Philosophical Logic is a clear and concise critical survey of nonclassical logics of philosophical interest written by one of the world's leading authorities on the subject. After giving an overview of classical logic, John Burgess introduces five central branches of nonclassical logic (temporal, modal, conditional, relevantistic, and intuitionistic), focusing on the sometimes problematic relationship between formal apparatus and intuitive motivation. Requiring minimal background and arranged to make the more technical material optional, the book offers a choice between an overview and in-depth study, and it balances the philosophical and technical aspects of the subject. – The book emphasizes the relationship between models and the traditional goal of logic, the evaluation of arguments, and critically examines apparatus and assumptions that often are taken for granted. Philosophical Logic provides an unusually thorough treatment of conditional logic, unifying probabilistic and model-theoretic approaches. It underscores the variety of approaches that have been taken to relevantistic and related logics, and it stresses the problem of connecting formal systems to the motivating ideas behind intuitionistic mathematics. Each chapter ends with a brief guide to further reading. – Philosophical Logic addresses students new to logic, philosophers working in other areas, and specialists in logic, providing both a sophisticated introduction and a new synthesis. – Chapter One, Classical Logic; – Ch. Two, Temporal Logic; – Ch. Three, Modal Logic; – Ch. Four, Conditional Logic; – Ch. Five, Relevantistic Logic; – Ch. Six, Intuitionistic Logic. M.-M. V.

This book is intended to provide a philosophically, and historically-based introduction to modal logic, offering to every reader, even those with little specific background, a conceptually clear path through the labyrinth of contemporary modal logic. This is done by emphasizing the notion of multimodality while delineating the formal side of the semantics and proof theory behind the topics in a smooth and gentle pace. The conceptual thread which ties the book together passes through topics like the development of modal logic from standard logic; the syntax and semantics of normal modal systems; the seminal ideas behind completeness, incompleteness, canonicity and finite models; the temporal logics, the logics of knowledge and belief; the generalized syntactical and semantical treatment of multimodalities and finally the pleasures and difficulties of quantified modal logic. – Multimodality is the notion which stands behind the most fertile investigations in modal logic, such as temporal logics, epistemic logics, dynamic logics and so on. By focusing on multimodal logic this book provides common ground for philosophers, logicians, linguists, mathematicians and computer scientists. The book is also designed to provide a repertoire of ideas and techniques for students interested in progressive inquiry in modal and multimodal logic. Each chapter is relatively independent, complemented with exercises and followed by a short bibliographical commentary intended for historically-minded readers. – Table of contents : Preface. - 1. Modal logic and standard logic. - 2. The syntax of normal modal systems. - 3. The semantics of normal modal systems. - 4. Completeness and canonicity. - 5. Incompleteness and finite models. - 6. Temporal logics. - 7. Epistemic logic: knowledge and belief. - 8. Multimodal logics. - 9. Towards quantified modal logic. M.-M. V.

Ted A. Warfield has recently employed modal logic to argue that compatibilism in the free-will/determinism debate entails the rejection of intuitively valid inferences. I show that Warfield's argument fails. A parallel argument leads to the false conclusion that the mere possibility of determinism, together with the necessary existence of any contingent propositions, entails the rejection of intuitively valid inferences. The error in both arguments involves a crucial equivocation, which can be revealed by replacing modal operators with explicit quantifiers over possible worlds. I conclude that the modal-logical apparatus used by Warfield obscures rather than clarifies, and distracts from the real philosophical issues involved in the metaphysical debate. These issues cannot be settled by logic alone.

It has been argued by Bernard Linsky and Edward Zalta, and independently by Timothy Williamson, that the best quantified modal logic is one that validates both the Barcan Formula and its converse. This requires that domains be fixed across all possible worlds. All objects exist necessarily; some – those we would usually consider contingent – are concrete at some worlds and non-concrete (but still existent) at others. Linsky and Zalta refer to such objects as ‘contingently non-concrete’. I defend the standard usage of the word ‘exists’, and the view that many objects exist only contingently. I argue that the Linsky/Zalta analysis, and to a lesser extent Williamson’s, suffers not only from a peculiar ontology but also from two related formal difficulties. Their analysis gives either counter-intuitive or ad hoc results about essences, and it fails to accommodate contingently existing abstracta.

We describe E. W. Beth’s use of nonclassical valuations (in his own terminology pseudo-valuations) in propositional logics. Three periods are distinguished. In the first period (1954) he develops the idea of pseudo-valuation intending to apply it to obtain a subformula theorem for arbitrary propositional logics. When this fails, he obtains in the second period (1958-1961) some simple but elegant applications of the idea, mainly with regard to proofs of independance of axioms systems. The thirs period (1961-1964) is the application of the idea towards the introduction of a semantics (his second one) for intuitionistic logics. We will show that it is highly likely that Beth discovered this version of “possible worlds semantics” for intuitionistic and some modal logics essentially independently from Kripke. The history of the concept of semantic tableaux is strongly bound to the birth of the concept of semantic tableaux, but we will touch the latter subject only in so far as is necessary for our considerations.

1, Introduction; 2, Une classe universelle anti-fondée pour les croyances; 3, Logique modale anti-fondée; 4, Logique modale anti-fondée et connaissance commune; 4, Conclusion et perspectives.

Introduction; – Normative Temporal Logic; – Symbolic Representations; – Model Checking; – Case Study : Traffic Control; – Discussion.

La Syllogistique d’Aristote de Łukasiewicz est écrite pour corriger les interprétations traditionnelles de la syllogistique d’Aristote en se plaçant « du point de vue de la logique formelle moderne ». Son interprétation contient plusieurs paradoxes forts : la description de la syllogistique comme une axiomatique qui utilise intuitivement les règles du calcul propositionnel, l’absence de quantificateurs et l’interprétation de la « nécessité syllogistique » comme un quantificateur universel, l’interprétation quadrivalente de la logique modale tout en admettant que la logique d’Aristote est bivalente. Tous ces paradoxes se comprennent mieux si l’on voit que Łukasiewicz veut construire un système logique cohérent conforme aux intentions d’Aristote en utilisant la logique moderne comme un outil, tout en réagissant contre les critiques de la logique moderne à l’encontre de la syllogistique d’Aristote. (Auteur)

Łukasiewicz’s Aristotle’s Syllogistic was written “from the standpoint of modern formal logic” as a correction of the traditional interpretations of Aristotle’s syllogistic. His interpretation includes many paradoxical views, such as the description of the syllogistic as an axiomatic system intuitively using the rules of propositional calculus, the absence of quantifiers alongside the interpretation of “logical necessity” as equivalent to a universal quantifier, and the four-valued interpretation of modal logic alongside the thesis that Aristotle’s logic is two-valued. All these paradoxes are better understood once one admits that Łukasiewicz wants to build up a coherent logical system upon Aristotle’s intentions with the help of modern logic as a tool, but also tries to react against the criticisms of Aristotle’s syllogistic from the standpoint of modern logic.

This article contains : 1. Introduction ; 2. Logical and Mathematical knowledge ; 3. Questions and answers : a new perspective on logical operators 4. Lewis' modal logic ; 5. Conclusion. – References, 138-139. F. F.

This book is about how to understand quantum mechanics by means of a modal interpretation. Modal interpretations provide a general framework within which quantum mechanics can be considered as a theory that describes reality in terms of physical systems possessing definite properties. Quantum mechanics is standardly understood to be a theory about probabilities with which measurements have outcomes. Modal interpretations are relatively new attempts to present quantum mechanics as a theory which, like other physical theories, describes an observer-independent reality. In this book, Pieter Vermaas summarises the results of this work. The book will be of great value to undergraduates, graduate students and researchers in philosophy of science, and physics departments with an interest in learning about modal interpretations of quantum mechanics. – Contents : – 1. Introduction; – 2. Quantum mechanics; – 3. Modal interpretations; – Part I. Formalism: – 4. The different versions; – 5. The full property ascription; – 6. Joint property ascriptions; – 7. Discontinuities, instabilities and other bad behaviour; – 8. Transition probabilities; – 9. Dynamical autonomy and locality; – Part II. Physics: – 10. The measurement problem; – 11. The Born rule; – Part III. Philosophy: – 12. Properties, states, measurement outcomes and effective states; – 13. Holism versus reductionism; – 14. Possibilities and impossibilities; – 15. Conclusions.

This revised and considerably expanded 2nd edition, published in 2008, brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area. – Contents : Preface to the first edition; Preface to the second edition; Mathematical prolegomenon. – Part I. Propositional Logic: – 1. Classical logic and the material conditional; – 2. Basic modal logic; – 3. Normal modal logics; – 4. Non-normal modal logics; strict conditionals; – 5. Conditional logics; – 6. Intuitionist logic; – 7. Many-valued logics; – 8. First degree entailment; – 9. Logics with gaps, gluts, and worlds; – 10. Relevant logics; – 11. Fuzzy logics; 11a. Appendix: Many valued modal logics; Postscript: An historical perspective on conditionals. – Part II. Qualification and Identity: – 12. Classical logic; – 13. Free logic; – 14. Constant domain modal logics; – 15. Variable domain modal logics; – 16. Necessary identity in modal logic; – 17. Contingent identity in modal logic; – 18. Non-normal modal logics; – 19. Conditional logics; – 20. Intuitionist logic; – 21. Many-valued logics; – 22. First degree entailment; – 23. Logics with gaps, gluts, and worlds; – 24. Relevant logics; – 25. Fuzzy logics. – Postscript: A methodological coda. – Includes bibliographical references (p. 587-602) and index.