Ontological Priority: Dependence or Determination? 4Structuralism in the Idiom of Determination 4.1Determining plurality 4.2Determining kind properties 5A Reinvigorated Eliminativism. (shrink)

Modern bioethics, which is based on Western moral philosophy and Western biomedical perspectives, has evolved within a complex, highly individualistic culture that draws a sharp distinction between church and state and tolerates a multitude of values. This discipline defines its principles in secular and objective terms that often are bewildering to people of non-Western origin. Despite much discourse, principlism remains the fundamental framework of bioethics. Principlism is held in such high regard that many bioethicists equate autonomy with personhood, as if (...) autonomy exists independently of specific beliefs and commitments.In addition, we continue to minimize the substantial differences in the way people of different cultures perceive, experience, and explain illness, although our views of the potential cultural limitations of Western medicine have grown and expanded in recent years. At the heart of it we continue to be tied to a biomedical focus that largely neglects the context of the situation. (shrink)

Does thought have distinctive experiential features? Is there, in addition to sensory phenomenology, a kind of cognitive phenomenology--phenomenology of a cognitive or conceptual character? Leading philosophers of mind debate whether conscious thought has cognitive phenomenology and whether it is part of conscious perception and conscious emotion.

A priori metaphysics has come under repeated attack by naturalistic metaphysicians, who take their closer connection to the sciences to confer greater epistemic credentials on their theories. But it is hard to see how this can be so unless the problem of theory change that has for so long vexed philosophers of science can be addressed in the context of scientific metaphysics. This paper argues that canonical metaphysical claims, unlike their scientific counterparts, cannot meaningfully be regarded as ‘approximately true,’ and (...) that this means that the epistemic progress that science arguably enjoys through episodes of theory change cannot be expected to transfer to its metaphysics. What the value of engaging in metaphysics of science before the emergence of a final theory becomes correspondingly unclear. (shrink)

This paper explores the value of the eros motif for critical pedagogy and citizenship education. The conceptual affinities between eros and democracy are identified and integrated into a theory of democratic political education. Long recognized as vital to the process of self knowledge, the ancient Greek concept of eros has nevertheless been largely erased from contemporary educational debate. By retrieving eros from the fringe of academic discourse and integrating it with critical pedagogy, the aims of radical democracy can be more (...) fully achieved. The essay emphasizes the civil society or cultural dimensions of democracy as against its legal or procedural aspects. Renewed emphasis on the associational qualities of democracy underscore the importance of eros as an educational principle. The ancient pedagogical motif of educating the desires is posited as an alternative to the liberal/modernist paradigm of education which de-values affective domains of knowledge. (shrink)

The phenomenal character of perceptual experience involves the representation of colour, shape and motion. Does it also involve the representation of high-level categories? Is the recognition of a tomato as a tomato contained within perceptual phenomenality? Proponents of a conservative view of the reach of phenomenal content say ’No’, whereas those who take a liberal view of perceptual phenomenality say ’Yes’. I clarify the debate between conservatives and liberals, and argue in favour of the liberal view that high-level content can (...) directly inform the phenomenal character of perception. (shrink)

Universals are putative objects like wisdom, morality, redness, etc. Although we believe in properties (which, we argue, are not a kind of object), we do not believe in universals. However, a number of ordinary, natural language constructions seem to commit us to their existence. In this paper, we provide a fictionalist theory of universals, which allows us to speak as if universals existed, whilst denying that any really do.

In 1997, a Scottish surgeon by the name of Robert Smith was approached by a man with an unusual request: he wanted his apparently healthy lower left leg amputated. Although details about the case are sketchy, the would-be amputee appears to have desired the amputation on the grounds that his left foot wasn’t part of him – it felt alien. After consultation with psychiatrists, Smith performed the amputation. Two and a half years later, the patient reported that his life had (...) been transformed for the better by the operation [1]. A second patient was also reported as having been satisfied with his amputation [2]. (shrink)

Against transmission -- For attention -- Education in the minor key -- Anthropology, art and the university.

The hypothesis that play behavior is more prevalent in larger-brained animals has recently been challenged. It may be, for example, that only certain brain structures are related to play. Here, we analyze social play behavior with regards to the cerebellum: a structure strongly implicated in motor-development, and possibly also in cognitive skills. We present an evolutionary analysis of social play and the cerebellum, using a phylogenetic comparative method. Social play frequency and relative cerebellum size are positively correlated. Hence, there appears (...) to be a link between the evolutionary elaboration of social play and the cerebellum. (shrink)

Modern bioethics, which is based on Western moral philosophy and Western biomedical perspectives, has evolved within a complex, highly individualistic culture that draws a sharp distinction between church and state and tolerates a multitude of values. This discipline defines its principles in secular and objective terms that often are bewildering to people of non-Western origin. Despite much discourse, principlism remains the fundamental framework of bioethics. Principlism is held in such high regard that many bioethicists equate autonomy with personhood, as if (...) autonomy exists independently of specific beliefs and commitments.In addition, we continue to minimize the substantial differences in the way people of different cultures perceive, experience, and explain illness, although our views of the potential cultural limitations of Western medicine have grown and expanded in recent years. At the heart of it we continue to be tied to a biomedical focus that largely neglects the context of the situation. (shrink)

This study presents a critical discourse analysis of YouTube comments below five videos of the Johnny Depp v Amber Heard trial, which was live streamed by the platform in April and May 2022. The analysis examines the discursive resources used by commenters to construct domestic abuse. Commenters draw on three interpretive repertoires: ‘Perfect Victim’, ‘Mutual Abuse’ and ‘Dangerous Women’. The analysis explores the way these repertoires are used to rebut Heard’s allegations of abuse by mobilising the perfect victim repertoire to (...) refute any claim she has to this experience, and the mutual abuse repertoire to implicate Heard in the abuse and minimise blame for Depp. Through establishing gender-symmetry in domestic abuse and drawing on traditional gender norms for each party, commenters construct the dangerous women repertoire to depict Heard as crazy, pathological and violent. The key implication of this study is that public constructions of domestic abuse can directly impact the attitudes and treatment of both victims and perpetrators. In this instance, they serve to maintain the oppression and control of women within anti-feminist narratives of female dominance, currently led by men’s rights activists and conservative outlets. (shrink)

A suite of questions concerning fundamentality lies at the heart of contemporary metaphysics. The relation of grounding, thought to connect the more to the less fundamental, sits at the heart of those debates in turn. Since most contemporary metaphysicians embrace the doctrine of physicalism and thus hold that reality is fundamentally physical, a natural question is how physics can inform the current debates over fundamentality and grounding. This Element introduces the reader to the concept of grounding and some of the (...) key issues that animate contemporary debates around it, such as the question of whether grounding is 'unified' or 'plural' and whether there exists a fundamental level of reality. It moves on to show how resources from physics can help point the way towards their answers - thus furthering the case for a naturalistic approach to even the most fundamental of questions in metaphysics. (shrink)

The number of colleges and universities with campus agriculture projects in the US has grown from an estimated 23 in 1992 to nearly 300 today with possible increased numbers predicted. The profile emerging from campus agriculture projects looks a lot different from the traditional land grant colleges of agriculture. In spite of this emergent trend and staunch advocacy for campus agriculture projects, limited empirical research on agriculture-based learning in higher education exists outside agriculture degrees and theoretical work of scholars such (...) as Liberty Hyde Bailey and David Orr. This study explored the diversity of characteristics and pedagogical objectives of emerging campus agriculture projects through a nationwide compilation, surveying campus agriculture project directors and educators, and multiple case studies. Data collected gives empirical evidence supporting claims agriculture is taking on a different identity in higher education. Issues of sustainability, food, and agriculture are not only influencing the physical workings of colleges and universities, but pedagogy on a departmental and institutional scale. Findings illustrate a re-visioning of how higher education is interfacing with agriculture and agriculture-based education beyond traditional agriculture degrees at land grant colleges of agriculture to focus teaching sustainability, critical thinking and inquiry skills, and fostering a sense of belonging to community. (shrink)

We outline a framework for analyzing episodes from the history of science in which the application of mathematics plays a constitutive role in the conceptual development of empirical sciences. Our starting point is the inferential conception of the application of mathematics, recently advanced by Bueno and Colyvan. We identify and discuss some systematic problems of this approach. We propose refinements of the inferential conception based on theoretical considerations and on the basis of a historical case study. We demonstrate the usefulness (...) of the refined, dynamical inferential conception using the well-researched example of the genesis of general relativity. Specifically, we look at the collaboration of the physicist Einstein and the mathematician Grossmann in the years 1912--1913, which resulted in the jointly published ``Outline of a Generalized Theory of Relativity and a Theory of Gravitation,'' a precursor theory of the final theory of general relativity. In this episode, an independently developed mathematical theory, the theory of differential invariants and the absolute differential calculus, was applied in the process of physical theorizing aiming at finding a relativistic theory of gravitation. We argue that the dynamical inferential conception not only provides a natural framework to describe and analyze this episode, but it also generates new questions and insights. We comment on the mathematical tradition on which Grossmann drew, and on his own contributions to mathematical theorizing. We argue that the dynamical inferential conception allows us to identify both the role of heuristics and of mathematical resources as well as the systematic role of problems and mistakes in the reconstruction of episodes of conceptual innovation and theory change. (shrink)

In this ingenious and powerfully argued book Tim Maudlin sets out a novel account of logic and semantics which allows him to deal with certain notorious paradoxes which have bedevilled philosophical theories of truth. All philosophers interested in logic and language will find this a stimulating read.

Ontic structural realism is at its core the view that “structure is ontologically fundamental.” Informed from its inception by the scientific revolutions that punctuated the 20th century, its advocates often present the position as the perspective on ontology best befitting of modern physics. But the idea that structure is fundamental has proved difficult to articulate adequately, and what OSR's claimed naturalistic credentials consist in is hard to precisify as well. Nor is it clear that the position is actually supported by (...) our most fundamental physical theories. What is clear, however, is that structuralists have revealed a seam of material at the core of modern physics that is replete with implications for metaphysics. This article will survey some positions subsumed under the rubric of OSR, considering both their warrant and the interconnections that exist between them. It will be argued that the fundamental kind properties pose a challenge to ontic structuralism, because it seems that these properties do not supervene upon the relevant structures. But it will also be argued that the development of structuralist metaphysics will require both an engagement with the details of modern physical theories and the deployment of tools more typically developed in a priori metaphysics. As such, it seems armchair metaphysicians have not just a stake in whether OSR's claims may ultimately be shown to stand up, but a crucial role to play in getting them to the point where they can be subjected to scrutiny in the first place. (shrink)

This paper proposes a reformulation of the treatment of boundaries, at parts and aggregates of entities in Basic Formal Ontology. These are currently treated as mutually exclusive, which is inadequate for biological representation since some entities may simultaneously be at parts, boundaries and/or aggregates. We introduce functions which map entities to their boundaries, at parts or aggregations. We make use of time, space and spacetime projection functions which, along the way, allow us to develop a simple temporal theory.

The present paper provides an analysis of Euler’s solutions to the Königsberg bridges problem. Euler proposes three different solutions to the problem, addressing their strengths and weaknesses along the way. I put the analysis of Euler’s paper to work in the philosophical discussion on mathematical explanations. I propose that the key ingredient to a good explanation is the degree to which it provides relevant information. Providing relevant information is based on knowledge of the structure in question, graphs in the present (...) case. I also propose computational complexity and logical strength as measures of relevant information. (shrink)

Michael Weisberg and Kenneth Reisman argue that the Volterra Principle can be derived from multiple predator-prey models and that, therefore, the Volterra Principle is a prime example for robustness analysis. In the current article, I give new results regarding the Volterra Principle, extending Weisberg’s and Reisman’s work, and I discuss the consequences of these results for robustness analysis. I argue that we do not end up with multiple, independent models but rather with one general model. I identify the kind of (...) situation in which this generalization approach may occur, and I analyze the generalized Volterra Principle from an explanatory perspective. (shrink)

Much of the neuroimaging research has focused on how mathematical operations are performed. Although this body of research has provided insight for the refinement of pedagogy, there are very few neuroimaging studies on how mathematical operations should be taught. In this article, we describe the teaching of algebra in Singapore schools and the imperatives that led us to develop two neuroimaging studies that examined questions of curricular concerns. One of the challenges was to condense issues from classrooms into tasks suitable (...) for neuroimaging studies. Another challenge, not particular to the neuroimaging method, was to draw suitable inferences from the findings and translate them into pedagogical practices. We describe our efforts and outline some continuing challenges. (shrink)

Philosophy and model theory frequently meet one another. Philosophy and Model Theory aims to understand their interactions -/- Model theory is used in every ‘theoretical’ branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging appeals to model theory have created a highly fragmented literature. On the one hand, many philosophically significant mathematical results are found only in mathematics textbooks: these are aimed squarely at mathematicians; (...) they typically presuppose that the reader has a significant background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are then scattered across disconnected pockets of papers, separated by decades or more. -/- The first aim of Philosophy and Model Theory, then, is to consider the philosophical uses of model theory. On a technical level, we try to show how philosophically significant results connect to one another, and also to state the best version of a result for philosophical purposes. On a philosophical level, we show how similar dialectical situations arise repeatedly, across fragmented debates in varied philosophical areas. -/- The second aim of Philosophy and Model Theory, though, is to consider the philosophy of model theory. Model theory itself is rarely taken as the subject matter of philosophising (contrast this, say, with the philosophy of biology, or the philosophy of set theory). But model theory is a beautiful part of pure mathematics, and worthy of philosophical study in its own right. (shrink)