In "God, Mind and Logical Space" Istvan Aranyosi takes the reader on a journey for the mind by revisiting the fundamental questions and the everlasting debates in philosophy of religion, ontology, and the philosophy of mind. The first part deals with issues in ontology, and the author puts forward a radical view according to which all thinkable objects and states of affairs have an equal claim to existence in a way that renders existence a relative notion. In the second part another radical view is argued for, according to which some objects and states of affairs that do not exist in our world are nevertheless present in our surroundings by being real in their consequences. The final part argues that the only way to prove the existence of God is to accept a view called Logical Pantheism, according to which God is identical to Logical Space.

Anil Gupta asks one of the key questions in philosophy: what is the contribution of experience of knowledge? Gupta develops an account of experience that allows it to inform knowledge while respecting two constraints - the contribution of experience to knowledge must be both rational and substantial. He says that these constraints cannot be met if we make the assumption that experience only aquaints us with partial truth about the world. Instead he uses tools from philosophical logic, specifically the logic of interdependent concepts, to show that a natural account of experience is available using the interdependence of views and perceptual judgements. In essence he argues for a reformed empiricism that embraces experience as conditional.

I was very happy when in 1997 Fiachra Long came to spend part of his sabbatical leave at the Archives Maurice Blondel at Louvain-Ia-Neuve. This allowed him to bring together and complete his translation of three important articles from Maurice Blondel, known as the philosopher of Aix-en-Province. These three articles fonn a unity: they make explicit certain aspects of the method used in the great thesis of 1893, Action. This thesis, it is well known, aroused many polemic debates after its appearance. Thomist theologians accused Blondel of turning back towards Kantian idealism whereas the philosophers of the Revue de metaphysique et de morale accused him on the contrary of falling back on a pre-critical realism. The three articles translated here, each in its own way, attempt to pass beyond these two opposite charges. The Idealist Illusion (1898) underlines the fact that the content of consciousness should be unfurled as it appears, by withdrawing from any idealist or realist prejudice, before judging the consistency of its content as a whole. In this way Blondel supports the "phenomenological" method used in his thesis. The Elementary Principle of a Logic of the Moral Life (1903) is a very well-worked text which shows that "the logic of possession and privation" is broader than "the logic of amnnation and negation. " Using these words, Blondel develops certain striking laws of action such as that of the "parallelogram of contrary forces.

Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.

This book revisits the definition of polemical discourse and deals with its functions in the democratic sphere. It first examines theoretical questions concerning the management of disagreement in democracy and the nature of polemical discourse. Next, it analyses case studies involving such issues as the place of women in the public space, illustrated by the case of the burqa in France and public controversy in the media on the exclusion of women from the public space. The book then explores reason, passion and violence in polemical discourse by means of cases involving confrontations between secular and ultra-orthodox circles, controversies about the Mexican Wall and fierce discussions about stock-options, and bonuses in times of financial crisis. Although polemical exchanges in the public sphere exacerbate dissent instead of resolving conflicts, they are quite frequent in the media and on the Net. How can we explain such a paradox? Most studies in argumentation avoid the question: they mainly focus on the verbal procedures leading to agreement. This focus stems from the centrality conferred upon consensus in our democratic societies, where decisions should be the result of a process of deliberation. What is then the social function of a confrontational management of dissent that does not primarily seek to achieve agreement? Is it just a sign of decadence, failure and powerlessness, or does it play a constructive role? This book answers these questions.

This book, translated from the French, is an introduction to first-order model theory. The first six chapters are very basic: starting from scratch, they quickly reach the essential, namely, the back-and-forth method and compactness, which are illustrated with examples taken from algebra. The next chapter introduces logic via the study of the models of arithmetic, and the following is a combinatorial tool-box preparing for the chapters on saturated and prime models. The last ten chapters form a rather complete but nevertheless accessible exposition of stability theory, which is the core of the subject.

It must be acknowledged that the essays presented here do not constitute a systematic account of any sort but represent occasional forays. Some deal with matters that happened to evoke Rescher's interest, others grew out of a chance encounter with a text he deemed to be of particular value. Throughout, challenges of the work itself more than compensated the author's efforts. Logic has always been of crucially important concern to philosophers. Rescher's own involvement with the history of logic goes back to his work on Leibniz in the 1950's (represented by Chapter 8 of the present book). Thereafter, during the 1960's he devoted considerable effort to the contributions of the medieval logicians of the Arabic-using world (here represented in Chapters 2-6). Moreover, Rescher have from time to time returned to the area to look at some aspects of the more recent scene, as Chapters 8-9 illustrate. In some instances the present essays have been overtaken by subsequent events-events which in fact helped to promote. This is true in particular in chapter 6's work on Arabic work regarding temporal modalities, which was instrumental in evoking the important contributions of Tony Street of Cambridge University.

The collective focus of the essays here presented consists of the attempt to overcome the deadlock between metaphysical and non- (or anti-) metaphysical Hegel interpretations. There is no doubt that Hegel rejects traditional and influential forms of metaphysical thought. There is also no doubt that he grounds his philosophical system on a metaphysical theory of thought and reality. The question asked by the contributors in this volume is therefore: what kind of metaphysics does Hegel reject, and what kind does he embrace? Some of the papers address the issue in general and comprehensive terms, but from different, even opposite perspectives: Hegel's claim of a 'unity' of logic and metaphysics; his potentially deflationary understanding of metaphysics; his overt metaphysical commitments; his subject-less notion of logical thought; and his criticism of Kant's critique of metaphysics. Other contributors discuss the same topics in view of very specific subject-matter in Hegel's corpus, to wit: the philosophy of self-consciousness; practical philosophy; teleology and holism; a particular brand of naturalism; language's relation to thought; 'true' and 'spurious' infinity as pivotal in philosophic thinking; and Hegel's conception of human agency and action.

The aim of this thematically unified anthology is to track the history of epistemic logic, to consider some important applications of these logics of knowledge and belief in a variety of fields, and finally to discuss future directions of research with particular emphasis on 'active agenthood' and multi-modal systems. It is accessible to researchers and graduate students in philosophy, computer science, game theory, economics and related disciplines utilizing the means and methods of epistemic logic.

Alfred Tarski was one of the two giants of the twentieth-century development of logic, along with Kurt Goedel. The four volumes of this collection contain all of Tarski's published papers and abstracts, as well as a comprehensive bibliography. Here will be found many of the works, spanning the period 1921 through 1979, which are the bedrock of contemporary areas of logic, whether in mathematics or philosophy. These areas include the theory of truth in formalized languages, decision methods and undecidable theories, foundations of geometry, set theory, and model theory, algebraic logic, and universal algebra.

George Boole (1815-1864) is well known to mathematicians for his research and textbooks on the calculus, but his name has spread world-wide for his innovations in symbolic logic and the development and applications made since his day. The utility of "Boolean algebra" in computing has greatly increased curiosity in the nature and extent of his achievements. His work is most accessible in his two books on logic, "A mathematical analysis of logic" (1947) and "An investigation of the laws of thought" (1954). But at various times he wrote manuscript essays, especially after the publication of the second book; several were intended for a non-technical work, "The Philosophy of logic," which he was not able to complete. This volume contains an edited selection which not only relates them to Boole's publications and the historical context of his time, but also describes their strange history of family, followers and scholars have treid to confect an edition. The book will appeal to logicians, mathematicians and philosophers, and those interested in the histories of the corresponding subjects; and also students of the early Victorian Britain in which they were written.

This skit of Bertrand Russell's philosophy was originally published in 1918 by Russell's correspondent friend Jourdain. The introduction explains that the contents purport to be lost papers written by Mr. B*rtr*nd R*ss*ll, a contemporary of Bertrand Russell. This politically humorous volume from the early 20th Century parodies the writing style of Russell as well as his theories.

What do philosophy and computer science have in common? It turns out, quite a lot! In providing an introduction to computer science (using Python), Daniel Lim presents in this book key philosophical issues, ranging from external world skepticism to the existence of God to the problem of induction. These issues, and others, are introduced through the use of critical computational concepts, ranging from image manipulation to recursive programming to elementary machine learning techniques. In illuminating some of the overlapping conceptual spaces of computer science and philosophy, Lim teaches the reader fundamental programming skills and also allows her to develop the critical thinking skills essential for examining some of the enduring questions of philosophy. Key Features Teaches readers actual computer programming, not merely ideas about computers Includes fun programming projects (like digital image manipulation and Game of Life simulation), allowing the reader to develop the ability to write larger computer programs that require decomposition, abstraction, and algorithmic thinking Uses computational concepts to introduce, clarify, and develop a variety of philosophical issues Covers various aspects of machine learning and relates them to philosophical issues involving science and induction as well as to ethical issues Provides a framework to critically analyze arguments in classic and contemporary philosophical debates

The Dialectical Forge identifies dialectical disputation (jadal) as a primary formative dynamic in the evolution of pre-modern Islamic legal systems, promoting dialectic from relative obscurity to a more appropriate position at the forefront of Islamic legal studies. The author introduces and develops a dialectics-based analytical method for the study of pre-modern Islamic legal argumentation, examines parallels and divergences between Aristotelian dialectic and early juridical jadal-theory, and proposes a multi-component paradigm-the Dialectical Forge Model-to account for the power of jadal in shaping Islamic law and legal theory.In addition to overviews of current evolutionary narratives for Islamic legal theory and dialectic, and expositions on key texts, this work shines an analytical light upon the considerably sophisticated "proto-system" of juridical dialectical teaching and practice evident in Islam's second century, several generations before the first "full-system" treatises of legal and dialectical theory were composed. This proto-system is revealed from analyses of dialectical sequences in the 2nd/8th century Kitab Ikhtilaf al-'Iraqiyyin / 'Iraqiyyayn (the "subject-text") through a lens molded from 5th/11th century jadal-theory treatises (the "lens-texts"). Specific features thus uncovered inform the elaboration of a Dialectical Forge Model, whose more general components and functions are explored in closing chapters.

Tadeusz Kotarbinski is one of towering figures in contemporary Polish philosophy. He was a great thinker, a great teacher, a great organizer of philosophical and scientific life (he was, among others, the rector of the Uni versi ty of t6dz, the president of the Polish Academy of Sciences, and the president of the International Institute of Philosophy), and, last but not least, a great moral authority. He died at the age of 96 on October 3, 1981. Kotarbinski was active in almost all branches of philosophy. He made many significant contributions to logic, semantics, ontology, epistemology, history of philosophy, and ethics. He created a new field, namely praxiology. Thus, using an ancient distinction, he contributed to theoretical as well as practical philoso hy. Kotarbinski regarded praxiology as his major philosophical "child." Doubtless, praxiology belongs to practical philosophy. This collection, howewer, is mainly devoted to Kotarbinski' s theoretical philosophy. Reism - Kotarbinski' s fundamental idea of ontology and semantics - is the central topic of most papers included here; even Pszczolowski' s essay on praxiology considers its ontological basis., Only two papers, namely that of Zarnecka-Bialy and that of Wolenski, are not linked with reism. However, both fall under the general label "Kotarbinski: logic, semantics and ontology." The collection partly consists of earlier published papers.

This book deals with a basic problem arising within the Bayesian approach 1 to scientific methodology, namely the choice of prior probabilities. The problem will be considered with special reference to some inference methods used within Bayesian statistics (BS) and the so-called theory of inductive 2 probabilities (T/P). In this study an important role will be played by the assumption - defended by Sir Karl Popper and the supporters of the current verisimilitude theory (VT) - that the cognitive goal of science is the achievement of a high degree of truthlikeness or verisimilitude. A more detailed outline of the issues and objectives of the book is given in Section 1. In Section 2 the historical background of the Bayesian approach and the verisimilitude theory is briefly illustrated. In Section 3, the methods used in TIP and BS for making multinomial inference~ are considered and some conceptual relationships between TIP and BS are pointed out. In Section 4 the main lines of a new approach to the problem of the choice of prior probabilities are illustrated. Lastly, in Section 5 >the structure of the book is described and a first explanation of some technical terms is provided.

This book is intended to be a survey of the most important results in mathematical logic for philosophers. It is a survey of results which have philosophical significance and it is intended to be accessible to philosophers. I have assumed the mathematical sophistication acquired. in an introductory logic course or in reading a basic logic text. In addition to proving the most philosophically significant results in mathematical logic, I have attempted to illustrate various methods of proof. For example, the completeness of quantification theory is proved both constructively and non-constructively and relative ad vantages of each type of proof are discussed. Similarly, constructive and non-constructive versions of Godel's first incompleteness theorem are given. I hope that the reader. will develop facility with the methods of proof and also be caused by reflect on their differences. I assume familiarity with quantification theory both in under standing the notations and in finding object language proofs. Strictly speaking the presentation is self-contained, but it would be very difficult for someone without background in the subject to follow the material from the beginning. This is necessary if the notes are to be accessible to readers who have had diverse backgrounds at a more elementary level. However, to make them accessible to readers with no background would require writing yet another introductory logic text. Numerous exercises have been included and many of these are integral parts of the proofs."

While post-Fregean logicians tend to ignore or even denigrate the traditional logic of Aristotle and the Scholastics, new work in recent years has shown the viability of a renewed, extended, and strengthened logic of terms that shares fundamental features of the old syllogistic. A number of logicians, following the lead of Fred Sommers, have built just such a term logic. It is a system of formal logic that not only matches the expressive and inferential powers of today's standard logic, but surpasses it and is far simpler and more natural. This book aims to substantiate this claim by exhibiting just how the term logic can shed need light on a variety of challenges that face any system of formal logic.

Philosophical Dimensions of Logic and Science is a collection of outstanding contributed papers presented at the 11th International Congress of Logic, Methodology, and Philosophy of Science held in Krakow in 1999. The Congress was a follow-up to the series of meetings, initiated once by Alfred Tarski, which aimed to provide an interdisciplinary forum for scientists, philosophers and logicians. The articles selected for publication in the book comply with that idea and innovatively address current issues in logic, metamathematics, philosophy of language, philosophy of science, and cognitive science, as well as philosophical problems of biology, chemistry and physics.
The volume will be of interest to philosophers, logicians and scientists interested in foundational problems of their disciplines."

"Necessity is the mother of invention. " Part I: What is in this book - details. There are several different types of formal proof procedures that logicians have invented. The ones we consider are: 1) tableau systems, 2) Gentzen sequent calculi, 3) natural deduction systems, and 4) axiom systems. We present proof procedures of each of these types for the most common normal modal logics: S5, S4, B, T, D, K, K4, D4, KB, DB, and also G, the logic that has become important in applications of modal logic to the proof theory of Peano arithmetic. Further, we present a similar variety of proof procedures for an even larger number of regular, non-normal modal logics (many introduced by Lemmon). We also consider some quasi-regular logics, including S2 and S3. Virtually all of these proof procedures are studied in both propositional and first-order versions (generally with and without the Barcan formula). Finally, we present the full variety of proof methods for Intuitionistic logic (and of course Classical logic too). We actually give two quite different kinds of tableau systems for the logics we consider, two kinds of Gentzen sequent calculi, and two kinds of natural deduction systems. Each of the two tableau systems has its own uses; each provides us with different information about the logics involved. They complement each other more than they overlap. Of the two Gentzen systems, one is of the conventional sort, common in the literature.

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 weIl 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 0/ Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook 0/ 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."

Dynamic Epistemic Logic is the logic of knowledge change. This book provides various logics to support such formal specifications, including proof systems. Concrete examples and epistemic puzzles enliven the exposition. The book also offers exercises with answers. It is suitable for graduate courses in logic. Many examples, exercises, and thorough completeness proofs and expressivity results are included. A companion web page offers slides for lecturers and exams for further practice.