'Electrifying ... A user manual for our polarized world' Adam Grant, #1 New York Times-bestselling author of Think Again By a two-time debating world champion, a dazzling look at how arguing better can transform your life - and the world - for the better Everyone debates, in some form, most days. Sometimes we do it to persuade; other times to learn, discover a truth, or simply to express something about ourselves. We argue to defend ourselves, our work, and our loved ones from external threat. We do it to get our way, or just to get ahead. As a two-time debating world champion, Bo has made a career out of arguing. Over the past few years, however, he's noticed how we're not only arguing more and more, but getting worse at it - a fact proven by our polarised politics. By tracing his own journey from immigrant kid to world champion, as well as those of illustrious participants in the sport such as Malcolm X, Edmund Burke and Sally Rooney, Seo shows how the skills of debating - information gathering, truth finding, lucidity, organization, and persuasion - are often the cornerstone of successful careers and happy lives. Along the way, he provides the reader with an unforgettable toolkit to use debate as a means to improve their own. This book is an everyperson's guide to disagreeing well, so that the outcome of having had an argument is better than not having it at all. Taking readers on a thrilling intellectual adventure into the eccentric and brilliant subculture of competitive debate, The Art of Disagreeing Well proves that good-faith debate can enrich and improve our lives, friendships, democracies and in the process, our world.

This book represents a major contribution to game theory. It offers this conception of equilibrium in games: strategic equilibrium. This conception arises from a study of expected utility decision principles, which must be revised to take account of the evidence a choice provides concerning its outcome. The argument for these principles distinguishes reasons for action from incentives, and draws on contemporary analyses of counterfactual conditionals. The book also includes a procedure for identifying strategic equilibria in ideal normal-form games. In synthesizing decision theory and game theory in a powerful way this book will be of particular interest to all philosophers concerned with decision theory and game theory as well as economists and other social scientists.

Over the past few years, the tree model of time has been widely employed to deal with issues concerning the semantics of tensed discourse. The thought that has motivated its adoption is that the most plausible way to make sense of indeterminism is to conceive of future possibilities as branches that depart from a common trunk, constituted by the past and the present. However, the thought still needs to be further articulated and defended, and several important questions remain open, such as the question of how actuality can be understood and formally represented in a branching framework. The present volume is intended to be a 360 degree reflection on the tree model. The contributions is gathers concern the model and its alternatives, both from a semantic and from a metaphysical point of view. "

This volume tells the story of the legacy and impact of the great German polymath Gottfried Wilhelm Leibniz (1646-1716). Leibniz made significant contributions to many areas, including philosophy, mathematics, political and social theory, theology, and various sciences. The essays in this volume explores the effects of Leibniz's profound insights on subsequent generations of thinkers by tracing the ways in which his ideas have been defended and developed in the three centuries since his death. Each of the 11 essays is concerned with Leibniz's legacy and impact in a particular area, and between them they show not just the depth of Leibniz's talents but also the extent to which he shaped the various domains to which he contributed, and in some cases continues to shape them today. With essays written by experts such as Nicholas Jolley, Pauline Phemister, and Philip Beeley, this volume is essential reading not just for students of Leibniz but also for those who wish to understand the game-changing impact made by one of history's true universal geniuses.

This book is a companion to logical thought and logical thinking in China with a comparative and interdisciplinary perspective. It introduces the basic ideas and theories of Chinese thought in a comprehensive and analytical way. It covers thoughts in ancient, pre-modern and modern China from a historical point of view. It deals with topics in logical (including logico-philosophical) concepts and theories rooted in China, Indian and Western Logic transplanted to China, and the development of logical studies in contemporary China and other Chinese communities. The term "philosophy of logic" or "logico-philosophical thought" is used in this book to represent "logical thought" in a broad sense which includes thinking on logical concepts, modes of reasoning, and linguistic ideas related to logic and philosophical logic. Unique in its approach, the book uses Western logical theories and philosophy of language, Chinese philology, and history of ideas to deal with the basic ideas and major problems in logical thought and logical thinking in China. In doing so, it advances the understanding of the lost tradition in Chinese philosophical studies.

This book introduces the principles of place and time by discussing the main roles they play in argumentation, unpacking the multifarious meanings of spatiality and temporality. Definitions of kairos are explored to yield suggestions as to how this concept, and that of 'place', can operate in argumentation. The chapters explore various related concepts such as the role of different arguments in different places, and how some places are not intended for argument; argumentation, time and temporality; visual argumentation; the effect of the passage of time on argument evaluation; and the image as a site of discursive production. This collection is of interest to students and researchers in argumentation studies, rhetoric, reasoning, and philosophy. Previously published in Argumentation Volume 34, issue 1, March 2020

At the turn of the century, Gottlob Frege and Edmund Husserl both participated in the discussion concerning the foundations of logic and mathematics. Since the 1960s, comparisons have been made between Frege's semantic views and Husserl's theory of intentional acts. In quite recent years, new approaches to the two philosophers' views have appeared. This collection of articles opens with the first English translation of Dagfinn Follesdal's early classic on Husserl and Frege of 1958. The book brings together a number of new contributions by well-known authors and gives a survey of recent developments in the field. It shows that Husserl's thought is coming to occupy a central role in the philosophy of logic and mathematics, as well as in the philosophy of mind and cognitive science. The work is primarily meant for philosophers, especially for those working on the problems of language, logic, mathematics, and mind. It can also be used as a textbook in advanced courses in philosophy. "

This book reconstructs the theory of signification implicit in Aristotle's De Interpretatione and its psychological background in his writing De Anima, a project often envisioned by scholars but never systematically undertaken. I begin by explaining what sort of phonetic material, according to Aristotle, can be a significans and a phone. To that end, I provide a physiological account of which animal sounds count as phone, as well as a psychological evaluation of the cognitive content of the phonai under consideration in De Interpretatione: names, verbs, and assertive sentences. I then turn to noemata, which, for Aristotle, are the psychological reference and significata of names, verbs and assertive sentences. I explain what, for Aristotle, are the logical properties a significatum must have in order to be signified by the phonetic material of a name, verb or assertive sentence, and why noemata can fulfil those logical conditions. Finally, I elucidate the significans-significatum relation without making use of the modern semantic triangle. This approach is consonant with Aristotle's methodology and breaks new ground by exploring the connection between the linguistic and psychological aspects of Aristotle's theory of signification.

This edited collection explores the philosophy of Clarence Irving Lewis through two major concepts that are integral to his conceptual pragmatism: the a priori and the given. The relation between these two elements of knowledge forms the core of Lewis's masterpiece Mind and the World Order . While Lewis's conceptual pragmatism is directed against any conception of the a priori as constraining the mind and experience, it also emphasizes the inalterability and the unavoidability of the given that remains the same through any interpretation of it by the mind. The chapters in this book probe Lewis's new account of the relation between the a priori and the given in dialogue with other notable figures in twentieth-century philosophy, including Goodman, Putnam, Quine, Russell, Sellars, and Sheffer. C.I. Lewis: The A Priori and the Given represents a focused treatment of a longneglected figure in twentieth-century American philosophy.

Gottlob Frege (1848-1925) is considered the father of modern logic and one of the founding figures of analytic philosophy. He was first and foremost a mathematician, but his major works also made important contributions to the philosophy of language. Frege's writings are difficult and deal with technical, abstract concepts. The Routledge Philosophy Guidebook to Frege On Sense and Reference helps the student to get to grips with Frege's thought, and introduces and assesses: the background of Frege's philosophical work Frege's main papers and arguments, focussing on his distinction between sense and reference the continuing importance of Frege's work to philosophy of logic and language. Ideal for those coming to Frege for the first time, and containing fresh insights for anyone interested in his philosophy, this Guidebook is essential reading for all students of philosophy of language, philosophical logic and the history of analytic philosophy.

Originally published in 1967. An introduction to the literature of nonstandard logic, in particular to those nonstandard logics known as many-valued logics. Part I expounds and discusses implicational calculi, modal logics and many-valued logics and their associated calculi. Part II considers the detailed development of various many-valued calculi, and some of the important metathereoms which have been proved for them. Applications of the calculi to problems in the philosophy are also surveyed. This work combines criticism with exposition to form a comprehensive but concise survey of the field.

Originally published in 1966. An introduction to current studies of kinds of inference in which validity cannot be determined by ordinary deductive models. In particular, inductive inference, predictive inference, statistical inference, and decision making are examined in some detail. The last chapter discusses the relationship of these forms of inference to philosophical notions of rationality. Special features of the monograph include a discussion of the legitimacy of various criteria for successful predictive inference, the development of an intuitive model which exhibits the difficulties of choosing probability measures over infinite sets, and a comparison of rival views on the foundations of probability in terms of the amount of information which the members of these schools believe suitable for fruitful formalization. The bibliographies include articles by statisticians accessible to students of symbolic logic.

This book addresses the argument in the history of the philosophy of science between the positivists and the anti-positivists. The author starts from a point of firm conviction that all science and philosophy must start with the given... But that the range of the given is not definite. He begins with an examination of science from the outside and then the inside, explaining his position on metaphysics and attempts to formulate the character of operational acts before a general theory of symbolism is explored. The last five chapters constitute a treatise to show that the development from one stage of symbolismto the next is inevitable, consequently that explanatory science represents the culmination of knowledge.

Originally published in 1973. This book presents a valid mode of reasoning that is different to mathematical probability. This inductive logic is investigated in terms of scientific investigation. The author presents his criteria of adequacy for analysing inductive support for hypotheses and discusses each of these criteria in depth. The chapters cover philosophical problems and paradoxes about experimental support, probability and justifiability, ending with a system of logical syntax of induction. Each section begins with a summary of its contents and there is a glossary of technical terms to aid the reader.

Originally published in 1964. This book is concerned with general arguments, by which is meant broadly arguments that rely for their force on the ideas expressed by all, every, any, some, none and other kindred words or phrases. A main object of quantificational logic is to provide methods for evaluating general arguments. To evaluate a general argument by these methods we must first express it in a standard form. Quantificational form is dealt with in chapter one and in part of chapter three; in the remainder of the book an account is given of methods by which arguments when formulated quantificationally may be tested for validity or invalidity. Some attention is also paid to the logic of identity and of definite descriptions. Throughout the book an attempt has been made to give a clear explanation of the concepts involved and the symbols used; in particular a step-by-step and partly mechanical method is developed for translating complicated statements of ordinary discourse into the appropriate quantificational formulae. Some elementary knowledge of truth-functional logic is presupposed.

The book aims to formalise tableau methods for the logics of propositions and names. The methods described are based on Set Theory. The tableau rule was reduced to an ordered n-tuple of sets of expressions where the first element is a set of premises, and the following elements are its supersets.

This book offers new insights into the nature of human rational capacities by engaging inferentialism with empirical research in the cognitive sciences. Inferentialism advocates that humans' unique kind of intelligence is discursive and rooted in competencies to make, assess and justify claims. This approach provides a rich source of valuable insights into the nature of our rational capacities, but it is underdeveloped in important respects. For example, little attempt has been made to assess inferentialism considering relevant scientific research on human communication, cognition or reasoning. By engaging philosophical and scientific approaches in a productive dialogue, this book shows how we can better understand human rational capacities by comparing their respective strengths and weaknesses. In this vein, the author critically revisits and constructively develops central themes from the work of Robert Brandom and other "language rationalists": the nature of the assertoric practice and its connection to reasoned discourse, the linguistic constitution of the shared space of reasons, the social nature and function of reasoning, the intersubjective roots of social-normative practices and the nature of objective thought. Practices of Reason will be of interest to scholars and advanced students working in philosophy of mind, philosophy of language and philosophy of logic.

How do we think? What does a faithful use of logic look like? Without even pausing to think about it, we exercise our capacity for rational thought. But how exactly does logic work? What makes some arguments valid and others not? In this Questions in Christian Philosophy volume, philosopher Forrest Baird offers an introduction to logic. He considers the basic building blocks of human reason, including types of arguments, fallacies, syllogisms, symbols, and proofs, all of which are demonstrated with exercises for students throughout. In addition, he reflects on the relationship between the use of reason and the Christian faith. With this academic but accessible primer, readers will be introduced to the basics of logic-and encouraged to reason better. The Questions in Christian Philosophy Series features introductory textbooks that offer students a Christian perspective on the various branches of philosophy, enabling them as they seek to understand all facets of life including existence, knowledge, ethics, art, and more.

Originally published in 1965. This is a textbook of modern deductive logic, designed for beginners but leading further into the heart of the subject than most other books of the kind. The fields covered are the Propositional Calculus, the more elementary parts of the Predicate Calculus, and Syllogistic Logic treated from a modern point of view. In each of the systems discussed the main emphases are on Decision Procedures and Axiomatisation, and the material is presented with as much formal rigour as is compatible with clarity of exposition. The techniques used are not only described but given a theoretical justification. Proofs of Consistency, Completeness and Independence are set out in detail. The fundamental characteristics of the various systems studies, and their relations to each other are established by meta-logical proofs, which are used freely in all sections of the book. Exercises are appended to most of the chapters, and answers are provided.

Originally published in 1973. This book is directed to the student of philosophy whose background in mathematics is very limited. The author strikes a balance between material of a philosophical and a formal kind, and does this in a way that will bring out the intricate connections between the two. On the formal side, he gives particular care to provide the basic tools from set theory and arithmetic that are needed to study systems of logic, setting out completeness results for two, three, and four valued logic, explaining concepts such as freedom and bondage in quantificational logic, describing the intuitionistic conception of the logical operators, and setting out Zermelo's axiom system for set theory. On the philosophical side, he gives particular attention to such topics as the problem of entailment, the import of the Loewenheim-Skolem theorem, the expressive powers of quantificational logic, the ideas underlying intuitionistic logic, the nature of set theory, and the relationship between logic and set theory. There are exercises within the text, set out alongside the theoretical ideas that they involve.

Originally published in 1962. This book gives an account of the concepts and methods of a basic part of logic. In chapter I elementary ideas, including those of truth-functional argument and truth-functional validity, are explained. Chapter II begins with a more comprehensive account of truth-functionality; the leading characteristics of the most important monadic and dyadic truth-functions are described, and the different notations in use are set forth. The main part of the book describes and explains three different methods of testing truth-functional aguments and agument forms for validity: the truthtable method, the deductive method and the method of normal forms; for the benefit mainly of readers who have not acquired in one way or another a general facility in the manipulation of symbols some of the procedures have been described in rather more detail than is common in texts of this kind. In the final chapter the author discusses and rejects the view, based largely on the so called paradoxes of material implication, that truth-functional logic is not applicable in any really important way to arguments of ordinary discourse.

Originally published in 1968. This is a critical study of the concept of 'rule' featuring in law, ethics and much philosophical analysis which the author uses to investigate the concept of 'rationality'. The author indicates in what manner the modes of reasoning involved in reliance upon rules are unique and in what fashion they provide an alternative both to the modes of logico-mathematical reasoning and to the modes of scientific reasoning. This prepares the groundwork for a methodology meeting the requirements of the fields using rules such as law and ethics which could be significant for communications theory and the use of computers in normative fields. Other substantive issues related to the mainstream of legal philosophy are discussed - theories of interpretation, the notion of purpose and the requirements of principled decision-making. The book utilizes examples drawn from English and American legal decisions to suggest how the positions of legal positivism and of natural law are equally artificial and misleading.

Originally published in 1962. A clear and simple account of the growth and structure of Mathematical Logic, no earlier knowledge of logic being required. After outlining the four lines of thought that have been its roots - the logic of Aristotle, the idea of all the parts of mathematics as systems to be designed on the same sort of plan as that used by Euclid and his Elements, and the discoveries in algebra and geometry in 1800-1860 - the book goes on to give some of the main ideas and theories of the chief writers on Mathematical Logic: De Morgan, Boole, Jevons, Pierce, Frege, Peano, Whitehead, Russell, Post, Hilbert and Goebel. Written to assist readers who require a general picture of current logic, it will also be a guide for those who will later be going more deeply into the expert details of this field.

Originally published in 1985. This book is about a single famous line of argument, pioneered by Descartes and deployed to full effect by Kant. That argument was meant to refute scepticism once and for all, and make the world safe for science. 'I think, so I exist' is valid reasoning, but circular as proof. In similar vein, Kant argues from our having a science of geometry to Space being our contribution to experience: a different conclusion, arrived at by a similar fallacy. Yet these arguments do show something: that certain sets of opinions, if professed, show an inbuilt inconsistency. It is this second-strike capacity that has kept transcendental arguments going for so long. Attempts to re-build metaphysics by means of such transcendental reasoning have been debated. This book offers an introduction to the field, and ventures its own assessment, in non-technical language, without assuming previous training in logic or philosophy.