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Language Truth And Logic In Mathematics
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Book Synopsis Language, Truth and Logic by : Alfred Jules Ayer
Download or read book Language, Truth and Logic written by Alfred Jules Ayer and published by Courier Corporation. This book was released on 2012-04-18 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Book Synopsis Language, Truth and Logic in Mathematics by : Jaakko Hintikka
Download or read book Language, Truth and Logic in Mathematics written by Jaakko Hintikka and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: One can distinguish, roughly speaking, two different approaches to the philosophy of mathematics. On the one hand, some philosophers (and some mathematicians) take the nature and the results of mathematicians' activities as given, and go on to ask what philosophical morals one might perhaps find in their story. On the other hand, some philosophers, logicians and mathematicians have tried or are trying to subject the very concepts which mathematicians are using in their work to critical scrutiny. In practice this usually means scrutinizing the logical and linguistic tools mathematicians wield. Such scrutiny can scarcely help relying on philosophical ideas and principles. In other words it can scarcely help being literally a study of language, truth and logic in mathematics, albeit not necessarily in the spirit of AJ. Ayer. As its title indicates, the essays included in the present volume represent the latter approach. In most of them one of the fundamental concepts in the foundations of mathematics and logic is subjected to a scrutiny from a largely novel point of view. Typically, it turns out that the concept in question is in need of a revision or reconsideration or at least can be given a new twist. The results of such a re-examination are not primarily critical, however, but typically open up new constructive possibilities. The consequences of such deconstructions and reconstructions are often quite sweeping, and are explored in the same paper or in others.
Book Synopsis Briefly: Ayer's Language Truth and Logic by : David Mills Daniel
Download or read book Briefly: Ayer's Language Truth and Logic written by David Mills Daniel and published by SCM Press. This book was released on 2013-01-03 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of the "SCM Briefly" series, which summarizes books by philosophers and theologians, this book provides a summary of Language, Truth and Logic. It also includes line by line analysis, short quotes, and a glossary of terms to help students with definitions of philosophical terms.
Book Synopsis Truth in Mathematics by : Harold G. Dales
Download or read book Truth in Mathematics written by Harold G. Dales and published by Oxford University Press. This book was released on 1998 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nature of truth in mathematics has exercised the minds of thinkers from at least the time of the ancient Greeks. The great advances in mathematics and philosophy in the twentieth century and in particular the work by G]odel and the development of the notion of independence in mathematics have led to new and complex views on this question. Collecting the work of a number of outstanding mathematicians and philosophers, including Yurii Manin, Vaughan Jones, and Per Martin-L]of, this volume provides an overview of the forefront of current thinking and a valuable introduction for researchers in the area.
Book Synopsis The Historical and Philosophical Significance of Ayer’s Language, Truth and Logic by : Adam Tamas Tuboly
Download or read book The Historical and Philosophical Significance of Ayer’s Language, Truth and Logic written by Adam Tamas Tuboly and published by Springer Nature. This book was released on 2020-10-23 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited collection provides the first comprehensive volume on A. J. Ayer’s 1936 masterpiece, Language, Truth and Logic. With eleven original chapters the volume reconsiders the historical and philosophical significance of Ayer’s work, examining its place in the history of analytic philosophy and its subsequent legacy. Making use of pioneering research in logical empiricism, the contributors explore a wide variety of topics, from ethics, values and religion, to truth, epistemology and philosophy of language. Among the questions discussed are: How did Ayer preserve or distort the views and conceptions of logical empiricists? How are Ayer's arguments different from the ones he aimed at reconstructing? And which aspects of the book were responsible for its immense impact? The volume expertly places Language, Truth and Logic in the intellectual and socio-cultural history of twentieth-century philosophical thought, providing both introductory and contextual chapters, as well as specific explorations of a variety of topics covering the main themes of the book. Providing important insights of both historical and contemporary significance, this collection is an essential resource for scholars interested in the legacy of the Vienna Circle and its effect on ethics and philosophy of mind.
Book Synopsis Language, Truth and Knowledge by : Thomas Bonk
Download or read book Language, Truth and Knowledge written by Thomas Bonk and published by Springer Science & Business Media. This book was released on 2003-09-30 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection will prove a valuable resource for our understanding of the historic Carnap and the living philosophical issues with which he grappled. It arose out of a symposium on Carnap's work (Vienna, 2001). With essays by Graham H. Bird, Jaakko Hintikka, Ilkka Niiniluoto, Jan Wolenski, this volume will interest graduate students of the philosophy of language and logic, as well as professional philosophers, historians of analytic philosophy, and philosophically inclined logicians.
Book Synopsis From a Logical Point of View by : Willard Van Orman Quine
Download or read book From a Logical Point of View written by Willard Van Orman Quine and published by Harvard University Press. This book was released on 1980-05-15 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of essays has a unity and bears throughout the imprint of Quine's powerful and original mind. It is written with the felicity in the choice of words which makes everything that Quine writes a pleasure to read, and which ranks him among the best contemporary writers on abstract subjects.
Download or read book Shadows of Syntax written by Jared Warren and published by Oxford University Press. This book was released on 2020-07-20 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the source of logical and mathematical truth? This volume revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. In Shadows of Syntax, Jared Warren offers the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. He argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims. In Part I, Warren explains exactly what conventionalism amounts to and what linguistic conventions are. Part II develops an unrestricted inferentialist theory of the meanings of logical constants that leads to logical conventionalism. This conventionalist theory is elaborated in discussions of logical pluralism, the epistemology of logic, and of the influential objections that led to the historical demise of conventionalism. Part III aims to extend conventionalism from logic to mathematics. Unlike logic, mathematics involves both ontological commitments and a rich notion of truth that cannot be generated by any algorithmic process. To address these issues Warren develops conventionalist-friendly but independently plausible theories of both metaontology and mathematical truth. Finally, Part IV steps back to address big picture worries and meta-worries about conventionalism. This book develops and defends a unified theory of logic and mathematics according to which logical and mathematical truths are reflections of our linguistic rules, mere shadows of syntax.
Book Synopsis Handbook of Logic and Language by : J. van Benthem
Download or read book Handbook of Logic and Language written by J. van Benthem and published by Elsevier. This book was released on 1997 with total page 1274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook documents the main trends in current research between logic and language, including its broader influence in computer science, linguistic theory and cognitive science. The history of the combined study of Logic and Linguistics goes back a long way, at least to the work of the scholastic philosophers in the Middle Ages. At the beginning of this century, the subject was revitalized through the pioneering efforts of Gottlob Frege, Bertrand Russell, and Polish philosophical logicians such as Kazimierz Ajdukiewicz. Around 1970, the landmark achievements of Richard Montague established a junction between state-of-the-art mathematical logic and generative linguistic theory. Over the subsequent decades, this enterprise of Montague Grammar has flourished and diversified into a number of research programs with empirical and theoretical substance. This appears to be the first Handbook to bring logic-language interface to the fore. Both aspects of the interaction between logic and language are demonstrated in the book i.e. firstly, how logical systems are designed and modified in response to linguistic needs and secondly, how mathematical theory arises in this process and how it affects subsequent linguistic theory. The Handbook presents concise, impartial accounts of the topics covered. Where possible, an author and a commentator have cooperated to ensure the proper breadth and technical content of the papers. The Handbook is self-contained, and individual articles are of the highest quality.
Book Synopsis The Principles of Mathematics Revisited by : Jaakko Hintikka
Download or read book The Principles of Mathematics Revisited written by Jaakko Hintikka and published by Cambridge University Press. This book was released on 1998-04-28 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous impossibility results by Gödel and Tarski that have dominated the field for the last sixty years turn out to be much less significant than has been thought. All of ordinary mathematics can in principle be done on this first-order level, thus dispensing with the existence of sets and other higher-order entities.
Book Synopsis Principia Mathematica by : Alfred North Whitehead
Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Philosophy of Language by : Alex Miller
Download or read book Philosophy of Language written by Alex Miller and published by Routledge. This book was released on 2007-09-12 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This engaging and accessible introduction to the philosophy of language provides an important guide to one of the liveliest and most challenging areas of study in philosophy. Interweaving the historical development of the subject with a thematic overview of the different approaches to meaning, the book provides students with the tools necessary to understand contemporary analytical philosophy. The second edition includes new material on: Chomsky, Wittgenstein and Davidson as well as new chapters on the causal theory of reference, possible worlds semantics and semantic externalism.
Book Synopsis Philosophy of Language by : Alex Miller
Download or read book Philosophy of Language written by Alex Miller and published by Taylor & Francis. This book was released on 2007-09-12 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This engaging and accessible introduction to the philosophy of language provides an important guide to one of the liveliest and most challenging areas of study in philosophy. Interweaving the historical development of the subject with a thematic overview of the different approaches to meaning, the book provides students with the tools necessary to understand contemporary analytical philosophy. The second edition includes new material on: Chomsky, Wittgenstein and Davidson as well as new chapters on the causal theory of reference, possible worlds semantics and semantic externalism.
Book Synopsis Philosophy of Language by : Alexander Miller
Download or read book Philosophy of Language written by Alexander Miller and published by Routledge. This book was released on 2018-01-17 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Philosophy of Language provides a comprehensive, meticulous survey of twentieth-century and contemporary philosophical theories of meaning. Interweaving the historical development of the subject with a thematic overview of the different approaches to meaning, the book provides students with the tools necessary to understand contemporary analytic philosophy. Beginning with a systematic look at Frege’s foundational theories on sense and reference, Alexander Miller goes on to offer a clear exposition of the development of subsequent arguments in the philosophy of language. Communicating a sense of active philosophical debate, the author confronts the views of the early theorists, taking in Frege, Russell, and logical positivism and going on to discuss the scepticism of Quine, Kripke, and Wittgenstein. The work of philosophers such as Davidson, Dummett, Searle, Fodor, McGinn, Wright, Grice, and Tarski is also examined in depth. The third edition has been fully revised for enhanced clarity and includes: · a short introduction for students, outlining the importance of the philosophy of language and the aims of the book; · two substantial new sections on Philip Pettit’s "ethocentric" account of rule-following and on Hannah Ginsborg’s "partial reductionism" about rule-following and meaning; · the addition of chapter summaries and study questions throughout, designed to promote greater understanding and engagement; · updated guides to further reading at the end of every chapter. This well-established and sophisticated introduction to the philosophy of language is an unrivalled guide to one of the liveliest and most challenging areas of philosophy and is suitable for use on undergraduate degrees and in postgraduate study.
Book Synopsis An Introduction to Mathematical Logic and Type Theory by : Peter B. Andrews
Download or read book An Introduction to Mathematical Logic and Type Theory written by Peter B. Andrews and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: In case you are considering to adopt this book for courses with over 50 students, please contact [email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.
Book Synopsis Summary of Alfred Jules Ayer's Language, Truth and Logic by : Everest Media,
Download or read book Summary of Alfred Jules Ayer's Language, Truth and Logic written by Everest Media, and published by Everest Media LLC. This book was released on 2022-05-10T22:59:00Z with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Please note: This is a companion version & not the original book. Sample Book Insights: #1 The traditional disputes between philosophers are, for the most part, as unwarranted as they are unfruitful. The surest way to end them is to establish beyond question what should be the purpose and method of a philosophical inquiry. And this is not difficult to do. #2 The author claims that the human mind is incapable of understanding things in themselves, and that we can only understand things as they relate to our own experience. This means we can never truly understand anything beyond our senses. #3 The criterion used to test the genuineness of apparent statements of fact is the verifiability criterion. A sentence is factually significant to a given person if, and only if, he knows how to verify the proposition that it purports to express. #4 The distinction between the strong and weak sense of the term verifiable is important. A proposition is said to be verifiable in the strong sense of the term if its truth can be conclusively proven in experience. But a proposition is verifiable in the weak sense if it is possible for experience to render it probable.
Download or read book Spandrels of Truth written by Jc Beall and published by Oxford University Press. This book was released on 2009-04-09 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jc Beall presents a new theory of 'transparent' truth. A prominent philosophical view of truth is as an entirely see-through device introduced for only practical (expressive) reasons. Beall's modest dialetheic theory shows how the notorious paradoxes associated with transparency can be dealt with.
