This book is dedicated to the work of Alasdair Urquhart. The book starts out with an introduction to and an overview of Urquhart's work, and an autobiographical essay by Urquhart. This introductory section is followed by papers on algebraic logic and lattice theory, papers on the complexity of proofs, and papers on philosophical logic and history of logic. The final section of the book contains a response to the papers by Urquhart. Alasdair Urquhart has made extremely important contributions to a variety of fields in logic. He produced some of the earliest work on the semantics of relevant logic. He provided the undecidability of the logics R (of relevant implication) and E (of relevant entailment), as well as some of their close neighbors. He proved that interpolation fails in some of those systems. Urquhart has done very important work in complexity theory, both about the complexity of proofs in classical and some nonclassical logics. In pure algebra, he has produced a representation theorem for lattices and some rather beautiful duality theorems. In addition, he has done important work in the history of logic, especially on Bertrand Russell, including editing Volume four of Russell's Collected Papers.

Logic Works is a critical and extensive introduction to logic. It asks questions about why systems of logic are as they are, how they relate to ordinary language and ordinary reasoning, and what alternatives there might be to classical logical doctrines. The book covers classical first-order logic and alternatives, including intuitionistic, free, and many-valued logic. It also considers how logical analysis can be applied to carefully represent the reasoning employed in academic and scientific work, better understand that reasoning, and identify its hidden premises. Aiming to be as much a reference work and handbook for further, independent study as a course text, it covers more material than is typically covered in an introductory course. It also covers this material at greater length and in more depth with the purpose of making it accessible to those with no prior training in logic or formal systems. Online support material includes a detailed student solutions manual with a running commentary on all starred exercises, and a set of editable slide presentations for course lectures. Key Features Introduces an unusually broad range of topics, allowing instructors to craft courses to meet a range of various objectives Adopts a critical attitude to certain classical doctrines, exposing students to alternative ways to answer philosophical questions about logic Carefully considers the ways natural language both resists and lends itself to formalization Makes objectual semantics for quantified logic easy, with an incremental, rule-governed approach assisted by numerous simple exercises Makes important metatheoretical results accessible to introductory students through a discursive presentation of those results and by using simple case studies

The theory of the square of opposition has been studied for over 2,000 years and has seen a resurgence in new theories and research since the second half of the twentieth century. This volume collects papers presented at the Sixth World Congress on the Square of Opposition, held in Crete in 2018, developing an interdisciplinary exploration of the theory. Chapter authors explore subjects such as Aristotle's ontological square, logical oppositions in Avicenna's hypothetical logic, and the power of the square of opposition to solve theological problems regarding predestination and theodicy. Other topics covered include: Hegel's opposition to diagrams De Morgan's unpublished octagon of opposition turnstile figures of opposition institutional model-theoretic treatment of oppositions Lacan's four formulas of sexuation the theory of oppositional poly-simplexes The Exoteric Square of Opposition will appeal to pure logicians, historians of logic, semioticians, philosophers, theologians, mathematicians, and psychoanalysts.

Providing a clear interpretation of Hegel's characterizations of possibility and actuality in the Science of Logic, this book departs from the standard understandings of these concepts to break new ground in Hegelian scholarship. The book draws out some of the implications of Hegel's view of immanent possibility, especially as it relates to Leibniz's thesis of modal optimism: his view that this world is the best of all possible worlds. Reading Hegel as a philosopher of possibility, against a tradition that has conceived of him primarily as a philosopher of necessity, rationality, and finitude, Nahum Brown demonstrates the historical background and philosophical traditions from which Hegel's concept of possibility emerges. Systematically outlining Hegel's conceptions of positive and negative freedom, Brown reveals the Hegelian underpinnings of our conception of reality and what it is to be in the world itself. Original and convincing, this book is crucial for philosophers approaching modality from any tradition.

This volume advances discussion between critics and defenders of the force-content distinction and opens up new ways of thinking about force and speech acts in relation to the unity problem. The force-content dichotomy has shaped the philosophy of language and mind since the time of Frege and Russell. Isn't it obvious that, for example, the clauses of a conditional are not asserted and must therefore be propositions and propositions the forceless contents of forceful acts? But, others have recently asked in response, how can a proposition be a truth value bearer if it is not unified through the forceful act of a subject that takes a position regarding how things are? Can we not instead think of propositions as being inherently forceful, but of force as being cancelled in certain contexts? And what do assertoric, but also directive and interrogative force indicators mean? Force, Content and the Unity of the Proposition will be of interest to researchers working in philosophy of language, philosophical logic, philosophy of mind and linguistics.

Absurdity, time, death-each poses a profound threat to Being, compelling us to face our limits and our finitude. Yet what does it mean to fully realize and experience these threats? Finite Transcendence: Existential Exile and the Myth of Home presents a thoughtful and thorough examination of these challenges and questions, arguing the universality of the realization of finitude in the experience of exile. By tracing the historical presence and experience of notions of "faith" and "exile" in Western thought from the Ancient Greeks to the present, Steven A. Burr demonstrates the character of each as fundamental constitutive components of what it means to be human. The book discusses essential elements of each, culminating in a compelling account of "existential exile" as a definitive name for the human experience of finitude. Burr follows with a comprehensive analysis of the writings of Albert Camus, demonstrating an edifying articulation of, engagement with, and reconciliation of the condition of existential exile. Finally, based on the model suggested in Camus's approach, Burr discusses responses to exile and articulates the meaning of home as the transcendence of exile. Finite Transcendence is a work that will be of great value to anyone working in or studying existentialism, philosophy of religion, hermeneutics, and social theory, as well as to anyone interested in questions of faith and society, religion, or secularity.

This book is the first detailed and focused defense of necessitarianism. The author's original account of necessitarianism encourages a reexamination of commonly held metaphysical positions as well as important issues in other, related areas of philosophy. Necessitarianism is the view that absolutely nothing about the world could have been otherwise in any way, whatsoever. Most philosophers believe that necessitarianism is just plain false and presume that some things could have been otherwise than what they are. In this book, the author argues that necessitarianism is true and the view that some things in the world are contingent-what the author terms contingentarianism-is false. The author assesses various theories of contingency, including the possible worlds theory, combinatorialism, and dispositionalism, and argues that no theory can successfully explain why an entity is such as it is rather than not. She then lays out a case for necessitarianism and provides responses to various objections. The book concludes with an explanation of the ways in which necessitarianism is relevant to issues in ethics, philosophy of mind, and social philosophy. A Case for Necessitarianism will be of interest to scholars and advanced students working in metaphysics, logic, and philosophy of science.

This book uncovers a logical fallacy underlying Afro-Pessimism and provides a formal theory of Articulation, teasing out new reflections on race and Blackness. Afro-Pessimism maintains that Blacks, subject to a subordinate position in society, suffer a cultural death. In this monograph, Victor Peterson rejects this theory, demonstrating that Black subjectivity is inherently multiple, articulating identities appropriate to the contexts in which it finds itself and yet remaining continuous across its individual but not mutually exclusive instantiations. Peterson argues that we should consider the mechanisms that produce the conditions under which individuals obtain positions of either dominance or subordination. By providing a working logical foundation for Articulation theory within cultural studies, Peterson encourages us to rethink the politics of racial identity and subjectivity in contemporary social life. Encouraging critical thought about the arbitrarily determined but instrumentally objective of our global racial order, this book will be of great interest to scholars of Black Studies, sociology, cultural studies, and philosophy.

1. Metaphors and Logic Metaphors are among the most vigorous offspring of the creative mind; but their vitality springs from the fact that they are logical organisms in the ecology of l- guage. I aim to use logical techniques to analyze the meanings of metaphors. My goal here is to show how contemporary formal semantics can be extended to handle metaphorical utterances. What distinguishes this work is that it focuses intensely on the logical aspects of metaphors. I stress the role of logic in the generation and int- pretation of metaphors. While I don't presuppose any formal training in logic, some familiarity with philosophical logic (the propositional calculus and the predicate c- culus) is helpful. Since my theory makes great use of the notion of structure, I refer to it as the structural theory of m etaphor (STM). STM is a semant ic theory of m etaphor : if STM is correct, then metaphors are cognitively meaningful and are n- trivially logically linked with truth. I aim to extend possible worlds semantics to handle metaphors. I'll argue that some sentences in natural languages like English have multiple meanings: "Juliet is the sun" has (at least) two meanings: the literal meaning "(Juliet is the sunkIT" and the metaphorical meaning "(Juliet is the sun)MET". Each meaning is a function from (possible) worlds to truth-values. I deny that these functions are identical; I deny that the metaphorical function is necessarily false or necessarily true.

Western philosophy and science are responsible for constructing some powerful tools of investigation, aiming at discovering the truth, delivering robust explanations, verifying conjectures, showing that inferences are sound and demonstrating results conclusively. By contrast reasoning that depends on analogies has often been viewed with suspicion. Professor Lloyd first explores the origins of those Western ideals, criticises some of their excesses and redresses the balance in favour of looser, admittedly non-demonstrative analogical reasoning. For this he takes examples both from ancient Greek and Chinese thought and from the materials of recent ethnography to show how different ancient and modern cultures have developed different styles of reasoning. He also develops two original but controversial ideas, that of semantic stretch (to cast doubt on the literal/metaphorical dichotomy) and the multidimensionality of reality (to bypass the realism versus relativism and nature versus nurture controversies).

This edited volume brings together 18 state-of-the art essays on pluralism about truth and logic. Parts I and II are dedicated to respectively truth pluralism and logical pluralism, and Part III to their interconnections. Some contributors challenge pluralism, arguing that the nature of truth or logic is uniform. The majority of contributors, however, defend pluralism, articulate novel versions of the view, or contribute to fundamental debates internal to the pluralist camp. The volume will be of interest to truth theorists and philosophers of logic, as well as philosophers interested in relativism, contextualism, metaphysics, philosophy of language, semantics, paradox, epistemology, or normativity.

This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory (CTT). The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning. According to this perspective the emergence of concepts are not only games of giving and asking for reasons (games involving Why-questions), they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How.

Originally published in 1982, this volume examines the sources of British Hegelian thinking, the lines of its development and intellectual relationships among members of the school. The sources in this book include twentieth century Marxians who pioneered the move 'back to Hegel' such as Gramsci and Lukacs. It includes brief biographical entries of the principal British Hegelians and of minor figures wo paved the way for Hegel's entry into British philosophy.

The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist.The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it. Which that is, and its extent, is determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference.

'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.

The late Mario Mignucci was one of the most authoritative, original, and influential scholars in the area of ancient philosophy, especially ancient logic. Collected here for the first time are sixteen of his most important essays on Ancient Logic, Language, and Metaphysics. These essays show a perceptive historian and a skillful logician philosophically engaged with issues that are still at the very heart of history and philosophy of logic, such as the nature of predication, identity, and modality. As well as essays found in disparate publications, often not easily available online, the volume includes an article on Plato and the relatives translated into English for the first time and an unpublished paper on De interpretatione 7. Mignucci thinks rigorously and writes clearly. He brings the deep knowledge of a scholar and the precision of a logician to bear on some of the trickiest topics in ancient philosophy. This collection deserves the close attention of anyone concerned with logic, language, and metaphysics, whether in ancient or contemporary philosophy.

Logic is, and has always been, an essential part of philosophy. It employs concepts which are crucial for understanding thought and language, and demands a mastery of procedures and techniques. With the same intellectual goals as the first edition, this innovative introductory logic textbook explores the relationship between natural language and logic, motivating the student to acquire skills and techniques of formal logic.

This new and revised edition includes substantial additions which make the text even more useful to students and instructors alike. Central to these changes is an Appendix, 'How to Learn Logic', which takes the student through fourteen compact and sharply directed lessons with exercises and answers. Other new material includes a discussion of the truth tree method for both Sentential and Predicate logics, an account of alternative notations, and the provision of answers to selected exercises that figure in the main body of the book.

Originally published in 1991, this volume examines Hegel's political philosophy from the perspective of his argument for constitutional monarchy. It offers an interpretation of Hegelian theory that is relevant for the understanding of modern republican constitutions. Modern republican theories are assessed together with those of Plato, Kant and Marx in order to put Hegel's model to the most rigorous test. The arguments are based on fresh analysis of Hegel's system and on new translations of key passages in Hegel's text.

Between the two world wars, Stanislaw Lesniewski (1886-1939), created the famous and important system of foundations of mathematics that comprises three deductive theories: Protothetic, Ontology, and Mereology. His research started in 1914 with studies on the general theory of sets (later named `Mereology'). Ontology followed between 1919 and 1921, and was the next step towards an integrated system. In order to combine these two systematically he constructed Protothetic - the system of `first principles'. Together they amount to what Z. Jordan called `... most thorough, original, and philosophically significant attempt to provide a logically secure foundation for the whole of mathematics'. The volume collects many of the most significant commentaries on, and contributions to, Protothetic. A Protothetic Bibliography is included.

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.

First published in 1993. Why do mirrors reverse left and right but not up and down? Does time flow at an even rate These are just two of the questions that won't be answered in Pseudo-Problems. This book explains how problems are dissolved rather than solved. Roy Sorenson takes the most important and interesting examples from one hundred years of analytic philosophy (and the odd one from the centuries before) to consolidate a new theory of dissolution. Pseudo-Problems is a fast-moving, fascinating alternative history of twentieth-century analytic philosophy, and a fine example of what philosophical analysis should be. Not least, it is an important contribution to the debates about creativity and problem solving.

This collection addresses metaphysical issues at the intersection between philosophy and science. A unique feature is the way in which it is guided both by history of philosophy, by interaction between philosophy and science, and by methodological awareness. In asking how metaphysics is possible in an age of science, the contributors draw on philosophical tools provided by three great thinkers who were fully conversant with and actively engaged with the sciences of their day: Kant, Husserl, and Frege. Part I sets out frameworks for scientifically informed metaphysics in accordance with the meta-metaphysics outlined by these three self-reflective philosophers. Part II explores the domain for co-existent metaphysics and science. Constraints on ambitious critical metaphysics are laid down in close consideration of logic, meta-theory, and specific conditions for science. Part III exemplifies the role of language and science in contemporary metaphysics. Quine's pursuit of truth is analysed; Cantor's absolute infinitude is reconstrued in modal terms; and sense is made of Weyl's take on the relationship between mathematics and empirical aspects of physics. With chapters by leading scholars, Metametaphysics and the Sciences is an in-depth resource for researchers and advanced students working within metaphysics, philosophy of science, and the history of philosophy.

Ludwig Wittgenstein's brief Tractatus Logico-Philosophicus (1922) is one of the most important philosophical works of the twentieth century, yet it offers little orientation for the reader. The first-time reader is left wondering what it could be about, and the scholar is left with little guidance for interpretation. In Tractatus in Context, James C. Klagge presents the vital background necessary for appreciating Wittgenstein's gnomic masterpiece. Tractatus in Context contains the early reactions to the Tractatus, including the initial reviews written in 1922-1924. And while we can't talk with Wittgenstein, we can do the next best thing-hear what he had to say about the Tractatus. Klagge thus presents what Wittgenstein thought about germane issues leading up to his writing the book, in discussions and correspondence with others about his ideas, and what he had to say about the Tractatus after it was written-in letters, lectures and conversations. It offers, you might say, Wittgenstein's own commentary on the book. Key Features: Illuminates what is at stake in the Tractatus, by providing the views of others that engaged Wittgenstein as he was writing it. Includes Wittgenstein's earlier thoughts on ideas in the book as recorded in his notebooks, letters, and conversations as well as his later, retrospective comments on those ideas. Draws on new or little-known sources, such as Wittgenstein's coded notebooks, Hermine's notes, Frege's letters, Hansel's diary, Ramsey's notes, and Skinner's dictations. Draws connections between the background context and specific passages in the Tractatus, using a proposition-by-proposition commentary.

First published in 1972, Philosophical Tasks was written to identify and examine some central themes in contemporary Anglo-American philosophy. The book explores the claim that philosophy is essentially linguistic, and considers in particular such topics as philosophy and science, fact and language, conceptual analysis, first- and second-order tasks, scepticism, ordinary language, and conceptual frameworks.

This volume discusses two distinct perspectives on the analysis of argumentative discourse: the dialectical and the rhetorical perspective. It intends to open a thorough discussion of the two approaches, their commonalities and differences, and the ways in which, in some combination or other, they can be used to further the development of sound analytic tools for dealing with argumentation.