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"

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

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 domain of nonlinear dynamical systems and its mathematical underpinnings has been developing exponentially for a century, the last 35 years seeing an outpouring of new ideas and applications and a concomitant confluence with ideas of complex systems and their applications from irreversible thermodynamics. A few examples are in meteorology, ecological dynamics, andsocial and economic dynamics. These new ideas have profound implications for our understanding and practice in domains involving complexity, predictability and determinism, equilibrium, control, planning, individuality, responsibility and so on.
Our intention is to draw together in this volume, we believe for the first time, a comprehensive picture of the manifold philosophically interesting impacts of recent developments in understanding nonlinear systems and the unique aspects of their complexity. The book will focus specifically on the philosophical concepts, principles, judgments and problems distinctly raised by work in the domain of complex nonlinear dynamical systems, especially in recent years.

-Comprehensive coverage of all main theories in the philosophy of Complex Systems

-Clearly written expositions of fundamental ideas and concepts

-Definitive discussions by leading researchers in the field

-Summaries of leading-edge research in related fields are also included"

This collection represents the primary reference work for researchers and students in the area of Temporal Reasoning in Artificial Intelligence. Temporal reasoning has a vital role to play in many areas, particularly Artificial Intelligence. Yet, until now, there has been no single volume collecting together the breadth of work in this area. This collection brings together the leading researchers in a range of relevant areas and provides an coherent description of the breadth of activity concerning temporal reasoning in the filed of Artificial Intelligence.
Key Features:
- Broad range: foundations; techniques and applications
- Leading researchers around the world have written the chapters
- Covers many vital applications
- Source book for Artificial Intelligence, temporal reasoning
- Approaches provide foundation for many future software systems
- Broad range: foundations; techniques and applications
- Leading researchers around the world have written the chapters
- Covers many vital applications
- Source book for Artificial Intelligence, temporal reasoning
- Approaches provide foundation for many future software systems

The present work is a continuation of the authors' acclaimed multi-volume A
Practical Logic of Cognitive Systems. After having investigated the notion of
relevance in their previous volume, Gabbay and Woods now turn to abduction. In
this highly original approach, abduction is construed as ignorance-preserving
inference, in which conjecture plays a pivotal role. Abduction is a response to a
cognitive target that cannot be hit on the basis of what the agent currently knows.
The abducer selects a hypothesis which were it true would enable the reasoner to attain his target. He concludes from this fact that the hypothesis may be conjectured. In allowing conjecture to stand in for the knowledge he fails to have, the abducer reveals himself to be a satisficer, since an abductive solution is not a solution from knowledge. Key to the authors' analysis is the requirement that a conjectured proposition is not just what a reasoner might allow himself to assume, but a proposition he must defeasibly release as a premiss for further inferences in the domain of enquiry in which the original abduction problem has arisen.

The coverage of the book is extensive, from the philosophy of science to
computer science and AI, from diagnostics to the law, from historical explanation to linguistic interpretation. One of the volume's strongest contributions is its exploration of the abductive character of criminal trials, with special attention given to the standard of proof beyond a reasonable doubt.

Underlying their analysis of abductive reasoning is the authors' conception of
practical agency. In this approach, practical agency is dominantly a matter of the
comparativemodesty of an agent's cognitive agendas, together with comparatively scant resources available for their advancement. Seen in these ways, abduction has a significantly practical character, precisely because it is a form of inference that satisfices rather than maximizes its response to the agent's cognitive target.

The Reach of Abduction will be necessary reading for researchers, graduate
students and senior undergraduates in logic, computer science, AI, belief dynamics, argumentation theory, cognitive psychology and neuroscience, linguistics, forensic science, legal reasoning and related areas.

Key features:

- Reach of Abduction is fully integrated with a background logic of cognitive systems.

- The most extensive coverage compared to competitive works.

- Demonstrates not only that abduction is a form of ignorance preserving
inference but that it is a mode of inference that is wholly rational.

- Demonstrates the satisficing rather than maximizing character of
abduction.

- The development of formal models of abduction is considerably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticated
conceptual analysis and extensive logical modelling.
- Reach of Abduction is fully integrated with a background logic of cognitive systems.
- The most extensive coverage compared to competitive works
- Demonstrates not only that abduction is a form of ignorance preserving
inference but that it is a mode of inference that is wholly rational.
- Demonstrates the satisficing rather than maximizing character of
abduction.
- The development of formal models of abduction isconsiderably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticated
conceptual analysis and extensive logical modelling.

Agenda Relevance is the first volume in the authors' omnibus investigation of
the logic of practical reasoning, under the collective title, A Practical Logic
of Cognitive Systems. In this highly original approach, practical reasoning is
identified as reasoning performed with comparatively few cognitive assets,
including resources such as information, time and computational capacity. Unlike
what is proposed in optimization models of human cognition, a practical reasoner
lacks perfect information, boundless time and unconstrained access to
computational complexity. The practical reasoner is therefore obliged to be a
cognitive economizer and to achieve his cognitive ends with considerable
efficiency. Accordingly, the practical reasoner avails himself of various
scarce-resource compensation strategies. He also possesses neurocognitive
traits that abet him in his reasoning tasks. Prominent among these is the
practical agent's striking (though not perfect) adeptness at evading irrelevant
information and staying on task. On the approach taken here, irrelevancies are
impediments to the attainment of cognitive ends. Thus, in its most basic sense,
relevant information is cognitively helpful information. Information can then be
said to be relevant for a practical reasoner to the extent that it advances or
closes some cognitive agenda of his. The book explores this idea with a
conceptual detail and nuance not seen the standard semantic, probabilistic and
pragmatic approaches to relevance; but wherever possible, the authors seek to
integrate alternative conceptions rather than reject them outright. A further
attraction of the agenda-relevance approach is the extent to which its principal
conceptual findings lend themselves to technically sophisticated re-expression
in formal models that marshal the resources of time and action logics and
label led deductive systems.

Agenda Relevance is necessary reading for researchers in logic, belief
dynamics, computer science, AI, psychology and neuroscience, linguistics,
argumentation theory, and legal reasoning and forensic science, and will repay
study by graduate students and senior undergraduates in these same fields.

Key features:

relevance
action and agendas
practical reasoning
belief dynamics
non-classical logics
labelled deductive systems

"

Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled "The logic of quantum mechanics" quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results.
Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate.
The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject.
The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras MV algebras, partially ordered Abelian groups and those structures underlying quantum probability.
- Written by eminent scholars in the field of logic
- A comprehensive presentation of the theory, approaches and results in the field of quantum logic
- Volume focuses on quantum structures

This book is a specialized monograph on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language. Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (second edition), J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2, and David J. Pym and Eike Ritter's Reductive Logic and Proof Search: Proof theory, semantics and control.

Modern applications of logic, in mathematics, theoretical computer science, and linguistics, require combined systems involving many different logics working together. In this book the author offers a basic methodology for combining - or fibring - systems. This means that many existing complex systems can be broken down into simpler components, hence making them much easier to manipulate.

Greek, Indian and Arabic Logic marks the initial appearance of the multi-volume Handbook of the History of Logic. Additional volumes will be published when ready, rather than in strict chronological order. Soon to appear are The Rise of Modern Logic: From Leibniz to Frege. Also in preparation are Logic From Russell to Godel, The Emergence of Classical Logic, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in Logic. Further volumes will follow, including Mediaeval and Renaissance Logic and Logic: A History of its Central.
In designing the Handbook of the History of Logic, the Editors have taken the view that the history of logic holds more than an antiquarian interest, and that a knowledge of logic's rich and sophisticated development is, in various respects, relevant to the research programmes of the present day. Ancient logic is no exception. The present volume attests to the distant origins of some of modern logic's most important features, such as can be found in the claim by the authors of the chapter on Aristotle's early logic that, from its infancy, the theory of the syllogism is an example of an intuitionistic, non-monotonic, relevantly paraconsistent logic. Similarly, in addition to its comparative earliness, what is striking about the best of the Megarian and Stoic traditions is their sophistication and originality.
Logic is an indispensably important pivot of the Western intellectual tradition. But, as the chapters on Indian and Arabic logic make clear, logic's parentage extends more widely than any direct line from the Greek city states. It is hardly surprising, therefore, that for centuries logic has been an unfetteredlyinternational enterprise, whose research programmes reach to every corner of the learned world.
Like its companion volumes, Greek, Indian and Arabic Logic is the result of a design that gives to its distinguished authors as much space as would be needed to produce highly authoritative chapters, rich in detail and interpretative reach. The aim of the Editors is to have placed before the relevant intellectual communities a research tool of indispensable value.
Together with the other volumes, Greek, Indian and Arabic Logic, will be essential reading for everyone with a curiosity about logic's long development, especially researchers, graduate and senior undergraduate students in logic in all its forms, argumentation theory, AI and computer science, cognitive psychology and neuroscience, linguistics, forensics, philosophy and the history of philosophy, and the history of ideas.

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

Scientists use concepts and principles that are partly specific for their subject matter, but they also share part of them with colleagues working in different fields. Compare the biological notion of a 'natural kind' with the general notion of 'confirmation' of a hypothesis by certain evidence. Or compare the physical principle of the 'conservation of energy' and the general principle of 'the unity of science'. Scientists agree that all such notions and principles aren't as crystal clear as one might wish.
An important task of the philosophy of the special sciences, such as philosophy of physics, of biology and of economics, to mention only a few of the many flourishing examples, is the clarification of such subject specific concepts and principles. Similarly, an important task of 'general' philosophy of science is the clarification of concepts like 'confirmation' and principles like 'the unity of science'. It is evident that clarfication of concepts and principles only makes sense if one tries to do justice, as much as possible, to the actual use of these notions by scientists, without however following this use slavishly. That is, occasionally a philosopher may have good reasons for suggesting to scientists that they should deviate from a standard use. Frequently, this amounts to a plea for differentiation in order to stop debates at cross-purposes due to the conflation of different meanings.
While the special volumes of the series of Handbooks of the Philosophy of Science address topics relative to a specific discipline, this general volume deals with focal issues of a general nature.
After an editorial introduction about the dominant method of clarifying concepts and principles in philosophy of science, called explication, the first five chapters deal with the following subjects. Laws, theories, and research programs as units of empirical knowledge (Theo Kuipers), various past and contemporary perspectives on explanation (Stathis Psillos), the evaluation of theories in terms of their virtues (Ilkka Niiniluto), and the role of experiments in the natural sciences, notably physics and biology (Allan Franklin), and their role in the social sciences, notably economics (Wenceslao Gonzalez).
In the subsequent three chapters there is even more attention to various positions and methods that philosophers of science and scientists may favor: ontological, epistemological, and methodological positions (James Ladyman), reduction, integration, and the unity of science as aims in the sciences and the humanities (William Bechtel and Andrew Hamilton), and logical, historical and computational approaches to the philosophy of science (Atocha Aliseda and Donald Gillies).
The volume concludes with the much debated question of demarcating science from nonscience (Martin Mahner) and the rich European-American history of the philosophy of science in the 20th century (Friedrich Stadler).
- Comprehensive coverage of the philosophy of science written by leading philosophers in this field
- Clear style of writing for an interdisciplinary audience
- No specific pre-knowledge required

Legal theory, political sciences, sociology, philosophy, logic, artificial intelligence: there are many approaches to legal argumentation. Each of them provides specific insights into highly complex phenomena. Different disciplines, but also different traditions in disciplines (e.g. analytical and continental traditions in philosophy) find here a rare occasion to meet. The present book contains contributions, both historical and thematic, from leading researchers in several of the most important approaches to legal rationality. One of the main issues is the relation between logic and law: the way logic is actually used in law, but also the way logic can make law explicit. An outstanding group of philosophers, logicians and jurists try to meet this issue. The book is more than a collection of papers. However different their respective conceptual tools may be, the authors share a common conception: legal argumentation is a specific argumentation context.

Lambda Calculi: A Guide Interpolation and Definability Discourse Representation Theory

Philosophy of Biology is a rapidly expanding field. It is concerned with explanatory concepts in evolution, genetics, and ecology. This collection of 25 essays by leading researchers provides an overview of the state of the field. These essays are wholly new; none of them could have been written even ten years ago. They demonstrate how philosophical analysis has been able to contribute to sometimes contested areas of scientific theory making.
-Written by internationally acknowledged leaders in the field
- Entries make original contributions as well as summarizing state of the art discoveries in the field
- Easy to read and understand

Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature. The issue of preservation of properties is addressed.

This is an overview of the current state of knowledge along with open problems and perspectives, clarified in such fields as non-standard inferences in description logics, logic of provability, logical dynamics and computability theory. The book includes contributions concerning the role of logic today, including unexpected aspects of contemporary logic and the application of logic. This book will be of interest to logicians and mathematicians in general.