This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts of the quantum-theoretic formalism used in quantum information. It then gives a synthetic presentation of the main "mathematical characters" of the quantum computational game: qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates the puzzling entanglement-phenomena and logically analyses the Einstein-Podolsky-Rosen paradox and introduces the reader to quantum computational logics, and new forms of quantum logic. The middle chapters investigate the possibility of a quantum computational semantics for a language that can express sentences like "Alice knows that everybody knows that she is pretty", explore the mathematical concept of quantum Turing machine, and illustrate some characteristic examples that arise in the framework of musical languages. The book concludes with an analysis of recent discussions, and contains a Mathematical Appendix which is a survey of the definitions of all main mathematical concepts used in the book.

Succinct representation and fast access to large amounts of data are challenges of our time. This unique book suggests general approaches of 'complexity of descriptions'. It deals with a variety of concrete topics and bridges between them, while opening new perspectives and providing promising avenues for the 'complexity puzzle'.

This collection will prove a valuable resource for our understanding of the historic Carnap and the living philosophical issues with which he grappled. It arose out of a symposium on Carnap's work (Vienna, 2001). With essays by Graham H. Bird, Jaakko Hintikka, Ilkka Niiniluoto, Jan Wolenski, this volume will interest graduate students of the philosophy of language and logic, as well as professional philosophers, historians of analytic philosophy, and philosophically inclined logicians.

In 1986, the emergence of a novel brain disease in British cattle presented a unique challenge to scientists. How that challenge was addressed has been the subject of a public inquiry and numerous academic studies conducted to date. However, none of these investigations has sought to examine the reasoning of scientists during this critical period in the public health of the UK. Using concepts and techniques in informal logic, argumentation and fallacy theory, this study reconstructs and evaluates the reasoning of scientists in the ten-year period between 1986 and 1996. Specifically, a form of presumptive reasoning is described in which extensive use is made of arguments traditionally identified as informal fallacies. In the context of the adverse epistemic conditions that confronted scientists during the BSE epidemic, these arguments were anything but fallacious, serving instead to confer a number of epistemic gains upon scientific inquiry. This book argues for a closer integration of philosophy with public health science, an integration that is exemplified by the case of scientific reasoning during the BSE affair. It will therefore be of interest to advanced students, academics, researchers and professionals in the areas of public health science and epidemiology, as well as philosophical disciplines such as informal logic, argumentation and fallacy theory and epistemology.

William G. Lycan offers a fresh original approach to the long-running debate among philosophers and logicians about the best way to analyse and understand conditional sentences. Lycan attends not just to the semantics of such sentences, but equally to their syntax, making use of insights from linguistic theory. Real Conditionals is the definitive presentation of Lycan's view, written in his characteristically lively style.

This book is dedicated to the life and work of the mathematician Joachim Lambek (1922-2014). The editors gather together noted experts to discuss the state of the art of various of Lambek's works in logic, category theory, and linguistics and to celebrate his contributions to those areas over the course of his multifaceted career. After early work in combinatorics and elementary number theory, Lambek became a distinguished algebraist (notably in ring theory). In the 1960s, he began to work in category theory, categorical algebra, logic, proof theory, and foundations of computability. In a parallel development, beginning in the late 1950s and for the rest of his career, Lambek also worked extensively in mathematical linguistics and computational approaches to natural languages. He and his collaborators perfected production and type grammars for numerous natural languages. Lambek grammars form an early noncommutative precursor to Girard's linear logic. In a surprising development (2000), he introduced a novel and deeper algebraic framework (which he called pregroup grammars) for analyzing natural language, along with algebraic, higher category, and proof-theoretic semantics. This book is of interest to mathematicians, logicians, linguists, and computer scientists.

Stoicism (third century BC to second century AD) is one of the richest and most influential intellectual traditions of antiquity. Leading scholars here contribute new studies of a set of topics which are the focus of current research in this area. They combine careful analytical attention to the original texts with historical sensitivity and philosophical acuity, to provide the basis for a better understanding of Stoic ethics, political theory, logic, and physics. Whereas till recently the study of Hellenistic philosophy has been mainly a historical enterprise, these essays demonstrate that a proper treatment of Stoicism engages us in philosophical questions of considerable current relevance and interest.

Gareth Matthews suggests that we can better understand the nature of philosophical inquiry if we recognize the central role played by perplexity. The seminal representation of philosophical perplexity is in Plato's dialogues; Matthews examines the intriguing shifts in Plato's attitude to perplexity and suggests that these may represent a course of philosophical development that philosophers follow even today.

In this innovative and groundbreaking work, the structure and evolution of scientific theories is examined in meticulous detail and rigorously analysed as never before. For the first time, scientific revolutions are presented as a natural consequence of the evolution of scientific theories and described with mathematical precision. Many new techniques are introduced and with the more precise understanding of the nature of the scientific enterprise obtained thereby, old philosophical problems are cast into a new light and shown to be susceptible to the same rigorous approach by which they may be completely solved. Numerous real examples from the sciences are given and discussed in detail, culminating in some startling results concerning the future development of science and that Holy Grail of physics, the possibility of a final, all-embracing Theory of Everything. Written in an eloquent and engaging style interspersed with occasional flashes of delicious humour, this book is destined to become a classic in the Philosophy of Science. It will doubtless be appreciated equally by philosophers and scientists alike as well as a wider, less specialised audience. Truly an important document and a major contribution to the literature; this is a work for the twenty-first century.

Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters. The book addresses the need for a theory of infinity, and reviews both old and new theories of infinity. It discussing the purposes of studying infinity and the troubles with traditional approaches to the problem, and concludes by offering a solution to some existing paradoxes.

This book offers a comprehensive critical survey of issues of historical interpretation and evaluation in Bertrand Russell's 1918 logical atomism lectures and logical atomism itself. These lectures record the culmination of Russell's thought in response to discussions with Wittgenstein on the nature of judgement and philosophy of logic and with Moore and other philosophical realists about epistemology and ontological atomism, and to Whitehead and Russell's novel extension of revolutionary nineteenth-century work in mathematics and logic. Russell's logical atomism lectures have had a lasting impact on analytic philosophy and on Russell's contemporaries including Carnap, Ramsey, Stebbing, and Wittgenstein. Comprised of 14 original essays, this book will demonstrate how the direct and indirect influence of these lectures thus runs deep and wide.

As philosophy departments attempt to define their unique value amid program closures in the humanities and the rise of interdisciplinary research, metaphilosophy has become an increasingly important area of inquiry. Richard Fumerton here lays out a cogent answer to the question asked in the book's title, What is Philosophy?. Against those who argue that philosophy is not sharply distinguishable from the sciences, Fumerton makes a case for philosophy as an autonomous discipline with its own distinct methodology. Over the course of nine engaging and accessible chapters, he shows that answering fundamental philosophical questions requires one to take a radical first-person perspective that divorces the truth conditions of philosophical claims from the kind of contingent truths investigated by the empirical sciences. Along the way, Fumerton briefly discusses the historical controversies that have surrounded the nature of philosophy, situating his own argument within the larger conversation. Key Features Illuminates the unique role of thought experiments and especially the "paradox of analysis" in understanding the purpose and value of philosophy. Shows that philosophy asks fundamental questions, unanswerable by the sciences, that are critical to thinking clearly and rationally about the world. Highlights the distinct character of philosophical questions in specific subject areas: philosophy of language, epistemology, ethics, philosophy of mind, and philosophy of science. Concludes by making a unique case for philosophy's contribution to cross-disciplinary work in ethics, politics, mathematics, and the empirical sciences. Written in a way to be engaging and accessible for advanced undergraduate readers.

This book discusses how scientific and other types of cognition make use of models, abduction, and explanatory reasoning in order to produce important or creative changes in theories and concepts. It includes revised contributions presented during the international conference on Model-Based Reasoning (MBR'015), held on June 25-27 in Sestri Levante, Italy. The book is divided into three main parts, the first of which focuses on models, reasoning and representation. It highlights key theoretical concepts from an applied perspective, addressing issues concerning information visualization, experimental methods and design. The second part goes a step further, examining abduction, problem solving and reasoning. The respective contributions analyze different types of reasoning, discussing various concepts of inference and creativity and their relationship with experimental data. In turn, the third part reports on a number of historical, epistemological and technological issues. By analyzing possible contradictions in modern research and describing representative case studies in experimental research, this part aims at fostering new discussions and stimulating new ideas. All in all, the book provides researchers and graduate students in the field of applied philosophy, epistemology, cognitive science and artificial intelligence alike with an authoritative snapshot of current theories and applications of model-based reasoning.

This text presents a clear and philosophically sound method for identifying, interpreting, and evaluating arguments as they appear in non-technical sources. It focuses on a more functional, real-world goal of argument analysis as a tool for figuring out what is reasonable to believe rather than as an instrument of persuasion. Methods are illustrated by applying them to arguments about different topics as they appear in a variety of contexts - e.g., newspaper editorials and columns, short essays, informal reports of scientific results, etc.

This book collects original essays on the epistemology of modality and related issues in modal metaphysics and philosophical methodology.

As philosophy departments attempt to define their unique value amid program closures in the humanities and the rise of interdisciplinary research, metaphilosophy has become an increasingly important area of inquiry. Richard Fumerton here lays out a cogent answer to the question asked in the book's title, What is Philosophy?. Against those who argue that philosophy is not sharply distinguishable from the sciences, Fumerton makes a case for philosophy as an autonomous discipline with its own distinct methodology. Over the course of nine engaging and accessible chapters, he shows that answering fundamental philosophical questions requires one to take a radical first-person perspective that divorces the truth conditions of philosophical claims from the kind of contingent truths investigated by the empirical sciences. Along the way, Fumerton briefly discusses the historical controversies that have surrounded the nature of philosophy, situating his own argument within the larger conversation. Key Features Illuminates the unique role of thought experiments and especially the "paradox of analysis" in understanding the purpose and value of philosophy. Shows that philosophy asks fundamental questions, unanswerable by the sciences, that are critical to thinking clearly and rationally about the world. Highlights the distinct character of philosophical questions in specific subject areas: philosophy of language, epistemology, ethics, philosophy of mind, and philosophy of science. Concludes by making a unique case for philosophy's contribution to cross-disciplinary work in ethics, politics, mathematics, and the empirical sciences. Written in a way to be engaging and accessible for advanced undergraduate readers.

What do philosophy and computer science have in common? It turns out, quite a lot! In providing an introduction to computer science (using Python), Daniel Lim presents in this book key philosophical issues, ranging from external world skepticism to the existence of God to the problem of induction. These issues, and others, are introduced through the use of critical computational concepts, ranging from image manipulation to recursive programming to elementary machine learning techniques. In illuminating some of the overlapping conceptual spaces of computer science and philosophy, Lim teaches the reader fundamental programming skills and also allows her to develop the critical thinking skills essential for examining some of the enduring questions of philosophy. Key Features Teaches readers actual computer programming, not merely ideas about computers Includes fun programming projects (like digital image manipulation and Game of Life simulation), allowing the reader to develop the ability to write larger computer programs that require decomposition, abstraction, and algorithmic thinking Uses computational concepts to introduce, clarify, and develop a variety of philosophical issues Covers various aspects of machine learning and relates them to philosophical issues involving science and induction as well as to ethical issues Provides a framework to critically analyze arguments in classic and contemporary philosophical debates

This contributed volume explores the ways logical skills have been perceived over the course of history. The authors approach the topic from the lenses of philosophy, anthropology, sociology, and history to examine two opposing perceptions of logic: the first as an innate human ability and the second as a skill that can be learned and mastered. Chapters focus on the social and political dynamics of the use of logic throughout history, utilizing case studies and critical analyses. Specific topics covered include: the rise of logical skills problems concerning medieval notions of idiocy and rationality decolonizing natural logic natural logic and the course of time Logical Skills: Social-Historical Perspectives will appeal to undergraduate and graduate students, as well as researchers in the fields of history, sociology, philosophy, and logic. Psychology and colonial studies scholars will also find this volume to be of particular interest.

This book introduces a new form of argumentative analysis: rhetorical heuremes. The method applies the concepts of heuristic thinking, probability, and contingency in order to develop a better understanding of complex arguments in classical oratory. A new theory is required because Greek and Roman rhetoric cannot provide detailed answers to problems of strategic argumentation in the analysis of speeches. Building on scholarship in Ciceronian oratory, this book moves beyond the extant terminology and employs a concept of heuristic reasoning derived from the psychology of decision making and mathematical problem solving. The author analyses selected passages from Cicero's forensic speeches where arguments of probability are deployed, and shows that the Sophistic concept of probability can link ancient rhetoric and modern theories of argumentation. Six groups of heuremes are identified, each of which represents a form of probabilistic reasoning by which the orator plays upon the perception of the jurors.

About the Series: The aim of this series is to bring together important recent writings in major areas of philosophical inquiry, selected from a variety of sources, mostly periodicals, which may not be conveniently available to the university student or the general reader. The editors of each volume contribute an introductory essay on the items chosen and on the questions with which they deal. A selective bibliography is appended as a guide to further reading. About this volume: When we say a certain rose is red, we seem to be attributing a property, redness, to it. But are there really such properties? If so, what are they like, how do we know about them, and how are they related to the objects which have them and the linguistic devices which we use to talk about them? This collection presents these ancient problems in a modern light. In particular, it makes accessible for the first time the most important contributions to the contemporary controversy about the nature of properties. Those new to the subject will find the clearly-written introduction, by two experts in the field, an invaluable guide to the intricacies of this debate. The volume illustrates very well the aims and methods of modern metaphysics and shows how a thorough understanding of the metaphysics of properties is crucial to most of analytic philosophy.

A N Prior has a special place in the history of postwar philosophy for his highly original work at the intersection of logic and metaphysics. His logical innovations have found many applications in the areas of philosophical logic, mathematics, linguistics, and, increasingly, computer science. In addition, he made seminal contributions to debates in metaphysics, particularly on modality and the nature of time. This volume presents a selection of current research in the areas that were of most interest to Prior: temporal and tense logic, modal logic, proof theory, quantification and individuation, and the logic of agency. Both title and contents reflect Prior's view that logic is 'about the real world', and the orientation of the volume is towards the application of logic, in philosophy, computer science, and elsewhere. Following Prior, modal syntax is now widely applied to the formalization of a variety of subject matters, and tense logic has found numerous applications in computing, for example in natural language processing, logical deduction involving time-dependent data, program-verification, and VLSI. A special feature of the volume is the inclusion of three hitherto unpublished pieces by Prior on modal logic and the philosophy of time, along with a complete bibliography of Prior's published philosophical writings.

The Topics is Aristotle's treatise on dialectical argument, a practice perhaps as old as human language, systemized for the first time by Aristotle. This seminal text offers many important insights into his conception of logic, his development of the notion of the predicables (the Five Terms), and his ideas on the method of philosophical inquiry itself. This volume contains a clear and accurate translation of Books I and VIII of Aristotle's Topics together with a philosophical commentary on these books and additional selections from Books II and III, and from the Sophistical Refutations . These books and selections best give a general view of the main ideas, arguments, and techniques expounded in the Topics . The volume is well suited to the requirements of students, including those who do not know Greek.

This is the first of two volumes of essays in commemoration of Alan Turing, whose pioneering work in the theory of artificial intelligence and computer science continues to be widely discussed today. A group of prominent academics from a wide range of disciplines focus on three questions famously raised by Turing: What, if any, are the limits on machine `thinking'? Could a machine be genuinely intelligent? Might we ourselves be biological machines, whose thought consists essentially in nothing more than the interaction of neurons according to strictly determined rules? The discussion of these fascinating issues is accessible to non-specialists and stimulating for all readers.