This anthology of original essays has been nearly .two and one-half years in the making, and reflects the generous effort of many persons. To begin with, we thank the contributors to the volume, who not only cooperated with regards to their own works, but who also provided valuable advice concerning the over-all volume. One of the contributors was outstanding in his assistance and warrants special mention: we thank Professor Michel Meyer, for his encouragement, counsel, and dedication to see this project to comple tion. We would also like to thank Professor Jaakko Hintikka for his encouragement and Mrs. Kuipers of Reidel for her patience and under standing along the way. A project such as this could never have been completed without the unique assistance of members of the Department of Communication, Ohio State University: Ms. Kimberly Pasi and Mr. Charles Mawhirtcr. Also, special thanks are due to our graduate research assistant Ms. Susan Jasko, for her proofreading and bibliographic work. The pressures of developing a Festschrift are considerable and could not have been met without the cooperation and enthusiasm of Mrs. Perelman, especially in allowing us to publish Professor Perelman's address to Ohio State University as our introduction."

This is not quite the book I originally intended to write. Since I first felt that linguistic application of categorial grammar merited a system- atic presentation, I have been subject to (what seemed to be) a series of demanding technical and foundational distractions. Inspite of a prej- udice that mathematical elegance was even inconsistent with linguistic practicality, repeated illumination of the latter by the former implied a new perspective on the field, one prompting formal innovation, and some re-examination of methods and goals. This piece collects and extends work over the last four years general- ising categorial grammar to a categorial logic. The state of the art at the beginning of that period was represented by the edited collections Oehrle, Bach and Wheeler (1988) and Buszkowski, Marciszewski and van Benthem (1988) (see Morrill 1991a, b), and by Moortgat (1988b). Familiarity with such work however is not strictly necessary for an un- derstanding of the present one, which attempts to map a self-contained, if intensive, course with Montague Grammar as its point of departure. This being the case, the reader should have an understanding of logical semantics and its technicalities, such as would be obtained from Dowty, Wall and Peters (1981), or Gamut (1991). Some familiarity with the issues raised by contemporary syntactic theories would also be useful, as would some familiarity with logical deduction.

This volume contains English translations of Frege's early writings in logic and philosophy and of relevant reviews by other leading logicians. Professor Bynum has contributed a biographical essay, introduction, and extensive bibliography.

A comprehensive survey of Martin-Loef's constructive type theory, considerable parts of which have only been presented by Martin-Loef in lecture form or as part of conference talks. Sommaruga surveys the prehistory of type theory and its highly complex development through eight different stages from 1970 to 1995. He also provides a systematic presentation of the latest version of the theory, as offered by Martin-Loef at Leiden University in Fall 1993. This presentation gives a fuller and updated account of the system. Earlier, brief presentations took no account of the issues related to the type-theoretical approach to logic and the foundations of mathematics, while here they are accorded an entire part of the book. Readership: Comprehensive accounts of the history and philosophy of constructive type theory and a considerable amount of related material. Readers need a solid background in standard logic and a first, basic acquaintance with type theory.

Action is conceived of as an intentional behavior of an individual or of an institutional subject; it is determined by information processing, namely by a process in which pieces of descriptive and practical information are involved. Action is explained by a formal and finalistic theory which is connected with a specific theory of institutions. The philosophical basis of the logic of norm sentences and of other systems of practical thinking (formal teleology, axiology, logic of preferences) is discussed. The author criticizes traditional deontic logic and argues in favor of a genuine logic of norms. The book gives a structure analysis of the so-called practical inference and of nomic causal propositions. Besides a critical account of von Wright's practical philosophy the author offers critical analyses of discourse rationality (Habermas, Apel, Alexy) and of Wittgenstein's views on philosophizing. The book addresses readers interested in philosophical logic, practical philosophy, sociology of institutions, legal philosophy, and theory democracy.

"Exposes the vast gap between the actual science underlying AI and the dramatic claims being made for it." -John Horgan "If you want to know about AI, read this book...It shows how a supposedly futuristic reverence for Artificial Intelligence retards progress when it denigrates our most irreplaceable resource for any future progress: our own human intelligence." -Peter Thiel Ever since Alan Turing, AI enthusiasts have equated artificial intelligence with human intelligence. A computer scientist working at the forefront of natural language processing, Erik Larson takes us on a tour of the landscape of AI to reveal why this is a profound mistake. AI works on inductive reasoning, crunching data sets to predict outcomes. But humans don't correlate data sets. We make conjectures, informed by context and experience. And we haven't a clue how to program that kind of intuitive reasoning, which lies at the heart of common sense. Futurists insist AI will soon eclipse the capacities of the most gifted mind, but Larson shows how far we are from superintelligence-and what it would take to get there. "Larson worries that we're making two mistakes at once, defining human intelligence down while overestimating what AI is likely to achieve...Another concern is learned passivity: our tendency to assume that AI will solve problems and our failure, as a result, to cultivate human ingenuity." -David A. Shaywitz, Wall Street Journal "A convincing case that artificial general intelligence-machine-based intelligence that matches our own-is beyond the capacity of algorithmic machine learning because there is a mismatch between how humans and machines know what they know." -Sue Halpern, New York Review of Books

Graham Priest presents an original exploration of philosophical questions concerning the one and the many. He covers a wide range of issues in metaphysics-including unity, identity, grounding, mereology, universals, being, intentionality, and nothingness-and deploys the techniques of paraconsistent logic in order to offer a radically new treatment of unity. Priest brings together traditions of Western and Asian thought that are usually kept separate in academic philosophy: he draws on ideas from Plato, Heidegger, and Nagarjuna, among other philosophers.

The first Symposium consisted of three people in a cafe in Warsaw in 1973. Since then, meetings have grown in size and have been held in Leyden, Copenhagen, Nijmegen, Rome, Oxford, Poitiers and Freiburg am-Breisgau. The ninth Symposium was held in St Andrews in June 1990, with 57 participants who listened to addresses by 28 speakers. It was very fitting that Scotland's oldest university, founded in the heyday of medievalleaming in 1411, should have been given the chance to bring together scholars from all over Europe and beyond to present their researches on the glorious past of scholastic rational thought. The topic of the Symposium was "Sophisms in Medieval Logic and Grammar." The present volume consists, for the most part, of the papers presented at the Symposium. In fact, however, it proved impossible to include five of the contributions. Two of the papers included here were intended for the Symposium but in the event not delivered, because of the unavoidable absence of the speakers. The Symposium received very helpful financial support from one of the major philosophical associations in Britain, the Mind Association, from the Philosophical Quarterly, a journal published at St Andrews, from the University of St Andrews, from the British Academy, and from Low and Bonarplc. In organising the programme for the conference and in preparing the papers for publication I received invaluable help from: Professor E.J."

The goal of this work is twofold. First, it aims to account for double genitive constructions in Serbian. Second, it aims to re-evaluate the DP hypothesis in light of their existence in Serbian. Based on evidence from the categorial status of possessives, argumenthood in the nominal domain, the morphosyntactic structure of nominalizations, and the assignment of the genitive case, it is argued that DP projection must be assumed in Serbian.

Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas.
This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical.
The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.

This volume deals with the connection between thinking-and-speaking and our form(s) of life. All contributions engage with Wittgenstein's approach to this topic. As a whole, the volume takes a stance against both biological and ethnological interpretations of the notion "form of life" and seeks to promote a broadly logico-linguistic understanding instead. The structure of this book is threefold. Part one focuses on lines of thinking that lead from Wittgenstein's earlier thought to the concept of form of life in his later work. Contributions to part two examine the concrete philosophical function of this notion as well as the ways in which it differs from cognate concepts. Contributions to part three put Wittgenstein's notion of form of life in perspective by relating it to phenomenology, ordinary language philosophy and problems in contemporary analytic philosophy.

This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three "dogmas of proof-theoretic semantics" are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.

Why is it so hard to learn critical thinking skills? Traditional textbooks focus almost exclusively on logic and fallacious reasoning, ignoring two crucial problems. As psychologists have demonstrated recently, many of our mistakes are not caused by formal reasoning gone awry, but by our bypassing it completely. We instead favor more comfortable, but often unreliable, intuitive methods. Second, the evaluation of premises is of fundamental importance, especially in this era of fake news and politicized science. This highly innovative text is psychologically informed, both in its diagnosis of inferential errors, and in teaching students how to watch out for and work around their natural intellectual blind spots. It also incorporates insights from epistemology and philosophy of science that are indispensable for learning how to evaluate premises. The result is a hands-on primer for real world critical thinking. The authors bring over four combined decades of classroom experience and a fresh approach to the traditional challenges of a critical thinking course: effectively explaining the nature of validity, assessing deductive arguments, reconstructing, identifying and diagramming arguments, and causal and probabilistic inference. Additionally, they discuss in detail, important, frequently neglected topics, including testimony, the nature and credibility of science, rhetoric, and dialectical argumentation. Key Features and Benefits: Uses contemporary psychological explanations of, and remedies for, pervasive errors in belief formation. There is no other critical thinking text that generally applies this psychological approach. Assesses premises, notably premises based on the testimony of others, and evaluation of news and other information sources. No other critical thinking textbook gives detailed treatment of this crucial topic. Typically, they only provide a few remarks about when to accept expert opinion / argument from authority. Carefully explains the concept of validity, paying particular attention in distinguishing logical possibility from other species of possibility, and demonstrates how we may mistakenly judge invalid arguments as valid because of belief bias. Instead of assessing an argument's validity using formal/mathematical methods (i.e., truth tables for propositional logic and Venn diagrams for categorical logic), provides one technique that is generally applicable: explicitly showing that it is impossible to make the conclusion false and the premises true together. For instructors who like the more formal approach, the text also includes standard treatments using truth tables and Venn diagrams. Uses frequency trees and the frequency approach to probability more generally, a simple method for understanding and evaluating quite complex probabilistic information Uses arguments maps, which have been shown to significantly improve students' reasoning and argument evaluation

Essays on Husserl's Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl's work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl's by considering their reception and elaboration by some of his disciples and followers, such as Oskar Becker and Jacob Klein, as well as their influence on some of the most significant logicians and mathematicians of the past century, such as Luitzen E. J. Brouwer, Rudolf Carnap, Kurt Goedel and Hermann Weyl. Most of the papers consider Husserl and another scholar - e.g. Leibniz, Kant, Bolzano, Brentano, Cantor, Frege - and trace out and contextualize lines of influence, points of contact, and points of disagreement. Each essay is written by an expert of the field, and the volume includes contributions both from the analytical tradition and from the phenomenological one.

Poland has played an enormous role in the development of mathematical logic. Leading Polish logicians, like Lesniewski, Lukasiewicz and Tarski, produced several works related to philosophical logic, a field covering different topics relevant to philosophical foundations of logic itself, as well as various individual sciences. This collection presents contemporary Polish work in philosophical logic which in many respects continue the Polish way of doing philosophical logic. This book will be of interest to logicians, mathematicians, philosophers, and linguists.

Aristotle's modal syllogistic has been an object of study ever since the time of Theophrastus; but these studies (apart from an intense flowering in the Middle Ages) have been somewhat desultory. Remarkably, in the 1990s several new lines of research have appeared, with series of original publications by Fred Johnson, Richard Patterson and Ulrich Nortmann. Johnson presented for the first time a formal semantics adequate to a de re reading of the apodeictic syllogistic; this was based on a simple intuition linking the modal syllogistic to Aristotelian metaphysics. Nortmann developed an ingenious de dicto analysis. Patterson articulated the links (both theoretical and genetic) between the modal syllogistic and the metaphysics, using an analysis which strictly speaking is neither de re nor de dicto. My own studies in this field date from 1976, when my colleague Peter Roeper and I jointly wrote a paper "Aristotle's apodeictic syllogisms" for the XXIInd History of Logic Conference in Krakow. This paper contained the disjunctive reading of particular affirmative apodeictic propositions, which I still favour. Nonetheless, I did not consider that paper's results decisive or comprehensive enough to publish, and my 1981 book The Syllogism contained no treatment of the modal syllogism. The paper's ideas lay dormant till 1989, when I read Johnson's and Patterson's initial articles. I began publishing on the topic in 1991. Gradually my thoughts acquired a certain comprehensiveness and systematicity, till in 1993 I was able to take a semester's sabbatical to write up a draft of this book.

The distinguished scholar of ancient philosophy J.L. Ackrill here presents the best of his essays on Plato and Aristotle from the past forty years. He brings philosophical acuity and philological expertise to a range of texts and topics in ancient thought - from ethics and logic to epistemology and metaphysics - which continue to be widely discussed today.

This volume is a culmination of years of development, and the first to introduce the concepts of superoptimum evaluative and explanatory reasoning. Stuart Nagel's new Quorum book will help academic and practicing attorneys in two important ways. First, by understanding evaluative reasoning, they will gain a better grasp of the appropriate behavior to be adopted if they wish to achieve certain desired goals. Second, by understanding the elements of explanatory reasoning, they will understand how and why decisions are reached.

Evaluative reasoning can take several forms. It can help decision-makers select from among several public policy choices. It can enhance individual decision-making and provide means to allocate scarce resources. It can also assist in advocating and influencing decisions, mediating disputes, representing divergent viewpoints, and in assigning people to specific tasks. Explanatory reasoning, on the other hand, will help explain public policy making, and assist users in generalizing from cases and facts, and in understanding relationships. The purpose of explanatory reasoning is also to explain why superoptimum solutions are infrequently adopted and why they are seldom successfully implemented. The use of both kinds of reasoning, says Nagel, are particularly important to those who want a better understanding and want to improve the legal system.

Temporal Logic: From Ancient Ideas to Artificial Intelligence deals with the history of temporal logic as well as the crucial systematic questions within the field. The book studies the rich contributions from ancient and medieval philosophy up to the downfall of temporal logic in the Renaissance. The modern rediscovery of the subject, which is especially due to the work of A. N. Prior, is described, leading into a thorough discussion of the use of temporal logic in computer science and the understanding of natural language. Temporal Logic: From Ancient Ideas to Artificial Intelligence thus interweaves linguistic, philosophical and computational aspects into an informative and inspiring whole.

Propositional Logics presents the history, philosophy, and mathematics of the major systems of propositional logic. Classical logic, modal logics, many-valued logics, intuitionism, paraconsistent logics, and dependent implication are examined in separate chapters. Each begins with a motivation in the originators' own terms, followed by the standard formal semantics, syntax, and completeness theorem. The chapters on the various logics are largely self-contained so that the book can be used as a reference. An appendix summarizes the formal semantics and axiomatizations of the logics. The view that unifies the exposition is that propositional logics comprise a spectrum. As the aspect of propositions under consideration varies, the logic varies. Each logic is shown to fall naturally within a general framework for semantics. A theory of translations between logics is presented that allows for further comparisons, and necessary conditions are given for a translation to preserve meaning. For this third edition the material has been re-organized to make the text easier to study, and a new section on paraconsistent logics with simple semantics has been added which challenges standard views on the nature of consequence relations. The text includes worked examples and hundreds of exercises, from routine to open problems, making the book with its clear and careful exposition ideal for courses or individual study.

Aristotle's modal syllogistic is his study of patterns of reasoning about necessity and possibility. Many scholars think the modal syllogistic is incoherent, a 'realm of darkness'. Others think it is coherent, but devise complicated formal modellings to mimic Aristotle's results. This volume provides a simple interpretation of Aristotle's modal syllogistic using standard predicate logic. Rini distinguishes between red terms, such as 'horse', 'plant' or 'man', which name things in virtue of features those things must have, and green terms, such as 'moving', which name things in virtue of their non-necessary features. By applying this distinction to the "Prior Analytics," Rini shows how traditional interpretive puzzles about the modal syllogistic melt away and the simple structure of Aristotle's own proofs is revealed. The result is an applied logic which provides needed links between Aristotle's views of science and logical demonstration. The volume is particularly valuable to researchers and students of the history of logic, Aristotle's theory of modality, and the philosophy of logic in general.

The articles in this volume deal with the main inferential methods that can be applied to different kinds of experimental evidence. These contributions - accompanied with critical comments - by renowned scholars in the field of philosophy of science aim at removing the traditional opposition between inductivists and deductivists. They explore the different methods of explanation and justification in the sciences in different contexts and with different objectives.
The volume contains contributions on methods of the sciences, especially on induction, deduction, abduction, laws, probability and explanation, ranging from logic, mathematics, natural to the social sciences. They present a highly topical pluralist re-evaluation of methodological and foundational procedures and reasoning, e.g. focusing in Bayesianism and Artificial Intelligence.
They document the second international conference in Vienna on "Induction and Deduction in the Sciences" as part of the Scientific Network on "Historical and Contemporary Perspectives of Philosophy of Science in Europe," funded by the European Science Foundation (ESF).

Fuzzy Sets, Logics and Reasoning about Knowledge reports recent results concerning the genuinely logical aspects of fuzzy sets in relation to algebraic considerations, knowledge representation and commonsense reasoning. It takes a state-of-the-art look at multiple-valued and fuzzy set-based logics, in an artificial intelligence perspective. The papers, all of which are written by leading contributors in their respective fields, are grouped into four sections. The first section presents a panorama of many-valued logics in connection with fuzzy sets. The second explores algebraic foundations, with an emphasis on MV algebras. The third is devoted to approximate reasoning methods and similarity-based reasoning. The fourth explores connections between fuzzy knowledge representation, especially possibilistic logic and prioritized knowledge bases. Readership: Scholars and graduate students in logic, algebra, knowledge representation, and formal aspects of artificial intelligence.