This book presents a set of historical recollections on the work of Martin Davis and his role in advancing our understanding of the connections between logic, computing, and unsolvability. The individual contributions touch on most of the core aspects of Davis' work and set it in a contemporary context. They analyse, discuss and develop many of the ideas and concepts that Davis put forward, including such issues as contemporary satisfiability solvers, essential unification, quantum computing and generalisations of Hilbert's tenth problem. The book starts out with a scientific autobiography by Davis, and ends with his responses to comments included in the contributions. In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis' work. As a whole, this book shows how Davis' scientific work lies at the intersection of computability, theoretical computer science, foundations of mathematics, and philosophy, and draws its unifying vision from his deep involvement in Logic.

J. Anthony Blair is a prominent international figure in argumentation studies. He is among the originators of informal logic, an author of textbooks on the informal logic approach to argument analysis and evaluation and on critical thinking, and a founder and editor of the journal Informal Logic. Blair is widely recognized among the leaders in the field for contributing formative ideas to the argumentation literature of the last few decades. This selection of key works provides insights into the history of the field of argumentation theory and various related disciplines. It illuminates the central debates and presents core ideas in four main areas: Critical Thinking, Informal Logic, Argument Theory and Logic, Dialectic and Rhetoric.

OndrejMajer, Ahti-VeikkoPietarinen, andTeroTulenheimo 1 Games and logic in philosophy Recent years have witnessed a growing interest in the unifying methodo- gies over what have been perceived as pretty disparate logical 'systems', or else merely an assortment of formal and mathematical 'approaches' to phi- sophical inquiry. This development has largely been fueled by an increasing dissatisfaction to what has earlier been taken to be a straightforward outcome of 'logical pluralism' or 'methodological diversity'. These phrases appear to re ect the everyday chaos of our academic pursuits rather than any genuine attempt to clarify the general principles underlying the miscellaneous ways in which logic appears to us. But the situation is changing. Unity among plurality is emerging in c- temporary studies in logical philosophy and neighbouring disciplines. This is a necessary follow-up to the intensive research into the intricacies of logical systems and methodologies performed over the recent years. The present book suggests one such peculiar but very unrestrained meth- ological perspective over the eld of logic and its applications in mathematics, language or computation: games. An allegory for opposition, cooperation and coordination, games are also concrete objects of formal study.

This study explores the theoretical relationship between Aristotle's theory of syllogism and his conception of demonstrative knowledge. More specifically, I consider why Aristotle's theory of demonstration presupposes his theory of syllogism. In reconsidering the relationship between Aristotle's two Analytics, I modify this widely discussed question. The problem of the relationship between Aristotle's logic and his theory of proof is commonly approached from the standpoint of whether the theory of demonstration presupposes the theory of syllogism. By contrast, I assume the theoretical relationship between these two theories from the start. This assumption is based on much explicit textual evidence indicating that Aristotle considers the theory of demonstration a branch of the theory of syllogism. I see no textual reasons for doubting the theoretical relationship between Aristotle's two Analytics so I attempt to uncover here the common theoretical assumptions that relate the syllogistic form of reasoning to the cognitive state (i. e. , knowledge), which is attained through syllogistic inferences. This modification of the traditional approach reflects the wider objective of this essay. Unlike the traditional interpretation, which views the Posterior Analytics in light of scientific practice, this study aims to lay the foundation for a comprehensive interpretation of the Posterior Analytics, considering this work from a metaphysical perspective. One of my major assertions is that Aristotle's conception of substance is essential for a grasp of his theory of demonstration in general, and of the role of syllogistic logic in particular.

This book consists of a series of chapters on Carnap's ideal of explication as an alternative to the naturalistic conceptions of science, setting it in its historical context, discussing specific cases of explications, and entiching the on-going debate on conceptual engineering and naturalism in analytic philosophy.

This book on proof theory centers around the legacy of Kurt Schutte and its current impact on the subject. Schutte was the last doctoral student of David Hilbert who was the first to see that proofs can be viewed as structured mathematical objects amenable to investigation by mathematical methods (metamathematics). Schutte inaugurated the important paradigm shift from finite proofs to infinite proofs and developed the mathematical tools for their analysis. Infinitary proof theory flourished in his hands in the 1960s, culminating in the famous bound 0 for the limit of predicative mathematics (a fame shared with Feferman). Later his interests shifted to developing infinite proof calculi for impredicative theories. Schutte had a keen interest in advancing ordinal analysis to ever stronger theories and was still working on some of the strongest systems in his eighties. The articles in this volume from leading experts close to his research, show the enduring influence of his work in modern proof theory. They range from eye witness accounts of his scientific life to developments at the current research frontier, including papers by Schutte himself that have never been published before.

This volume covers a wide range of topics in the most recent debates in the philosophy of mathematics, and is dedicated to how semantic, epistemological, ontological and logical issues interact in the attempt to give a satisfactory picture of mathematical knowledge. The essays collected here explore the semantic and epistemic problems raised by different kinds of mathematical objects, by their characterization in terms of axiomatic theories, and by the objectivity of both pure and applied mathematics. They investigate controversial aspects of contemporary theories such as neo-logicist abstractionism, structuralism, or multiversism about sets, by discussing different conceptions of mathematical realism and rival relativistic views on the mathematical universe. They consider fundamental philosophical notions such as set, cardinal number, truth, ground, finiteness and infinity, examining how their informal conceptions can best be captured in formal theories. The philosophy of mathematics is an extremely lively field of inquiry, with extensive reaches in disciplines such as logic and philosophy of logic, semantics, ontology, epistemology, cognitive sciences, as well as history and philosophy of mathematics and science. By bringing together well-known scholars and younger researchers, the essays in this collection - prompted by the meetings of the Italian Network for the Philosophy of Mathematics (FilMat) - show how much valuable research is currently being pursued in this area, and how many roads ahead are still open for promising solutions to long-standing philosophical concerns. Promoted by the Italian Network for the Philosophy of Mathematics - FilMat

It is usually assumed that Wittgenstein's philosophical development is determined either by one dramatic or one subtle change of mind. This book challenges the one-change view. Wittgenstein had many changes of mind and they are so substantial that he can be understood as holding several different philosophies in the late twenties and early thirties. Early in 1929, Wittgenstein envisages a complementary (phenomenological) symbolism in order to carry out the Tractarian task of giving the limits of language and thought. The symbolism failed and he then developed a comprehensive notion of 'grammar' that, he hoped, would fulfill the task. This notion of 'grammar' leads in 1930-1 to the calculus conception of language, which is still defended in the Big Typescript (1932-3). As a complementary tool of the calculus conception, Wittgenstein invents the genetic method, which aims at dissolving philosophical puzzles by the understanding of how they come about. After the Big Typescript, Wittgenstein assimilates an anthropological perspective and puts the genetic method at the center of the stage of his philosophy. The use of the genetic method (associated with an anthropological perspective) develops gradually, taking various forms of application: in the Blue Book, in the versions of the Brown Book (1934-6), and in the Philosophical Investigations.

This book is both dif?cult and rewarding, affording a new perspective on logic and reality, basically seen in terms of change and stability, being and becoming. Most importantly it exemplifies a mode of doing philosophy of science that seems a welcome departure from the traditional focus on purely analytic arguments. The author approaches ontology, metaphysics, and logic as having offered a number of ways of constructing the description of reality, and aims at deepening their relationships in a new way. Going beyond the mere abstract and formal aspects of logical analysis, he offers a new architecture of logic that sees it as applied not only to the "reasoning processes" belonging to the first disciplinary group - ontology - but also directly concerned with en- ties, events, and phenomena studied by the second one - metaphysics. It is the task of the book to elaborate such a constructive logic, both by offering a lo- cal view of the structure of the reality in general and by proffering a wealth of models able to encompass its implications for science. In turning from the merely formal to the constructive account of logic Brenner overcomes the limitation of logic to linguistic concepts so that it can be not only a logic "of" reality but also "in" that reality which is constitutively characterized by a number of fundamental dualities (observer and observed, self and not-self, internal and external, etc.

The twelve original studies collected in this volume examine different aspects of Edmund Husserl's Logical Investigations. They are authored by scholars and specialists internationally recognized for their expertise in the fields of logic, phenomenology, history of philosophy and philosophy of mind. They approach Husserl's groundwork from different angles and perspectives and shed new light on a number of issues such as meaning, intentionality, ontology, logic, etc.

This book provides an accessible and thorough analysis of "The Doctrine of Being," the first part of Hegel's Science of Logic. Though it received much scholarly attention in the past, interpreters of this text have generally refrained from examining it in a sufficiently detailed manner. Through a rigorous and critical reading of Hegel's speculative arguments, Mehmet Tabak illustrates that Hegel meant his logic to be both a presuppositionless analysis and development of the basic categories of thought, on the one hand, and a post-Kantian ontology on the other. However, the analysis of the text demonstrates that Hegel fails to deliver such logic. This volume promises to be an indispensable guide to those who wish to understand the first book of Science of Logic.

Stewart Shapiro's aim in Vagueness in Context is to develop both a philosophical and a formal, model-theoretic account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases. A person can be tall with respect to male accountants and not tall (even short) with respect to professional basketball players. The main feature of Shapiro's account is that the extensions (and anti-extensions) of vague terms also vary in the course of a conversation, even after the external contextual features, such as the comparison class, are fixed. A central thesis is that in some cases, a competent speaker of the language can go either way in the borderline area of a vague predicate without sinning against the meaning of the words and the non-linguistic facts. Shapiro calls this open texture, borrowing the term from Friedrich Waismann. The formal model theory has a similar structure to the supervaluationist approach, employing the notion of a sharpening of a base interpretation. In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity. The ultimate goal of the technical aspects of the work is to delimit a plausible notion of logical consequence, and to explore what happens with the sorites paradox. Later chapters deal with what passes for higher-order vagueness - vagueness in the notions of 'determinacy' and 'borderline' - and with vague singular terms, or objects. In each case, the philosophical picture is developed by extending and modifying the original account. This is followed with modifications to the model theory and the central meta-theorems. As Shapiro sees it, vagueness is a linguistic phenomenon, due to the kinds of languages that humans speak. But vagueness is also due to the world we find ourselves in, as we try to communicate features of it to each other. Vagueness is also due to the kinds of beings we are. There is no need to blame the phenomenon on any one of those aspects.

This book provides a new, linguistic approach to Argumentation Theory. Its main goal is to integrate the logical, dialectical and rhetorical dimensions of argumentation in a model providing a unitary treatment of its justificatory and persuasive powers. This model takes as its basis Speech Acts Theory in order to characterize argumentation as a second-order speech act complex. The result is a systematic and comprehensive theory of the interpretation, analysis and evaluation of arguments. This theory sheds light on the many faces of argumentative communication: verbal and non-verbal, monological and dialogical, literal and non-literal, ordinary and specialized.
The book takes into consideration the major current comprehensive accounts of good argumentation (Perelman's New Rhetoric, Pragma-dialectics, the ARG model, the Epistemic Approach) and shows that these accounts have fundamental weaknesses rooted in their instrumentalist conception of argumentation as an activity oriented to a goal external to itself. Furthermore, the author addresses some challenging meta-theoretical questions such as the justification problem for Argumentation Theory models and the relationship between reasoning and arguing.

This book is for bioethicists, ethicists (theologians/philosophers), professionals in biotechnology, EU and national policymakers, and professors/teachers of courses in applied ethics. It presents an interdisciplinary reflection on the nature and scope of current biotechnology in Europe. It offers a concise presentation of the current biotechnological arena in Europe with its ethical implications and provides a survey of topical Council of Europe documents and treaties.

This edited volume presents new lines of research dealing with the language of thought and its philosophical implications in the time of Ockham. It features more than 20 essays that also serve as a tribute to the ground-breaking work of a leading expert in late medieval philosophy: Claude Panaccio. Coverage addresses topics in the philosophy of mind and cognition (externalism, mental causation, resemblance, habits, sensory awareness, the psychology, illusion, representationalism), concepts (universal, transcendental, identity, syncategorematic), logic and language (definitions, syllogisms, modality, supposition, obligationes, etc.), action theory (belief, will, action), and more. A distinctive feature of this work is that it brings together contributions in both French and English, the two major research languages today on the main theme in question. It unites the most renowned specialists in the field as well as many of Claude Panaccio's former students who have engaged with his work over the years. In furthering this dialogue, the essays render key topics in fourteenth-century thought accessible to the contemporary philosophical community without being anachronistic or insensitive to the particularities of the medieval context. As a result, this book will appeal to a general population of philosophers and historians of philosophy with an interest in logic, philosophy of language, philosophy of mind, and metaphysics.

This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman's work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman's work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Goedel's incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth theories, and category theory. In his philosophical research, Feferman explored questions such as "What is logic?" and proposed particular positions regarding the foundations of mathematics including, for example, his "conceptual structuralism." The contributing authors of the volume examine all of the above issues. Their papers are accompanied by an autobiography presented by Feferman that reflects on the evolution and intellectual contexts of his work. The contributing authors critically examine Feferman's work and, in part, actively expand on his concrete mathematical projects. The volume illuminates Feferman's distinctive work and, in the process, provides an enlightening perspective on the foundations of mathematics and logic.

This monograph addresses the question of the increasing irrelevance of philosophy, which has seen scientists as well as philosophers concluding that philosophy is dead and has dissolved into the sciences. It seeks to answer the question of whether or not philosophy can still be fruitful and what kind of philosophy can be such. The author argues that from its very beginning philosophy has focused on knowledge and methods for acquiring knowledge. This view, however, has generally been abandoned in the last century with the belief that, unlike the sciences, philosophy makes no observations or experiments and requires only thought. Thus, in order for philosophy to once again be relevant, it needs to return to its roots and focus on knowledge as well as methods for acquiring knowledge. Accordingly, this book deals with several questions about knowledge that are essential to this view of philosophy, including mathematical knowledge. Coverage examines such issues as the nature of knowledge; plausibility and common sense; knowledge as problem solving; modeling scientific knowledge; mathematical objects, definitions, diagrams; mathematics and reality; and more. This monograph presents a new approach to philosophy, epistemology, and the philosophy of mathematics. It will appeal to graduate students and researchers with interests in the role of knowledge, the analytic method, models of science, and mathematics and reality.

Andinmy haste, I said: "Allmenare Liars" 1 -Psalms 116:11 The Original Lie Philosophical analysis often reveals and seldom solves paradoxes. To quote Stephen Read: A paradox arises when an unacceptable conclusion is supported by a plausible argument from apparently acceptable premises. [...] So three di?erent reactions to the paradoxes are possible: to show that the r- soning is fallacious; or that the premises are not true after all; or that 2 the conclusion can in fact be accepted. There are sometimes elaborate ways to endorse a paradoxical conc- sion. One might be prepared to concede that indeed there are a number of grains that make a heap, but no possibility to know this number. However, some paradoxes are more threatening than others; showing the conclusiontobeacceptableisnotaseriousoption,iftheacceptanceleads to triviality. Among semantic paradoxes, the Liar (in any of its versions) 3 o?ers as its conclusion a bullet no one would be willing to bite. One of the most famous versions of the Liar Paradox was proposed by Epimenides, though its attribution to the Cretan poet and philosopher has only a relatively recent history. It seems indeed that Epimenides was mentioned neither in ancient nor in medieval treatments of the Liar 1 Jewish Publication Society translation. 2 Read [1].

Gottfried Wilhelm Leibniz was an outstanding contributor to many fields of human knowledge. The historiography of philosophy has tagged him as a "rationalist." But what does this exactly mean? Is he a "rationalist" in the same sense in Mathematics and Politics, in Physics and Jurisprudence, in Metaphysics and Theology, in Logic and Linguistics, in Technology and Medicine, in Epistemology and Ethics? What are the most significant features of his "rationalism," whatever it is?

For the first time an outstanding group of Leibniz researchers, some acknowledged as leading scholars, others in the beginning of a promising career, who specialize in the most significant areas of Leibniz's contributions to human thought and action, were requested to spell out the nature of his rationalism in each of these areas, with a view to provide a comprehensive picture of what it amounts to, both in its general drive and in its specific features and eventual inner tensions.

The chapters of the book are the result of intense discussion in the course of an international conference focused on the title question of this book, and were selected in view of their contribution to this topic. They are clustered in thematically organized parts. No effort has been made to hide the controversies underlying the different interpretations of Leibniz's "rationalism" - in each particular domain and as a whole. On the contrary, the editor firmly believes that only through a variety of conflicting interpretive perspectives can the multi-faceted nature of an oeuvre of such a magnitude and variety as Leibniz's be brought to light and understood as it deserves.

Alfred Tarski was one of the two giants of the twentieth-century development of logic, along with Kurt Goedel. The four volumes of this collection contain all of Tarski's published papers and abstracts, as well as a comprehensive bibliography. Here will be found many of the works, spanning the period 1921 through 1979, which are the bedrock of contemporary areas of logic, whether in mathematics or philosophy. These areas include the theory of truth in formalized languages, decision methods and undecidable theories, foundations of geometry, set theory, and model theory, algebraic logic, and universal algebra.

The Handbook of Deontic Logic and Normative Systems presents a detailed overview of the main lines of research on contemporary deontic logic and related topics. Although building on decades of previous work in the field, it is the first collection to take into account the significant changes in the landscape of deontic logic that have occurred in the past twenty years. These changes have resulted largely, though not entirely, from the interaction of deontic logic with a variety of other fields, including computer science, legal theory, organizational theory, economics, and linguistics. This first volume of the Handbook is divided into three parts, containing nine chapters in all, each written by leading experts in the field. The first part concentrates on historical foundations. The second examines topics of central interest in contemporary deontic logic. The third presents some new logical frameworks that have now become part of the mainstream literature. A second volume of the Handbook is currently in preparation, and there may be a third after that.

This is a collection of Isaac Levi's philosophical papers. Over the period represented by the work here, Professor Levi has developed an interrelated set of views, in the tradition of Peirce and Dewey, on epistemology and the philosophy of science and social science. This focus has been on the problem of induction and the growth of knowledge, the foundations of probability and the theory of rational decision making. His most important essays in these areas are assembled here, with an introduction setting out their main themes and connections. Part I considers how the aims of scientific inquiry should constrain its practice, employing the crucial notion of 'epistemic utility'. The essays in Part II explain Professor Levi's conception of human knowledge; those in Part III consider objective or statistical probability and evaluate the notion of potential surprise; while Part IV extends his views to central questions of individual and collective decision making. As a whole the volume presents a coherent, elaborated position which will be of great interest to a range of philosophers, decision theorists, welfare and social choice theorists and cognitive scientists.

In his new study, Beyond Atheism, Beyond God, author Philip A. Stahl uses atheism as a rational stepping stone to arrive at an emergent conception of the universe, exposing features that might be described as transcendent.

He presents an impersonal approach to Being that is devoid of any specific religious overtones or affi liations. Each person becomes a quantum-based co-creator in his or her own right, according to physicist Henry Stapp. As such, we are able to thereby see ourselves and our humanity in a new light, as opposed to being merely reactive cogs in a vast mechanical-reductionist machine. Effectively, we emerge as much more than assemblies of molecules.

This volume, the fourth and final entry in Stahl's series on atheism, seeks to arrive at a transcendent concept of being that also surpasses absolutism and naive or dogmatic deity templates. It considers the development of a more realistic, cogent and effective ethics and morality less likely to be exploited by the power mongers or sacred source apologists, and it answers the question of whether God exists-though not in the way one would normally assume.

This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz's work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics and Theoretical Computer Science.

The range of contributions includes material on the extension of natural deduction with higher-order rules, as opposed to higher-order connectives, and a paper discussing the application of natural deduction rules to dealing with equality in predicate calculus. The volume continues with a key chapter summarizing work on the extension of the Curry-Howard isomorphism (itself a by-product of the work on natural deduction), via methods of category theory that have been successfully applied to linear logic, as well as many other contributions from highly regarded authorities. With an illustrious group of contributors addressing a wealth of topics and applications, this volume is a valuable addition to the libraries of academics in the multiple disciplines whose development has been given added scope by the methodologies supplied by natural deduction. The volume is representative of the rich and varied directions that Prawitz work has inspired in the area of natural deduction.
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Pondering on Problems of Argumentation is a collection of twenty essays brought together for anyone who is interested in theoretical issues in the study of argumentation. This collection of papers gives the reader an insightful and balanced view of the kind of theoretical issues argumentation theorists are currently concerned with. Because most of the perspectives on argumentation that are en vogue are represented, this volume provides a multidisciplinary and even interdisciplinary outlook on the current state of affairs in argumentation theory. Some of the contributions in Pondering on Problems of Argumentation deal with problems of argumentation that have been recognized as theoretical issues for a considerable time, like the problems of fallaciousness and identifying argumentation structures. Other contributions discuss issues that have become a focus of attention only recently or regained their prominence, such as the relationship between dialectic and rhetoric, and the strategic use of the argumentative technique of dissociation. In five separate sections papers are included dealing with argumentative strategies, problems of norms of reasonableness and fallaciousness, types of argument and argument schemes the structure of argumentation and rules for advocacy and discussion.