This volume is number five in the 11-volume "Handbook of the History of Logic." It covers the first 50 years of the development of mathematical logic in the 20th century, and concentrates on the achievements of the great names of the period--Russell, Post, Godel, Tarski, Church, and the like. This was the period in which mathematical logic gave mature expression to its four main parts: set theory, model theory, proof theory and recursion theory. Collectively, this work ranks as one of the greatest achievements of our intellectual history. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, and artificial intelligence, for whom the historical background of his or her work is a salient consideration.
The entire range of modal logic is covered
Serves as a singular contribution to the intellectual history of the 20th century
Contains the latest scholarly discoveries and interpretative insights"

Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration
Serves as a singular contribution to the intellectual history of the 20th centuryContains the latest scholarly discoveries and interpretative insights

"Philosophy of Linguistics" investigates the foundational concepts and methods of linguistics, the scientific study of human language. This groundbreaking collection, the most thorough treatment of the philosophy of linguistics ever published, brings together philosophers, scientists and historians to map out both the foundational assumptions set during the second half of the last century and the unfolding shifts in perspective in which more functionalist perspectives are explored. The opening chapter lays out the philosophical background in preparation for the papers that follow, which demonstrate the shift in the perspective of linguistics study through discussions of syntax, semantics, phonology and cognitive science more generally. The volume serves as a detailed introduction for those new to the field as well as a rich source of new insights and potential research agendas for those already engaged with the philosophy of linguistics.

Part of the Handbook of the Philosophy of Science series edited by:

Dov M. Gabbay, King's College, London, UK; Paul Thagard, University of Waterloo, Canada; and John Woods, University of British Columbia, Canada.
Provides a bridge between philosophy and current scientific findingsEncourages multi-disciplinary dialogueCovers theory and applications

This volume covers a wide range of conceptual, epistemological and methodological issues in the philosophy of science raised by reflection upon medical science and practice. Several chapters examine such general meta-scientific concepts as discovery, reduction, theories and models, causal inference and scientific realism as they apply to medicine or medical science in particular. Some discuss important concepts specific to medicine (diagnosis, health, disease, brain death). A topic such as evidence, for instance, is examined at a variety of levels, from social mechanisms for guiding evidence-based reasoning such as evidence-based medicine, consensus conferences, and clinical trials, to the more abstract analysis of experimentation, inference and uncertainty. Some chapters reflect on particular domains of medicine, including psychiatry, public health, and nursing.

The contributions span a broad range of detailed cases from the science and practice of medicine, as well as a broad range of intellectual approaches, from conceptual analysis to detailed examinations of particular scientific papers or historical episodes.
Chapters view philosophy of medicine from quite different angles Considers substantive cases from both medical science and practiceChapters from a distinguished array of contributors

This volume is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic - as this handbook attests - is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration.

Chapter on the Port Royal contributions to probability theory and decision theory

Serves as a singular contribution to the intellectual history of the 20th century Contains the latest scholarly discoveries and interpretative insights"

The most pressing problems facing humanity today - over-population, energy shortages, climate change, soil erosion, species extinctions, the risk of epidemic disease, the threat of warfare that could destroy all the hard-won gains of civilization, and even the recent fibrillations of the stock market - are all ecological or have a large ecological component. in this volume philosophers turn their attention to understanding the science of ecology and its huge implications for the human project.
To get the application of ecology to policy or other practical concerns right, humanity needs a clear and disinterested philosophical understanding of ecology which can help identify the practical lessons of science. Conversely, the urgent practical demands humanity faces today cannot help but direct scientific and philosophical investigation toward the basis of those ecological challenges that threaten human survival. This book will help to fuel the timely renaissance of interest in philosophy of ecology that is now occurring in the philosophical profession.
Provides a bridge between philosophy and current scientific findingsCovers theory and applicationsEncourages multi-disciplinary dialogue"

Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy and
language in ancient times; they were studied by traditional informal
methods until the 20th century. In the last century the tools became
highly mathematical, and both modal logic and quantification found numerous applications in Computer Science. At the same time many other kinds of nonclassical logics were investigated and applied to Computer Science.
Although there exist several good books in propositional modal logics, this book is the first detailed monograph in nonclassical first-order quantification. It includes results obtained during the past thirty years. The field is very large, so we confine ourselves with only two kinds of logics: modal and superintuitionistic. The main emphasis of Volume 1 is model-theoretic, and it concentrates on descriptions of different sound semantics and completeness problem --- even for these seemingly simple questions we have our hands full. The major part of the presented material has never been published before. Some results are very recent, and for other results we either give new proofs or first proofs in full detail.

Information is a recognized fundamental notion across the sciences and humanities, which is crucial to understanding physical computation, communication, and human cognition. The Philosophy of Information brings together the most important perspectives on information. It includes major technical approaches, while also setting out the historical backgrounds of information as well as its contemporary role in many academic fields. Also, special unifying topics are high-lighted that play across many fields, while we also aim at identifying relevant themes for philosophical reflection. There is no established area yet of Philosophy of Information, and this Handbook can help shape one, making sure it is well grounded in scientific expertise. As a side benefit, a book like this can facilitate contacts and collaboration among diverse academic milieus sharing a common interest in information.
- First overview of the formal and technical issues involved in the philosophy of information
- Integrated presentation of major mathematical approaches to information, form computer science, information theory, and logic
- Interdisciplinary themes across the traditional boundaries of natural sciences, social sciences, and humanities.

This volume concerns philosophical issues that arise from the practice of anthropology and sociology. The essays cover a wide range of issues, including traditional questions in the philosophy of social science as well as those specific to these disciplines. Authors attend to the historical development of the current debates and set the stage for future work.
. Comprehensive survey of philosophical issues in anthropology and sociology
. Historical discussion of important debates
. Applications to current research in anthropology and sociology

The Handbook of the History of Logic is a multi-volume research instrument that brings to the development of logic the best in modern techniques of historical and interpretative scholarship. It is the first work in English in which the history of logic is presented so extensively. The volumes are numerous and large. Authors have been given considerable latitude to produce chapters of a length, and a level of detail, that would lay fair claim on the ambitions of the project to be a definitive research work. Authors have been carefully selected with this aim in mind. They and the Editors join in the conviction that a knowledge of the history of logic is nothing but beneficial to the subject's present-day research programmes. One of the attractions of the Handbook's several volumes is the emphasis they give to the enduring relevance of developments in logic throughout the ages, including some of the earliest manifestations of the subject.
Covers in depth the notion of logical consequenceDiscusses the central concept in logic of modalityIncludes the use of diagrams in logical reasoning

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.

One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind?
It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume.
Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed.
The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics.
-Comprehensive coverage of all main theories in the philosophy of mathematics
-Clearly written expositions of fundamental ideas and concepts
-Definitive discussions by leading researchers in the field
-Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included

Paraconsistent logics are logics which allow solid deductive reasoning under contradictions by offering a mathematical and philosophical support to contradictory yet non-trivial theories. Due to its role in models of scientific reasoning and to its philosophical implications, as well as to its connections to topics such as abduction, automated reasoning, logic programming, and belief revision, paraconsistency has becoming a fast growing area. During the III World Congress on Paraconsistency (WCP3) held in Toulouse, France, in July, 2003, it became apparent that there is a need for a Handbook covering the most recent results on several aspects of paraconsistent logic, including philosophical debates on paraconsistency and its connections to philosophy of language, argumentation theory, computer science, information theory, and artificial intelligence. This book is a basic tool for those who want to know more about paraconsistent logic, its history and philosophy, the various systems of paraconsistent logic and their applications. The present volume is edited by Jean-Yves Beziau, Walter Carnielli and Dov Gabbay, expert logicians versed in a variety of logics.

Part of the Handbook of the Philosophy of Science Series edited by:

Dov M. Gabbay King's College, London, UK; Paul Thagard University of Waterloo, Canada; and John Woods University of British Columbia, Canada.

"Philosophy of Economics" investigates the foundational concepts and methods of economics, the social science that analyzes the production, distribution and consumption of goods and services. This groundbreaking collection, the most thorough treatment of the philosophy of economics ever published, brings together philosophers, scientists and historians to map out the central topics in the field. The articles are divided into two groups. Chapters in the first group deal with various philosophical issues characteristic of economics in general, including realism and Lakatos, explanation and testing, modeling and mathematics, political ideology and feminist epistemology. Chapters in the second group discuss particular methods, theories and branches of economics, including forecasting and measurement, econometrics and experimentation, rational choice and agency issues, game theory and social choice, behavioral economics and public choice, geographical economics and evolutionary economics, and finally the economics of scientific knowledge. This volume serves as a detailed introduction for those new to the field as well as a rich source of new insights and potential research agendas for those already engaged with the philosophy of economics.
Provides a bridge between philosophy and current scientific findingsEncourages multi-disciplinary dialogueCovers theory and applications

In this book the authors present new results on interpolation for nonmonotonic logics, abstract (function) independence, the Talmudic Kal Vachomer rule, and an equational solution of contrary-to-duty obligations. The chapter on formal construction is the conceptual core of the book, where the authors combine the ideas of several types of nonmonotonic logics and their analysis of 'natural' concepts into a formal logic, a special preferential construction that combines formal clarity with the intuitive advantages of Reiter defaults, defeasible inheritance, theory revision, and epistemic considerations. It is suitable for researchers in the area of computer science and mathematical logic.

In this book the authors present new results on interpolation for nonmonotonic logics, abstract (function) independence, the Talmudic Kal Vachomer rule, and an equational solution of contrary-to-duty obligations. The chapter on formal construction is the conceptual core of the book, where the authors combine the ideas of several types of nonmonotonic logics and their analysis of 'natural' concepts into a formal logic, a special preferential construction that combines formal clarity with the intuitive advantages of Reiter defaults, defeasible inheritance, theory revision, and epistemic considerations. It is suitable for researchers in the area of computer science and mathematical logic.

This text offers an extension to the traditional Kripke semantics for non-classical logics by adding the notion of reactivity. Reactive Kripke models change their accessibility relation as we progress in the evaluation process of formulas in the model. This feature makes the reactive Kripke semantics strictly stronger and more applicable than the traditional one. Here we investigate the properties and axiomatisations of this new and most effective semantics, and we offer a wide landscape of applications of the idea of reactivity. Applied topics include reactive automata, reactive grammars, reactive products, reactive deontic logic and reactive preferential structures. Reactive Kripke semantics is the next step in the evolution of possible world semantics for non-classical logics, and this book, written by one of the leading authorities in the field, is essential reading for graduate students and researchers in applied logic, and it offers many research opportunities for PhD students.

This second edition of the Handbook of Philosophical Logic reflects great changes in the landscape of philosophical logic since the first edition. It gives readers an idea of that landscape and its relation to computer science and formal language and artificial intelligence. It shows how the increased demand for philosophical logic from computer science and artificial intelligence and computational linguistics accelerated the development of the subject directly and indirectly. This development in turn, directly pushed research forward, stimulated by the needs of applications. New logic areas became established and old areas were enriched and expanded. At the same time, it socially provided employment for generations of logicians residing in computer science, linguistics and electrical engineering departments which of course helped keep the logic community to thrive. The many contributors to this Handbook are active in these application areas and are among the most famous leading figures of applied philosophical logic of our times.

"Handbook of the History of Logic" brings to the development of logic the best in modern techniques of historical and interpretative scholarship. Computational logic was born in the twentieth century and evolved in close symbiosis with the advent of the first electronic computers and the growing importance of computer science, informatics and artificial intelligence. With more than ten thousand people working in research and development of logic and logic-related methods, with several dozen international conferences and several times as many workshops addressing the growing richness and diversity of the field, and with the foundational role and importance these methods now assume in mathematics, computer science, artificial intelligence, cognitive science, linguistics, law and many engineering fields where logic-related techniques are used inter alia to state and settle correctness issues, the field has diversified in ways that even the pure logicians working in the early decades of the twentieth century could have hardly anticipated.

Logical calculi, which capture an important aspect of human thought, are now amenable to investigation with mathematical rigour and computational support and fertilized the early dreams of mechanised reasoning: Calculemus . The Dartmouth Conference in 1956 - generally considered as the birthplace of artificial intelligence - raised explicitly the hopes for the new possibilities that the advent of electronic computing machinery offered: logical statements could now be executed on a machine with all the far-reaching consequences that ultimately led to logic programming, deduction systems for mathematics and engineering, logical design and verification of computer software and hardware, deductive databases and software synthesis as well as logical techniques for analysis in the field of mechanical engineering. This volume covers some of the main subareas of computational logic and its applications.
Chapters by leading authorities in the fieldProvides a forum where philosophers and scientists interactComprehensive reference source on the history of logic"

Trends in Belief Revision and Argumentation Dynamics contains a collection of original essays on diverse aspects where these two areas of research converge. The essays are the result of the synergistic interactions that took place during the 2012 Workshop on Belief Revision and Argumentation in Funchal, Madeira. The Island of Madeira provided a stimulating environment for the presentation of research results and the subsequent lively discussions held. The dynamic exchange of ideas contributed to refining the approaches and to discovering new insights that undoubtedly will positively affect the field by advancing the individual research lines. The authors of the chapters in this book have made an effort to reflect these discussions, successfully addressing many of the important points raised during the workshop. The present book encompasses work that comes from the two areas of research, which are different but that are concerned with the epistemic state of an agent. As such, these essays reflect dissimilar perspectives that have contributed to advance the understanding of such a puzzling and thrilling problem. At the same time, with this collection we hope to reach a wider audience by disseminating and stimulating research on this topic, as we strongly believe that the interaction between the two areas will lead to a better understanding of each of them.

This book regards Dung's abstract argumentation frames as a general network, comparable to other networks such as general logics neural-nets, ecology nets, electrical networks, flow networks and so on. As such the book imports general meta-logical methods and applies them to argumentation and exports ideas from argumentation to general logics and networks.

Belief Revision Refutation and systems in Propositional Logic. A Quantifier Scope in Formal Linguistics and Non-deterministic Semantics for Logical Systems.

Lambda Calculi: A Guide Interpolation and Definability Discourse Representation Theory

"Philosophy of Chemistry" investigates the foundational concepts and methods of chemistry, the science of the nature of substances and their transformations. This groundbreaking collection, the most thorough treatment of the philosophy of chemistry ever published, brings together philosophers, scientists and historians to map out the central topics in the field. The 33 articles address the history of the philosophy of chemistry and the philosophical importance of some central figures in the history of chemistry; the nature of chemical substances; central chemical concepts and methods, including the chemical bond, the periodic table and reaction mechanisms; and chemistry s relationship to other disciplines such as physics, molecular biology, pharmacy and chemical engineering. This volume serves as a detailed introduction for those new to the field as well as a rich source of new insights and potential research agendas for those already engaged with the philosophy of chemistry.
Provides a bridge between philosophy and current scientific findingsEncourages multi-disciplinary dialogueCovers theory and applications
"