An engaging and accessible introduction to mathematical proof incorporating ideas from real analysis A mathematical proof is an inferential argument for a mathematical statement. Since the time of the ancient Greek mathematicians, the proof has been a cornerstone of the science of mathematics. The goal of this book is to help students learn to follow and understand the function and structure of mathematical proof and to produce proofs of their own. An Introduction to Proof through Real Analysis is based on (...) course material developed and refined over thirty years by Professor Daniel J. Madden and was designed to function as a complete text for both first proofs and first analysis courses. Written in an engaging and accessible narrative style, this book systematically covers the basic techniques of proof writing, beginning with real numbers and progressing to logic, set theory, topology, and continuity. The book proceeds from natural numbers to rational numbers in a familiar way, and justifies the need for a rigorous definition of real numbers. The mathematical climax of the story it tells is the Intermediate Value Theorem, which justifies the notion that the real numbers are sufficient for solving all geometric problems. • Concentrates solely on designing proofs by placing instruction on proof writing on top of discussions of specific mathematical subjects • Departs from traditional guides to proofs by incorporating elements of both real analysis and algebraic representation • Written in an engaging narrative style to tell the story of proof and its meaning, function, and construction • Uses a particular mathematical idea as the focus of each type of proof presented • Developed from material that has been class-tested and fine-tuned over thirty years in university introductory courses An Introduction to Proof through Real Analysis is the ideal introductory text to proofs for second and third-year undergraduate mathematics students, especially those who have completed a calculus sequence, students learning real analysis for the first time, and those learning proofs for the first time. Daniel J. Madden, PhD, is an Associate Professor of Mathematics at The University of Arizona, Tucson, Arizona, USA. He has taught a junior level course introducing students to the idea of a rigorous proof based on real analysis almost every semester since 1990. Dr. Madden is the winner of the 2015 Southwest Section of the Mathematical Association of America Distinguished Teacher Award. Jason A. Aubrey, PhD, is Assistant Professor of Mathematics and Director, Mathematics Center of the University of Arizona. (shrink)

English education policy has increasingly focused on the need to intervene in an intergenerational cycle of poverty and low attainment. The accompanying policy discourse has tended to emphasise the impact of family background on educational outcomes. However, as the capacity of parents to secure positive educational outcomes for their children is closely linked to the quality of their own education, low attainment is rather more closely connected to what happens in schools than this focus suggests. Pupils from groups known to (...) be at increased risk of low attainment are also known to be at increased risk of involvement in the disciplinary processes of schools. This paper draws on the findings of a small-scale qualitative study to highlight some of the limitations in the educational provision accessed by Secondary age pupils involved in school exclusion processes. The assumptions and tensions at practice level that underpinned this provision are also discussed. In the conclusion it is argued that a much stronger focus on the learning of these pupils could improve their attainment and contribute to a reduction in social and educational inequalities in the future. (shrink)

Written by one of Ireland's leading medical law academics, this practical book comprehensively covers case law and regulations regarding the healthcare system, the law relating to human reproduction, and the key issues of consent and treatment. Designed to be used by lawyers and healthcare professionals, Medicine, Ethics and the Law in Ireland provides an invaluable reference tool for anybody who requires accurate information and guidance on this area of Irish law. This new edition includes: Medical research and clinical trials; Organ (...) donation and transportation; Patient safety and QA; and Biobanking. (shrink)

Thinking About Thinking: Mind and Meaning in the Era of Techno-Nihilism addresses our existential crisis by reminding us of the conditions for meaning that have been obscured by the modern technological mentality. Madden weaves together disparate insights from Wittgenstein, Hegel, Aristotle, Heidegger, Merleau-Ponty, Nietzsche, Sophocles, and others in an attempt to account for our mindedness in terms of its inextricable connection to a world capable of inspiring our care. The mind is not a discrete entity locked behind the skull or (...) withdrawn into a ghostly realm, but a participation in an inheritance (biological and cultural) held in common with other participants, and taking responsibility for that world is crucial for the meaning. The ever-increasing technological mediation of our lives undermines this worldliness. We are subsequently "losing our minds," and as our mindedness fades, so goes our sense of dignity and value. Madden makes this case deploying insights from phenomenology, analytic philosophy, Aristotelianism, neuroscience, and cognitive science, and along the way confronts the mind-body problem, freedom, artificial intelligence, transhumanism, and nihilism. More importantly, he invites the reader into an accessible dialogue concerning issues of grave importance to the meaning of our lives. (shrink)

From whence spring the sparks of creativity? It is to this very question that the field of depth psychology--especially that of C.G. Jung and his intellectual descendants--has much to contribute. Just as the Muses were the offspring of Mnemosyne, the goddess of memory, our memories are the ancestors of our creativity that finds its multifaceted expression in the written word, image, theater, dance, and music. The Unconscious Roots of Creativity seeks to push the investigation into that domain of memory that (...) is beyond our conscious reach. With articles from 16 contributors, the "red thread" running through each of the offerings in this volume is that, whatever its ultimate expression, the creative impulse has its roots deep in the psyche. Edited By Kathryn Madden, Leonard Cruz and Steven Buser with articles by Linda Carter, Anna Maria Costantino, Carol Thayer Cox, Leonard Cruz, Lisa Raye Garlock, James Hollis, Naomi Ruth Lowinsky, Ian Livingston, Kathryn Madden, Jordan S. Potash, Susan Rowland, Murray Stein, Ann Ulanov, Tjeu van den Berk, Robin van Loben Sels, and Heidi S. Volf. (shrink)

In 'Law as a Leap of Faith' Gardner's analogy of faith in law to faith in God may seem outlandish. But consider the implications of the positions Gardner's jurisprudential views assemble: law can give us reason to do what we would otherwise not have reason to do - in fact it can give us reason to do what would otherwise be immoral. This is the implication of a commitment to law's capacity to give exclusive reasons, on one hand, together with (...) the commitment, on the other, that any given law is valid because of its sources and not its moral merits. (shrink)

Generative AI appears to threaten argument creativity. Because of its capacity to generate coherent texts, individuals are likely to integrate its ideas, and not their own, into arguments, thereby reducing their creative contribution. This article argues that this view is mistaken—it rests on a misunderstanding of the nature of creativity. Within arguments, creative and critical thinking cannot be separated. Because creativity is enmeshed with skills such as analysis and evaluation, the use of generative AI in the construction of arguments, especially (...) in the role as universal audience, has the potential to heighten, not diminish argument creativity. (shrink)

Among semanticists and philosophers of language, there has been a recent outburst of interest in predicates such as delicious, called predicates of personal taste (PPTs, e.g. Lasersohn 2005). Somewhat surprisingly, the question of whether or how we can distinguish aesthetic predicates from PPTs has hardly been addressed at all in this recent work. It is precisely this question that we address. We investigate linguistic criteria that we argue can be used to delineate the class of specifically aesthetic adjectives. We show (...) that there are, in fact, good motivations for keeping PPTs and aesthetic predicates apart: the semantic structure of the former, but not the latter, entails an experiencer. There are many adjectives whose semantic structure arguably also entails an experiencer, yet which are readily used in expressing aesthetic judgments. Adjectives such as provocative or moving are a case in point, since as adjectives they arguably maintain the experiencer argument from the verb they are derived from. Nevertheless, when we describe, say, a sculpture as provocative, or a theater performance as moving, we clearly make aesthetic judgments. The difficult question, then, is to articulate the relationship between an aesthetic predicate (of which beautiful and ugly are paradigms) and other predicates that just happen to be used in making an aesthetic judgment. Tightly related to this point is the more general question of the relationship between an evaluative predicate and a predicate that occurs in an evaluative judgment. One of our aims is to make some progress in addressing these questions. (shrink)

Written for students, Mind, Matter, and Nature presumes no prior philosophical training on the part of the reader. The book nevertheless holds the arguments discussed to rigorous standards and is conversant with recent literature, thus making it useful as well to more advanced students and professionals interested in a resource on Thomistic hylomorphism in the philosophy of mind.

What Indiana Jones can teach us about the ethics of practicing and teaching archeology.

Abstract Few theoretical insights have emerged from the extensive literature discussions of petitio principii argument. In particular, the pattern of petitio analysis has largely been one of movement between the two sides of a dichotomy, that of form and content. In this paper, I trace the basis of this dichotomy to a dualist conception of mind and world. I argue for the rejection of the form/content dichotomy on the ground that its dualist presuppositions generate a reductionist analysis of certain concepts (...) which are central to the analysis of petitio argument. I contend, for example, that no syntactic relation can assimilate within its analysis the essentially holistic nature of a notion like justification. In this regard, I expound a form of dialectical criticism which has been frequently employed in the philosophical arguments of Hilary Putnam. Here the focus of analysis is upon the way in which the proponent of a position proceeds to explain or argue for his/her own particular theses. My conclusion points to the use of such dialectic within future analyses of petitio principii. (shrink)

In much eighteenth-century British literary criticism, passion distinguishes poetry from philosophy, whose ideas are too abstract to evoke emotion. At the end of the century, however, William Wordsworth radically refuses this distinction between poetry and philosophy, rejecting the centrality of passion for poetry. Instead, developing ideas latent in the work of James Beattie, he places affection at the heart of his poetic theory. This essay uncovers "the affections" as a major site of meaning for Wordsworth: calm, rationalized emotions, they yoke (...) together the philosophical and the poetical, enabling poetry not merely to stimulate emotion but moreover to think through it. (shrink)

Whilst care imperatives have arisen across the breadth of Western societies, within the education sector they appear both prolific and urgent. This paper explores the deployment of care discourses within education generally and draws upon the case of Australian Health and Physical Education (HPE) more specifically, to undertake a Foucauldian interrogation of care. In so doing I demonstrate the usefulness of Foucault's pastoral power lens and its capacity to provide insight into the moral and ethical work conducted by caring teachers (...) on behalf of the state (Acker, 1995). Following a brief overview of the advocacy, challenges and debates surrounding the issue of caring teaching within education, I draw on the work of Hunter (1994) and three case studies from a genealogical interrogation of HPE that employed Foucualt's ethical fourfold as a heuristic device to reveal the ethical practices and objectives of the good HPE teacher. Drawing on this genealogical work, I argue that HPE teachers and their colleagues have been purposefully incited to constitute themselves as agents of pastoral power. From this Foucauldian perspective, I conclude with an exploration of the unintended and possibly ‘dangerous’ practices of caring teaching that may emerge within the complex and messy nexus of contemporary self‐constitution. (shrink)

A picture book about the importance of following rules and taking responsibility.

When a chimpanzee stockpiles rocks as weapons or when a frog sends out mating calls, we might easily assume these animals know their own motivations--that they use the same psychological mechanisms that we do. But as Beyond the Brain indicates, this is a dangerous assumption because animals have different evolutionary trajectories, ecological niches, and physical attributes. How do these differences influence animal thinking and behavior? Removing our human-centered spectacles, Louise Barrett investigates the mind and brain and offers an alternative (...) approach for understanding animal and human cognition. Drawing on examples from animal behavior, comparative psychology, robotics, artificial life, developmental psychology, and cognitive science, Barrett provides remarkable new insights into how animals and humans depend on their bodies and environment--not just their brains--to behave intelligently. Barrett begins with an overview of human cognitive adaptations and how these color our views of other species, brains, and minds. Considering when it is worth having a big brain--or indeed having a brain at all--she investigates exactly what brains are good at. Showing that the brain's evolutionary function guides action in the world, she looks at how physical structure contributes to cognitive processes, and she demonstrates how these processes employ materials and resources in specific environments. Arguing that thinking and behavior constitute a property of the whole organism, not just the brain, Beyond the Brain illustrates how the body, brain, and cognition are tied to the wider world. (shrink)

Renowned as the chief challenger of traditional views of morality, man's freedom, and religion from 1650-1750, Benedict de Spinoza (1632-77) spread alarm and ...

This book investigates the nature of Feminist interventions in psychoanalysis by comparing the status and treatment of women in two different psychoanalytic ...

This chapter argues that gustatory properties such as sweetness or saltiness are not proprietary to the sense of taste. Rather, we can maintain the common-sense view that such properties can be smelled as well as tasted.

"Gill's and Ryan's Parmenides is, simply, superb: the Introduction, more than a hundred pages long, is transparently clear, takes the reader meticulously through the arguments, avoids perverseness, and still manages to make sense of the dialogue as a whole; there is a fine selective bibliography; and those parts of the translation I have looked at in detail suggest that it too is very good indeed." --Christopher Rowe, _Phronesis_.

Quelle lumière l'idée d'athéisme et la figure de l'athée jettent-elle sur les concepts de tolérance, de liberté de conscience et de laïcité? Pour répondre à cette question, cet ouvrage fait le choix d'éclairer le présent par une perspective historique, en analysant la manière dont l'athéisme est apparu et s'est développé dans le questionnement théologico-politique et philosophique depuis le XVIIe siècle."--Page 4 of cover.

This book evaluates some of the most common ethical issues confronted by reproductive endocrinologists, embryologists, and their teams. The authors apply core ethical principles and approaches to problem solving to each of the cases raised. This work is a guide for both those on the front lines of patient care as well as for students in the field, whatever their background. By outlining sample cases, the book is an instigator for ethical discussions among ethicists, medical practitioners and students.

Presents a set-theoretic version of the analysis of "there be" as predicating instantiation of a property, a property-theoretic version of which was developed in McNally 1992. This paper provides a solution to the criticism that McNally 1992's analysis could not account for sentences in which postverbal nominal contains a monotone decreasing or nonmonotonic determiner.

In this volume leading researchers present new work on the semantics and pragmatics of adjectives and adverbs, and their interfaces with syntax. Its concerns include the semantics of gradability; the relationship between adjectival scales and verbal aspect; the relationship between meaning and the positions of adjectives and adverbs in nominal and verbal projections; and the fine-grained semantics of different subclasses of adverbs and adverbs. Its goals are to provide a comprehensive vision of the linguistically significant structural and interpretive properties of (...) adjectives and adverbs, to highlight the similarities between these two categories, and to signal the importance of a careful and detailed integration of lexical and compositional semantics. The editors open the book with an overview of current research before introducing and contextualizing the remaining chapters. The work is aimed at scholars and advanced students of syntax, semantics, formal pragmatics, and discourse. It will also appeal to researchers in philosophy, psycholinguistics, and language acquisition interested in the syntax and semantics of adjectives and adverbs. (shrink)

In a quiet London office, a software designer muses on the algorithms that will make possible the risk flags to be visualized on the screens of border guards from Heathrow to St Pancras International. There is, he says, ‘real time decision making’ – to detain, to deport, to secondarily question or search – but there is also the ‘offline team who run the analytics and work out the best set of rules’. Writing the code that will decide the association rules (...) between items of data, prosaic and mundane – flight route, payment type, passport – the analysts derive a novel preemptive security measure. This paper proposes the analytic of the data derivative – a visualized risk flag or score drawn from an amalgam of disaggregated fragments of data, inferred from across the gaps between data and projected onto an array of uncertain futures. In contrast to disciplinary and enclosed techniques of collecting data to govern population, the data derivative functions via ‘differential curves of normality’, imagining a range of potential futures through the association rule, thus ‘opening up to let things happen’. In some senses akin to the risk orientation of the financial derivative, itself indifferent to actual underlying people, places or events by virtue of modulated norms, the contemporary security derivative is not centred on who we are, nor even on what our data say about us, but on what can be imagined and inferred about who we might be – on our very proclivities and potentialities. (shrink)