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An entertaining introduction to logic and reasoning, packed with puzzles and thought experiments for the reader to try "Peter Cave takes us on an edifying tour through the world of paradoxes, and there is much to be learned, as well as much enjoyment to be had, in the process." -Adrian W. Moore, University of Oxford, UK "'This sentence is false' is a sentence printed on the cover of this book. A sentence is not a name. So what is the name of the book? This book (whatever its name) is full of intriguing philosophical puzzles ... Paradoxes may seem trivial at first glance, but further thought reveals them to be challenges to some of our most fundamental beliefs and preconceptions. Peter Cave entertainingly escorts the reader through a great variety of these fascinating puzzles, shining light that is fresh and bright." -Laurence Goldstein, University of Kent, UK "This is a truly wonderful book. The topic is tough, but Peter Cave brings it to life. He manages to give new insights on old topics, which is itself remarkable, and he also brings in plenty of less familiar topics ... All in all, it is a joy to see such cleverness and clarity of thought coexisting with such an easy (and light and amusing) writing style." -Professor Imre Leader, Cambridge University, UK Put your neurons through their paces with this lively and engaging introduction to paradoxes. From "Buridan's Ass" and the "Surprise Examination" to "The Liar" and "Sleeping Beauty," This Sentence is False introduces all the key philosophical paradoxes. This fascinating guide to logic and reasoning is packed with puzzles and thought experiments to actively engage the reader in critical thinking. As well as paradoxes that occur in our everyday lives, topics also include God, ethics, political philosophy, space, and time. This Sentence is False will put your mind to the test, challenge what you think you know, and lead you on a fascinating journey through logical reasoning.
Consider the sentence 'This sentence is not true'. Certain notorious paradoxes like this have bedevilled philosophical theories of truth. Tim Maudlin presents an original account of logic and semantics which deals with these paradoxes, and allows him to set out a new theory of truth-values and the norms governing claims about truth.
Bringing together powerful new tools from set theory and the philosophy of language, this book proposes a solution to one of the few unresolved paradoxes from antiquity, the Paradox of the Liar. Barwise and Etchemendy model and compare Russellian and Austinian conceptions of propositions, and develop a range of model-theoretic techniques--based on Aczel's work--that open up new avenues in logical and formal semantics.
The Liar paradox raises foundational questions about logic, language, and truth (and semantic notions in general). A simple Liar sentence like 'This sentence is false' appears to be both true and false if it is either true or false. For if the sentence is true, then what it says is the case; but what it says is that it is false, hence it must be false. On the other hand, if the statement is false, then it is true, since it says (only) that it is false. How, then, should we classify Liar sentences? Are they true or false? A natural suggestion would be that Liars are neither true nor false; that is, they fall into a category beyond truth and falsity. This solution might resolve the initial problem, but it beckons the Liar's revenge. A sentence that says of itself only that it is false or beyond truth and falsity will, in effect, bring back the initial problem. The Liar's revenge is a witness to the hydra-like nature of Liars: in dealing with one Liar you often bring about another. JC Beall presents fourteen new essays and an extensive introduction, which examine the nature of the Liar paradox and its resistance to any attempt to solve it. Written by some of the world's leading experts in the field, the papers in this volume will be an important resource for those working in truth studies, philosophical logic, and philosophy of language, as well as those with an interest in formal semantics and metaphysics.
This brief book takes readers to the very heart of what it is that philosophy can do well. Completed shortly before Donald Davidson's death at 85, Truth and Predication brings full circle a journey moving from the insights of Plato and Aristotle to the problems of contemporary philosophy. In particular, Davidson, countering many of his contemporaries, argues that the concept of truth is not ambiguous, and that we need an effective theory of truth in order to live well. Davidson begins by harking back to an early interest in the classics, and an even earlier engagement with the workings of grammar; in the pleasures of diagramming sentences in grade school, he locates his first glimpse into the mechanics of how we conduct the most important activities in our life--such as declaring love, asking directions, issuing orders, and telling stories. Davidson connects these essential questions with the most basic and yet hard to understand mysteries of language use--how we connect noun to verb. This is a problem that Plato and Aristotle wrestled with, and Davidson draws on their thinking to show how an understanding of linguistic behavior is critical to the formulating of a workable concept of truth. Anchored in classical philosophy, Truth and Predication nonetheless makes telling use of the work of a great number of modern philosophers from Tarski and Dewey to Quine and Rorty. Representing the very best of Western thought, it reopens the most difficult and pressing of ancient philosophical problems, and reveals them to be very much of our day.
"A delightful book … I should like to have written it myself." — Bertrand Russell First published in 1936, this first full-length presentation in English of the Logical Positivism of Carnap, Neurath, and others has gone through many printings to become a classic of thought and communication. It not only surveys one of the most important areas of modern thought; it also shows the confusion that arises from imperfect understanding of the uses of language. A first-rate antidote for fuzzy thought and muddled writing, this remarkable book has helped philosophers, writers, speakers, teachers, students, and general readers alike. Mr. Ayers sets up specific tests by which you can easily evaluate statements of ideas. You will also learn how to distinguish ideas that cannot be verified by experience — those expressing religious, moral, or aesthetic experience, those expounding theological or metaphysical doctrine, and those dealing with a priori truth. The basic thesis of this work is that philosophy should not squander its energies upon the unknowable, but should perform its proper function in criticism and analysis.
Priest advocates and defends the view that there are true contradictions (dialetheism), a perspective that flies in the face of orthodoxy in Western philosophy since Aristole and remains at the centre of philosophical debate. This edition contains the author's reflections on developments since 1987.
Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.