Of the four chapters in this book, the first two discuss (albeit in consider ably modified form) matters previously discussed in my papers 'On the Logic of Conditionals' [1] and 'Probability and the Logic of Conditionals' [2], while the last two present essentially new material. Chapter I is relatively informal and roughly parallels the first of the above papers in discussing the basic ideas of a probabilistic approach to the logic of the indicative conditional, according to which these constructions do not have truth values, but they do have probabilities (equal to conditional probabilities), and the appropriate criterion of soundness for inferences involving them is that it should not be possible for all premises of the inference to be probable while the conclusion is improbable. Applying this criterion is shown to have radically different consequences from the orthodox 'material conditional' theory, not only in application to the standard 'fallacies' of the material conditional, but to many forms (e. g. , Contraposition) which have hitherto been regarded as above suspi cion. Many more applications are considered in Chapter I, as well as certain related theoretical matters. The chief of these, which is the most important new topic treated in Chapter I (i. e.

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 commu 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 organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.

Papers from more than three decades reflect the development of thinkingover the dialogical framework that shapes verbal expression of comprehending experience and that has to be exhibited in responsible argumentations. With dialogical reconstructions of experience owing to the methodical constructivism of the a oeErlangen Schoola it is possible to uncover the origin of many conceptual oppositions in traditional philosophical talk, like natural vs. artificial/cultural, subjective vs. objective, etc., and to solve philosophical riddles connected with them.

This volume deals with formal, mechanizable reasoning in modal logics, that is, logics of necessity, possibility, belief, time computations etc. It is therefore of immense interest for various interrelated disciplines such as philosophy, AI, computer science, logic, cognitive science and linguistics. The book consists of 15 original research papers, divided into three parts. The first part contains papers which give a profound description of powerful proof-theoretic methods as applied to the normal modal logic S4. Part II is concerned with a number of generalizations of the standard proof-theoretic formats, while the third part presents new and important results on semantics-based proof systems for modal logic.

This book features mathematical and formal philosophers' efforts to understand philosophical questions using mathematical techniques. It offers a collection of works from leading researchers in the area, who discuss some of the most fascinating ways formal methods are now being applied. It covers topics such as: the uses of probable and statistical reasoning, rational choice theory, reasoning in the environmental sciences, reasoning about laws and changes of rules, and reasoning about collective decision procedures as well as about action. Utilizing mathematical techniques has been very fruitful in the traditional domains of formal philosophy - logic, philosophy of mathematics and metaphysics - while formal philosophy is simultaneously branching out into other areas in philosophy and the social sciences. These areas particularly include ethics, political science, and the methodology of the natural and social sciences. Reasoning about legal rules, collective decision-making procedures, and rational choices are of interest to all those engaged in legal theory, political science and economics. Statistical reasoning is also of interest to political scientists and economists.

The present volume of the "Handbook of the History of Logic" is designed to establish 19th century Britain as a substantial force in logic, developing new ideas, some of which would be overtaken by, and other that would anticipate, the century's later capitulation to the mathematization of logic.
"British Logic in the Nineteenth Century" is indispensable reading and a definitive research resource for anyone with an interest in the history of logic.
- Detailed and comprehensive chapters covering the entire range of modal logic
- Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic

In 1911, Bertrand Russell began a historically formative interchange about the nature of logic and cognition with his student, Ludwig Wittgenstein. In 1913, Russell set to work on a manuscript, the "Theory of Knowledge", designed to move from the analysis of perception to judgement and on to knowledge of the world. After Wittgenstein interrupted Russell's daily writing with a series of objections to his doctrine of judgement and conception of logic, Russell abandoned his project in despair, leaving it unfinished. His subsequent work can be understood largely as an attempt to assimilate and respond to Wittgenstein's challenge in 1913. "Russell and Wittgenstein on the Nature of Judgement" is the first book-length treatment of Russell's decisive 1913 exchanges with Wittgenstein. Rosalind Carey incorporates little-known notes and diagrams into a new analysis of the problems Russell was facing. She also evaluates the numerous interpretations of Russell's positions and Wittgenstein's objections to them. The result is a new perspective on both these great thinkers, at a crucial point in the development of twentieth-century philosophy.

Free logic - i.e., logic free of existential presuppositions in general and with respect to singular terms in particular- began to come into its own as a field of research in the 1950s. As is the case with so many developments in Western philosophy, its roots can be traced back to ancient Greek philo sophy. It is only during the last fifty years, however, that it has become well established as a branch of modern logic. The name of Karel Lambert is most closely connected with this development: he gave it its name and its profile as a well defined field of research. After a development of fifty years, it is time to look back and take stock while at the same time scanning for new perspectives. This is the purpose of the papers collected in this volume. The first paper is written by Karel Lambert himself who also comments on all the papers of the other authors. In an introductory essay we give a survey of the present status of and new directions in free logic."

This book attempts to explicate and expand upon Frank Ramsey's notion of the realistic spirit. In so doing, it provides a systematic reading of his work, and demonstrates the extent of Ramsey's genius as evinced by both his responses to the Tractatus Logico-Philosophicus, and the impact he had on Wittgenstein's later philosophical insights.

ways of doing it, but it is wrong to project it far into the past: it did not exist at the turn of the century and only became clearly apparent after the Second World War. I recently taught at an American university on the his tory of philosophy from Balzano to Husserl. The course title had to come from a fixed pool and gave trouble. Was it philosophical logic, the nine teenth century, or phenomenology? A logic title would connote over this period Frege, Russell, Carnap, perhaps a mention of Boole: not continental enough. The nineteenth century? The century of Kant's successors: Fichte, Hegel, Schopenhauer, Feuer bach, Marx, Nietzsche? What have they to do with Balzano, Lotze, Brentano, Meinong, Husserl and Twardowski? Even tually 'Phenomenology' was chosen, misdescribing more than half of the course. That illustrates the problems one faces in trying to work against the picture of the period which is ingrained in minds and syllabuses. This book arises from my efforts to combat that picture. I backed into writing about the history of recent philosophy rather than setting out to do so. The beginning was chance. In Manchester in the early seventies, at a time when most English philosophy departments breathed re cycled Oxford air, the intellectual atmosphere derived from Cambridge and Warsaw, spiced with a breath of Freiburg and Paris."

Ludwig Wittgenstein's brief Tractatus Logico-Philosophicus (1922) is one of the most important philosophical works of the twentieth century, yet it offers little orientation for the reader. The first-time reader is left wondering what it could be about, and the scholar is left with little guidance for interpretation. In Tractatus in Context, James C. Klagge presents the vital background necessary for appreciating Wittgenstein's gnomic masterpiece. Tractatus in Context contains the early reactions to the Tractatus, including the initial reviews written in 1922-1924. And while we can't talk with Wittgenstein, we can do the next best thing-hear what he had to say about the Tractatus. Klagge thus presents what Wittgenstein thought about germane issues leading up to his writing the book, in discussions and correspondence with others about his ideas, and what he had to say about the Tractatus after it was written-in letters, lectures and conversations. It offers, you might say, Wittgenstein's own commentary on the book. Key Features: Illuminates what is at stake in the Tractatus, by providing the views of others that engaged Wittgenstein as he was writing it. Includes Wittgenstein's earlier thoughts on ideas in the book as recorded in his notebooks, letters, and conversations as well as his later, retrospective comments on those ideas. Draws on new or little-known sources, such as Wittgenstein's coded notebooks, Hermine's notes, Frege's letters, Hansel's diary, Ramsey's notes, and Skinner's dictations. Draws connections between the background context and specific passages in the Tractatus, using a proposition-by-proposition commentary.

Hilbert's Programs & Beyond presents the foundational work of David Hilbert in a sequence of thematically organized essays. They first trace the roots of Hilbert's work to the radical transformation of mathematics in the 19th century and bring out his pivotal role in creating mathematical logic and proof theory. They then analyze techniques and results of "classical" proof theory as well as their dramatic expansion in modern proof theory. This intellectual experience finally opens horizons for reflection on the nature of mathematics in the 21st century: Sieg articulates his position of reductive structuralism and explores mathematical capacities via computational models.

Wittgenstein's Tractatus Logico-Philosophicus, first published in 1921, has had a profound influence on modern philosophic thought. Prototractatus is a facsimile reproduction of an early version of Tractatus, only discovered in 1965. The original text has a parallel English translation and the text is edited to indicate all relevant deviations from the final version.

It is the aim of the present study to introduce the reader to the ways of thinking of those contemporary philosophers who apply the tools of symbolic logic to classical philosophical problems. Unlike the "conti nental" reader for whom this work was originally written, the English speaking reader will be more familiar with most of the philosophers dis cussed in this book, and he will in general not be tempted to dismiss them indiscriminately as "positivists" and "nominalists." But the English version of this study may help to redress the balance in another respect. In view of the present emphasis on ordinary language and the wide spread tendency to leave the mathematical logicians alone with their technicalities, it seems not without merit to revive the interest in formal ontology and the construction of formal systems. A closer look at the historical account which will be given here, may convince the reader that there are several points in the historical develop ment whose consequences have not yet been fully assessed: I mention, e. g., the shift from the traditional three-level semantics of sense and deno tation to the contemporary two-level semantics of representation; the relation of extensional structure and intensional content in the extensional systems of Wittgenstein and Carnap; the confusing changes in labelling the different kinds of analytic and apriori true sentences; etc. Among the philosophically interesting tools of symbolic logic Lesniewski's calculus of names deserves special attention."

Axiomatic Formal Ontology is a fairly comprehensive systematic treatise on general metaphysics. The axiomatic method is applied throughout the book. Its main theme is the construction of a general non-set-theoretical theory of intensional entities. Other important matters discussed are the metaphysics of modality, the nature of actual existence, mereology and the taxonomy of entities.

This monograph is a detailed study, and systematic defence, of the Growing Block Theory of time (GBT), first conceived by C.D. Broad. The book offers a coherent, logically perspicuous and ideologically lean formulation of GBT, defends it against the most notorious objections to be found in the extant philosophical literature, and shows how it can be derived from a more general theory, consistent with relativistic spacetime, on the pre-relativistic assumption of an absolute and total temporal order. The authors devise axiomatizations of GBT and its competitors which, against the backdrop of a shared quantified tense logic, significantly improves the prospects of their comparative assessment. Importantly, neither of these axiomatizations involves commitment to properties of presentness, pastness or futurity. The authors proceed to address, and defuse, a number of objections that have been marshaled against GBT, including the so-called epistemic objection according to which the theory invites skepticism about our temporal location. The challenge posed by relativistic physics is met head-on, by replacing claims about temporal variation by claims about variation across spacetime. The book aims to achieve the greatest possible rigor. The background logic is set out in detail, as are the principles governing the notions of precedence and temporal location. The authors likewise devise a novel spacetime logic suited for the articulation, and comparative assessment, of relativistic theories of time. The book comes with three technical appendices which include soundness and completeness proofs for the systems corresponding to GBT and its competitors, in both their pre-relativistic and relativistic forms. The book is primarily directed at researchers and graduate students working on the philosophy of time or temporal logic, but is of interest to metaphysicians and philosophical logicians more generally.

This wide-ranging book introduces information as a key concept not only in physics, from quantum mechanics to thermodynamics, but also in the neighboring sciences and in the humanities. The central part analyzes dynamical processes as manifestations of information flows between microscopic and macroscopic scales and between systems and their environment. Quantum mechanics is interpreted as a reconstruction of mechanics based on fundamental limitations of information processing on the smallest scales. These become particularly manifest in quantum chaos and in quantum computing. Covering subjects such as causality, prediction, undecidability, chaos, and quantum randomness, the book also provides an information-theoretical view of predictability. More than 180 illustrations visualize the concepts and arguments. The book takes inspiration from the author's graduate-level topical lecture but is also well suited for undergraduate studies and is a valuable resource for researchers and professionals.

When asked in 1962 on what he was working Kazimierz Ajdukiewicz replied: Several years ago Polish Scientific Publishers suggested that I pre pare a new edition of The Logical Foundations of Teaching, which I wrote 1 before 1939 as a contribution to The Encyclopaedia of Education. It was a small booklet covering elementary information about logical semantics and scientific methodology, information which in my opinion was necessary as a foundation of teaching and as an element of the education of any teacher. When I recently set to preparing the new edition, I rewrote practically everything, and a booklet of some 100 pages swelled into a bulky volume almost five times bigger. The issues have remained practically the same, but they are now analysed much more thoroughly and the threshold of difficulty is much higher now. The main stress has been laid on the methods used in the empirical sciences, and within that field, on the theory of measurement and the methods of statistical inference. I am now working on the last chapter of the book, concerned with explanation procedures and theory construction in the empirical sciences. When that book, which I intend to entitle Pragmatic Logic, is com pleted I intend to prepare for the press Vol. 2 of my minor writings, 2 Language and Cognition, which will cover some of my post-war pa pers."

1. STRUCTURE AND REFERENCES 1.1. The main part of the dictionary consists of alphabetically arranged articles concerned with basic logical theories and some other selected topics. Within each article a set of concepts is defined in their mutual relations. This way of defining concepts in the context of a theory provides better understand ing of ideas than that provided by isolated short defmitions. A disadvantage of this method is that it takes more time to look something up inside an extensive article. To reduce this disadvantage the following measures have been adopted. Each article is divided into numbered sections, the numbers, in boldface type, being addresses to which we refer. Those sections of larger articles which are divided at the first level, i.e. numbered with single numerals, have titles. Main sections are further subdivided, the subsections being numbered by numerals added to the main section number, e.g. I, 1.1, 1.2, ..., 1.1.1, 1.1.2, and so on. A comprehensive subject index is supplied together with a glossary. The aim of the latter is to provide, if possible, short defmitions which sometimes may prove sufficient. As to the use of the glossary, see the comment preceding it."

The importance of Stoicism for Gilles Deleuze's Logic of Sense and Michel Foucault's Hermeneutics of the Subject and The Care of the Self is well known. However, few students of either classics or philosophy are aware of the breadth of French and Italian receptions of Stoicism. This book firstly presents this broad field to readers, and secondly advances it by renewing dialogues with ancient Stoic texts. The authors in this volume, who combine expertise in continental and Hellenistic philosophy, challenge our understanding of both modern and ancient concepts, arguments, exercises, and therapies. It conceives of Stoicism as a vital strand of philosophy which contributes to the life of contemporary thought. Flowing through the sustained, varied engagement with Stoicism by continental thinkers, this volume covers Jean-Paul Sartre, Gilles Deleuze, Michel Foucault, Julia Kristeva, Alain Badiou, Emile Brehier, Barbara Cassin, Giorgio Agamben, and Pierre Hadot. Stoic sources addressed range from doxography and well-known authors like Epictetus and Seneca to more obscure authorites like Musonius Rufus and Cornutus.

CENGAGE ADVANTAGE BOOKS: UNDERSTANDING ARGUMENTS, CONCISE EDITION, 1E uses everyday life experiences to teach the basics of informal logic. By taking out the non-essential instruction, this edition hones in on the "argument construction" involved in day-to-day life, and how to do it better. Plus, to round out the discussion, CENGAGE ADVANTAGE BOOKS: UNDERSTANDING ARGUMENTS, CONCISE EDITION, 1E includes a three-chapter overview of formal logic as well.

This book is the first to provide a critical history of analytic philosophy from its inception in the late nineteenth century to the present day. Quentin Smith focuses on the connections between the four leading movements in analytic philosophy -- logical realism, logical positivism, ordinary language analysis, and linguistic essentialism -- and corresponding twentieth-century theories of ethics and of religion. Through a critical evaluation of each school's theoretical positions, Smith counters the widespread view of analytic philosophy as indifferent to important questions about fight and wrong and human meaning. He argues that analytic philosophy throughout its history has revolved around the central issues of existence, and he offers a new ethics and philosophy of religion.

The author develops a positive ethical theory based on a method of ethics first formulated by Robert Adams. Smith's theory belongs to the tradition of perfectionism or self-realization ethics and builds on Thomas Hurka's recent theory of perfectionism. In his consideration of philosophy of religion, Smith concludes that there is a sound "logical argument from evil" that takes into account Alvin Plantinga's free-will defense and undermines monotheism, paving the way to a naturalistic pantheism.

"Smith's book is original not only in intent but frequently in the detailed argument involved in evaluating the merits of the philosophies of language and their implications for ethics and philosophy of religion". -- John F. Post, Vanderbilt University