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Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.
From the author of Wittgenstein's Poker and Would You Kill the Fat Man?, the story of an extraordinary group of philosophers during a dark chapter in Europe's history On June 22, 1936, the philosopher Moritz Schlick was on his way to deliver a lecture at the University of Vienna when Johann Nelboeck, a deranged former student of Schlick's, shot him dead on the university steps. Some Austrian newspapers defended the madman, while Nelboeck himself argued in court that his onetime teacher had promoted a treacherous Jewish philosophy. David Edmonds traces the rise and fall of the Vienna Circle-an influential group of brilliant thinkers led by Schlick-and of a philosophical movement that sought to do away with metaphysics and pseudoscience in a city darkened by fascism, anti-Semitism, and unreason. The Vienna Circle's members included Otto Neurath, Rudolf Carnap, and the eccentric logician Kurt Goedel. On its fringes were two other philosophical titans of the twentieth century, Ludwig Wittgenstein and Karl Popper. The Circle championed the philosophy of logical empiricism, which held that only two types of propositions have cognitive meaning, those that can be verified through experience and those that are analytically true. For a time, it was the most fashionable movement in philosophy. Yet by the outbreak of World War II, Schlick's group had disbanded and almost all its members had fled. Edmonds reveals why the Austro-fascists and the Nazis saw their philosophy as such a threat. The Murder of Professor Schlick paints an unforgettable portrait of the Vienna Circle and its members while weaving an enthralling narrative set against the backdrop of economic catastrophe and rising extremism in Hitler's Europe.
In times of crisis, we all ask, "What's the point?". It turns out the answer to the question is hidden in plain sight and is connected to the fundamental purpose and very essence of our existence. There is only one point in living but it may not be what you think. "Paul Koberg doesn't shy away from the tough questions. His answers to 'what is ego?', what is evil?' and 'is life simply the absence of death?' will fascinate and engage you. In today's times of crisis, Paul Koberg's book is a gift. Recommended for readers who appreciate a deep look into the deep questions of life." Reviewed by Stacie Haas for Readers' Favorite - 5 Stars
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).
Stresses the importance of argumentation in everyday life Critical Thinking and Communication, 7/e, encourages students to develop skills in constructing and refuting arguments in contexts ranging from informal conversations to structured debates. The authors stress the importance of argumentation in everyday life while building student competence and critical awareness. Through exercises and examples, students learn to create arguments and develop, understand, and interpret extended cases.
Although Hegel considered Science of Logic essential to his philosophy, it has received scant commentary compared with the other three books he published in his lifetime. Here philosopher Stanley Rosen rescues the Science of Logic from obscurity, arguing that its neglect is responsible for contemporary philosophy's fracture into many different and opposed schools of thought. Through deep and careful analysis, Rosen sheds new light on the precise problems that animate Hegel's overlooked book and their tremendous significance to philosophical conceptions of logic and reason. Rosen's overarching question is how, if at all, rationalism can overcome the split between monism and dualism. Monism--which claims a singular essence for all things--ultimately leads to nihilism, while dualism, which claims multiple, irreducible essences, leads to what Rosen calls "the endless chatter of the history of philosophy." The Science of Logic, he argues, is the fundamental text to offer a new conception of rationalism that might overcome this philosophical split. Leading readers through Hegel's book from beginning to end, Rosen's argument culminates in a masterful chapter on the Idea in Hegel. By fully appreciating the Science of Logic and situating it properly within Hegel's oeuvre, Rosen in turn provides new tools for wrangling with the conceptual puzzles that have brought so many other philosophers to disaster.
Philosophy of logic is a fundamental part of philosophical study, and one which is increasingly recognized as being immensely important in relation to many issues in metaphysics, metametaphysics, epistemology, philosophy of mathematics, and philosophy of language. This textbook provides a comprehensive and accessible introduction to topics including the objectivity of logical inference rules and its relevance in discussions of epistemological relativism, the revived interest in logical pluralism, the question of logic's metaphysical neutrality, and the demarcation between logic and mathematics. Chapters in the book cover the state of the art in contemporary philosophy of logic, and allow students to understand the philosophical relevance of these debates without having to contend with complex technical arguments. This will be a major new resource for students working on logic, as well as for readers seeking a better understanding of philosophy of logic in its wider context.
In the history of mathematics, Charles Lutwidge Dodgson (1832-1898), better known as Lewis Carroll, stands out as the rare mathematician who also was an exceptional literary figure.
In "The Pamphlets of Lewis Carroll, " each volume of a projected six volumes deals with a particular aspect of his work. When the series is complete, it will include all of his works that were not originally issued in hard cover with the exception of his poetry and fiction.
This fourth volume focuses on his writings on logic. It includes pamphlets and sheets privately printed by Dodgson, unpublished manuscript sheets, rare previously published documents, and early versions of published works. These are collected together for the first time, organized by subject, and presented with suitable commentary so that the reader can fully appreciate Dodgson's contributions to the logic of his time and of ours.
The general introduction to the book describes the importance of logic in Dodgson's life and work and provides a historical perspective on the state of logic that existed during his lifetime. The sections of the book that follow contain introductory essays that provide analyses and context both for the general reader and for the specialist, followed by the items in transcription or facsimile.
Distributed for the Lewis Carroll Society of North America
For centuries, the sorites paradox has spurred philosophers to think and argue about the problem of vagueness. This volume offers a guide to the paradox which is both an accessible survey and an exposition of the state of the art, with a chapter-by-chapter presentation of all of the main solutions to the paradox and of all its main areas of influence. Each chapter offers a gentle introduction to its topic, gradually building up to a final discussion of some open problems. Students will find a comprehensive guide to the fundamentals of the paradox, together with lucid explanations of the challenges it continues to raise. Researchers will find exciting new ideas and debates on the paradox.
Logic is often perceived as having little to do with the rest of philosophy, and even less to do with real life. In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, the basics of formal logic are explained in simple, non-technical terms, showing that logic is a powerful and exciting part of modern philosophy. In this new edition Graham Priest expands his discussion to cover the subjects of algorithms and axioms, and proofs in mathematics. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
This powerful book introduces core critical thinking concepts and principles as an empowering problem-solving framework for every profession, course of study, and indeed every area of life. The Miniature Guide to Critical Thinking Concepts and Tools distills the groundbreaking work of Richard Paul and Linda Elder, targeting how to deconstruct thinking through the elements of reasoning and how to assess the quality of our thinking. The eighth edition of this guide further details the foundations of critical thinking and how they can be applied in instruction to improve teaching and learning at all levels; it also reveals how we can learn to identify and avoid egocentric and sociocentric thought, which lead to close-mindedness, self-deception, arrogance, hypocrisy, greed, selfishness, herd mentality, prejudice, and the like. With more than half a million copies sold, Richard Paul and Linda Elder's bestselling book in the Thinker's Guide Library is used in secondary and higher education courses and professional development seminars across the globe. In a world of conflicting information and clashing ideologies, this guide clears a path for advancing fairminded critical societies.
Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naive and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics.
All of us are faced countless times with the challenge of persuading others, whether we're trying to win a trivial argument with a friend or convince our coworkers about an important decision. Instead of relying on untrained instinct--and often floundering or failing as a result--we'd win more arguments if we learned the timeless art of verbal persuasion, rhetoric. How to Win an Argument gathers the rhetorical wisdom of Cicero, ancient Rome's greatest orator, from across his works and combines it with passages from his legal and political speeches to show his powerful techniques in action. The result is an enlightening and entertaining practical introduction to the secrets of persuasive speaking and writing--including strategies that are just as effective in today's offices, schools, courts, and political debates as they were in the Roman forum. How to Win an Argument addresses proof based on rational argumentation, character, and emotion; the parts of a speech; the plain, middle, and grand styles; how to persuade no matter what audience or circumstances you face; and more. Cicero's words are presented in lively translations, with illuminating introductions; the book also features a brief biography of Cicero, a glossary, suggestions for further reading, and an appendix of the original Latin texts. Astonishingly relevant, this unique anthology of Cicero's rhetorical and oratorical wisdom will be enjoyed by anyone who ever needs to win arguments and influence people--in other words, all of us.
A fascinating history that reveals the ways in which the pursuit of rationality often leads to an explosion of irrationality It's a story we can't stop telling ourselves. Once, humans were benighted by superstition and irrationality, but then the Greeks invented reason. Later, the Enlightenment enshrined rationality as the supreme value. Discovering that reason is the defining feature of our species, we named ourselves the "rational animal." But is this flattering story itself rational? In this sweeping account of irrationality from antiquity to today-from the fifth-century BC murder of Hippasus for revealing the existence of irrational numbers to the rise of Twitter mobs and the election of Donald Trump-Justin Smith says the evidence suggests the opposite. From sex and music to religion and war, irrationality makes up the greater part of human life and history. Rich and ambitious, Irrationality ranges across philosophy, politics, and current events. Challenging conventional thinking about logic, natural reason, dreams, art and science, pseudoscience, the Enlightenment, the internet, jokes and lies, and death, the book shows how history reveals that any triumph of reason is temporary and reversible, and that rational schemes, notably including many from Silicon Valley, often result in their polar opposite. The problem is that the rational gives birth to the irrational and vice versa in an endless cycle, and any effort to permanently set things in order sooner or later ends in an explosion of unreason. Because of this, it is irrational to try to eliminate irrationality. For better or worse, it is an ineradicable feature of life. Illuminating unreason at a moment when the world appears to have gone mad again, Irrationality is fascinating, provocative, and timely.
This text provides a straightforward, lively but rigorous, introduction to truth-functional and predicate logic, complete with lucid examples and incisive exercises, for which Warren Goldfarb is renowned.
This reissue, first published in 1971, provides a brief historical account of the Theory of Logical Types; and describes the problems that gave rise to it, its various different formulations (Simple and Ramified), the difficulties connected with each, and the criticisms that have been directed against it. Professor Copi seeks to make the subject accessible to the non-specialist and yet provide a sufficiently rigorous exposition for the serious student to see exactly what the theory is and how it works.
First published in 1952, professor 's Strawson 's highly influential Introduction to Logical Theory provides a detailed examination of the relationship between the behaviour of words in common language and the behaviour of symbols in a logical system. He seeks to explain both the exact nature of the discipline known as Formal Logic, and also to reveal something of the intricate logical structure of ordinary unformalised discourse.
We all engage in the process of reasoning, but we don't always pay attention to whether we are doing it well. This book offers the opportunity to practise reasoning in a clear-headed and critical way, with the aims of developing an awareness of the importance of reasoning well and of improving the reader's skill in analyzing and evaluating arguments.
In this third edition, Anne Thomson has updated and revised the book to include fresh and topical examples which will guide students through the processes of critical reasoning in a clear and engaging way. In addition, two new chapters on evaluating the credibility of evidence and decision making and dilemmas will fully equip students to reason well. By the end of the book students should be able to:
According to Bayesian epistemology, rational learning from experience is consistent learning, that is learning should incorporate new information consistently into one's old system of beliefs. Simon M. Huttegger argues that this core idea can be transferred to situations where the learner's informational inputs are much more limited than Bayesianism assumes, thereby significantly expanding the reach of a Bayesian type of epistemology. What results from this is a unified account of probabilistic learning in the tradition of Richard Jeffrey's 'radical probabilism'. Along the way, Huttegger addresses a number of debates in epistemology and the philosophy of science, including the status of prior probabilities, whether Bayes' rule is the only legitimate form of learning from experience, and whether rational agents can have sustained disagreements. His book will be of interest to students and scholars of epistemology, of game and decision theory, and of cognitive, economic, and computer sciences.
This book contains a selection of the papers presented at the Logic, Reasoning and Rationality 2010 conference (LRR10) in Ghent. The conference aimed at stimulating the use of formal frameworks to explicate concrete cases of human reasoning, and conversely, to challenge scholars in formal studies by presenting them with interesting new cases of actual reasoning. According to the members of the Wiener Kreis, there was a strong connection between logic, reasoning, and rationality and that human reasoning is rational in so far as it is based on (classical) logic. Later, this belief came under attack and logic was deemed inadequate to explicate actual cases of human reasoning. Today, there is a growing interest in reconnecting logic, reasoning and rationality. A central motor for this change was the development of non-classical logics and non-classical formal frameworks. The book contains contributions in various non-classical formal frameworks, case studies that enhance our apprehension of concrete reasoning patterns, and studies of the philosophical implications for our understanding of the notions of rationality.
This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area.
Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations to weak Heyting algebras and implicative semilattices. The book also dives into the Blok-Esakia theorem and provides an outline of the intuitionistic modal logic KM which is closely related to the Godel-Lob provability logic GL. One chapter scrutinizes Esakia s work interpreting modal diamond as the derivative of a topological space within the setting of point-free topology. The final chapter in the volume is dedicated to the derivational semantics of modal logic and other related issues."
Hermeneutics is the branch of knowledge that deals with interpretation, a behaviour that is intrinsic to our daily lives. As humans, we decipher the meaning of newspaper articles, books, legal matters, religious texts, political speeches, emails, and even dinner conversations every day . But how is knowledge mediated through these forms? What constitutes the process of interpretation? And how do we draw meaning from the world around us so that we might understand our position in it? In this Very Short Introduction Jens Zimmermann traces the history of hermeneutic theory, setting out its key elements, and demonstrating how they can be applied to a broad range of disciplines: theology; literature; law; and natural and social sciences. Demonstrating the longstanding and wide-ranging necessity of interpretation, Zimmermann reveals its significance in our current social and political landscape. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
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