Intensional logic has emerged, since the 1960' s, as a powerful theoretical and practical tool in such diverse disciplines as computer science, artificial intelligence, linguistics, philosophy and even the foundations of mathematics. The present volume is a collection of carefully chosen papers, giving the reader a taste of the frontline state of research in intensional logics today. Most papers are representative of new ideas and/or new research themes. The collection would benefit the researcher as well as the student. This book is a most welcome addition to our series. The Editors CONTENTS PREFACE IX JOHAN VAN BENTHEM AND NATASHA ALECHINA Modal Quantification over Structured Domains PATRICK BLACKBURN AND WILFRIED MEYER-VIOL Modal Logic and Model-Theoretic Syntax 29 RUY J. G. B. DE QUEIROZ AND DOV M. GABBAY The Functional Interpretation of Modal Necessity 61 VLADIMIR V. RYBAKOV Logics of Schemes for First-Order Theories and Poly-Modal Propositional Logic 93 JERRY SELIGMAN The Logic of Correct Description 107 DIMITER VAKARELOV Modal Logics of Arrows 137 HEINRICH WANSING A Full-Circle Theorem for Simple Tense Logic 173 MICHAEL ZAKHARYASCHEV Canonical Formulas for Modal and Superintuitionistic Logics: A Short Outline 195 EDWARD N. ZALTA 249 The Modal Object Calculus and its Interpretation NAME INDEX 281 SUBJECT INDEX 285 PREFACE Intensional logic has many faces. In this preface we identify some prominent ones without aiming at completeness.

What role, if any, does formal logic play in characterizing epistemically rational belief? Traditionally, belief is seen in a binary way - either one believes a proposition, or one doesn't. Given this picture, it is attractive to impose certain deductive constraints on rational belief: that one's beliefs be logically consistent, and that one believe the logical consequences of one's beliefs. A less popular picture sees belief as a graded phenomenon. This picture (explored more by decision-theorists and philosophers of science thatn by mainstream epistemologists) invites the use of probabilistic coherence to constrain rational belief. But this latter project has often involved defining graded beliefs in terms of preferences, which may seem to change the subject away from epistemic rationality.
Putting Logic in its Place explores the relations between these two ways of seeing beliefs. It argues that the binary conception, although it fits nicely with much of our commonsense thought and talk about belief, cannot in the end support the traditional deductive constraints on rational belief. Binary beliefs that obeyed these constraints could not answer to anything like our intuitive notion of epistemic rationality, and would end up having to be divorced from central aspects of our cognitive, practical, and emotional lives.
But this does not mean that logic plays no role in rationality. Probabilistic coherence should be viewed as using standard logic to constrain rational graded belief. This probabilistic constraint helps explain the appeal of the traditional deductive constraints, and even underlies the force of rationally persuasive deductive arguments. Graded belief cannot bedefined in terms of preferences. But probabilistic coherence may be defended without positing definitional connections between beliefs and preferences. Like the traditional deductive constraints, coherence is a logical ideal that humans cannot fully attain. Nevertheless, it furnishes a compelling way of understanding a key dimension of epistemic rationality.

Are people rational? This question was central to Greek thought; and has been at the heart of psychology and philosophy for millennia. This book provides a radical and controversial reappraisal of conventional wisdom in the psychology of reasoning, proposing that the Western conception of the mind as a logical system is flawed at the very outset. It argues that cognition should be understood in terms of probability theory, the calculus of uncertain reasoning, rather than in terms of logic, the calculus of certain reasoning.

As philosophy departments attempt to define their unique value amid program closures in the humanities and the rise of interdisciplinary research, metaphilosophy has become an increasingly important area of inquiry. Richard Fumerton here lays out a cogent answer to the question asked in the book's title, What is Philosophy?. Against those who argue that philosophy is not sharply distinguishable from the sciences, Fumerton makes a case for philosophy as an autonomous discipline with its own distinct methodology. Over the course of nine engaging and accessible chapters, he shows that answering fundamental philosophical questions requires one to take a radical first-person perspective that divorces the truth conditions of philosophical claims from the kind of contingent truths investigated by the empirical sciences. Along the way, Fumerton briefly discusses the historical controversies that have surrounded the nature of philosophy, situating his own argument within the larger conversation. Key Features Illuminates the unique role of thought experiments and especially the "paradox of analysis" in understanding the purpose and value of philosophy. Shows that philosophy asks fundamental questions, unanswerable by the sciences, that are critical to thinking clearly and rationally about the world. Highlights the distinct character of philosophical questions in specific subject areas: philosophy of language, epistemology, ethics, philosophy of mind, and philosophy of science. Concludes by making a unique case for philosophy's contribution to cross-disciplinary work in ethics, politics, mathematics, and the empirical sciences. Written in a way to be engaging and accessible for advanced undergraduate readers.

Is truth objective or relative? What exists independently of our minds? This book is about these two questions. The essays in its pages variously defend and critique answers to each, grapple over the proper methodology for addressing them, and wonder whether either question is worth pursuing. In so doing, they carry on a long and esteemed tradition - for our two questions are among the oldest of philosophical issues, and have vexed almost every major philosopher, from Plato, to Kant to Wittgenstein. Fifteen eminent contributors bring fresh perspectives, renewed energy and original answers to debates which have been the focus of a tremendous amount of interest in the last three decades both within philosophy and the culture at large.

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

In Contradiction advocates and defends the view that there are true contradictions (dialetheism), a view that flies in the face of orthodoxy in Western philosophy since Aristotle. The book has been at the center of the controversies surrounding dialetheism ever since its first publication in
1987. This second edition of the book substantially expands upon the original in various ways, and also contains the author's reflections on developments over the last two decades. Further aspects of dialetheism are discussed in the companion volume, Doubt Truth to be a Liar, also published by
Oxford University Press in 2006.

Can OUGHT be derived from IS? This book presents an investigation of this time-honored problem by means of alethic-deontic predicate logic. New in this study is the leitmotif of relevance: is-ought inferences indeed exist, but they are all irrelevant in a precise logical sense. New proof techniques establish this result for very broad classes of logics. A profound philosophical analysis of is-ought bridge principles supplements the logical study. The final results imply incisive limitations for the justifiability of ethics as opposed to empirical science.

In the fall of 1985 Carnegie Mellon University established a Department of Philosophy. The focus of the department is logic broadly conceived, philos- ophy of science, in particular of the social sciences, and linguistics. To mark the inauguration of the department, a daylong celebration was held on April 5, 1986. This celebration consisted of two keynote addresses by Patrick Sup- pes and Thomas Schwartz, seminars directed by members of the department, and a panel discussion on the computational model of mind moderated by Dana S. Scott. The various contributions, in modified and expanded form, are the core of this collection of essays, and they are, I believe, of more than parochial interest: they turn attention to substantive and reflective interdis- ciplinary work. The collection is divided into three parts. The first part gives perspec- tives (i) on general features of the interdisciplinary enterprise in philosophy (by Patrick Suppes, Thomas Schwartz, Herbert A. Simon, and Clark Gly- mour) , and (ii) on a particular topic that invites such interaction, namely computational models of the mind (with contributions by Gilbert Harman, John Haugeland, Jay McClelland, and Allen Newell). The second part con- tains (mostly informal) reports on concrete research done within that enter- prise; the research topics range from decision theory and the philosophy of economics through foundational problems in mathematics to issues in aes- thetics and computational linguistics. The third part is a postscriptum by Isaac Levi, analyzing directions of (computational) work from his perspective.

Does game theory ? the mathematical theory of strategic interaction ? provide genuine explanations of human behaviour? Can game theory be used in economic consultancy or other normative contexts? Explaining Games: The Epistemic Programme in Game Theory ? the first monograph on the philosophy of game theory ? is a bold attempt to combine insights from epistemic logic and the philosophy of science to investigate the applicability of game theory in such fields as economics, philosophy and strategic consultancy. De Bruin proves new mathematical theorems about the beliefs, desires and rationality principles of individual human beings, and he explores in detail the logical form of game theory as it is used in explanatory and normative contexts. He argues that game theory reduces to rational choice theory if used as an explanatory device, and that game theory is nonsensical if used as a normative device. A provocative account of the history of game theory reveals that this is not bad news for all of game theory, though. Two central research programmes in game theory tried to find the ultimate characterisation of strategic interaction between rational agents. Yet, while the Nash Equilibrium Refinement Programme has done badly thanks to such research habits as overmathematisation, model-tinkering and introversion, the Epistemic Programme, De Bruin argues, has been rather successful in achieving this aim.

Abductive Reasoning: Logical Investigations into Discovery and Explanation is a much awaited original contribution to the study of abductive reasoning, providing logical foundations and a rich sample of pertinent applications. Divided into three parts on the conceptual framework, the logical foundations, and the applications, this monograph takes the reader for a comprehensive and erudite tour through the taxonomy of abductive reasoning, via the logical workings of abductive inference ending with applications pertinent to scientific explanation, empirical progress, pragmatism and belief revision.

In the twenty-first century, humanity is reaching new heights of scientific understanding - and at the same time appears to be losing its mind. How can a species that discovered vaccines for Covid-19 in less than a year produce so much fake news, quack cures and conspiracy theorizing?

In Rationality, Pinker rejects the cynical cliché that humans are simply an irrational species - cavemen out of time fatally cursed with biases, fallacies and illusions. After all, we discovered the laws of nature, lengthened and enriched our lives and set the benchmarks for rationality itself. Instead, he explains, we think in ways that suit the low-tech contexts in which we spend most of our lives, but fail to take advantage of the powerful tools of reasoning we have built up over millennia: logic, critical thinking, probability, causal inference, and decision-making under uncertainty. These tools are not a standard part of our educational curricula, and have never been presented clearly and entertainingly in a single book - until now.

Rationality matters. It leads to better choices in our lives and in the public sphere, and is the ultimate driver of social justice and moral progress. Brimming with insight and humour, Rationality will enlighten, inspire and empower.

"Euthydemus is Plato's defense of Socratic dialogue as a means to pursue truth. In Euthydemus, Plato has Socrates engage in a conversation with the title character and his brother Dionysodorus, both famous Sophists. They are representative of a type of argument, which Plato calls 'eristic', that emphasizes verbal trickery in order to humiliate your opponent and win your debate. This is contrasted with Socrates' dialectic, where words are a means of discerning reality, not gaining victory. In the process, Plato makes a case for the Socratic method as a means of educating youth, something he was attempting to do in his own newly-opened Academy. Presented in Plato's usual dramatic style, Euthydemus is simultaneously an engaging read and a passionate pedagogical manifesto.

This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. The third category contains papers on Avicenna's logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community.

As philosophy departments attempt to define their unique value amid program closures in the humanities and the rise of interdisciplinary research, metaphilosophy has become an increasingly important area of inquiry. Richard Fumerton here lays out a cogent answer to the question asked in the book's title, What is Philosophy?. Against those who argue that philosophy is not sharply distinguishable from the sciences, Fumerton makes a case for philosophy as an autonomous discipline with its own distinct methodology. Over the course of nine engaging and accessible chapters, he shows that answering fundamental philosophical questions requires one to take a radical first-person perspective that divorces the truth conditions of philosophical claims from the kind of contingent truths investigated by the empirical sciences. Along the way, Fumerton briefly discusses the historical controversies that have surrounded the nature of philosophy, situating his own argument within the larger conversation. Key Features Illuminates the unique role of thought experiments and especially the "paradox of analysis" in understanding the purpose and value of philosophy. Shows that philosophy asks fundamental questions, unanswerable by the sciences, that are critical to thinking clearly and rationally about the world. Highlights the distinct character of philosophical questions in specific subject areas: philosophy of language, epistemology, ethics, philosophy of mind, and philosophy of science. Concludes by making a unique case for philosophy's contribution to cross-disciplinary work in ethics, politics, mathematics, and the empirical sciences. Written in a way to be engaging and accessible for advanced undergraduate readers.

This volume is the first extensive study of the historical and philosophical connections between technology and mathematics. Coverage includes the use of mathematics in ancient as well as modern technology, devices and machines for computation, cryptology, mathematics in technological education, the epistemology of computer-mediated proofs, and the relationship between technological and mathematical computability. The book also examines the work of such historical figures as Gottfried Wilhelm Leibniz, Charles Babbage, Ada Lovelace, and Alan Turing.

This volume comprises a selection of contributions to the theorizing about argumentation that have been presented at the 9th conference of the International Society for the Study of Argumentation (ISSA), held in Amsterdam in July 2018. The chapters included provide a general theoretical perspective on central topics in argumentation theory, such as argument schemes and the fallacies. Some contributions concentrate on the treatment of the concept of conductive argument. Other contributions are dedicated to specific issues such as the justification of questions, the occurrence of mining relations, the role of exclamatives, argumentative abduction, eudaimonistic argumentation and a typology of logical ways to counter an argument. In a number of cases the theoretical problems addressed are related to a specific type of context, such as the burden of proof in philosophical argumentation, the charge of committing a genetic fallacy in strategic manoeuvring in philosophy, the necessity of community argument, and connection adequacy for arguments with institutional warrants. The volume offers a great deal of diversity in its breadth of coverage of argumentation theory and wide geographic representation from North and South America to Europe and China.

This monograph is a defence of the Fregean take on logic. The author argues that Freges projects, in logic and philosophy of language, are essentially connected and that the formalist shift produced by the work of Peano, Boole and Schroeder and continued by Hilbert and Tarski is completely alien to Frege's approach in the Begriffsschrift. A central thesis of the book is that judgeable contents, i.e. propositions, are the primary bearers of logical properties, which makes logic embedded in our conceptual system. This approach allows coherent and correct definitions of logical constants, logical consequence, and truth and connects their use to the practices of rational agents in science and everyday life.

This book provides readers with a guide to both ordinal analysis, and to proof theory. It mainly focuses on ordinal analysis, a research topic in proof theory that is concerned with the ordinal theoretic content of formal theories. However, the book also addresses ordinal analysis and basic materials in proof theory of first-order or omega logic, presenting some new results and new proofs of known ones.Primarily intended for graduate students and researchers in mathematics, especially in mathematical logic, the book also includes numerous exercises and answers for selected exercises, designed to help readers grasp and apply the main results and techniques discussed.

This book collects a renowned scholar's essays from the past five decades and reflects two main concerns: an approach to logic that stresses argumentation, reasoning, and critical thinking and that is informal, empirical, naturalistic, practical, applied, concrete, and historical; and an interest in Galileo's life and thought-his scientific achievements, Inquisition trial, and methodological lessons in light of his iconic status as "father of modern science." These republished essays include many hard to find articles, out of print works, and chapters which are not available online. The collection provides an excellent resource of the author's lifelong dedication to the subject. Thus, the book contains critical analyses of some key Galilean arguments about the laws of falling bodies and the Copernican hypothesis of the earth's motion. There is also a group of chapters in which Galileo's argumentation is compared and contrasted with that of other figures such as Socrates, Karl Marx, Giordano Bruno, and his musicologist father Vincenzo Galilei. The chapters on Galileo's trial illustrate an approach to the science-vs-religion issue which Finocchiaro labels "para-clerical" and conceptualizes in terms of a judicious consideration of arguments for and against Galileo and the Church. Other essays examine argumentation about Galileo's life and thought by the major Galilean scholars of recent decades. The book will be of interest to scholars in philosophy, logic, philosophy of science, history of science, history of religion, philosophy of religion, argumentation, rhetoric, and communication studies.

Logic is fundamental to thought and language. But which logical principles are correct? The paradoxes play a crucial role in answering that question. The so-called Liar and Heap paradoxes challenge our basic ideas about logic; at the very least, they teach us that the correct logical principles are not as obvious as common sense would have it. The essays in this volume, written by leading figures in the field, discuss novel thoughts about the paradoxes.

This book explores the research of Professor Hilary Putnam, a Harvard professor as well as a leading philosopher, mathematician and computer scientist. It features the work of distinguished scholars in the field as well as a selection of young academics who have studied topics closely connected to Putnam's work. It includes 12 papers that analyze, develop, and constructively criticize this notable professor's research in mathematical logic, the philosophy of logic and the philosophy of mathematics. In addition, it features a short essay presenting reminiscences and anecdotes about Putnam from his friends and colleagues, and also includes an extensive bibliography of his work in mathematics and logic. The book offers readers a comprehensive review of outstanding contributions in logic and mathematics as well as an engaging dialogue between prominent scholars and researchers. It provides those interested in mathematical logic, the philosophy of logic, and the philosophy of mathematics unique insights into the work of Hilary Putnam.

Gareth Matthews suggests that we can better understand the nature of philosophical inquiry if we recognize the central role played by perplexity. The seminal representation of philosophical perplexity is in Plato's dialogues; Matthews invites us to view this as a response to something inherently problematic in the basic notions that philosophy deals with. He examines the intriguing shifts in Plato's attitude to perplexity and suggests that this development may be seen as an archetypal pattern that philosophers follow even today. So it is that one may be won over to philosophy in the first place by the example of a Socratic teacher who displays an uncanny gift at getting one perplexed about something one thought one understood perfectly well. Later, however, wanting like Plato to move beyond perplexity to produce philosophical 'results', one may be chagrined to discover that one's very best attempt to develop a philosophical theory induces its own perplexity. Then, like late Plato and like Aristotle, the philosopher may seek to 'normalize' perplexity in a way that both allows for progress and yet respects the peculiarly baffling character of philosophical questions.

Stephen Schiffer presents a groundbreaking account of meaning and belief, and shows how it can illuminate a range of crucial problems regarding language, mind, knowledge, and ontology. He introduces the new doctrine of 'pleonastic propositions' to explain what the things we mean and believe
are. He discusses the relation between semantic and psychological facts, on the one hand, and physical facts, on the other; vagueness and indeterminacy; moral truth; conditionals; and the role of propositional content in information acquisition and explanation. This radical new treatment of meaning
will command the attention of everyone who works on fundamental questions about language, and will attract much interest from other areas of philosophy.

This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts of the quantum-theoretic formalism used in quantum information. It then gives a synthetic presentation of the main "mathematical characters" of the quantum computational game: qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates the puzzling entanglement-phenomena and logically analyses the Einstein-Podolsky-Rosen paradox and introduces the reader to quantum computational logics, and new forms of quantum logic. The middle chapters investigate the possibility of a quantum computational semantics for a language that can express sentences like "Alice knows that everybody knows that she is pretty", explore the mathematical concept of quantum Turing machine, and illustrate some characteristic examples that arise in the framework of musical languages. The book concludes with an analysis of recent discussions, and contains a Mathematical Appendix which is a survey of the definitions of all main mathematical concepts used in the book.