The present collection represents an attempt to bring together several contributions to the ongoing debate pertaining to supervenience of the normative in law and morals and strives to be the first work that addresses the topic comprehensively. It addresses the controversies surrounding the idea of normative supervenience and the philosophical conceptions they generated, deserve a recapitulation, as well as a new impulse for further development. Recently, there has been renewed interest in the concepts of normativity and supervenience. The research on normativity - a term introduced to the philosophical jargon by Edmund Husserl almost one hundred years ago - gained impetus in the 1990s through the works of such philosophers as Robert Audi, Christine Korsgaard, Robert Brandom, Paul Boghossian or Joseph Raz. The problem of the nature and sources of normativity has been investigated not only in morals and in relation to language, but also in other domains, e.g. in law or in the c ontext of the theories of rationality. Supervenience, understood as a special kind of relation between properties and weaker than entailment, has become analytic philosophers' favorite formal tool since 1980s. It features in the theories pertaining to mental properties, but also in aesthetics or the law. In recent years, the 'marriage' of normativity and supervenience has become an object of many philosophical theories as well as heated debates. It seems that the conceptual apparatus of the supervenience theory makes it possible to state precisely some claims pertaining to normativity, as well as illuminate the problems surrounding it.

We do not perceive the present as it is and in totality, nor do we infer the future from the present with any high degree of dependability, nor yet do we accurately know the consequences of our own actions. In addition, there is a fourth source of error to be taken into account, for we do not execute actions in the precise form in which they are imaged and willed. Frank H. Knight [R4.34, p. 202] The "degree" of certainty of confidence felt in the conclusion after it is reached cannot be ignored, for it is of the greatest practical signi- cance. The action which follows upon an opinion depends as much upon the amount of confidence in that opinion as it does upon fav- ableness of the opinion itself. The ultimate logic, or psychology, of these deliberations is obscure, a part of the scientifically unfathomable mystery of life and mind. Frank H. Knight [R4.34, p. 226-227] With some inaccuracy, description of uncertain consequences can be classified into two categories, those which use exclusively the language of probability distributions and those which call for some other principle, either to replace or supplement.

Arguing that our attachment to Aristotelian modes of discourse makes a revision of their conceptual foundations long overdue, the author proposes the consideration of unacknowledged factors that play a central role in argument itself. These are in particular the subjective imprint and the dynamics of argumentation. Their inclusion in a four-dimensional framework (subjective-objective, structural-procedural) and the focus on thesis validity allow for a more realistic view of our discourse practice. Exhaustive analyses of fascinating historical and contemporary arguments are provided. These range from Columbus s advocacy of the Western Passage to India, over the trial of King Louis XVI during the French Revolution, to today s highly charged controversies surrounding euthanasia and embryo research.

Excavating foundational issues such as the purpose of argument itself (assent of an audience or critical examination of validity claims) and the contested role of argument as a generator of knowledge, the book culminates in a discussion of the relationship between rationality and reasonableness and criticizes the restrictions of rational argument relying on fixed logical, economic or cultural criteria that in reality are mutable. Here, a true, open argument requires the infusion of Paul Lorenzen s principle of transsubjectivity, which recognizes but transcends the partiality of the individual and which can be seen in the pragmatic and expanding consensus that humanity can control itself to safeguard the future of a fragile, damaged world."

The rise of scientific (analytic) philosophy since the turn of the twentieth century is linked to the philosophical interaction between, on the one hand, Ernst Mach, the Vienna Circle around Moritz Schlick and Otto Neurath, the Berlin Group (Hans Reichenbach, Carl G. Hempel), and the Prague Group (Rudolf Carnap, Philipp Frank), and, on the other, philosophers and scientists in Denmark (Niels Bohr, Joergen Joergensen), Finland (Eino Kaila, Georg Henrik von Wright and their disciples), Norway (Arne Naess and his students), and Sweden (Ake Petzall, the journal Theoria and a younger generation of philosophers in Uppsala). In addition, the pure theory of law of Hans Kelsen achieved wide dissemination in the Nordic countries (through, for example, Alf Ross). One of the key events in the relations between the Central European philosophers and those of the Nordic countries was the Second International Congress for the Unity of Science which was arranged in Copenhagen in 1936.

Besides considering the interactions of these groups, the book also pays special attention to their interactions, in the context of the Cold War period following the Second World War, with the so-called Third Vienna Circle and with the Forum Alpbach/Austrian College around Viktor Kraft and Bela Juhos (along with Ludwig Wittgenstein and Paul Feyerabend), where the issues of (philosophical and scientific) realism and "psychologism"-the relationship between psychology and philosophy-were matters of controversy.

By comparison with the more extensively investigated and better known transatlantic transfer and transformation of "positivism" and logical empiricism, the developments outlined above remain

neglected and marginalized topics in historiography. The symposium aims to reveal the remarkable continuity of the philosophical enlightened "Nordic Connection." We intend to shed light on this forgotten communication and to reconstruct these hidden scholarly networks from an historical and logical point of view, thereby evaluating their significance for today's research."

Foundational questions in logic, mathematics, computer science and physics are constant sources of epistemological debate in contemporary philosophy. To what extent is the transfinite part of mathematics completely trustworthy? Why is there a general 'malaise' concerning the logical approach to the foundations of mathematics? What is the role of symmetry in physics? Is it possible to build a coherent worldview compatible with a macroobjectivistic position and based on the quantum picture of the world? What account can be given of opinion change in the light of new evidence? These are some of the questions discussed in this volume, which collects 14 lectures on the foundation of science given at the School of Philosophy of Science, Trieste, October 1989. The volume will be of particular interest to any student or scholar engaged in interdisciplinary research into the foundations of science in the context of contemporary debates.

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. "

Church's Thesis (CT) was first published by Alonzo Church in 1935. CT is a proposition that identifies two notions: an intuitive notion of a effectively computable function defined in natural numbers with the notion of a recursive function. Despite of the many efforts of prominent scientists, Church's Thesis has never been falsified. There exists a vast literature concerning the thesis. The aim of the book is to provide one volume summary of the state of research on Church's Thesis. These include the following: different formulations of CT, CT and intuitionism, CT and intensional mathematics, CT and physics, the epistemic status of CT, CT and philosophy of mind, provability of CT and CT and functional programming.

This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area.

Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations to weak Heyting algebras and implicative semilattices. The book also dives into the Blok-Esakia theorem and provides an outline of the intuitionistic modal logic KM which is closely related to the Godel-Lob provability logic GL. One chapter scrutinizes Esakia s work interpreting modal diamond as the derivative of a topological space within the setting of point-free topology. The final chapter in the volume is dedicated to the derivational semantics of modal logic and other related issues."

How can we advance knowledge? Which methods do we need in order to make new discoveries? How can we rationally evaluate, reconstruct and offer discoveries as a means of improving the 'method' of discovery itself? And how can we use findings about scientific discovery to boost funding policies, thus fostering a deeper impact of scientific discovery itself? The respective chapters in this book provide readers with answers to these questions. They focus on a set of issues that are essential to the development of types of reasoning for advancing knowledge, such as models for both revolutionary findings and paradigm shifts; ways of rationally addressing scientific disagreement, e.g. when a revolutionary discovery sparks considerable disagreement inside the scientific community; frameworks for both discovery and inference methods; and heuristics for economics and the social sciences.

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.

Over the past few years, the tree model of time has been widely employed to deal with issues concerning the semantics of tensed discourse. The thought that has motivated its adoption is that the most plausible way to make sense of indeterminism is to conceive of future possibilities as branches that depart from a common trunk, constituted by the past and the present. However, the thought still needs to be further articulated and defended, and several important questions remain open, such as the question of how actuality can be understood and formally represented in a branching framework. The present volume is intended to be a 360 degree reflection on the tree model. The contributions is gathers concern the model and its alternatives, both from a semantic and from a metaphysical point of view. "

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.

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.

This book reconstructs the theory of signification implicit in Aristotle's De Interpretatione and its psychological background in his writing De Anima, a project often envisioned by scholars but never systematically undertaken. I begin by explaining what sort of phonetic material, according to Aristotle, can be a significans and a phone. To that end, I provide a physiological account of which animal sounds count as phone, as well as a psychological evaluation of the cognitive content of the phonai under consideration in De Interpretatione: names, verbs, and assertive sentences. I then turn to noemata, which, for Aristotle, are the psychological reference and significata of names, verbs and assertive sentences. I explain what, for Aristotle, are the logical properties a significatum must have in order to be signified by the phonetic material of a name, verb or assertive sentence, and why noemata can fulfil those logical conditions. Finally, I elucidate the significans-significatum relation without making use of the modern semantic triangle. This approach is consonant with Aristotle's methodology and breaks new ground by exploring the connection between the linguistic and psychological aspects of Aristotle's theory of signification.

This volume presents different conceptions of logic and mathematics and discuss their philosophical foundations and consequences. This concerns first of all topics of Wittgenstein's ideas on logic and mathematics; questions about the structural complexity of propositions; the more recent debate about Neo-Logicism and Neo-Fregeanism; the comparison and translatability of different logics; the foundations of mathematics: intuitionism, mathematical realism, and formalism. The contributing authors are Matthias Baaz, Francesco Berto, Jean-Yves Beziau, Elena Dragalina-Chernya, Gunther Eder, Susan Edwards-McKie, Oliver Feldmann, Juliet Floyd, Norbert Gratzl, Richard Heinrich, Janusz Kaczmarek, Wolfgang Kienzler, Timm Lampert, Itala Maria Loffredo D'Ottaviano, Paolo Mancosu, Matthieu Marion, Felix Muhlhoelzer, Charles Parsons, Edi Pavlovic, Christoph Pfisterer, Michael Potter, Richard Raatzsch, Esther Ramharter, Stefan Riegelnik, Gabriel Sandu, Georg Schiemer, Gerhard Schurz, Dana Scott, Stewart Shapiro, Karl Sigmund, William W. Tait, Mark van Atten, Maria van der Schaar, Vladimir Vasyukov, Jan von Plato, Jan Wolenski and Richard Zach.

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.

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.

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.

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."

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.

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.

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 bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students.