We prove that there exists a nonzero recursively enumerable Turing degree possessing a strong minimal cover.

My ultimate purpose here is to examine, discuss, and interpret a difficult excerpt in Stobaeus’ 5th c. AD anthology, alleging to report—uniquely, it appears—a distinction Chrysippus drew between three different applications of the term stoixe›on or element (i.e., physical element).1 Stobaeus lists this passage as giving opinions specifically of Chrysippus “about the elements out of substance” (per‹ t«n §k t∞w oÈs€aw stoixe€vn), though in holding them he says Chrysippus was following Zeno, the leader of his sect. Hermann Diels (1879) identified (...) this selection as an excerpt (his fr. 21) from Arius Didymus’ late first century BC Epitome of Physical Doctrines.2 I print a translation below, with the text in an Appendix, as it is given in von Arnim (1903). The text is not without its problems, and I indicate in footnotes to the text which of the principal editors’ textual interventions I accept and follow in my translation. Whether this text presents a single, continuous excerpt from Arius Didymus, or instead some compilation of Stobaeus (or an earlier anthologist whose work Stobaeus employed) from dispersed passages of.. (shrink)

Educational policy and discussion, in Britain and the USA, are increasingly dominated by the confused ideology of egalitarianism. David E. Cooper begins by identifying the principles hidden among the confusions, and argues that these necessarily conflict with the ideal of educational excellence - in which conflict it is this ideal that must be preserved. He goes on to criticize the use of education as a tool for promoting wider social equality, focussing especially on the muddles surrounding 'equal opportunities', 'social mix' (...) and 'reverse discrimination'. Further chapters criticize the 'new egalitarianism' favoured, on epistemological grounds, by various sociologists of knowledge in recent years and 'cultural egalitarianism' according to which standard criteria of educational value merely reflect parochial and economic interests. (shrink)

Any account of knowledge has to take account both of the contribution of the world and the contribution of man. Every human endeavour, every activity, every art, every science is a product of a unique interaction between man and the world. Where man is most passive, he merely reflects and reports the world; this is pure discovery, if it ever exists. Where man is most active, the world's contribution lies merely in the provision of the raw material; this is pure (...) invention, if it ever exists. All the arts, all the sciences can be ordered in a continuous array or spectrum ranging from pure discovery to pure invention. That they are all at some point on this continuum gives them a common but fragile thread, justifying our thinking and talking of the unity of the arts and sciences. Philosophy is neither pure discovery nor pure invention; it bears resemblances to both a science and an art. In this paper I propose to try to give reasons why we should regard the philosopher as an artist and philosophy as an art; or, at any rate, I shall try to show that there is an Art of Philosophy. (shrink)

_ The Routledge Encyclopaedia of Educational Thinkers_ comprises 128 essays by leading scholars analysing the most important, influential, innovative and interesting thinkers on education of all time. Each of the chronologically arranged entries explores why a particular thinker is significant for those who study education and explores the social, historical and political contexts in which the thinker worked. Ranging from Confucius and Montessori to Dewey and Edward de Bono, the entries form concise, accessible summaries of the greatest or most influential (...) educational thinkers of past and present times. Each essay includes the following features; concise biographical information on the individual, an outline of the individual’s key achievements and activities, an assessment of their impact and influence, a list of their major writings, suggested further reading. Carefully brought together to present a balance of gender and geographical contexts as well as areas of thought and work in the broad field of education, this substantial volume provides a unique history and overview of figures who have shaped education and educational thinking throughout the world. Combining and building upon two internationally renowned volumes, this collection is deliberately broad in scope, crossing centuries, boundaries and disciplines. The Encyclopaedia therefore provides a perfect introduction to the huge range and diversity of educational thought. Offering an accessible means of understanding the emergence and development of what is currently seen in the classroom, this Encyclopaedia is an invaluable reference guide for all students of education, including undergraduates and post-graduates in education or teacher training and students of related disciplines. (shrink)

Andrew Cooper presents the first systematic study of Kant's account of natural history. Cooper contends that Kant made a decisive contribution to one of the most explosive and understudied revolutions in the history of science: the addition of time to the frame in which explanations are required, sought, and justified in natural science. Through addressing a wide range of Kant's works, Cooper challenges the claim that Kant's theory of science denies a developmental conception of nature and argues instead that it (...) establishes a method by which natural historians can genuinely dispute historical claims and potentially come to consensus. This method, Cooper argues, can be used to expose serious flaws in Kant's own historical reasoning, including the formation and defence of his racist views. The book will be valuable to philosophers seeking to discern both the power and limitations of Kant's theory of science, and to historians of science working on the fractured landscape of eighteenth-century Newtonianism. (shrink)

Computability theory concerns information with a causal–typically algorithmic–structure. As such, it provides a schematic analysis of many naturally occurring situations. Emil Post was the first to focus on the close relationship between information, coded as real numbers, and its algorithmic infrastructure. Having characterised the close connection between the quantifier type of a real and the Turing jump operation, he looked for more subtle ways in which information entails a particular causal context. Specifically, he wanted to find simple relations on reals (...) which produced richness of local computability-theoretic structure. To this extent, he was not just interested in causal structure as an abstraction, but in the way in which this structure emerges in natural contexts. Post’s programme was the genesis of a more far reaching research project. In this article we will firstly review the history of Post’s programme, and look at two interesting developments of Post’s approach. The first of these developments concerns the extension of the core programme, initially restricted to the Turing structure of the computably enumerable sets of natural numbers, to the Ershov hierarchy of sets. The second looks at how new types of information coming from the recent growth of research into randomness, and the revealing of unexpected new computability-theoretic infrastructure. We will conclude by viewing Post’s programme from a more general perspective. We will look at how algorithmic structure does not just emerge mathematically from information, but how that emergent structure can model the emergence of very basic aspects of the real world. (shrink)

I Deliberation, Practical Syllogisms , and Intuition. Introduction Aristotle's views on moral reasoning are a difficult and much disputed subject. ...

It has been suggested that the enterprise of developing mechanistic theories of the human cognitive architecture is flawed because the theories produced are not directly falsifiable. Newell attempted to sidestep this criticism by arguing for a Lakatosian model of scientific progress in which cognitive architectures should be understood as theories that develop over time. However, Newell's own candidate cognitive architecture adhered only loosely to Lakatosian principles. This paper reconsiders the role of falsification and the potential utility of Lakatosian principles in (...) the development of cognitive architectures. It is argued that a lack of direct falsifiability need not undermine the scientific development of a cognitive architecture if broadly Lakatosian principles are adopted. Moreover, it is demonstrated that the Lakatosian concepts of positive and negative heuristics for theory development and of general heuristic power offer methods for guiding the development of an architecture and for evaluating the contribution and potential of an architecture's research program. (shrink)

This engaging volume explores and defends the claim that misanthropy is a justified attitude towards humankind in the light of how human beings both compare with and treat animals. Reflection on differences between humans and animals helps to confirm the misanthropic verdict, while reflection on the moral and other failings manifest in our treatment of animals illuminates what is wrong with this treatment. Human failings, it is argued, are too entrenched to permit optimism about the future of animals, but ways (...) are proposed in which individual people may accommodate to the truth of misanthropy through cultivating mindful, humble and compassionate relationships to animals. Drawing on both Eastern and Western philosophical traditions David E. Cooper offers an original and challenging approach to the complex field of animal ethics. (shrink)

Classifying Madness (Springer, 2005) concerns philosophical problems with the Diagnostic and Statistical Manual of Mental Disorders, more commonly known as the D.S.M. The D.S.M. is published by the American Psychiatric Association and aims to list and describe all mental disorders. The first half of Classifying Madness asks whether the project of constructing a classification of mental disorders that reflects natural distinctions makes sense. Chapters examine the nature of mental illness, and also consider whether mental disorders fall into natural kinds. The (...) second half of the book addresses epistemic worries. Even supposing a natural classification system to be possible in principle, there may be reasons to be suspicious of the categories included in the D.S.M. I examine the extent to which the D.S.M. depends on psychiatric theory, and look at how it has been shaped by social and financial factors. I aim to be critical of the D.S.M. without being antagonistic towards it. Ultimately, however, I am forced to conclude that although the D.S.M. is of immense practical importance, it is unlikely to come to reflect the natural structure of mental disorders. (shrink)

Outstanding translations by leading contemporary scholars--many commissioned especially for this volume--are presented here in the first single edition to include the entire surviving corpus of works attributed to Plato in antiquity. In his introductory essay, John Cooper explains the presentation of these works, discusses questions concerning the chronology of their composition, comments on the dialogue form in which Plato wrote, and offers guidance on approaching the reading and study of Plato's works. Also included are concise introductions by Cooper and Hutchinson (...) to each translation, meticulous annotation designed to serve both scholar and general reader, and a comprehensive index. This handsome volume offers fine paper and a high-quality Smyth-sewn cloth binding in a sturdy, elegant edition. (shrink)

We shall argue that there is adequate moral justification for capital punishment with linkage, that is, with linkage to keeping non‐murderers from dying. We present the argument with two aims in mind. The first is to question the conventional wisdom, seldom challenged even by proponents of capital punishment, that being an abolitionist is closely connected to having a civilized respect for human life. This conventional wisdom, we hope to show, is somewhat off the mark. To this end we exhibit structural (...) similarities between so‐called lifeboat dilemmas and the public's relationship to a murderer. In a lifeboat dilemma one must choose between saving this life or that, since the lifeboat will not hold both persons. Now if this life were an innocent's and that one a murderer's, a choice to save the latter would not be met with accusations of callousness towards human life. We hope to project everyone's intuitions about this case onto the more baffling case of a society's relationship to the murderers and dying innocents in its midst. (shrink)

Throughout the twentieth century, aestheticians and art theorists declared the 'death' of beauty as a serious, meaningful concept for aesthetics and art practice. Such declarations are better understood as polemical provocations, making their obituarism premature. Careful attention to the writings of those cited testify to the persistence of beauty, albeit in new, 'difficult', 'challenging' forms. Beauty persists, taking on new forms and inflections.

Why do gardens matter so much and mean so much to people? That is the intriguing question to which David Cooper seeks an answer in this book. Given the enthusiasm for gardens in human civilization ancient and modern, Eastern and Western, it is surprising that the question has been so long neglected by modern philosophy. Now at last there is a philosophy of gardens. David Cooper identifies garden appreciation as a special human phenomenon distinct from both from the appreciation of (...) art and the appreciation of nature. He discusses the contribution of gardening and other garden-related pursuits to "the good life." And he distinguishes the many kinds of meanings that gardens may have, from their representation of nature to their spiritual significance. A Philosophy of Gardens will open up this subject to students and scholars of aesthetics, ethics, and cultural and environmental studies, and to anyone with a reflective interest in things horticultural. (shrink)

The logical properties of the 'if-then' connective of ordinary English differ markedly from the logical properties of the material conditional of classical, two-valued logic. This becomes apparent upon examination of arguments in conversational English which involve (noncounterfactual) usages of if-then'. A nonclassical system of propositional logic is presented, whose conditional connective has logical properties approximating those of 'if-then'. This proposed system reduces, in a sense, to the classical logic. Moreover, because it is equivalent to a certain nonstandard three-valued logic, its (...) decision procedure is almost as efficient as that of the classical logic. It therefore provides a rational and convenient system in which to formalize English arguments. (shrink)

Mabel Cooper and Gloria Ferris lived in St Lawrence's Hospital one of the large learning disability institutions which were built round the edges of London. In this paper, Mabel and Gloria share their memories of three nurses at St Lawrence's, supported by Jane Abraham and in this process reveal a number of ethical issues that remain relevant today.

This paper aims to strengthen the liberal theory of public justification defended by John Rawls and his followers, by arguing that advocates of political liberalism can have more to say about how citizens can come to endorse and give priority to liberal justice than has been commonly supposed. The political conception of the person, complete with the two powers of moral personality, contains within it all the resources we need to illustrate why reasonable persons would have at least one good (...) reason to endorse and uphold liberal justice, and to make it regulative of their pursuit of their conceptions of the good. This is achieved by citizens’ feelings of care and affective concern toward their higher-order interests—their sense of justice, and their conception of the good. (shrink)