Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics, and computer science. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated.

Wittgenstein et Spinoza construisent, l'un dans le Tractatus, l'autre dans l'A0/00thique, des systA]mes philosophiques rA(c)unissant le monde, l'homme et Dieu dans lesquels ils s'opposent sur de nombreux points. C'est ainsi par exemple que, suivant Spinoza, l'homme est assurA(c) que rien ne se produit sans cause alors que Wittgenstein rejette la possibilitA(c) de rapports d'ordre causal entre les A(c)vA(c)nements. Le prA(c)sent travail dissA]que dans une premiA]re partie l'A"uvre de Wittgenstein, il analyse dans une deuxiA]me partie la doctrine de Spinoza, et il compare enfin dans la troisiA]me partie les deux systA]mes dont il fait ressortir les points de concordance et de dissemblance dans leurs constructions respectives. Il traite les A"uvres philosophiques que sont le Tractatus et l'A0/00thique comme si elles relevaient de sciences telles que la mA(c)canique, l'astronomie, etc., et utilise des modA]les gA(c)omA(c)triques appropriA(c)s A leur interprA(c)tation. L'A(c)tude comparative du Tractatus et de l'A0/00thique, qui ne cessent d'exercer leur influence sur la pensA(c)e humaine, permet de conclure que le Tractatus, A"uvre du XXe siA]cle, renoue avec le rationalisme du XVIIe siA]cle exprimA(c) par Spinoza.

This volume presents a selection of papers reflecting key theoretical issues in argumentation theory. Its six sections are devoted to specific themes, including the analysis and evaluation of argumentation, argument schemes and the contextual embedding of argumentation. The section on general perspectives on argumentation discusses the trends of empiricalization, contextualization and formalization, offers descriptions of the analytical and evaluative tools of informal logic, and highlights selected principles that argumentation theorists do and do not agree upon. In turn, the section on linguistic approaches to argumentation focuses on the problem of distinguishing between explanation and argument, while also elaborating on the role of verbal indicators of argument schemes. All essays included in this volume point out notable recent developments in the study of argumentation.

Representational systems such as language, mind and perhaps even the brain exhibit a structure that is often assumed to be compositional. That is, the semantic value of a complex representation is determined by the semantic value of their parts and the way they are put together. Dating back to the late 19th century, the principle of compositionality has regained wide attention recently. Since the principle has been dealt with very differently across disciplines, the aim of the two volumes is to bring together the diverging approaches. They assemble a collection of original papers that cover the topic of compositionality from virtually all perspectives of interest in the contemporary debate. The well-chosen international list of authors includes psychologists, neuroscientists, computer scientists, linguists, and philosophers.

This book offers an original philosophical perspective on exemplarity. Inspired by Wittgenstein's later work and Derrida's theory of deconstruction, it argues that examples are not static entities but rather oscillate between singular and universal moments. There is a broad consensus that exemplary cases mediate between singular instances and universal concepts or norms. In the first part of the book, Macha contends that there is a kind of differance between singular examples and general exemplars or paradigms. Every example is, in part, also an exemplar, and vice versa. Furthermore, he develops a paracomplete approach to the logic of exemplarity, which allows us to say of an exemplar of X neither that it is an X nor that it is not an X. This paradox is structurally isomorphic to Russell's paradox and can be addressed in similar ways. In the second part of the book, Macha presents four historical studies that exemplify the ideas developed in the first part. This part begins with Plato's Forms, understood as standards/paradigms, before considering Kant's theory of reflective judgment as a general epistemological account of exemplarity. This is then followed by analyses of Hegel's conceptual moment of particularity and Kuhn's concept of paradigm. The book concludes by discussing the speculative hypothesis that all our knowledge is based on paradigms, which, following the logic of exemplarity, are neither true nor false. The Philosophy of Exemplarity will be of interest to scholars and advanced students working in philosophy of language, logic, history of philosophy, and literary theory.

The Routledge Companion to Pragmatism offers 44 cutting-edge chapters-written specifically for this volume by an international team of distinguished researchers-that assess the past, present, and future of pragmatism. Going beyond the exposition of canonical texts and figures, the collection presents pragmatism as a living philosophical idiom that continues to devise promising theses in contemporary debates. The chapters are organized into four major parts: Pragmatism's history and figures Pragmatism and plural traditions Pragmatism's reach Pragmatism's relevance Each chapter provides up-to-date research tools for philosophers, students, and others who wish to locate pragmatist options in their contemporary research fields. As a whole, the volume demonstrates that the vitality of pragmatism lies in its ability to build upon, and transcend, the ideas and arguments of its founders. When seen in its full diversity, pragmatism emerges as one of the most successful and influential philosophical movements in Western philosophy.

In the twenty-first century, humanity is reaching new heights of scientific understanding - and at the same time appears to be losing its mind. How can a species that discovered vaccines for Covid-19 in less than a year produce so much fake news, quack cures and conspiracy theorizing?

In Rationality, Pinker rejects the cynical cliché that humans are simply an irrational species - cavemen out of time fatally cursed with biases, fallacies and illusions. After all, we discovered the laws of nature, lengthened and enriched our lives and set the benchmarks for rationality itself. Instead, he explains, we think in ways that suit the low-tech contexts in which we spend most of our lives, but fail to take advantage of the powerful tools of reasoning we have built up over millennia: logic, critical thinking, probability, causal inference, and decision-making under uncertainty. These tools are not a standard part of our educational curricula, and have never been presented clearly and entertainingly in a single book - until now.

Rationality matters. It leads to better choices in our lives and in the public sphere, and is the ultimate driver of social justice and moral progress. Brimming with insight and humour, Rationality will enlighten, inspire and empower.

This book explores a large variety of topics involved in Arabic philosophy. It examines concepts and issues relating to logic and mathematics, as well as metaphysics, ethics and aesthetics. These topics are all studied by different Arabic philosophers and scientists from different periods ranging from the 9th century to the 20th century, and are representative of the Arabic tradition. This is the first book dealing with the Arabic thought and philosophy and written only by women. The book brings together the work and contributions of an international group of female scholars and researchers specialized in the history of Arabic logic, philosophy and mathematics. Although all authors are women, the book does not enter into any kind of feminist trend. It simply highlights the contributions of female scholars in order to make them available to the large community of researchers interested in Arabic philosophy and to bring to the fore the presence and representativeness of female scholars in the field.

This accessible book provides a practical discussion of the main elements of argumentation as illustrated by 30 public arguments from a recent year on a wide variety of social, cultural, and scientific topics. Arguing is an important form of communication in any society and a principal way in which ideas are exposed, discussed, and modified. The real-life examples examined in this book reflect the different considerations that go into composing arguments and the range of strategies that can be chosen as vehicles for our positions. They demonstrate the roles that emotion can play along with other modes of conveying evidence, from the use of images to the use of gestures. They show the power of threats, comparisons, and consequences. What emerges is an instructive discussion that illustrates the way we argue and that shows argument, invention, and evaluation in action. This book is a stimulating read for anyone interested in argument and public discourse and can be used as a supplemental text for courses in argumentation, persuasive communication, critical thinking, composition, and informal logic.

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.

The book analyses the concept of discoverability, and some current epistemological problems related to it, with a special attention to science. It shows that discoverability is closely related to the sustainability of human creativity in an "eco-cognitive" perspective. Advocating the need of an integral ecology and leveraging the important concept of abduction, it demonstrates that an ecology of human creativity should have priority over other needs, i.e that the first ecological duty is to protect and sustain discoverability. Enhancing discoverability will protect human creativity, and it is exactly human creativity, a form of innovative abductive cognition, that can promote the implementation of the other kinds of ecology. The author guides readers through a comprehensive discussion on the concept of discoverability, eco-cognitive situatedness, and eco-cognitive openness and closure alike. By describing some key real-world examples, he highlights the main challenges that are currently posed to human creativity and epistemic integrity. He also describes future eco-cognitive settings, discussing the problem of overcomputationalism and suggesting a reinterpretation of the role of human knowledge. Overall, this book fills an important gap in the literature on the nexus abduction - creativity - discovery, offering a source of inspiration to philosophers, epistemologists, and cognitive scientists. Yet, it also addresses researchers in other disciplines interested in the problems of scientific discovery and epistemic integrity of research.

Propositions are routinely invoked by philosophers, linguists, logicians, and other theorists engaged in the study of meaning, communication, and the mind. To investigate the nature of propositions is to investigate the very nature of our connection to each other, and to the world around us. As one of the only volumes of its kind, The Routledge Handbook of Propositions provides a comprehensive overview of the philosophy of propositions, from both historical and contemporary perspectives. Comprising 33 original chapters by an international team of scholars, the volume addresses both traditional and emerging questions concerning the nature of propositions, and our capacity to engage with them in thought and in communication. The chapters are clearly organized into the following three sections: I. Foundational Issues in the Theory of Propositions II. Historical Theories of Propositions III. Contemporary Theories of Propositions Essential reading for philosophers of language and mind, and for those working in neighboring areas, The Routledge Handbook of Propositions is suitable for upper-level undergraduate study, as well as graduate and professional research.

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.

Russell's first book on philosophy and a fascinating insight into his early thinking A classic in the history and philosophy of mathematics and logic by one of the greatest philosophers of the 20th century This Routledge Classics edition includes a new foreword by Michael Potter, a renowned expert on analytic philosophy

Brilliant introduction to the philosophy of mathematics, from the question 'what is a number?' up to the concept of infinity, descriptions, classes and axioms Russell deploys all his skills and brilliant prose to write an introductory book - a real gem by one of the 20th century's most celebrated philosophers New foreword by Michael Potter to the Routledge Classics edition places the book in helpful context and explains why it's a classic

Superb insight into the development of Russell's thinking by the master himself Clearly and engaging written, charting his intellectual development from young idealist to celebrated sceptic This Routledge Classics edition includes a new foreword by Nicholas Griffin Ideal companion to Russell's own Autobiography, which is concerned with his incredibly colourful life rather than philosophy

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the seventh publication in the Lecture Notes in Logic series, Font and Jansana develop a very general approach to the algebraization of sentential logics and present its results on a number of particular logics. The authors compare their approach, which uses abstract logics, to the classical approach based on logical matrices and the equational consequence developed by Blok, Czelakowski, Pigozzi and others. This monograph presents a systematized account of some of the work on the algebraic study of sentential logics carried out by the logic group in Barcelona in the 1970s.

If numbers were objects, how could there be human knowledge of number? Numbers are not physical objects: must we conclude that we have a mysterious power of perceiving the abstract realm? Or should we instead conclude that numbers are fictions? This book argues that numbers are not objects: they are magnitude properties. Properties are not fictions and we certainly have scientific knowledge of them. Much is already known about magnitude properties such as inertial mass and electric charge, and much continues to be discovered. The book says the same is true of numbers. In the theory of magnitudes, the categorial distinction between quantity and individual is of central importance, for magnitudes are properties of quantities, not properties of individuals. Quantity entails divisibility, so the logic of quantity needs mereology, the a priori logic of part and whole. The three species of quantity are pluralities, continua and series, and the book presents three variants of mereology, one for each species of quantity. Given Euclid's axioms of equality, it is possible without the use of set theory to deduce the axioms of the natural, real and ordinal numbers from the respective mereologies of pluralities, continua and series. Knowledge and the Philosophy of Number carries out these deductions, arriving at a metaphysics of number that makes room for our a priori knowledge of mathematical reality.

What is the true worth of Wittgenstein's contribution to philosophy? Answers to this question are strongly divided. However, most assessments rest on certain popular misreadings of his purpose. This book challenges both "theoretical" and "therapeutic" interpretations. In their place, it seeks to establish that, from beginning to end, Wittgenstein regarded clarification as the true end of philosophy. It argues that, properly understood, his approach exemplifies rather than betrays critical philosophy and provides a viable alternative to other contemporary offerings.

Real Essentialism presents a comprehensive defence of neo-Aristotelian essentialism. Do objects have essences? Must they be the kinds of things they are in spite of the changes they undergo? Can we know what things are really like - can we define and classify reality? Many, if not most, philosophers doubt this, influenced by centuries of empiricism, and by the anti-essentialism of Wittgenstein, Quine, Popper, and other thinkers. Real Essentialism reinvigorates the tradition of realist, essentialist metaphysics, defending the reality and knowability of essence, the possibility of objective, immutable definition, and its relevance to contemporary scientific and metaphysical issues such as whether essence transcends physics and chemistry, the essence of life, the nature of biological species, and the nature of the person.

This Handbook offers students and more advanced readers a valuable resource for understanding linguistic reference; the relation between an expression (word, phrase, sentence) and what that expression is about. The volume's forty-one original chapters, written by many of today's leading philosophers of language, are organized into ten parts: I Early Descriptive Theories II Causal Theories of Reference III Causal Theories and Cognitive Significance IV Alternate Theories V Two-Dimensional Semantics VI Natural Kind Terms and Rigidity VII The Empty Case VIII Singular (De Re) Thoughts IX Indexicals X Epistemology of Reference Contributions consider what kinds of expressions actually refer (names, general terms, indexicals, empty terms, sentences), what referring expressions refer to, what makes an expression refer to whatever it does, connections between meaning and reference, and how we know facts about reference. Many contributions also develop connections between linguistic reference and issues in metaphysics, epistemology, philosophy of mind, and philosophy of science.

This book argues that there is a common cognitive mechanism underlying all indexical thoughts, in spite of their seeming diversity. Indexical thoughts are mental representations, such as beliefs and desires. They represent items from a thinker's point of view or her cognitive perspective. We typically express them by means of sentences containing linguistic expressions such as 'this (F)' or 'that (F)', adverbs like 'here', 'now', and 'today', and the personal pronoun 'I'. While generally agreeing that representing the world from a thinker's cognitive perspective is a key feature of indexical thoughts, philosophers disagree as to whether a thinker's cognitive perspective can be captured and rationalized by semantic content and, if so, what kind of content this is. This book surveys competing views and then advances its own positive account. Ultimately, it argues that a thinker's cognitive perspective - or her indexical point of view - is to be explained in terms of the content that is believed and asserted as the only kind of content that there is which thereby serves as the bearer of cognitive significance. The Indexical Point of View will be of interest to philosophers of mind and language, linguists, and cognitive scientists.