This book covers a wide variety of topics in combinatorics and graph theory.

Richard Peters argued for a general education based largely on the study of truth-seeking subjects for its own sake. His arguments have long been acknowledged as problematic. There are also difficulties with Paul Hirst's arguments for a liberal education, which in part overlap with Peters'. Where justification fails, can historical explanation illuminate? Peters was influenced by the prevailing idea that a secondary education should be based on traditional, largely knowledge-orientated subjects, pursued for intrinsic as well as practical ends. Does (...) history reveal good reasons for this view? The view itself has roots going back to the 16th century and the educational tradition of radical Protestantism. Religious arguments to do with restoring the image of an omniscient God in man made good sense, within their own terms, of an encyclopaedic approach to education. As these faded in prominence after 1800, old curricular patterns persisted in the drive for ‘middle-class schools’, and new, less plausible justifications grew in salience. These were based first on faculty psychology and later on the psychology of individual differences. The essay relates the views of Peters and Hirst to these historical arguments, asking how far their writings show traces of the religious argument mentioned, and how their views on education and the development of mind relate to the psychological arguments. (shrink)

Hirst always highlighted knowledge when reflecting on the school curriculum. He replaced his early focus on liberal education, the development of mind and theoretical knowledge by emphasizing the practical and practices as a curriculum starting point and for the framing of educational aims. In this paper I explore links between Hirst’s philosophical treatment of knowledge and some currently contested aspects of UK government education policies. I also note some ways in which his work relates to selected present-day debates (...) in philosophy of education. Examples of UK government policy will include Ofsted’s definition of learning as a ‘change in long-term memory’ and the ways in which they place ‘logical sequencing’ at the heart of teaching, learning, and curriculum. Their learning definition treats knowledge as an individual asset rather than something about individuals as embedded in the social world of practices, a perspective more in keeping with Hirst’s later views. The critique of individualistic notions of knowledge and learning includes some explorations of how learners move into the ‘space of reasons’. Where I draw attention to relationships between Hirst’s thought and contemporary philosophy of education debates, I do not always draw any definite conclusions. (shrink)

In a candid autobiographical chapter (Hirst 2010), which numbers among his last writings, Paul Hirst subjects his upbringing within a fundamentalist Christian sect to searching moral appraisal. He concludes that his parents wronged him by religiously indoctrinating him, stifling his emotional development, and arbitrarily restricting his range of valuable morally permissible experiences. This upbringing undermined his autonomy and—more fundamentally, on his account—kept him from living the life he had most reason to live. Surprisingly, however, Hirst suggests that (...) his parents had a right to initiate him into this conservative religious life, though the wider community owed him a more non-directive form of religious education to temper it. This is a striking concession to the scope of parental rights, especially in view of Hirst’s complaint that the emotional repression required by his parents was to ‘distort [his] experience and understanding of [himself] and others in ways that persisted well into [his] adult life’. Engaging with Hirst's evaluation of his upbringing, I argue for a narrower range of parental rights than Hirst–one which excludes a parental moral right to religious initiation–and provide an account of the kind of emotional experiences to which children plausibly have a right. (shrink)

In his contribution to Human Senses and Perception, R. J. Hirst has made a number of important suggestions about perceptual consciousness, He has emphasised the need to describe ‘what the percipient is or may be conscious of’ from the percipient's own point of view. This mode of description is contrasted with stimulus or neurological description. Perceptual consciousness of one object is distinguished from perceptual consciousness of another object ‘only by or on the evidence of, the person concerned’. The method (...) of obtaining descriptions of perceptual consciousness is either to question a percipient or to reflect on our own experience, The second important point stressed by Hirst is that the end product of perceiving is ‘the conscious experience of external objects’. Such an obvious point is often lost sight of in behavioural, dispositional, or neurophysiological analyses, The third and final suggestion made by Hirst to which I want to call attention is the usefulness of a genetic hypothesis to explain and account for perceptual consciousness. Hirst feels that perceptual consciousness is ‘unanalysable at the conscious level’, meaning that it is ‘a unitary awareness of objects or scenes’ and that the ‘various interacting unconscious activities’ which coexist with awareness ‘cannot be brought forward into consciousness’. The various analytical theories of perception have been designed to break perceptual consciousness into its components. This has resulted in their being false to perceptual consciousness. A genetic explanation of awareness has several advantages, prime among them being its ability to explain the complexity and development of awareness. (shrink)

In his contribution to Human Senses and Perception, R. J. Hirst has made a number of important suggestions about perceptual consciousness, He has emphasised the need to describe ‘what the percipient is or may be conscious of’ from the percipient's own point of view. This mode of description is contrasted with stimulus or neurological description. Perceptual consciousness of one object is distinguished from perceptual consciousness of another object ‘only by or on the evidence of, the person concerned’. The method (...) of obtaining descriptions of perceptual consciousness is either to question a percipient or to reflect on our own experience, The second important point stressed by Hirst is that the end product of perceiving is ‘the conscious experience of external objects’. Such an obvious point is often lost sight of in behavioural, dispositional, or neurophysiological analyses, The third and final suggestion made by Hirst to which I want to call attention is the usefulness of a genetic hypothesis to explain and account for perceptual consciousness. Hirst feels that perceptual consciousness is ‘unanalysable at the conscious level’, meaning that it is ‘a unitary awareness of objects or scenes’ and that the ‘various interacting unconscious activities’ which coexist with awareness ‘cannot be brought forward into consciousness’. The various analytical theories of perception have been designed to break perceptual consciousness into its components. This has resulted in their being false to perceptual consciousness. A genetic explanation of awareness has several advantages, prime among them being its ability to explain the complexity and development of awareness. (shrink)

This chapter contains sections titled: 1. 2. 3. 4. 5. 6. 7. 8. 9. Notes References.

The study of remembering is both compelling and challenging, in part, because of the multiplicity and the complexity of influences on memory. Whatever their interests, memory researchers are always aware of the many different factors that can drive the processes they care about. A search for the phrase ‘influences on memory’ confirms this daunting and exhilarating array of influences, of many different kinds, operating at many different timescales, and presumably often interacting in ways that we can’t yet imagine, let alone (...) model. There are hormonal and neuromodulatory, genetic and pharmacological, developmental and age-related influences; there are influences of arousal, stress, gender, mood, emotion, sleep and personality; there are unconscious, schematic or semantic influences, and there are influences of context, situation, task and environment. There are many aspects of ‘media influence on memory’ (Loftus and Banaji, 1989; Strange and Garry, 2007), and, of course, there are both ‘social influences on memory’ (Echterhoff and Hirst, 2009) and ‘cultural influences on memory’ (Gutchess and Indeck, 2009). Notoriously, there are numerous ‘suggestive influences’ on memory (Loftus, 2003): influences of misinformation (Seifert, 2002; Wright and Loftus, 1998), or of ‘memory conformity’ (Gabbert et al., 2006) and ‘memory contagion’ (Roediger et al., 2002). People who know each other well, such as intimate couples, ‘may be well practised in yielding to each other’s influence and incorporating their partner’s information into their own memories of the past’ (French et al., 2008: 264). (shrink)

This paper focuses on recent debates over the nature ofliberalism and its central feature of reason, both inside and outside ofeducational philosophy. Central ideas from Jonathan and Hirst contributeas do those from Rawls, Gadamer, Wittgenstein, Taylor, and Ackermantoward a less traditional contextualized and contingent view.

A reflection on the aesthetic status of some typical objects of everyday life, and the relationship we have with them, may originate from the development of “aesthetic experience” by John Dewey and Neopragmatism. The continuity between the common practices and aesthetic ones determines the significance of ordinary objects if they are linked to a project of enrichment and fulfillment of experience. A case that thematizes the richness of these practices in the contemporary world, and also the related theoretical and (...) critical problems, is the production of skateboards. An established artist like Damien Hirst collaborates with the NYC-based streetwear brand Supreme; a new London-based brand, Palace Skateboards, and Tate realize together a few skateboard and a video. (shrink)

Paul Hirst’s philosophical ‘conversion’ from forms of knowledge to forms of social practices was largely prompted by his radical reappraisal of the philosophical underpinnings that had validated his classic conception of liberal education. The primary motivation for Hirst’s later works was to remedy his own neglect of practical reason, whose sharp distinction from theoretical reason he acknowledged he had failed to appreciate. There is much to commend in his ‘practical’ turn. The main challenge that remains, however, is that (...) the social practices view is something of a ‘foundationalist’ two-part picture, where overwhelming priority is given to practical reason. I appreciate the importance of the two issues Hirst puts on the table, in his debate with Wilfred Carr particularly and in his later works more generally: the issues of cultivating phronesis and of making sense of the practical character of critical-reflective activities. But I argue that addressing these issues fully requires us to recognize that neither theoretical nor practical rationality can be intelligible apart from the other. To press the point home, I review the analogous debate between Hubert Dreyfus and John McDowell over whether to accept, and how to understand, the view that rational conceptuality in a relevant sense pervades not only deliberation and propositional thinking but also perception and embodied coping skills. I conclude by briefly considering the prospect that the legacy of Hirst and recent discussions around human nature, practical rationality, and the formation of reason will interactively enrich our philosophical-educational scholarship. (shrink)

We show that a statement HIL, which is motivated by a lemma of Hilbert and close in formulation to Hindman’s theorem, is actually much weaker than Hindman’s theorem. In particular, HIL is finitistically reducible in the sense of Hilbert’s program, while Hindman’s theorem is not.

With precision and profundity born of 30 years of devoted study, John Boyle offers an essential introduction to St. Thomas Aquinas on Scripture, shedding helpful light on the goals, methods, and commitments that animate the Angelic Doctor's engagement with the sacred page. Because the genius of St. Thomas's approach to the Bible lies not so much in its novelty but rather in the fidelity and clarity with which he recapitulates the riches of the preceding interpretive Tradition, this initiation into (...) St. Thomas's vision of Scripture is itself an orientation to the Church's vision of Scripture, from the Fathers through and beyond the Middle Ages. St. Thomas's embeddedness within the Church's Tradition and his own historical context is integral to his approach to Scripture, yet it sets him at some distance from modern readers, for whom his interpretive vision may seem perplexing or even impenetrable. In this Primer, Boyle first provides an acclimation to this medieval context through a survey and explanation of pertinent technical terminology used by St. Thomas and characteristic of the scholastic theology of the time. With an eye to the medieval practice of considering Scripture according to the fourfold division of causes, Boyle builds on this initial foundation by exploring in turn St. Thomas's accounts of the end or use of Scripture (final cause), its divine and human authorship (efficient cause), its order and division (material cause), and its literary styles or genres (formal cause). Drawing on writings from across St. Thomas's corpus, but especially his work On the Commendation and Division of Sacred Scripture and the prologues to his biblical commentaries, Boyle masterfully elucidates both the hermeneutical principles and deep wisdom of the Angelic Doctor's approach to Scripture, imparting invaluable guidance not only for reading and understanding St. Thomas and other great masters of the Tradition, but also-and ultimately-for understanding Scripture in light of this Tradition and reading it with greater benefit and joy. (shrink)

One of the earliest applications of Cantor's Normal Form Theorem is Jacobstahl's proof of the existence of prime factorizations of ordinals. Applying the techniques of reverse mathematics, we show that the full strength of the Normal Form Theorem is used in this proof.

The notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master. In particular, undergraduate mathematics students often experience difficulties in understanding and constructing proofs. Understanding Mathematical Proof describes the nature of mathematical proof, explores the various techniques that mathematicians adopt to prove their results, and offers advice and strategies for constructing proofs. It will improve students’ ability to understand proofs and construct correct proofs of their own. The (...) first chapter of the text introduces the kind of reasoning that mathematicians use when writing their proofs and gives some example proofs to set the scene. The book then describes basic logic to enable an understanding of the structure of both individual mathematical statements and whole mathematical proofs. It also explains the notions of sets and functions and dissects several proofs with a view to exposing some of the underlying features common to most mathematical proofs. The remainder of the book delves further into different types of proof, including direct proof, proof using contrapositive, proof by contradiction, and mathematical induction. The authors also discuss existence and uniqueness proofs and the role of counter examples. (shrink)

Despite recurring efforts, a gap exists across a variety of contexts between the protection of patients' safety in theory and in practice. This timely Research Handbook highlights these critical issues and suggests both legal and policy changes are necessary to better protect patients' safety. Multidisciplinary in nature, this Research Handbook features contributions from eminent academics, policy makers and medical practitioners from the Global North and South, discussing the essential facets concerning patient safety and the law. It highlights how the role (...) of legislation and case law has the potential to influence, both positively and negatively, medical practice and the quality of care. Chapters explore patient safety and the global health agenda; physiotherapy; 'non-therapeutic' clinical research with children; patient safety awareness in healthcare education; and the increasing use of robotics and artificial intelligence in healthcare. Outlining a wide range of international perspectives on patient safety and the law, this Research Handbook will appeal to academics and researchers specialising in health and medical law, human rights and healthcare regulation. It will also serve as a valuable resource for legal and medical practitioners alike, as well as clinicians and professionals working in healthcare governance. (shrink)

Samkara (c. 700 CE), the great Indian Advaitin thinker, was a commentator on sacred text and an Advaitin teacher. This book provides an introduction to the thought of Samkara, who is the most well-known and most perhaps the most authoritative Hindu thinker of all time. The author develops an innovative approach using Samkara's method of interpreting sacred texts and creatively examines the profound interrelationship between sacred text, content and method in Samkara's thought. In particular Samkara's teaching method is the main (...) focus of this book; it is a method that is based on Upanisadic truth and expects teachers to skillfully draw pupils towards it. This book will be of interest to students and scholars of Indian philosophy. (shrink)

For this second edition, the editors have returned to Austin's original lecture notes, amending the printed text where it seemed necessary.

Is the assimilation of these two formulations of the moral principle by Kant and some of his expositors justified? In the Analytic of Pure Practical Reason Kant claims that his view of morality agrees with the ancient command that man should love his neighbour as himself. Also in the Fundamental Principles of the Metaphysic of Morals he regards the Golden Rule as a deduction, though with several limitations, from the second version of the Categorical Imperative.

Recently, several authors have explored the connections between NP-complete problems for finite objects and the complexity of their analogs for infinite objects. In this paper, we will categorize infinite versions of several problems arising from finite complexity theory in terms of their recursion theoretic complexity and proof theoretic strength. These infinite analogs can behave in a variety of unexpected ways.

Dewey's book on Democracy and Education established his credentials in the field of education and once counted as his most important book. It has been re-published in many editions and continuously in print ever since the original publication in 1916.

Though the revised edition of A Theory of Justice, published in 1999, is the definitive statement of Rawls's view, so much of the extensive literature on Rawls's theory refers to the first edition. This reissue makes the first edition once again available for scholars and serious students of Rawls's work.

We prove that the statement “there is aksuch that for everyfthere is ak-bounded diagonally nonrecursive function relative tof” does not imply weak König’s lemma over${\rm{RC}}{{\rm{A}}_0} + {\rm{B\Sigma }}_2^0$. This answers a question posed by Simpson. A recursion-theoretic consequence is that the classic fact that everyk-bounded diagonally nonrecursive function computes a 2-bounded diagonally nonrecursive function may fail in the absence of${\rm{I\Sigma }}_2^0$.

Theories of discourse bring to realism new ideas about how knowledge develops and how representations of reality are influenced. We gain an understanding of the conceptual aspect of social life and the processes by which meaning is produced. This collection reflects the growing interest realist critics have shown towards forms of discourse theory and deconstruction. The diverse range of contributions address such issues as the work of Derrida and deconstruction, discourse theory, Eurocentrism and poststructuralism. What unites all of the contributions (...) is a sense that it is essential to provide a realist alternative to the hitherto dominance of social constructionism, hermeneutics and postmodernism, over many of the issues discussed. By developing a realist perspective the different authors attempt to embed discourse within the structured nature of the reality of the world. Realism can situate language, discourse and ideology within context specific, or 'causally efficacious' circumstances. Realism can help to uncover issues of power, representation, and subjectivity and how discursive and other social practices produce real effects. This can help us understand the manner in which social structures are reproduced through various forms of ideology and discourse. And by knowing this, we can start to address questions concerning human emancipation and how the world is to be transformed. (shrink)

This book continues and revises the ideas of justice as fairness that John Rawls presented in _A Theory of Justice_ but changes its philosophical interpretation in a fundamental way. That previous work assumed what Rawls calls a "well-ordered society," one that is stable and relatively homogenous in its basic moral beliefs and in which there is broad agreement about what constitutes the good life. Yet in modern democratic society a plurality of incompatible and irreconcilable doctrines--religious, philosophical, and moral--coexist within (...) the framework of democratic institutions. Recognizing this as a permanent condition of democracy, Rawls asks how a stable and just society of free and equal citizens can live in concord when divided by reasonable but incompatible doctrines? This edition includes the essay "The Idea of Public Reason Revisited," which outlines Rawls ' plans to revise _Political Liberalism,_ which were cut short by his death. "An extraordinary well-reasoned commentary on _A Theory of Justice_...a decisive turn towards political philosophy." --_Times Literary Supplement_. (shrink)

The book also includes a chronological table of significant events, select bibliography, succinct explanatory notes, and an index--all of which supply ...

The renowned philosopher John Searle reveals the fundamental nature of social reality. What kinds of things are money, property, governments, nations, marriages, cocktail parties, and football games? Searle explains the key role played by language in the creation, constitution, and maintenance of social reality. We make statements about social facts that are completely objective, for example: Barack Obama is President of the United States, the piece of paper in my hand is a twenty-dollar bill, I got married in London, (...) etc. And yet these facts only exist because we think they exist. How is it possible that we can have factual objective knowledge of a reality that is created by subjective opinions? This is part of a much larger question: How can we give an account of ourselves, with our peculiar human traits DS mind, reason, freedom, society - in a world that we know independently consists of mindless, meaningless particles? How can we account for our social and mental existence in a realm of brute physical facts? In answering this question, Searle avoids postulating different realms of being, a mental and a physical, or worse yet, a mental, a physical, and a social. There is just one reality: Searle shows how the human reality fits into that one reality. Mind, language, and civilization are natural products of the basic facts of the physical world described by physics, chemistry and biology. Searle explains how language creates and maintains the elaborate structures of human social institutions. These institutions serve to create and distribute power relations that are pervasive and often invisible. These power relations motivate human actions in a way that provides the glue that holds human civilization together. Searle shows how this account illuminates human rationality, free will, political power, and human rights. Our social world is a world created and maintained by language. (shrink)

In The Construction of Social Reality, John Searle argues that there are two kinds of facts--some that are independent of human observers, and some that require..

A Norton Library edition of Locke's Second Treatise of Government, edited by A. John Simmons.

This book comprises all of John Bell's published and unpublished papers in the field of quantum mechanics, including two papers that appeared after the first edition was published. It also contains a preface written for the first edition, and an introduction by Alain Aspect that puts into context Bell's great contribution to the quantum philosophy debate. One of the leading expositors and interpreters of modern quantum theory, John Bell played a major role in the development of our current (...) understanding of the profound nature of quantum concepts. First edition Hb (1987): 0-521-33495-0 First edition Pb (1988): 0-521-36869-3. (shrink)

Reissued here in its corrected second edition of 1864, this essay by John Stuart Mill argues for a utilitarian theory of morality. Originally printed as a series of three articles in Fraser's Magazine in 1861, the work sought to refine the 'greatest happiness' principle that had been championed by Jeremy Bentham, defending it from common criticisms, and offering a justification of its validity. Following Bentham, Mill holds that actions can be judged as right or wrong depending on whether they (...) promote happiness or 'the reverse of happiness'. Although attracted by Bentham's consequentialist framework based on empirical evidence rather than intuition, Mill separates happiness into 'higher' and 'lower' pleasures, arguing for a weighted system of measurement when making and judging decisions. Dissected and debated since its first appearance, the essay is Mill's key discussion on the topic and remains a fundamental text in the study of ethics. (shrink)