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• Contributors.- Introduction.- Irving H. Anellis: Preface and Prospectus.- Irving H. Anellis and Francine F. Abeles: The Historical Sources of Tree Graphs and the Tree Method in the Work of Peirce and Gentzen.- Jean Paul Van Bendegem: Logic and Argumentation in Belgium: The Role of Leo Apostel.- Philippe de Rouilhan: Tarski's Recantation: Reading the Postscript to "Wahrheitsbegriff".- Jan Wolenski: The Paradox of Analyticity and Related Issues.- David DeVidi and Herbert Korte: Naturalizing Natural Deduction.- Alberto Peruzzi: Category Theory and the Search for Universals: A Very Short Guide for Philosophers.- Roman Murawski: On the Way to Modern Logic - The Case of Polish Logic.- Valentin A. Bazhanov: Russian Origins of Non-Classical Logics.- Vladik Kreinovich: Constructive Mathematics in St. Petersburg, Russia: A (Somewhat Subjective) View from Within.- Jonathan P. Seldin: On Normalizing Disjunctive Intermediate Logic.- R.E. Hodel: A Natural Axiom System for Boolean Algebras with Applications.
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This book presents diverse topics in mathematical logic such as proof theory, meta-mathematics, and applications of logic to mathematical structures. The collection spans the first 100 years of modern logic and is dedicated to the memory of Irving Anellis, founder of the journal 'Modern Logic', whose academic work was essential in promoting the algebraic tradition of logic, as represented by Charles Sanders Peirce. Anellis's association with the Russian logic community introduced their school of logic to a wider audience in the USA, Canada and Western Europe. In addition, the collection takes a historical perspective on proof theory and the development of logic and mathematics in Eastern Logic, the Soviet Union and Russia. The book will be of interest to historians and philosophers in logic and mathematics, and the more specialized papers will also appeal to mathematicians and logicians.
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"Since antiquity, opposed concepts such as the One and the Many, the Finite and the Infinite, and the Absolute and the Relative, have been a driving force in philosophical, scientific, and mathematical thought. Yet they have also given rise to perplexing problems and conceptual paradoxes which continue to haunt scientists and philosophers. In Oppositions and Paradoxes, John L. Bell explains and investigates the paradoxes and puzzles that arise out of conceptual oppositions in physics and mathematics. In the process, Bell not only motivates abstract conceptual thinking about the paradoxes at issue, he also offers a compelling introduction to central ideas in such otherwise-difficult topics as non-Euclidean geometry, relativity, and quantum physics. These paradoxes are often as fun as they are flabbergasting. Consider, for example, the famous Tristram Shandy paradox: an immortal man composing an autobiography so slowly as to require a year of writing to describe each day of his life and he would, if he had infinite time, presumably never complete the work, although no individual part of it would remain unwritten. Or imagine an English professor who time-travels back to 1599 to offer a printing of Hamlet to Shakespeare, so as to help the Bard overcome writer's block and author the play which will centuries later inspire an English professor to travel back in time. These and many other paradoxes straddle the boundary between physics and metaphysics, and demonstrate the hidden difficulty in many of our most basic concepts."-- Provided by publisher.

• Preface--
• 1. Introduction--
• 2. Game theory--
• 3. First-order logic--
• 4. Independence-friendly (IF) logic--
• 5. Properties of IF logic--
• 6. Expressive power of IF logic--
• 7. Probabilistic IF logic--
• 8. Further topics-- References-- Index.
• (source: Nielsen Book Data)

Bringing together over twenty years of research, this book gives a complete overview of independence-friendly logic. It emphasizes the game-theoretical approach to logic, according to which logical concepts such as truth and falsity are best understood via the notion of semantic games. The book pushes the paradigm of game-theoretical semantics further than the current literature by showing how mixed strategies and equilibria can be used to analyze independence-friendly formulas on finite models. The book is suitable for graduate students and advanced undergraduates who have taken a course on first-order logic. It contains a primer of the necessary background in game theory, numerous examples and full proofs.
(source: Nielsen Book Data)

This complete text and software package provides a self-contained introduction to the basic concepts of logic: language, truth, argument, consequence, proof and counterexample. Assuming no prior study of logic, Barwide and Etchemendy provide a clear and comprehensive outline of the field - a text appropriate for introductory or secondary courses in logic that incorporates more than enough material to be of use to philosophers, computer scientists, and mathematicians as well. The price of a new text/software package includes one Registration ID, which must be used each time work is submitted to the grading service. Once activated, the Registration ID is not transferable.
(source: Nielsen Book Data)

Modal logic is the logic of necessity and possibility. Unlike non-modal logic, it codifies structures which represent how things could be as well as how things are. This text guides readers through the most basic systems of modal predicate logic with identity. Dealing with both technical developments such as completeness and incompleteness and finite and infinite models, it discusses philosophical applications, especially in the area of predicate logic.
(source: Nielsen Book Data)
Modal logic is the logic of necessity and possibility, of 'must be' and 'may be'. Unlike non-modal logic, it codifies structures which represent how things could be as well as how things are. This book is intended to replace the widely used Introduction to Modal Logic and the more recent, Companion to Modal Logic , by the same authors. The principle changes include the incorporation of developments that have taken place since 1968 both in modal propositional logic and in modal predicate logic, but without sacrificing the clarity of exposition and the accessiblity of the material which were essential features of the earlier books. Most importantly, the book has been completely rewritten and in no sense is a 'new edition' of either book. A New Introduction to Modal Logic guides readers through the most basic systems of modal predicate logic with identity. It deals with both technical developments such as completeness and incompleteness, and finite and infinite models, and discusses philosophical applications, especially in the area of predicate logic. Written for students of logic and for their lecturers, philosophers, linguistics, mathematicians, computer scientists and those studying cognitive science or semantics. A New Introduction to Modal Logic is the only textbook you will need.
(source: Nielsen Book Data)

• 1. GL and other systems of propositional modal logic--
• 2. Peano arithmetic--
• 3. The box as Bew(x)--
• 4. Semantics for GL and other modal logics--
• 5. Completeness and decidability of GL and K, K4, T, B, S4, and S5--
• 6. Canonical models--
• 7. On GL--
• 8. The fixed point theorem--
• 9. The arithmetical completeness theorems for GL and GLS--
• 10. Trees for GL--
• 11. An incomplete system of modal logic--
• 12. An S4 -preserving proof-theoretical treatment of modality--
• 13. Modal logic within set theory--
• 14. Modal logic within analysis--
• 15. The joint provability logic of consistency and w-consistency--
• 16. On GLB: the fixed point theorem, letterless sentences, and analysis--
• 18. Quantified provability logic with one one-place predicate letter-- Notes-- Bibliography-- Index.
• (source: Nielsen Book Data)

This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency (1979). Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians. Here it receives its first scientific application since its invention. Modal logic is concerned with the notions of necessity and possibility. What George Boolos does is to show how the concepts, techniques, and methods of modal logic shed brilliant light on the most important logical discovery of the twentieth century: the incompleteness theorems of Kurt Godel and the 'self-referential' sentences constructed in their proof. The book explores the effects of reinterpreting the notions of necessity and possibility to mean provability and consistency.
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• How to use this book--
• 1. How to use Tarski's World--
• 2. Exercises on propositional logic--
• 3. Exercises on first-order logic--
• 4. More theoretical exercises-- Appendices-- Index.
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Tarski's World 4.0 is an innovative and enjoyable way to introduce your students to the language of first-order logic. Using this program, students quickly master the meaning of the connectives and quantifiers, and soon become fluent in the symbolic language at the core of modern logic. Tarski's World allows the students to build three-dimensional worlds, and to describe them in first-order logic. They evaluate the sentences in the constructed worlds, and if their evaluation is incorrect, the program provides them with a game that leads them to understand where they went wrong. The package is intended as a supplement to any standard logic text, or for use by anyone who wants to learn the language. The disk and manual contain over a hundred exercises from very basic to highly sophisticated.
(source: Nielsen Book Data)

• Introduction--
• 1. Classical propositional logic--
• 2. Classical monadic predicate logic--
• 3. The system S5--
• 4. System T--
• 5. System S4--
• 6. Hilbert-type axiomatizations-- Exercises.
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Modal Logic can be characterized as the logic of necessity and possibility, of 'must be' and 'may be'. A Short Introduction to Modal Logic presents both semantic and syntactic features of the subject and illustrates them by detailed analyses of the three best-known modal systems S5, S4 and T. The book concentrates on the logical aspects of the subject and provides philosophical motivations to show the point of the formal work. The coverage is self-contained, including a summary of the necessary aspects of classical logic which it presupposes. A set of exercises is included in the final chapter.
(source: Nielsen Book Data)

• Introduction C. Anthony Anderson and Joseph Owens--
• 1. Quine on quantifying in Kit Fine--
• 2. Prolegomena to a structural theory of belief and other attitudes Hans Kemp--
• 3. A study in comparative semantics Ernest LePore and Barry Loewer--
• 4. Wherin is language social? Tyler Burge--
• 5. Narrow content Robert Stalnaker--
• 6. Cognitive access and semantic puzzles Joseph Owens--
• 7. On some thought-experiments about mind and meaning John Wallace and H. E. Mason--
• 8. Belief and the indentity of reference Keith S. Donnellan--
• 9. A millian heir rejects the wages of sinn Nathan Salmon--
• 10. The mode-of-presentation problem Stephen Schiffer--
• 11. Consciousness, unconsciousness, and intentionality John R. Searle--
• 12. Consciousness and intentionality: Robots with and without the right stuff Keith Gunderson-- Bibliography-- Subject index-- Name index.
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These papers treat those issues involved in formulating a logic of propositional attitudes and consider the relevance of the attitudes to the continuing study of both the philosophy of language and the philosophy of mind. C. Anthony Anderson is professor of philosophy and Joseph Owens is assistant professor of philosophy, both at the University of Minnesota.
(source: Nielsen Book Data)

• Preface-- Part I. Situation Theory:
• 1. Constraints, channels, and the flow of information Jon Barwise--
• 2. Extended Kamp notation: a graphical notation for situation theory Jon Barwise and Robin Cooper--
• 3. States of affairs without parameters Mark Crimmins-- Part II. Logical Applications:
• 4. Labelled deductive systems and situation theory D. M. Gabbay--
• 5. Events and processes in situation semantics Michael Georgeff, David Morley and Anand Rao--
• 6. Nonmonotonic projection, causation and induction Robert C. Koons--
• 7. Modal situation theory Stephen M. Schulz-- Part III. Linguistic Applications:
• 8. Generalized quantifiers and resource situations Robin Cooper--
• 9. Situation theory and cooperative action Keith Devlin and Duska Rosenberg--
• 10. Propositional and non-propositional attitudes Jonathan Ginzburg--
• 11. Episodic logic: a situational logic for natural language processing Chung Hee Hwang and Lenhart K. Schubert--
• 12. A situation-theoric formalization of definite description interpretation in plan elaboration dialogues Massimo Poessio--
• 13. A situation-theoretic representation of text meaning-- anaphora, quantification, and negation Dag Westerstahl, Bjorn Haglund and Torbjorn Lager-- Name index-- Subject index.
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• Preface-- Contributors-- Part I. Situation Theory:
• 1. Replacement systems and the axiomatization of situation theory Peter Aczel--
• 2. Information, infons, and inference Jon Barwise and John Etchemendy--
• 3. Infons and types in an information-based logic Keith Devlin--
• 4. On the logic of situation theory Tim Fernando--
• 5. Partial sets Michael W. Mislove, Lawrence S. Moss, and Frank J. Oles--
• 6. An illative theory of relations Gordon Plotkin--
• 7. Perspectives in situation theory Jerry Seligman--
• 8. Parametric types and propositions in first-order situation theory Dag Westerstahl-- Part II. Logical Applications:
• 9. Dewey on defeasibility Thomas Burke--
• 10. Three indexical solutions to the liar paradox Robert Koons--
• 11. The complexity of paradox William C. Rounds-- Part III. Linguistic Applications:
• 12. Situating word meaning Nick Braisby--
• 13. Information in the early stages of language acquisitions Robin Cooper--
• 14. Locations now and then Judith Merriam Crow--
• 15. Argument roles and anaphora Elisabet Engdahl--
• 16. Some puzzles about pronouns Jean Mark Gawron and Stanley Peters--
• 17. Out of the mouths of babes Elizabeth Macken--
• 18. Situations, games, and ambiguity Prashant Parikh--
• 19. Conditionals and unconditionals in universal grammar and situation semantics Dietmar Zaefferer-- Name index-- Subject index.
• (source: Nielsen Book Data)

Situation theory is the result of an interdisciplinary effort to create a full-fledged theory of information. Created by scholars and scientists from cognitive science, computer science and AI, linguistics, logic, philosophy, and mathematics, it aims to provide a common set of tools for the analysis of phenomena from all these fields. Unlike Shannon-Weaver type theories of information, which are purely quantitative theories, situation theory aims at providing tools for the analysis of the specific content of a situation (signal, message, data base, statement, or other information-carrying situation). The question addressed is not how much information is carried, but what information is carried.
(source: Nielsen Book Data)
Situation Theory grew out of attempts by Jon Barwise in the late 1970s to provide a semantics for 'naked-infinitive' perceptual reports such as 'Claire saw Jon run'. Barwise's intuition was that Claire didn't just see Jon, an individual, but Jon doing something, a situation. Situations are individuals having properties and standing in relations. A theory of situations would allow us to study and compare various types of situations or situation-like entitles, such as facts, events, and scenes. One of the central themes of situation theory of meaning and reference should be set within a general theory of information, one moreover that is rich enough to do justice to perception, communication, and thought. By now many people have contributed by the need to give a rigorous mathematical account of the principles of information that underwrite the theory.
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• Part 1 The origins of the problem: an outline of the issues-- the Baconian tradition in the philosophy of induction-- the rise of Pascalian probability-- the combination of Baconian and Pascalian themes.
• Part 2 The controversy about the nature of Pascalian probability: some general considerations-- indifference theories-- frequency theories-- propensity theories-- personalist theories-- multi-valued logic theories-- logical relation theories.
• Part 3 The foundations of pluralism in the analysis of probability: some logical distinctions exploited by differing analyses of Pascalian probability-- the appropriateness of different conceptions of Pascalian probability to different purposes-- the need to supplement Pascalian judgements by non-Pascalian ones-- how are different conceptions of probability possible?
• Part 4 The Pascalian gradation of ampliative induction: inductive probability under a realist construal-- inductive probability under a range-theoretical construal-- Pascalian gradation for variative induction-- inductive probability under a personalist construal.
• Part 5 The Baconian gradation of ampliative induction: inductive support by the method of relevant variables-- the logical syntax of the method of relevant variables-- some non-standard interpretations of Baconian logical syntax.
• Part 6 Four paradoxes about induction: the classical problem of induction-- the paradox of the ravens-- the "grue" paradox-- the lottery paradox.
• (source: Nielsen Book Data)

This book is concerned with two philosophical problems about the gradation of certainty which emerged in the 17th century and which, the author argues, are still alive today. One is concerned with the evaluation of inductive reasoning, whether in science, in jurisprudence or elsewhere; the other with the interpretation of the mathematical calculus of chance. At a non-specialist level, this book investigates both problems and the extent to which they are interconnected. The author aims to explore the diversity of logical structures that are available for judgements of probability, and to explore the rationale for their appropriateness to different contexts of application. Cohen's aim is to face up to the complexity of the underlying philosophical issues rather than to rehearse familiar mathematical findings or statistical procedures.
(source: Nielsen Book Data)

• The physical foundations of inference, or the world as the logician regards it: an exposition of the principal assumptions demanded for the establishment of a material or objective system of logic The foundations of logic considered more in detail, and especially in respect of what is demanded for inference-- (I) Sequences of phenomena, or laws of causation Continuation of the previous subject in respect of (II) Co-existences-- and comparison of these with sequences through the same three stages of advancing precision and completeness The uniformity of nature-- or that wide conception of regularity in the external world, which is the objective counterpart of inferribility The subjective foundations of induction, or the principal postulates demanded on the mental side Language: a discussion of the principal questions involved in its reference, functions, medium, and varieties Terms-- as interpreted and subdivided in logic Propositions: their general nature and composition The schedule of propositions: the various ways in which they may be arranged and subdivided for logical purposes Hypothetical and disjunctive judgments-- their distinctive characteristics, and the circumstances of their origin Definition-- in logic and in science Division, in its old interpretation: the simple analysis of the denotation of terms Division scientifically considered: further analysis and development Induction-- or the process of generalizing an attribute, observed in certain objects, over the whole class to which they belong The syllogism in relation to induction: modified acceptance of Mill's view Analysis and synthesis, regarded as correlated applications of the general process of hypothesis Inductive methods: the analysis of the antecedents, and exclusion of all but the cause Standards and units, as applicable to physical objects or events Standards and units as applied directly to psychical data Geometrical data: discussion of some of the difficulties commonly felt in their realization Explanation and verification, as steps towards the methodization and establishment of our knowledge of nature A universal or perfect language Extensions of our general powers of observation-- or the nature and limits of our control over space and time The ideal of logic and methodology-- or the degree and kind of knowledge at which induction may legitimately aim Speculation and action-- or the logical and scientific view of the world as modified by our practical tendencies.
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Venn, best known for his diagrams for set theory, primarily studied logic and probability theory. The present book is a study of the principles of logic, with special emphasis on inference and induction. From the Preface to the first edition (1889): 'As many readers will probably perceive, the main original guiding influence with me - as with most of those of the middle generation, and especially with most of those who approached logic with previous mathematical or scientific training - was that of Mill...I still continue to regard the general attitude towards phenomena, which Mill took up as a logician, to be the soundest and most useful for scientific study'.From the Preface to the Second Edition (1907): 'Though thus leaving the main outlines unaltered I have done what I could to improve the work, and to try to bring it up to date...A number of paragraphs have been altered, others have been re-written, and many hundreds of minor alterations, additions and corrections inserted'.
(source: Nielsen Book Data)