Recently, G. ASSER has obtained two interesting characterizations of the class of unary primitive recursive string-functions over a fixed alphabet as Robinson algebras. Both characterizations use a somewhat artificial string-function, namely the string-function lexicographically associated with the number-theoretical excess-over-a-square function. Our aim is to offer two new and natural Robinson algebras which are equivalent to ASSER’S algebras.

I hope you have had no trouble identifying this issue of our journal, even if the cover has been changed slightly. I would like to draw your attention to a more essential improvement in the journal's affairs: namely, that the Editorial Board has been enlarged by four new members. These are the following: Douglas Bridges , Ulrich Kohlenbach , H. Dugald Macpherson , and Pavel Pudlak . Please don't hesitate to contact a fellow editor, in particular the managing editor, if (...) you have suggestions for improving either the editorial procedures or the content and form of MLQ.The aims and scope of our journal are unchanged from the original ones developed by Günter Asser. His name is indissolubly connected with the former “Zeitschrift für Mathematische Logik und Grundlagen der Mathematik ”, now known as “Mathematical Logic Quarterly ”. He was one of the two founding editors and then the editor-in-chief of the journal until the 50th volume appeared about one year ago. Single-handedly, and almost incredibly, he showed that it is possible for one man to be the main editor of a successful highlevel scientific journal throughout half a century. He remains involved in and concerned with the editorial process of MLQ. For example, he carefully looks at every article to be published, faithfully checking almost every line of the final layout.On 26 February 2006, Professor Dr. Günter Asser celebrates his 80th birthday. I would like to take this opportunity, on behalf of the whole readership and of all fellow editors of ZML and MLQ throughout the last 51 years, to congratulate him cordially and to wish him good health and all the best for the future.The present issue starts with a paper directly related to G. Asser's spectrum conjecture. Then there are some papers specially dedicated to him, as well as further contributions, as always scrutinised and then recommended by expert referees. So this turns out to be an appropriate birthday issue. (shrink)

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

Given the sordid history of injustices linking genetics to race and ethnicity, considerations of justice are central to ensuring the responsible development of precision medicine programmes around the world. While considerations of justice may be in tension with other areas of concern, such as scientific value or privacy, there are also tensions between different aspects of justice. This paper focuses on three particular aspects of justice relevant to this precision medicine: social justice, distributive justice and human rights. We describe the (...) implications of each for the use of race and ethnicity in precision medicine, and also how they intersect and potentially conflict with each another. By attending to these intersections, we aim to enrich and add nuance to debates over how best to proceed with precision medicine initiatives. (shrink)

John Buridan was a fourteenth-century philosopher who enjoyed an enormous reputation for about two hundred years, was then totally neglected, and is now being 'rediscovered' through his relevance to contemporary work in philosophical logic. The final chapter of Buridan's Sophismata deals with problems about self-reference, and in particular with the semantic paradoxes. He offers his own distinctive solution to the well-known 'Liar Paradox' and introduces a number of other paradoxes that will be unfamiliar to most logicians. Buridan also moves on (...) from these problems to more general questions about the nature of propositions, the criteria of their truth and falsity and the concepts of validity and knowledge. This edition of that chapter is intended to make Buridan's ideas and arguments accessible to a wider range of readers. The volume should interest many philosophers, linguists and logicians, who are increasingly finding in medieval work striking anticipations of their own concerns. (shrink)

Graduate-level historical study is ideal for students intending to specialize in the topic, as well as those who only need a general treatment. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics, emphasizing Hilbert’s metamathematics. Part III focuses on the philosophy of mathematics. Each chapter has extensive supplementary notes; a detailed appendix charts modern developments.

Currently fashionable among critics of enlightenment thought is the charge that Kant's ethics fails to provide an adequate account of character and its formation in moral and political life. G. Felicitas Munzel challenges this reading of Kant's thought, claiming not only that Kant has a very rich notion of moral character, but also that it is a conception of systematic importance for his thought, linking the formal moral with the critical, aesthetic, anthropological, and biological aspects of his philosophy. The first (...) book to focus on character formation in Kant's moral philosophy, it builds on important recent work on Kant's aesthetics and anthropology, and brings these to bear on moral issues. Munzel traces Kant's multifaceted definition of character through the broad range of his writings, and then explores the structure of character, its actual exercise in the world, and its cultivation. An outstanding work of original textual analysis and interpretation, _Kant's Conception of Moral Character_ is a major contribution to Kant studies and moral philosophy in general. (shrink)

This volume is a critical edition of the eight-year correspondence between Gottfried Wilhelm Leibniz and Burcher de Volder, professor of philosophy and mathematics at Leiden University. Containing the surviving correspondence between Leibniz and De Volder, the volume also presents a generous selection from the letters between Leibniz and his friend Johann Bernoulli, through whose intercession the correspondence began. Bernoulli acted as intermediary throughout, and the often candid discussions between Leibniz and Bernoulli provide illuminating background to the correspondence proper. Each of (...) the selections appears both in the original Latin and in English translation. (shrink)

Taking a set of central issues from ancient Greek medicine and biology, this book studies firstly, the interaction between scientific theorising and folklore or popular assumptions; secondly, the ideological character of scientific inquiry. Topics of interest in the philosphy and sociology of science illuminated here include the relationship between primitive thought and early science, the roles of the consensus on the scientific community, tradition and the authority of the written text, in the development of science.

Philosophers and logicians have long debated how best to understand conditional or hypothetical sentences. William G. Lycan has a distinctive approach to this debate, attending not just to the semantics of such sentences, but equally to their syntax. He shows how insights from linguistic theory help to illuminate problems about the meaning and function of conditionals. For instance, philosophers and logicians have had problems analysing the locutions 'only if', 'unless', and 'even if'. Lycan sets out a general semantic theory of (...) conditionals which works for all such sentences; he assigns meanings to them in a way that explains how and why those meanings depend upon features of utterance context. According to Lycan's theory the 'if'-clauses refer to items called 'events', 'circumstances', or 'conditions'.Real Conditionals gives at last the definitive presentation of this original approach to a topic at the intersection of philosophy, logic, and linguistics. Lycan's characteristically lively and witty expository style ensures that it can be enjoyed by readers from all three disciplines. (shrink)

In their recent article, Koplin, Gyngell and Savulescu (2019) assess the viability of the precautionary principle as a decision-making tool to determine whether and under what circumstances germline gene editing should proceed. While their survey of different forms of the precautionary principle is illuminating, the most novel contribution is a new account of the precautionary principle, what they dub the Sufficientarian Precautionary Principle (SPP). SPP is meant to avoid several problems with existing accounts, while comporting with at least some of (...) the intuitive force behind the general idea of the precautionary principle. However, as it is only one subsection of a larger paper, SPP is not fully worked out. In this brief response, I will flesh out some problems with SPP as a decision-making tool – particularly that there is a lack of adequate normative justification for adopting it. While this does not constitute a decisive refutation of the approach, SPP needs considerable refinement and clarification before it can be considered viable for use in decision-making. (shrink)

Dr Lloyd writes for those who want to discover and explore Aristotle's work for themselves. He acts as mediator between Aristotle and the modern reader. The book is divided into two parts. The first tells the story of Aristotle's intellectual development as far as it can be reconstructed; the second presents the fundamentals of his thought in the main fields of inquiry which interested him: logic and metaphysics, physics, psychology, ethics, politics, and literary criticism. The final chapter considers the unity (...) and coherence of Aristotle's philosophy, and records briefly his later influence on European thought. This is a concise and lucid account of the work of a difficult and profound thinker. Dr Lloyd's business is only with the essentials; but he does not shirk the difficulties which arise in their interpretation, nor does he invest Aristotle with a spurious modernity. (shrink)

This book explores the universe and its subsystems from the three lenses of evolutionary (diversifying), developmental (converging), and complex (adaptive) processes at all scales. It draws from prolific experts within the academic disciplines of complexity science, physical science, information and computer science, theoretical and evo-devo biology, cosmology, astrobiology, evolutionary theory, developmental theory, and philosophy. The chapters come from a Satellite Meeting, "Evolution, Development and Complexity" (EDC) hosted at the Conference on Complex Systems, in Cancun, 2017. The contributions will be peer-reviewed (...) and contributors from outside the conference will be invited to submit chapters to ensure full coverage of the topics. This book explores many issues within the field of EDC such as the interaction of evolutionary stochasticity and developmental determinism in biological systems and what they might teach us about these twin processes in other complex systems. This text will appeal to students and researchers within the complex systems and EDC fields.. (shrink)

“THE ONLY THING NECESSARY IS NOT THEORETICAL LEARNING, but the Bildung of human beings, both in regard to their talents and their character.” Kant’s epigrammatic observation in his 1778 letter to Christian Wolke, director of the Philanthropin, adumbrates not only his mature sense of “enlightenment” but also the pedagogical role of his critical philosophy and his own life’s work. Over a decade earlier, his reading of Rousseau’s Emile: or, On Education had “set him straight” about what constitutes the true dignity (...) of humanity, namely, that it did not consist in the advance of knowledge by scholarly inquiry as he had believed. The primary thing was, instead, the “restoration of the rights of humanity,” an objective articulated in Kant’s mature moral thought as that pedagogical method which facilitates the self-consciousness and efficacy of the moral law in the individual. In another 1778 letter, this time to his former student, Marcus Herz, Kant states that the “main purpose of his academic life,” which he “at all times keeps before him,” is to “cultivate good characters.” In both his lectures on anthropology and on pedagogy, Kant repeatedly emphasizes the need for education and, by extension, for attending to the education of the educator. Human beings are nothing save what education makes of them, but they can only be educated by other human beings who must themselves first be educated. As early as his 1775/ 76 anthropology lectures, Kant observes that “if teachers and priests were educated, if the concepts of pure morality would prevail among them, then... the whole could afterwards be educated.” The resulting task is clear: it is incumbent on every generation to work on the plan of a more purposive education,” a task Kant describes as the “greatest and most difficult problem that can be assigned to humankind.”. (shrink)

The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der Töne. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der Töne in 1990. The conceptual basis has been vastly generalized to topos-theoretic foundations, including a corresponding thoroughly geometric musical logic. The theoretical models and results now include topologies for rhythm, melody, and harmony, as well as a classification theory of musical (...) objects that comprises the topos-theoretic concept framework. Classification also implies techniques of algebraic moduli theory. The classical models of modulation and counterpoint have been extended to exotic scales and counterpoint interval dichotomies. The probably most exciting new field of research deals with musical performance and its implementation on advanced object-oriented software environments. This subject not only uses extensively the existing mathematical music theory, it also opens the language to differential equations and tools of differential geometry, such as Lie derivatives. Mathematical performance theory is the key to inverse performance theory, an advanced new research field which deals with the calculation of varieties of parameters which give rise to a determined performance. This field uses techniques of algebraic geometry and statistics, approaches which have already produced significant results in the understanding of highest-ranked human performances. The book's formal language and models are currently being used by leading researchers in Europe and Northern America and have become a foundation of music software design. This is also testified by the book's nineteen collaborators and the included CD-ROM containing software and music examples. (shrink)

Modern science faces a series of problems that undermine confidence in its reliability. To solve these problems, we must reflect on what makes science work and what leads it astray. This book is about Science, its strengths and weaknesses. The papers that scientists write form a vast resource of evidence and theory that is doubling about every ten years, along with the number of scientists. The size of this resource makes it hard for it to be used effectively by scientists, (...) and along with this are growing concerns about its integrity and reliability. This book looks at the scientific method, as currently applied and as understood philosophically by scientists, the social structure of science, and the structure of scientific communication through journals. It includes case studies of controversies, and looks at how fields develop over time. (shrink)

Anscombe on thought, experience, sensation, and the ethics of virtue Gertrude Elizabeth Margaret Anscombe is one of analytical philosophy's most prominent figures, the founder of consequentialism, and a leading mind in the field of virtue ethics. Metaphysics and the Philosophy of Mind: The collected Philosophical Papers of G.E.M. Anscombe, Volume 2, is part of a multivolume compilation of her life's work, providing insight into the mind of a groundbreaking 20th century philosopher. This volume's work explores memory, intentionality, causality and time, (...) delving into the language, actions, and logic of perception, sensation, and more. (shrink)

The influence of Nazism on German culture was a key concern for many Anglo-American writers, who struggled to reconcile the many contributions of Germany to European civilization, with the barbarity of the new regime. In _German Literature Through Nazi Eyes_, H.G. Atkins gives an account of how the Nazis undertook a re-evaluation of German literature, making it sub-ordinate to their own interests. All reference to Jewish writers and influence was virtually eliminated, and key writers such as Goethe and Lessing were (...) re-interpreted. What was left was a military history that was avowedly militant and propagandist. (shrink)