This book, provides a critical approach to all major logical paradoxes: from ancient to contemporary ones. There are four key aims of the book: 1. Providing systematic and historical survey of different approaches - solutions of the most prominent paradoxes discussed in the logical and philosophical literature. 2. Introducing original solutions of major paradoxes like: Liar paradox, Protagoras paradox, an unexpected examination paradox, stone paradox, crocodile, Newcomb paradox. 3. Explaining the far-reaching significance of paradoxes of vagueness and change for philosophy and ontology. 4. Proposing a novel, well justified and, as it seems, natural classification of paradoxes. "

This volume is a collation of original contributions from the key actors of a new trend in the contemporary theory of knowledge and belief, that we call "dynamic epistemology." It brings the works of these researchers under a single umbrella by highlighting the coherence of their current themes, and by establishing connections between topics that, up until now, have been investigated independently. It also illustrates how the new analytical toolbox unveils questions about the theory of knowledge, belief, preference, action, and rationality, in a number of central axes in dynamic epistemology: temporal, social, probabilistic and even deontic dynamics.

Aristotle's Prior Analytics marks the beginning of formal logic. For Aristotle himself, this meant the discovery of a general theory of valid deductive argument, a project that he had described as either impossible or impracticable, probably not very long before he actually came up with syllogistic reasoning. A syllogism is the inferring of one proposition from two others of a particular form, and it is the subject of the Prior Analytics. The first book, to which this volume is devoted, offers a fairly coherent presentation of Aristotle's logic as a general theory of deductive argument.

In this volume, the author investigates and argues for, a particular answer to the question: What is the right way to logically analyze modalities from natural language within formal languages? The answer is: by formalizing modal expressions in terms of predicates. But, as in the case of truth, the most intuitive modal principles lead to paradox once the modal notions are conceived as predicates. The book discusses the philosophical interpretation of these modal paradoxes and argues that any satisfactory approach to modality will have to face the paradoxes independently of the grammatical category of the modal notion. By systematizing modal principles with respect to their joint consistency and inconsistency, Stern provides an overview of the options and limitations of the predicate approach to modality that may serve as a useful starting point for future work on predicate approaches to modality. Stern also develops a general strategy for constructing philosophically attractive theories of modal notions conceived as predicates. The idea is to characterize the modal predicate by appeal to its interaction with the truth predicate. This strategy is put to use by developing the modal theories Modal Friedman-Sheard and Modal Kripke-Feferman.

This book offers a detailed study of the truth-bearers problem, that is, the question of which category of items the predicates a ~truea (TM) and a ~falsea (TM) are predicated. The book has two dimensions: historical and systematic. Both focus around Tarskia (TM)s semantic theory of truth. The author locates Tarskia (TM)s ideas in a broad context of Austrian philosophy, in particular, Brentanoa (TM)s tradition. However, Bolzano and phenomenology (Husserl and Reinach) are also taken into account. The historical perspective is completed by showing how Tarski was rooted in Polish philosophical tradition originated with Twardowski and his version of Brentanism. The historical considerations are the basis for showing how the idea of truth-bearers as acts of judging was transformed into the theory of truth-bearers as sentences. In particular, the author analyses the way to nominalism in Polish philosophy, culminating in Lesniewski, Kotarbinski and Tarski. This book is indispensable for everybody interested in the evolution of Austrian philosophy from descriptive psychology to semantics. It is also a fundamental contribution toward a deeper understanding of the philosophical background of Tarskia (TM)s theory of truth.

Luciano Floridi presents a book that will set the agenda for the philosophy of information. PI is the philosophical field concerned with (1) the critical investigation of the conceptual nature and basic principles of information, including its dynamics, utilisation, and sciences, and (2) the elaboration and application of information-theoretic and computational methodologies to philosophical problems. This book lays down, for the first time, the conceptual foundations for this new area of research. It does so systematically, by pursuing three goals. Its metatheoretical goal is to describe what the philosophy of information is, its problems, approaches, and methods. Its introductory goal is to help the reader to gain a better grasp of the complex and multifarious nature of the various concepts and phenomena related to information. Its analytic goal is to answer several key theoretical questions of great philosophical interest, arising from the investigation of semantic information.

The volume analyses and develops David Makinson s efforts to make classical logic useful outside its most obvious application areas. The book contains chapters that analyse, appraise, or reshape Makinson s work and chapters that develop themes emerging from his contributions. These are grouped into major areas to which Makinsons has made highly influential contributions and the volume in its entirety is divided into four sections, each devoted to a particular area of logic: belief change, uncertain reasoning, normative systems and the resources of classical logic.

Among the contributions included in the volume, one chapter focuses on the inferential preferential method, i.e. the combined use of classical logic and mechanisms of preference and choice and provides examples from Makinson s work in non-monotonic and defeasible reasoning and belief revision. One chapter offers a short autobiography by Makinson which details his discovery of modern logic, his travels across continents and reveals his intellectual encounters and inspirations. The chapter also contains an unusually explicit statement on his views on the (limited but important) role of logic in philosophy."

such questions for centuries (unrestricted by the capabilities of any ha- ware). Theprinciplesgoverningtheinteractionofseveralprocesses, forexample, are abstract an similar to principles governing the cooperation of two large organisation. A detailed rule based e?ective but rigid bureaucracy is very much similar to a complex computer program handling and manipulating data. My guess is that the principles underlying one are very much the same as those underlying the other. Ibelievethedayisnotfarawayinthefuturewhenthecomputerscientist will wake up one morning with the realisation that he is actually a kind of formal philosopher! The projected number of volumes for this Handbook is about 18. The subjecthasevolvedanditsareashavebecomeinterrelatedtosuchanextent that it no longer makes sense to dedicate volumes to topics. However, the volumes do follow some natural groupings of chapters. I would like to thank our authors and readers for their contributions and their commitment in making this Handbook a success. Thanksalso to our publication administrator Mrs J. Spurr for her usual dedication and excellence and to Kluwer Academic Publishers (now Springer) for their continuing support for the Handbook. Dov Gabbay King's College London x PREFACE TO THE SECOND EDITION Logic IT Natural Program Arti?cialin- Logic p- language control spec- telligence gramming processing i?cation, veri?cation, concurrency Temporal Expressive Expressive Planning. Extension of logic power of tense power for re- Time depen- Horn clause operators. currentevents. dent data. with time Temporal Speci?cation Eventcalculus. capability. indices. Sepa- of tempo- Persistence Eventcalculus. ration of past ral control. through time- Temporal logic from future Decision prob- the Frame programming.

In three comprehensive volumes, Logic of the Future presents a full panorama of Charles S. Peirce's most important late writings. Among the most influential American thinkers, Peirce took his existential graphs to be a significant contribution to human thought. The manuscripts from 1895-1913, with many of them being published here for the first time, testify to the richness and open-endedness of his theory of logic and its applications. They also invite us to reconsider our ordinary conceptions of reasoning as well as the conventional stories concerning the evolution of modern logic. This first volume of Logic of the Future is on the historical development, theory and application of Peirce's graphical method and diagrammatic reasoning. It also illustrates the abundant further developments and applications Peirce envisaged existential graphs to have on the analysis of mathematics, language, meaning and mind.

Hegelian philosophy is now enjoying an enormous renaissance in the English-speaking world. At the very centre of his work is the monumental "Science of Logic." Hegel's theory of subjectivity, which comprises the final third of the "Science of Logic," has been comparatively neglected. This volume collects 15 essays on various aspects of Hegel's theory of subjectivity. For Hegel, "substance is subject." Anyone aspiring to understand Hegel's philosophy cannot afford to neglect this central topic.

The book is about Gentzen calculi for (the main systems of) modal logic. It is divided into three parts. In the first partwe introduce and discuss the main philosophical ideas related to proof theory, and we try to identify criteria for distinguishing good sequent calculi. In the second part we present the several attempts made from the 50's until today to provide modal logic with Gentzen calculi. In the third and and final part we analyse new calculi for modal logics, called tree-hypersequent calculi, which were recently introduced by the author. We show in a precise and clear way the main results that can be proved with and about them.

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.

Is it possible to quantify over absolutely all there is? Or must all of our quantifiers range over a less-than-all-inclusive domain? It has commonly been thought that the question of absolute generality is intimately connected with the set-theoretic antinomies. But the topic of absolute generality has enjoyed a surge of interest in recent years. It has become increasingly apparent that its ramifications extend well beyond the foundations of set theory. Connections include semantic indeterminacy, logical consequence, higher-order languages, and metaphysics. Rayo and Uzquiano present for the first time a collection of essays on absolute generality. These newly commissioned articles - written by an impressive array of international scholars - draw the reader into the forefront of contemporary research on the subject. The volume represents a variety of approaches to the problem, with some of the contributions arguing for the possibility of all-inclusive quantification and some of them arguing against it. An introduction by the editors draws a helpful map of the philosophical terrain.

This book describes argumentative tools and strategies that can be used to guide policy decisions under conditions of great uncertainty. Contributing authors explore methods from philosophical analysis and in particular argumentation analysis, showing how it can be used to systematize discussions about policy issues involving great uncertainty. The first part of the work explores how to deal in a systematic way with decision-making when there may be plural perspectives on the decision problem, along with unknown consequences of what we do. Readers will see how argumentation tools can be used for prioritizing among uncertain dangers, for determining how decisions should be framed, for choosing a suitable time frame for a decision, and for systematically choosing among different decision options. Case studies are presented in the second part of the book, showing argumentation in practice in the areas of climate geoengineering, water governance, synthetic biology, nuclear waste, and financial markets. In one example, argumentation analysis is applied to proposals to solve the climate problem with various technological manipulations of the natural climate system, such as massive dispersion of reflective aerosols into the stratosphere. Even after a thorough investigation of such a proposal, doubt remains as to whether all the potential risks have been identified. In such discussions, conventional risk analysis does not have much to contribute since it presupposes that the risks have been identified, whereas the argumentative approach to uncertainty management can be used to systematize discussions.

This text centers around three main subjects. The first is the concept of modularity and independence in classical logic and nonmonotonic and other nonclassical logic, and the consequences on syntactic and semantical interpolation and language change. In particular, we will show the connection between interpolation for nonmonotonic logic and manipulation of an abstract notion of size. Modularity is essentially the ability to put partial results achieved independently together for a global result. The second aspect of the book is the authors' uniform picture of conditionals, including many-valued logics and structures on the language elements themselves and on the truth value set. The third topic explained by the authors is neighbourhood semantics, their connection to independence, and their common points and differences for various logics, e.g., for defaults and deontic logic, for the limit version of preferential logics, and for general approximation. The book will be of value to researchers and graduate students in logic and theoretical computer science.

It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good! The first edition was the second handbook published for the logic com- nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organi- tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.

Since the pioneering work of Donald Davidson on action, many philosophers have taken critical stances on his causal account. This book criticizes Davidson's event-causal view of action, and offers instead an agent causal view both to describe what an action is and to set a framework for how actions are explained.

Chapter 1 Introduction introduction 3 Chapter 1 Introduction ; ; / 2 4 F F # D . < 4 " % %+ " % )+ " % '+ 4 G G % & % : 2 < 4 4 = . % > 2 " % (+ 4 chapter one 1.1 Argument Assistants 4 4 , 2 # 4 2 < H ! H 4 H F H H / ! H ! " # 4 H H H H F H introduction 5 H H 2 . H H G 2 4 2 2 1.2 Defeasible Argumentation in the Field of Law 4 4 3 " 8 2 2 , < 2 " # < , # 6 chapter one " + 4 # 4 6 1 G G 6 4 G " + , G < # # A # 0 # # 4 2 # # D G %@*$ # 4 "%@:*+ F , introduction 7 , 9 2 2 , 3 . G # , " + D F < H 4 H H 4 H 4 4 1.3 Theory Construction and the Application of Law to Cases 4 I H # " ", % %+ 8 chapter one " + 8 4 G , 2 D 2 < " + " + 4 # #< 2 introduction 9 2 4 # , 2 4 # 9 < # ! / 2 6 # I ", % )J % '+ 9 G # 9 2

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 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 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.