This book is a survey of the theory of formal deformation quantization of Poisson manifolds, in the formalism developed by Kontsevich. It is intended as an educational introduction for mathematical physicists who are dealing with the subject for the first time. The main topics covered are the theory of Poisson manifolds, star products and their classification, deformations of associative algebras and the formality theorem. Readers will also be familiarized with the relevant physical motivations underlying the purely mathematical construction.

Analytical jurisprudence has been mostly silent on the role of precedent in legal adjudication. What is the content of a judge's precedent ideology,or the rule of precedent-recognition, by means of which the ratio of a case is to be distinguished from mere dicta? In this study, the author identifies six types of judicial precedent-ideology, among them judicial legislation, systemic construction of the underlying reasons of law in the Dworkinian sense, and a radical re-evaluation of the merits of a prior case in later adjudication, as envisioned by the American Realists. These competing models are tested against judicial experiences in the UK, US, France, Italy, Germany and Finland. By this means Lon Fuller's famous 'internal morality of law' is shown to function rather poorly in the context of precedents, and the author therefore suggests a redefinition of the rule which makes it work for precedent. This, in turn leads the author to confront fundamental questions about the normative nature of law. Is Kelsen's grundnorm or Hart's ultimate rule of recognition a valid rule, in the image of legal rules proper, or is it merely a social fact, observable only in the practices and behaviour of judges and other officials? The author claims that Hart is caught between Kelsen and J.L. Borges, the late Argentinian fabulist, in so far as the ontology and epistemology of the rule of recognition are concerned. This leads the author to the conclusion that the two predicaments affecting analytical positivism, namely the threat of endless self-referentiality, or infinite regress, can only be accounted for by means of recourse to the philosophy of deconstruction as posited by Jacques Derrida.

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 uses of model theory have created a highly fragmented literature. On the one hand, many philosophically significant results are found only in mathematics textbooks: these are aimed squarely at mathematicians; they typically presuppose that the reader has a serious background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are scattered across disconnected pockets of papers. The first aim of this book, then, is to explore the philosophical uses of model theory, focusing on the central topics of reference, realism, and doxology. Its second aim is to address important questions in the philosophy of model theory, such as: sameness of theories and structure, the boundaries of logic, and the classification of mathematical structures. Philosophy and Model Theory will be accessible to anyone who has completed an introductory logic course. It does not assume that readers have encountered model theory before, but starts right at the beginning, discussing philosophical issues that arise even with conceptually basic model theory. Moreover, the book is largely self-contained: model-theoretic notions are defined as and when they are needed for the philosophical discussion, and many of the most philosophically significant results are given accessible proofs.

This book presents formalizations of three important medieval logical theories: supposition, consequence and obligations. These are based on innovative vantage points: supposition theories as algorithmic hermeneutics, theories of consequence analyzed with tools borrowed from model-theory and two-dimensional semantics, and obligations as logical games. The analysis of medieval logic is relevant for the modern philosopher and logician. This is the first book to render medieval logical theories accessible to the modern philosopher.

Introduction : why is formality so unpopular? -- A redefinition of the concept of formality -- Legal formality and graphical planning languages -- Certainty of the law : reasons, situation-types, analogy, and equilibrium -- The social structure of liquidity : flexibility in markets, states, and organizations / Bruce G. Carruthers, Arthur L. Stinchcombe -- Formalizing rightlessness in immigration law and administration -- Formalizing epistemological stratification of knowledge -- Conclusion : the varieties of formality.

In Fallacies and Judgments of Reasonableness, Frans H. van Eemeren, Bart Garssen and Bert Meuffels report on their systematic empirical research of the conventional validity of the pragma-dialectical discussion rules. The experimental studies they carried out during more than ten years start from the pragma-dialectical theory of argumentation developed at the University of Amsterdam, their home university. In these studies they test methodically the intersubjective acceptability of the rules for critical discussion proposed in this theory by confronting ordinary arguers who have not received any special education in argumentation and fallacies with discussion fragments containing both fallacious and non-fallacious argumentative moves. The research covers a wide range of informal fallacies. In this way, the authors create a basis for comparing the theoretical reasonableness conception of pragma-dialectics with the norms for judging argumentative moves prevailing in argumentative practice. Fallacies and Judgments of Reasonableness provides a unique insight into the relationship between theoretical and practical conceptions of reasonableness, supported by extensive empirical material gained by means of sophisticated experimental research.

This volume contains the proceedings of the Workshop on Homotopy Theory of Function Spaces and Related Topics, which was held at the Mathematisches Forschungsinstitut Oberwolfach, in Germany, from April 5-11, 2009. This volume contains fourteen original research articles covering a broad range of topics that include: localization and rational homotopy theory, evaluation subgroups, free loop spaces, Whitehead products, spaces of algebraic maps, gauge groups, loop groups, operads, and string topology. In addition to reporting on various topics in the area, this volume is supposed to facilitate the exchange of ideas within Homotopy Theory of Function Spaces, and promote cross-fertilization between Homotopy Theory of Function Spaces and other areas. With these latter aims in mind, this volume includes a survey article which, with its extensive bibliography, should help bring researchers and graduate students up to speed on activity in this field as well as a problems list, which is an expanded and edited version of problems discussed in sessions held at the conference. The problems list is intended to suggest directions for future work.

The Natural Philosophy Alliance (NPA) sponsors regular international conferences for presenting high-quality papers discussing aspects of philosophy in the sciences. Many papers offer challenges to accepted orthodoxy in the sciences, especially in physics. Everything from the micro-physics of quantum mechanics to the macro-physics of cosmology is entertained.Though the main interest of the NPA is in challenging orthodoxy in the sciences, it will also feature papers defending such orthodoxy. Our ultimate propose is to enable participants to articulate their own understanding of the truth. All papers are reviewed by society officers, and sometimes by other members, before presentation in conferences and they are edit, sometimes very significantly prior to publication in the Proceedings of the NPA.

This is the first volume of a collection of papers in honor of the fiftieth birthday of Jean-Yves Béziau. These 25 papers have been written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Arnon Avron, John Corcoran, Wilfrid Hodges, Laurence Horn, Lloyd Humbertsone, Dale Jacquette, David Makinson, Stephen Read, and Jan Woleński. It is a state-of-the-art source of cutting-edge studies in the new interdisciplinary field of universal logic. The papers touch upon a wide range of topics including combination of logic, non-classical logic, square and other geometrical figures of opposition, categorical logic, set theory, foundation of logic, philosophy and history of logic (Aristotle, Avicenna, Buridan, Schröder, MacColl). This book offers new perspectives and challenges in the study of logic and will be of interest to all students and researchers interested the nature and future of logic.