Two books have been particularly influential in contemporary philosophy of science: Karl R. Popper's Logic of Scientific Discovery, and Thomas S. Kuhn's Structure of Scientific Revolutions. Both agree upon the importance of revolutions in science, but differ about the role of criticism in science's revolutionary growth. This volume arose out of a symposium on Kuhn's work, with Popper in the chair, at an international colloquium held in London in 1965. The book begins with Kuhn's statement of his position followed by seven essays offering criticism and analysis, and finally by Kuhn's reply. The book will interest senior undergraduates and graduate students of the philosophy and history of science, as well as professional philosophers, philosophically inclined scientists, and some psychologists and sociologists.

Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Godel's incompleteness theorem, using an information theoretic approach based on the size of computer programs. One half of the book is concerned with studying the halting probability of a universal computer if its program is chosen by tossing a coin. The other half is concerned with encoding the halting probability as an algebraic equation in integers, a so-called exponential diophantine equation.

This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures.

Frank Ramsey was the greatest of the remarkable generation of Cambridge philosophers and logicians which included G. E. Moore, Bertrand Russell, Ludwig Wittgenstein and Maynard Keynes. Before his tragically early death in 1930 at the age of twenty-six, he had done seminal work in mathematics and economics as well as in logic and philosophy. This volume, with a new and extensive introduction by D. H. Mellor, contains all Ramsey's previously published writings on philosophy and the foundations of mathematics. The latter gives the definitive form and defence of the reduction of mathematics to logic undertaken in Russell and Whitehead's Principia Mathematica; the former includes the most profound and original studies of universals, truth, meaning, probability, knowledge, law and causation, all of which are still constantly referred to, and still essential reading for all serious students of these subjects.

The two notions of proofs and calculations are intimately related. Proofs can involve calculations, and the algorithm underlying a calculation should be proved correct. This volume explores this key relationship and introduces simple type theory. Starting from the familiar propositional calculus, the author develops the central idea of an applied lambda-calculus. This is illustrated by an account of Gödel's T, a system that codifies number-theoretic function hierarchies. Each of the book's 52 sections ends with a set of exercises, some 200 in total. An appendix contains complete solutions of these exercises.

Karl Popper (1902-1994) is one of this century's most influential philosophers, but his life in fin-de siecle and interwar Vienna, and his exile in New Zealand during World War II, have so far remained shrouded in mystery. This intellectual 2001 biography recovers the legacy of the young Popper; the progressive, cosmopolitan, Viennese socialist who combated fascism, revolutionized the philosophy of science, and envisioned the Open Society. Malachi Hacohen delves into his archives (as well as the archives of his colleagues) and draws a compelling portrait of the philosopher, the assimilated Jewish intelligentsia, and the vanished culture of Red Vienna, which was decimated by Nazism. Hacohen's adventurous biography restores Popper's works to their original Central European contexts and, at the same time, shows that they have urgent messages for contemporary politics and philosophy.

This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading.

A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers an up-to-date and reliable guide essential for the student.

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This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.

D-branes represent a key theoretical tool in the understanding of strongly coupled superstring theory and M-theory. They have led to many striking discoveries, including the precise microphysics underlying the thermodynamic behaviour of certain black holes, and remarkable holographic dualities between large-N gauge theories and gravity. This book provides a self-contained introduction to the technology of D-branes, presenting the recent developments and ideas in a pedagogical manner. It is suitable for use as a textbook in graduate courses on modern string theory and theoretical particle physics, and will also be an indispensable reference for seasoned practitioners. The introductory material is developed by first starting with the main features of string theory needed to get rapidly to grips with D-branes, uncovering further aspects while actually working with D-branes. Many advanced applications are covered, with discussions of open problems which could form the basis for other avenues of research.

This short introduction to category theory is for readers with relatively little mathematical background. At its heart is the concept of a universal property, important throughout mathematics. After a chapter introducing the basic definitions, separate chapters present three ways of expressing universal properties: via adjoint functors, representable functors, and limits. A final chapter ties the three together.
For each new categorical concept, a generous supply of examples is provided, taken from different parts of mathematics. At points where the leap in abstraction is particularly great (such as the Yoneda lemma), the reader will find careful and extensive explanations.

The reign of King Baldwin IV of Jerusalem (1174-85) has traditionally been seen as a period of decline when, because of the king's illness, power came to be held by those who made the wrong policy decisions. Notably, they ignored the advice of Raymond of Tripoli and attacked Saladin. This book challenges that view, arguing that peace with Saladin was not a viable option; and that the young king, despite suffering from lepromatous leprosy, presided over a society that was (contrary to what is often said) vigorous and self-confident.

This clearly written and engaging book brings together anthropology, psychology and economics to show how these three human science disciplines address fundamental questions related to the psychology of economic life in human societies - questions that matter for people from every society and every background. Based around vivid examples drawn from field research in China and Taiwan, the author encourages anthropologists to take the psychological dimensions of economic life more seriously, but also invites psychologists and economists to pay much more attention than they currently do to cultural and historical variables. In the end, this intrinsically radical book challenges us to step away from disciplinary assumptions and to reflect more deeply on what really matters to us in our collective social and economic life.

Sir Reginald Fleming Johnston (1874-1938) was a colonial administrator and scholar with a lifelong fascination with China who was appointed tutor to the young Puyi (1906-1967), who became emperor at the age of two. Johnston was highly favoured by the emperor, receiving several imperial titles and residing in the Forbidden City. His account of his time as Puyi's tutor, Twilight in the Forbidden City, also reissued in this series, was dramatised in the film The Last Emperor. Previously, Johnston had served in a variety of colonial service positions, including three years as commissioner of the British-held territory of Weihaiwai. This book, first published in 1910, is Johnston's examination of Weihaiwei, which he considered to be a microcosm of Chinese life. Writing with obvious affection, Johnston outlines the history, culture, festivals and local folklore of Weihaiwei and explores what the future could hold for the city.

English language and linguistics shares many of its writing conventions with those of other disciplines, but there are certain features and expectations that distinguish it as a subject. This book is written specifically to help undergraduate students of English language and linguistics develop the art of writing essays, projects and reports. Written by an author with over 30 years' experience of lecturing in the subject, it is a comprehensive and very readable resource and contains numerous discipline-related examples, practice exercises and an answer key. It includes chapters on referencing (including plagiarism, paraphrase and guidance on referencing styles), stylistic issues that often get overlooked, and writing a dissertation. The book offers practical guidance and a layout that guides students as they work though their project. It will be an invaluable reference tool that students can read cover to cover or dip into as and when required.

Introducing the reader to classical integrable systems and their applications, this book synthesizes the different approaches to the subject, providing a set of interconnected methods for solving problems in mathematical physics. The authors introduce and explain each method, and demonstrate how it can be applied to particular examples. Rather than presenting an exhaustive list of the various integrable systems, they focus on classical objects which have well-known quantum counterparts, or are the semi-classical limits of quantum objects. They thus enable readers to understand the literature on quantum integrable systems.

The 2003 second volume of this account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. Proofs of the Lefschetz theorem on hyperplane sections, the Picard-Lefschetz study of Lefschetz pencils, and Deligne theorems on the degeneration of the Leray spectral sequence and the global invariant cycles follow. The main results of the second part are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly Nori's connectivity theorem, which generalizes the above. The last part of the book is devoted to the relationships between Hodge theory and algebraic cycles. The book concludes with the example of cycles on abelian varieties, where some results of Bloch and Beauville, for example, are expounded. The text is complemented by exercises giving useful results in complex algebraic geometry. It will be welcomed by researchers in both algebraic and differential geometry.