This comprehensive account of the concept and practices of deduction is the first to bring together perspectives from philosophy, history, psychology and cognitive science, and mathematical practice. Catarina Dutilh Novaes draws on all of these perspectives to argue for an overarching conceptualization of deduction as a dialogical practice: deduction has dialogical roots, and these dialogical roots are still largely present both in theories and in practices of deduction. Dutilh Novaes' account also highlights the deeply human and in fact social nature of deduction, as embedded in actual human practices; as such, it presents a highly innovative account of deduction. The book will be of interest to a wide range of readers, from advanced students to senior scholars, and from philosophers to mathematicians and cognitive scientists.

The perception of what he calls 'aspects' preoccupied Wittgenstein and gave him considerable trouble in his final years. The Wittgensteinian aspect defies any number of traditional philosophical dichotomies: the aspect is neither subjective (inner, metaphysically private) nor objective; it presents perceivable unity and sense that are (arguably) not (yet) conceptual; it is 'subject to the will', but at the same time is normally taken to be genuinely revelatory of the object perceived under it. This Element begins with a grammatical and phenomenological characterization of Wittgensteinian 'aspects'. It then challenges two widespread ideas: that aspects are to be identified with concepts; and that aspect perception has a continuous version that is characteristic of (normal) human perception. It concludes by proposing that aspect perception brings to light the distinction between the world as perceived and the world as objectively construed, and the role we play in the constitution of the former.

The purpose of this book is to present unpublished papers at the cutting edge of research on dialetheism and to reflect recent work on the applications of the theory. It includes contributions from some of the most respected scholars in the field, as well as from young, up-and-coming philosophers working on dialetheism. Moving from the fringes of philosophy to become a main player in debates concerning truth and the logical paradoxes, dialetheism has thrived since the publication of Graham Priest's In Contradiction, and several of the papers find their roots in a conference on dialetheism held in Glasgow to mark the 25th anniversary of Priest's book. The content presented here demonstrates the considerable body of work produced in this field in recent years. With a broad focus, this book also addresses the applications of dialetheism outside the more familiar area of the logical paradoxes, and includes pieces discussing the application of dialetheism in metaphysics, philosophy of language, and philosophy of mind.

W. V. Quine was one of the most influential figures of twentieth-century American analytic philosophy. Although he wrote predominantly in English, in Brazil in 1942 he gave a series of lectures on logic and its philosophy in Portuguese, subsequently published as the book O Sentido da Nova Logica. The book has never before been fully translated into English, and this volume is the first to make its content accessible to Anglophone philosophers. Quine would go on to develop revolutionary ideas about semantic holism and ontology, and this book provides a snapshot of his views on logic and language at a pivotal stage of his intellectual development. The volume also includes an essay on logic which Quine also published in Portuguese, together with an extensive historical-philosophical essay by Frederique Janssen-Lauret. The valuable and previously neglected works first translated in this volume will be essential for scholars of twentieth-century philosophy.

In A Companion to David Lewis, Barry Loewer and Jonathan Schaffer bring together top philosophers to explain, discuss, and critically extend Lewis's seminal work in original ways. Students and scholars will discover the underlying themes and complex interconnections woven through the diverse range of his work in metaphysics, philosophy of language, logic, epistemology, philosophy of science, philosophy of mind, ethics, and aesthetics. * The first and only comprehensive study of the work of David Lewis, one of the most systematic and influential philosophers of the latter half of the 20th century * Contributions shed light on the underlying themes and complex interconnections woven through Lewis's work across his enormous range of influence, including metaphysics, language, logic, epistemology, science, mind, ethics, and aesthetics * Outstanding Lewis scholars and leading philosophers working in the fields Lewis influenced explain, discuss, and critically extend Lewis's work in original ways * An essential resource for students and researchers across analytic philosophy that covers the major themes of Lewis's work

Plural predication is a pervasive part of ordinary language. We can say that some people are fifty in number, are surrounding a building, come from many countries, and are classmates. These predicates can be true of some people without being true of any one of them; they are non-distributive predications. Yet the apparatus of predication and quantification in standard modern logic does not allow a place for such non-distributive predicates. Thomas McKay's book explores the enrichment of modern logic with plural predication and quantification. We can have genuinely non-distributive predication without relying on singularizing procedures from set theory and mereology. The fundamental 'among' relation can be understood in a way that does not generate any hierarchy of plurals analogous to a hierarchy of types or a hierarchy of higher-order logics. Singular quantification can be understood as a special case, with the general type being quantifiers that allow both singular and plural quantification. The 'among' relation is formally similar to a 'part of' relation, but the relations are distinct, so that mass quantification and plural quantification cannot be united in the same way that plural and singular are united. Analysis of singular and plural definite descriptions follows, with a defense of a fundamentally Russellian analysis, but coupled with some new ideas about how to be sensitive to the role of context. This facilitates an analysis of some central features of the use of pronouns, both singular and plural.

In the past 15 years a host of critical thinking books have appeared that teach students to find flaws in the arguments of others by learning to detect a number of informal fallacies. This book is not in that tradition. The authors of this book believe that while students learn to become vicious critics, they still continue to make the very mistakes they criticize in others. Thus, this book has adopted the approach of teaching the construction of good arguments first and then introducing criticism as a secondary skill. Moreover, the emphasis of the book is not on learning to name fallacies, but on being able to identify weaknesses in an argument so as to be able to construct an effective critique of that argument. The book is accompanied by a workbook featuring a wealth of examples to help students acquire the material.

This book aims to lay bare the logical foundations of tractable reasoning. It draws on Marvin Minsky's seminal work on frames, which has been highly influential in computer science and, to a lesser extent, in cognitive science. Only very few people have explored ideas about frames in logic, which is why the investigation in this book breaks new ground. The apparent intractability of dynamic, inferential reasoning is an unsolved problem in both cognitive science and logic-oriented artificial intelligence. By means of a logical investigation of frames and frame concepts, Andreas devises a novel logic of tractable reasoning, called frame logic. Moreover, he devises a novel belief revision scheme, which is tractable for frame logic. These tractability results shed new light on our logical and cognitive means to carry out dynamic, inferential reasoning. Modularity remains central for tractability, and so the author sets forth a logical variant of the massive modularity hypothesis in cognitive science. This book conducts a sustained and detailed examination of the structure of tractable and intelligible reasoning in cognitive science and artificial intelligence. Working from the perspective of formal epistemology and cognitive science, Andreas uses structuralist notions from Bourbaki and Sneed to provide new foundational analyses of frames, object-oriented programming, belief revision, and truth maintenance. Andreas then builds on these analyses to construct a novel logic of tractable reasoning he calls frame logic, together with a novel belief revision scheme that is tractable for frame logic. Put together, these logical analyses and tractability results provide new understandings of dynamic and inferential reasoning. Jon Doyle, North Carolina State University

A relative change occurs when some item changes a relation. This Element examines how Plato, Aristotle, Stoics and Sextus Empiricus approached relative change. Relative change is puzzling because the following three propositions each seem true but cannot be true together: (1) No relative changes are intrinsic changes; (2) Only intrinsic changes are proper changes; (3) Some relative changes are proper changes. Plato's Theaetetus and Phaedo property relative change. I argue that these dialogues assume relative changes to be intrinsic changes, so denying (1). Aristotle responds differently, by denying (3) that relative change is proper change. The Stoics claimed that some non-intrinsic changes are changes (denying (2)). Finally, I discuss Sextus' argument that relative change shows that there are no relatives at all.

For more than six decades, and for thousands of students, Introduction to Logic has been the gold standard in introductory logic texts. In this fifteenth edition, Carl Cohen and Victor Rodych update Irving M. Copi's classic text, improving on its many strengths and introducing new and helpful material that will greatly assist both students and instructors. In particular, chapters 1, 8, and 9 have been greatly enhanced without disturbing the book's clear and gradual pedagogical approach. Specifically: Chapter 1 now uses a simpler and better definition of "deductive validity," which enhances the rest of the book (especially chapters 1 and 8-10, and their new components). Chapter 8 now has: Simpler definitions of "simple statement" and "compound statement" More and more detailed examples of the Complete Truth-Table Method. Chapter 9 now has: A detailed, step-by-step account of the Shorter Truth-Table Method (with detailed step-by-step examples for conclusions of different types) A more complete and detailed account of Indirect Proof A detailed justification for Indirect Proof treating each of the three distinct ways in which an argument can be valid A new section on Conditional Proof, which complements the 19 Rules of Inference and Indirect Proof Explications of proofs of tautologies using both Indirect Proof and Conditional Proof A new section at the end of the chapter explaining the important difference between sound and demonstrative arguments. The Appendices now include: A new appendix on making the Shorter Truth-Table Technique (STTT) more efficient by selecting the most efficient sequence of STTT steps A new appendix on Step 1 calculations for multiple-line shorter truth tables A new appendix on unforced truth-value assignments, invalid arguments, and Maxims III-V. In addition, a Companion Website will offer: for Students: A Proof Checker Complete Truth Table Exercises Shorter Truth-Table Exercises A Truth-Table Video Venn Diagram Testing of Syllogisms Hundreds of True/False and Multiple Choice Questions for Instructors: An Instructor's Manual A Solutions Manual www.routledge.com/cw/9781138500860

Our beliefs come in degrees. I'm 70% confident it will rain tomorrow, and 0.001% sure my lottery ticket will win. What's more, we think these degrees of belief should abide by certain principles if they are to be rational. For instance, you shouldn't believe that a person's taller than 6ft more strongly than you believe that they're taller than 5ft, since the former entails the latter. In Dutch Book arguments, we try to establish the principles of rationality for degrees of belief by appealing to their role in guiding decisions. In particular, we show that degrees of belief that don't satisfy the principles will always guide action in some way that is bad or undesirable. In this Element, we present Dutch Book arguments for the principles of Probabilism, Conditionalization, and the Reflection Principle, among others, and we formulate and consider the most serious objections to them.

This volume gathers selected papers presented at the Fourth Asian Workshop on Philosophical Logic, held in Beijing in October 2018. The contributions cover a wide variety of topics in modal logic (epistemic logic, temporal logic and dynamic logic), proof theory, algebraic logic, game logics, and philosophical foundations of logic. They also reflect the interdisciplinary nature of logic - a subject that has been studied in fields as diverse as philosophy, linguistics, mathematics, computer science and artificial intelligence. More specifically. The book also presents the latest developments in logic both in Asia and beyond.

This book reports on cutting-edge research concerning social practices. Merging perspectives from various disciplines, including philosophy, biology, and cognitive science, it discusses theoretical aspects of social behavior along with models to investigate them, and also presents key case studies. Further, It describes concepts related to habits, routines, and rituals and examines important features of human action, such as intentionality and choice, exploring the influence of specific social practices in different situations. Based on a workshop held in June 2018 at the 6th World Congress of Universal Logic, UNILOG2018, in Vichy, and including additional invited chapters, the book offers fresh insights into the fields of social practice and the cognitive, computational, and philosophical tools to understand them.

Wittgenstein's 'middle period' is often seen as a transitional phase connecting his better-known early and later philosophies. The fifteen essays in this volume focus both on the distinctive character of his teaching and writing in the 1930s, and on its pivotal importance for an understanding of his philosophy as a whole. They offer wide-ranging perspectives on the central issue of how best to identify changes and continuities in his philosophy during those years, as well as on particular topics in the philosophy of mind, religion, ethics, aesthetics, and the philosophy of mathematics. The volume will be valuable for all who are interested in this formative period of Wittgenstein's development.

This edited book focuses on non-classical logics and their applications, highlighting the rapid advances and the new perspectives that are emerging in this area. Non-classical logics are logical formalisms that violate or go beyond classical logic laws, and their specific features make them particularly suited to describing and reason about aspects of social interaction. The richness and diversity of non-classical logics mean that this area is a natural catalyst for ideas and insights from many different fields, from information theory to game theory and business science. This volume is the post-proceedings of the 8th International Conference on Logic and Cognition, held at Sun Yat-Sen University Institute of Logic and Cognition (ILC) in Guangzhou, China in December 2016. The conference series started in 2001, and is organized by the ILC, often in collaboration with various international research groups. This eighth installment was jointly organized by ILC and Alessandra Palmigiano's Applied Logic research group. The conference series aims to foster the development of effective logical tools to study social behavior from a philosophical, cognitive and formal perspective in order to challenge the field of logic in ways that open up new and exciting research directions. Chapter "The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms" of this book is available open access under a CC BY 4.0 license at link.springer.com

I have been thinking about the philosophical issue of truth for more than two decades. It is one of several fascinating philosophical issues that motivated me to change my primary re ective interest to philosophy after receiving BS in mathem- ics in 1982. Some serious academic work in this connection started around the late eighties when I translated into Chinese a dozen of Donald Davidson's representative essays on truth and meaning and when I assumed translator for Adam Morton who gave a series of lectures on the issue in Beijing (1988), which was co-sponsored by my then institution (Institute of Philosophy, Chinese Academy of Social Science). I have loved the issue both for its own sake (as one speci c major issue in the phil- ophy of language and metaphysics) and for the sake of its signi cant involvement in many philosophical issues in different subjects of philosophy. Having been attracted to the analytic approach, I was then interested in looking at the issue both from the points of view of classical Chinese philosophy and Marxist philosophy, two major styles or frameworks of doing philosophy during that time in China, and from the point of view of contemporary analytic philosophy, which was then less recognized in the Chinese philosophical circle.

Metamathematics and the Philosophical Tradition is the first work to explore in such historical depth the relationship between fundamental philosophical quandaries regarding self-reference and meta-mathematical notions of consistency and incompleteness. Using the insights of twentieth-century logicians from Goedel through Hilbert and their successors, this volume revisits the writings of Aristotle, the ancient skeptics, Anselm, and enlightenment and seventeenth and eighteenth century philosophers Leibniz, Berkeley, Hume, Pascal, Descartes, and Kant to identify ways in which these both encode and evade problems of a priori definition and self-reference. The final chapters critique and extend more recent insights of late 20th-century logicians and quantum physicists, and offer new applications of the completeness theorem as a means of exploring "metatheoretical ascent" and the limitations of scientific certainty. Broadly syncretic in range, Metamathematics and the Philosophical Tradition addresses central and recurring problems within epistemology. The volume's elegant, condensed writing style renders accessible its wealth of citations and allusions from varied traditions and in several languages. Its arguments will be of special interest to historians and philosophers of science and mathematics, particularly scholars of classical skepticism, the Enlightenment, Kant, ethics, and mathematical logic.

This book presents the research achievements of Jin Yuelin, the first logician and a prominent philosopher in China, who founded a new philosophical system combining elements from Western and Chinese philosophical traditions, especially the concept of Tao. It consists of three sections: the first section interprets Jin's studies on Chinese philosophy, Russell's ideology and other general discussions in the field; section 2 includes Jin's studies on logic, which made him the founding father of modern logic in China; and section 3 presents Jin's ideas on politics, including his studies on Thomas Hill Green.

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 is a collection of, mostly unpublished, papers on topics surrounding decision theory. It addresses the most important areas in the philosophical study of rationality and knowledge, for example: causal vs. evidential decision theory, game theory, backwards induction, bounded rationality, counterfactual reasoning in games and in general, and analyses of the famous common knowledge assumptions in game theory.

We talk about irrationality when behaviour defies explanation or prediction, when decisions are driven by emotions or instinct rather than by reflection, when reasoning fails to conform to basic principles of logic and probability, and when beliefs lack coherence or empirical support. Depending on the context, agents exhibiting irrational behaviour may be described as foolish, ignorant, unwise or even insane. In this clear and engaging introduction to current debates on irrationality, Lisa Bortolotti presents the many facets of the concept and offers an original account of the importance of judgements of irrationality as value judgements. The book examines the standards against which we measure human behaviour, and reviews the often serious implications of judgements of irrationality for ethics and policy. Bortolotti argues that we should adopt a more critical stance towards accepted standards of rationality in the light of the often surprising outcomes of philosophical inquiry and cognitive science research into decision making. Irrationality is an accessible guide to the concept and will be essential reading for students and scholars interested in the limitations of human cognition and human agency.

In this book we deal with combinations of concepts defining individuals in the Talmud. Consider for example Yom Kippur and Shabbat. Each concept has its own body of laws. Reality forces us to combine them when they occur on the same day. This is a case of "Identity Merging." As the combined body of laws may be inconsistent, we need a belief revision mechanism to reconcile the conflicting norms. The Talmud offers three options: 1 Take the union of the sets of the rules side by side 2. Resolve the conflicts using further meta-level Talmudic principles (which are new and of value to present day Artificial Intelligence) 3. Regard the new combined concept as a new entity with its own Halachic norms and create new norms for it out of the existing ones. This book offers a clear and precise logical model showing how the Talmud deals with these options.

This edited book brings together research work in the field of constructive semantics with scholarship on the phenomenological foundations of logic and mathematics. It addresses one of the central issues in the epistemology and philosophy of mathematics, namely the relationship between phenomenological meaning constitution and constructive semantics. Contributing authors explore deep structural connections and fundamental differences between phenomenology and constructivism. Papers are drawn from contributions to a prestigious workshop held at the University of Friedrichshafen. Readers will discover insight into structural connections between the phenomenological concept of meaning constitution and constructivist concepts of meaning. Discussion ranges from more specific conceptualizations in the philosophy of logic and mathematics to more general considerations in epistemology, inferential semantics and phenomenology. Questions such as a possible phenomenological understanding of the relationship between structural rules and particle rules in dialogical logic are explored. Significant aspects of both phenomenology and dialectics, and dialectics and constructivism emerge. Graduates and researchers of philosophy, especially logic, as well as scholars of mathematics will all find something of interest in the expert insights presented in this volume.

THINK ABOUT IT, International Edition aims to help users become more critical, active, academic thinkers by teaching nine essential intellectual practices that span the university. Beginning with overarching strategies for critical thinking and ending with interactive outlines that guide users into greater development and organization, THINK ABOUT IT, International Edition provides key methods for users to think critically and powerfully.