This book discusses major milestones in Rohit Jivanlal Parikh's scholarly work. Highlighting the transition in Parikh's interest from formal languages to natural languages, and how he approached Wittgenstein's philosophy of language, it traces the academic trajectory of a brilliant scholar whose work opened up various new avenues in research. This volume is part of Springer's book series Outstanding Contributions to Logic, and honours Rohit Parikh and his works in many ways. Parikh is a leader in the realm of ideas, offering concepts and definitions that enrich the field and lead to new research directions. Parikh has contributed to a variety of areas in logic, computer science and game theory. In mathematical logic his contributions have been in recursive function theory, proof theory and non-standard analysis; in computer science, in the areas of modal, temporal and dynamic logics of programs and semantics of programs, as well as logics of knowledge; in artificial intelligence in the area of belief revision; and in game theory in the formal analysis of social procedures, with a strong undercurrent of philosophy running through all his work.This is not a collection of articles limited to one theme, or even directly connected to specific works by Parikh, but instead all papers are inspired and influenced by Parikh in some way, adding structures to and enriching "Parikh-land". The book presents a brochure-like overview of Parikh-land before providing an "introductory video" on the sights and sounds that you experience when reading the book.

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With the publication of the present volume, the Handbook of the History of Logic turns its attention to the rise of modern logic. The period covered is 1685-1900, with this volume carving out the territory from Leibniz to Frege. What is striking about this period is the earliness and persistence of what could be called 'the mathematical turn in logic'. Virtually every working logician is aware that, after a centuries-long run, the logic that originated in antiquity came to be displaced by a new approach with a dominantly mathematical character. It is, however, a substantial error to suppose that the mathematization of logic was, in all essentials, Frege's accomplishment or, if not his alone, a development ensuing from the second half of the nineteenth century. The mathematical turn in logic, although given considerable torque by events of the nineteenth century, can with assurance be dated from the final quarter of the seventeenth century in the impressively prescient work of Leibniz. It is true that, in the three hundred year run-up to the Begriffsschrift, one does not see a smoothly continuous evolution of the mathematical turn, but the idea that logic is mathematics, albeit perhaps only the most general part of mathematics, is one that attracted some degree of support throughout the entire period in question. Still, as Alfred North Whitehead once noted, the relationship between mathematics and symbolic logic has been an "uneasy" one, as is the present-day association of mathematics with computing. Some of this unease has a philosophical texture. For example, those who equate mathematics and logic sometimes disagree about the directionality of the purported identity. Frege and Russell made themselves famous by insisting (though for different reasons) that logic was the senior partner. Indeed logicism is the view that mathematics can be re-expressed without relevant loss in a suitably framed symbolic logic. But for a number of thinkers who took an algebraic approach to logic, the dependency relation was reversed, with mathematics in some form emerging as the senior partner. This was the precursor of the modern view that, in its four main precincts (set theory, proof theory, model theory and recursion theory), logic is indeed a branch of pure mathematics. It would be a mistake to leave the impression that the mathematization of logic (or the logicization of mathematics) was the sole concern of the history of logic between 1665 and 1900. There are, in this long interval, aspects of the modern unfolding of logic that bear no stamp of the imperial designs of mathematicians, as the chapters on Kant and Hegcl make clear. Of the two, Hcgel's influence on logic is arguably the greater, serving as a spur to the unfolding of an idealist tradition in logic - a development that will be covered in a further volume, British Logic in the Nineteenth Century.

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.

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.

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.

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.

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 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.

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.

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.

"Exposes the vast gap between the actual science underlying AI and the dramatic claims being made for it." -John Horgan "If you want to know about AI, read this book...It shows how a supposedly futuristic reverence for Artificial Intelligence retards progress when it denigrates our most irreplaceable resource for any future progress: our own human intelligence." -Peter Thiel Ever since Alan Turing, AI enthusiasts have equated artificial intelligence with human intelligence. A computer scientist working at the forefront of natural language processing, Erik Larson takes us on a tour of the landscape of AI to reveal why this is a profound mistake. AI works on inductive reasoning, crunching data sets to predict outcomes. But humans don't correlate data sets. We make conjectures, informed by context and experience. And we haven't a clue how to program that kind of intuitive reasoning, which lies at the heart of common sense. Futurists insist AI will soon eclipse the capacities of the most gifted mind, but Larson shows how far we are from superintelligence-and what it would take to get there. "Larson worries that we're making two mistakes at once, defining human intelligence down while overestimating what AI is likely to achieve...Another concern is learned passivity: our tendency to assume that AI will solve problems and our failure, as a result, to cultivate human ingenuity." -David A. Shaywitz, Wall Street Journal "A convincing case that artificial general intelligence-machine-based intelligence that matches our own-is beyond the capacity of algorithmic machine learning because there is a mismatch between how humans and machines know what they know." -Sue Halpern, New York Review of Books

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 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 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 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.

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 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.

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.

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.

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].

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.