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| tarski logic semantics metamathematics: Logic, Semantics, Metamathematics Alfred Tarski, 1983-01-01 |
| tarski logic semantics metamathematics: Logic, Semantics, Metamathematics Alfred Tarski, John Corcoran, 1983 Published with the aid of a grant from the National Endowment for the Humanities. Contains the only complete English-language text of The Concept of Truth in Formalized Languages. Tarski made extensive corrections and revisions of the original translations for this edition, along with new historical remarks. It includes a new preface and a new analytical index for use by philosophers and linguists as well as by historians of mathematics and philosophy. |
| tarski logic semantics metamathematics: Editor's Introduction to Alfred Tarski's Logic, Semantics, Metamathematics : Papers from 1923 to 1938 John Corcoran, Alfred Tarski, 1983 |
| tarski logic semantics metamathematics: Alfred Tarski, Logic, semantics, metamathematics Heinrich Scholz, 1957 |
| tarski logic semantics metamathematics: Alfred Tarski and the "Concept of Truth in Formalized Languages" Monika Gruber, 2016-09-02 This book provides a detailed commentary on the classic monograph by Alfred Tarski, and offers a reinterpretation and retranslation of the work using the original Polish text and the English and German translations. In the original work, Tarski presents a method for constructing definitions of truth for classical, quantificational formal languages. Furthermore, using the defined notion of truth, he demonstrates that it is possible to provide intuitively adequate definitions of the semantic notions of definability and denotation and that the notion in a structure can be defined in a way that is analogous to that used to define truth. Tarski’s piece is considered to be one of the major contributions to logic, semantics, and epistemology in the 20th century. However, the author points out that some mistakes were introduced into the text when it was translated into German in 1935. As the 1956 English version of the work was translated from the German text, those discrepancies were carried over in addition to new mistakes. The author has painstakingly compared the three texts, sentence-by-sentence, highlighting the inaccurate translations, offering explanations as to how they came about, and commenting on how they have influenced the content and suggesting a correct interpretation of certain passages. Furthermore, the author thoroughly examines Tarski’s article, offering interpretations and comments on the work. |
| tarski logic semantics metamathematics: Logic, semantics, metamathematics : papers from 1923 to 1938 Alfred Tarski, 1969 |
| tarski logic semantics metamathematics: Alfred Tarski and the Vienna Circle Jan Wolenski, Eckehart Köhler, 2013-03-09 The larger part of Yearbook 6 of the Institute Vienna Circle constitutes the proceedings of a symposium on Alfred Tarski and his influence on and interchanges with the Vienna Circle, especially those on and with Rudolf Carnap and Kurt Gödel. It is the first time that this topic has been treated on such a scale and in such depth. Attention is mainly paid to the origins, development and subsequent role of Tarski's definition of truth. Some contributions are primarily historical, others analyze logical aspects of the concept of truth. Contributors include Anita and Saul Feferman, Jan Wolenski, Jan Tarski and Hans Sluga. Several Polish logicians contributed: Gzegorczyk, Wójcicki, Murawski and Rojszczak. The volume presents entirely new biographical material on Tarski, both from his Polish period and on his influential career in the United States: at Harvard, in Princeton, at Hunter, and at the University of California at Berkeley. The high point of the analysis involves Tarski's influence on Carnap's evolution from a narrow syntactical view of language, to the ontologically more sophisticated but more controversial semantical view. Another highlight involves the interchange between Tarski and Gödel on the connection between truth and proof and on the nature of metalanguages. The concluding part of Yearbook 6 includes documentation, book reviews and a summary of current activities of the Institute Vienna Circle. Jan Tarski introduces letters written by his father to Gödel; Paolo Parrini reports on the Vienna Circle's influence in Italy; several reviews cover recent books on logical empiricism, on Gödel, on cosmology, on holistic approaches in Germany, and on Mauthner. |
| tarski logic semantics metamathematics: Alfred Tarski Anita Burdman Feferman, Solomon Feferman, 2004-10-04 Publisher Description |
| tarski logic semantics metamathematics: The Concept of Logical Consequence John Etchemendy, 1999 The aim of this book is to correct a common misunderstanding of a technique of mathematical logic. |
| tarski logic semantics metamathematics: Logic, Semantics, Metamathematics , 1969 |
| tarski logic semantics metamathematics: Principles of Truth Volker Halbach, Leon Horsten, 2013-05-02 On the one hand, the concept of truth is a major research subject in analytic philosophy. On the other hand, mathematical logicians have developed sophisticated logical theories of truth and the paradoxes. Recent developments in logical theories of the semantical paradoxes are highly relevant for philosophical research on the notion of truth. And conversely, philosophical guidance is necessary for the development of logical theories of truth and the paradoxes. From this perspective, this volume intends to reflect and promote deeper interaction and collaboration between philosophers and logicians investigating the concept of truth than has existed so far.Aside from an extended introductory overview of recent work in the theory of truth, the volume consists of articles by leading philosophers and logicians on subjects and debates that are situated on the interface between logical and philosophical theories of truth. The volume is intended for graduate students in philosophy and in logic who want an introduction to contemporary research in this area, as well as for professional philosophers and logicians |
| tarski logic semantics metamathematics: Introduction to Logic Alfred Tarski, 2013-07-04 This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout. |
| tarski logic semantics metamathematics: The Oxford Handbook of The History of Analytic Philosophy Michael Beaney, 2013-06-20 The main stream of academic philosophy, in Anglophone countries and increasingly worldwide, is identified by the name 'analytic'. The study of its history, from the 19th century to the late 20th, has boomed in recent years. These specially commissioned essays by forty leading scholars constitute the most comprehensive book on the subject. |
| tarski logic semantics metamathematics: The Unity of Science Rudolf Carnap, 2013-05-13 As a leading member of the Vienna Circle, Rudolph Carnap's aim was to bring about a unified science by applying a method of logical analysis to the empirical data of all the sciences. This work, first published in English in 1934, endeavors to work out a way in which the observation statements required for verification are not private to the observer. The work shows the strong influence of Wittgenstein, Russell, and Frege. |
| tarski logic semantics metamathematics: The Bounds of Logic Gila Sher, 1991 The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic developments. Extracting central philosophical ideas from Tarski's early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic exemplified in numerous recent mathematical and linguistic writings. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her development of the notion of logicality for quantifiers of many variables and her work on branching are of great importance, for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinnings of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications. |
| tarski logic semantics metamathematics: Kotarbiński: Logic, Semantics and Ontology Jan Wolenski, 2012-12-06 Tadeusz Kotarbinski is one of towering figures in contemporary Polish philosophy. He was a great thinker, a great teacher, a great organizer of philosophical and scientific life (he was, among others, the rector of the Uni versi ty of t6dz, the president of the Polish Academy of Sciences, and the president of the International Institute of Philosophy), and, last but not least, a great moral authority. He died at the age of 96 on October 3, 1981. Kotarbinski was active in almost all branches of philosophy. He made many significant contributions to logic, semantics, ontology, epistemology, history of philosophy, and ethics. He created a new field, namely praxiology. Thus, using an ancient distinction, he contributed to theoretical as well as practical philoso~hy. Kotarbinski regarded praxiology as his major philosophical child. Doubtless, praxiology belongs to practical philosophy. This collection, howewer, is mainly devoted to Kotarbinski' s theoretical philosophy. Reism - Kotarbinski' s fundamental idea of ontology and semantics - is the central topic of most papers included here; even Pszczolowski' s essay on praxiology considers its ontological basis. ,Only two papers, namely that of Zarnecka-Bialy and that of Wolenski, are not linked with reism. However, both fall under the general label Kotarbinski: logic, semantics and ontology. The collection partly consists of earlier published papers. |
| tarski logic semantics metamathematics: Logical Syntax of Language Rudolf Carnap, 2014-06-23 This is IV volume of eight in a series on Philosophy of the Mind and Language. For nearly a century mathematicians and logicians have been striving hard to make logic an exact science. But a book on logic must contain, in addition to the formulae, an expository context which, with the assistance of the words of ordinary language, explains the formulae and the relations between them; and this context often leaves much to be desired in the matter of clarity and exactitude. Originally published in 1937, the purpose of the present work is to give a systematic exposition of such a method, namely, of the method of logical syntax. |
| tarski logic semantics metamathematics: Metamathematics of Fuzzy Logic Petr Hájek, 2013-12-01 This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. Some important systems of real-valued propositional and predicate calculus are defined and investigated. The aim is to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named `fuzzy inference' can be naturally understood as logical deduction. |
| tarski logic semantics metamathematics: A Concise Introduction to Logic Craig DeLancey, 2017-02-06 |
| tarski logic semantics metamathematics: Proceedings of the Boston Colloquium for the Philosophy of Science 1966/1968 Robert S. Cohen, Marx W. Wartofsky, 2012-12-06 The fourth volume of Boston Studies in the Philosophy of Science consists mainly of papers which were contributed to our Colloquium during the past few years. The volume represents a wide range of interests in contem porary philosophy of science: issues in the philosophy of mind and of language, the neurophysiology of perceptual and linguistic behavior, philosophy of history and of the social sciences, and studies in the fun damental categories and methods of philosophy and the inter-relation ships of the sciences with ethics and metaphysics. Papers on the logic and methods of the natural sciences, including biological, physical and mathematical topics appear in the fifth volume of our series. We have included in the present volume the first English translation of the classic and fundamental work on aphasia by Carl Wernicke, together with a lucid and appreciative guide to his work by Dr. Norman Geschwind. The papers were not written to form a coherent volume, nor have they been edited with such a purpose. They represent current work-in progress, both in the United States and in Europe. Although most of the authors are philosophers, it is worth noting that we have essays of philosophical significance here written by a sociologist, an anthropologist, a political scientist, and by three neurophysiologists. We hope that collaboration among working scientists and working philosophers may develop further. |
| tarski logic semantics metamathematics: The Semantic Conception of Logic Gil Sagi, Jack Woods, 2021-09-09 This collection of new essays presents cutting-edge research on the semantic conception of logic, the invariance criteria of logicality, grammaticality, and logical truth. Contributors explore the history of the semantic tradition, starting with Tarski, and its historical applications, while central criticisms of the tradition, and especially the use of invariance criteria to explain logicality, are revisited by the original participants in that debate. Other essays discuss more recent criticism of the approach, and researchers from mathematics and linguistics weigh in on the role of the semantic tradition in their disciplines. This book will be invaluable to philosophers and logicians alike. |
| tarski logic semantics metamathematics: Philosophical Logic John MacFarlane, 2020-11-29 Introductory logic is generally taught as a straightforward technical discipline. In this book, John MacFarlane helps the reader think about the limitations of, presuppositions of, and alternatives to classical first-order predicate logic, making this an ideal introduction to philosophical logic for any student who already has completed an introductory logic course. The book explores the following questions. Are there quantificational idioms that cannot be expressed with the familiar universal and existential quantifiers? How can logic be extended to capture modal notions like necessity and obligation? Does the material conditional adequately capture the meaning of 'if'—and if not, what are the alternatives? Should logical consequence be understood in terms of models or in terms of proofs? Can one intelligibly question the validity of basic logical principles like Modus Ponens or Double Negation Elimination? Is the fact that classical logic validates the inference from a contradiction to anything a flaw, and if so, how can logic be modified to repair it? How, exactly, is logic related to reasoning? Must classical logic be revised in order to be applied to vague language, and if so how? Each chapter is organized around suggested readings and includes exercises designed to deepen the reader's understanding. Key Features: An integrated treatment of the technical and philosophical issues comprising philosophical logic Designed to serve students taking only one course in logic beyond the introductory level Provides tools and concepts necessary to understand work in many areas of analytic philosophy Includes exercises, suggested readings, and suggestions for further exploration in each chapter |
| tarski logic semantics metamathematics: Logic and Structure Dirk van Dalen, 2013-11-11 Logic appears in a 'sacred' and in a 'profane' form. The sacred form is dominant in proof theory, the profane form in model theory. The phenomenon is not unfamiliar, one observes this dichotomy also in other areas, e.g. set theory and recursion theory. For one reason or another, such as the discovery of the set theoretical paradoxes (Cantor, Russell), or the definability paradoxes (Richard, Berry), a subject is treated for some time with the utmost awe and diffidence. As a rule, however, sooner or later people start to treat the matter in a more free and easy way. Being raised in the 'sacred' tradition, I was greatly surprised (and some what shocked) when I observed Hartley Rogers teaching recursion theory to mathema ticians as if it were just an ordinary course in, say, linear algebra or algebraic topology. In the course of time I have come to accept his viewpoint as the didac tically sound one: before going into esoteric niceties one should develop a certain feeling for the subject and obtain a reasonable amount of plain working knowledge. For this reason I have adopted the profane attitude in this introductory text, reserving the more sacred approach for advanced courses. Readers who want to know more about the latter aspect of logic are referred to the immortal texts of Hilbert-Bernays or Kleene. |
| tarski logic semantics metamathematics: Methodological and Historical Essays in the Natural and Social Sciences Robert S. Cohen, 1974-04-30 Proceedings of the Boston Colloquium for the Philosophy of Science 1969/1972 |
| tarski logic semantics metamathematics: Axiomatic Theories of Truth Volker Halbach, 2014-02-27 At the centre of the traditional discussion of truth is the question of how truth is defined. Recent research, especially with the development of deflationist accounts of truth, has tended to take truth as an undefined primitive notion governed by axioms, while the liar paradox and cognate paradoxes pose problems for certain seemingly natural axioms for truth. In this book, Volker Halbach examines the most important axiomatizations of truth, explores their properties and shows how the logical results impinge on the philosophical topics related to truth. In particular, he shows that the discussion on topics such as deflationism about truth depends on the solution of the paradoxes. His book is an invaluable survey of the logical background to the philosophical discussion of truth, and will be indispensable reading for any graduate or professional philosopher in theories of truth. |
| tarski logic semantics metamathematics: From Symbolic Logic-- to Mathematical Logic Charles L. Silver, 1994 This text aims to unify mathematical logic and symbolic logic, and outlines how mathematical logic emerged from symbolic logic. Derivations are extended to encompass mathematical principles. Godel's theorems are covered, including philosophical and historical issues. |
| tarski logic semantics metamathematics: The Many and the One Salvatore Florio, Øystein Linnebo, 2021 Plural logic has seen a surge of interest in recent years. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? The result is a more nuanced picture of plural logic's applications than has been given thus far. |
| tarski logic semantics metamathematics: The Logic of Typed Feature Structures Bob Carpenter, 1992-06-26 This book develops the theory of typed feature structures and provides a logical foundation for logic programming and constraint-based reasoning systems. |
| tarski logic semantics metamathematics: Assessment Sensitivity John Gordon MacFarlane, 2014 John MacFarlane debates how we might make sense of the idea that truth is relative, and how we might use this idea to give satisfying accounts of parts of our thought and talk that have resisted traditional methods of analysis. Although there is a substantial philosophical literature on relativism about truth, going back to Plato's Theaetetus, this literature (both pro and con) has tended to focus on refutations of the doctrine, or refutations of these refutations, at the expense of saying clearly what the doctrine is. In contrast, Assessment Sensitivity begins with a clear account of what it is to be a relativist about truth, and uses this view to give satisfying accounts of what we mean when we talk about what is tasty, what we know, what will happen, what might be the case, and what we ought to do. The book seeks to provide a richer framework for the description of linguistic practices than standard truth-conditional semantics affords: one that allows not just standard contextual sensitivity (sensitivity to features of the context in which an expression is used), but assessment sensitivity (sensitivity to features of the context from which a use of an expression is assessed). The Context and Content series is a forum for outstanding original research at the intersection of philosophy, linguistics, and cognitive science. The general editor is Francois Recanati (Institut Jean-Nicod, Paris). |
| tarski logic semantics metamathematics: Semantics of Natural Language D. Davidson, Gilbert Harman, 2012-12-06 The idea that prompted the conferenee for which many of these papers were written, and that inspired this book, is stated in the Editorial Introduction reprinted below from Volume 21 of Synthese. The present volume contains the artieles in Synthese 21, Numbers 3-4 and Synthese 22, Numbers 1-2. In addition, it ineludes new papers by Saul Kripke, James McCawley, John R. Ross, and Paul Ziff, and reprints 'Grammar and Philosophy' by P. F. Strawson. Strawson's artiele first appeared in the Proceedings of the Aristotelian Society, Volume 70, and is reprinted with the kind permission of the author and the Aristotelian Society. We also repeat our thanks to the Olivetti Companyand Edizione di Comunita of Milan for permission to inelude the paper by Dana Scott; it also appeared in Synthese 21. DONALO DAVIDSON GILBERT HARMAN EDITORIAL INTRODUCTION The success of linguistics in treating naturallanguages as formal syntactic systems has aroused the interest of a number of linguists in a paralleI or related development of semantics. For the most part quite independ ently, many philosophers and logicians have reeently been applying formai semantic methods to structures increasingly like naturallanguages. While differenees in training, method and vocabulary tend to veil the fact, philosophers and linguists are converging, it seerns, on a common set of interrelated probiems. Sinee philosophers and linguists are working on the same, or very similar, probiems, it would obviously be instructive to compare notes. -- |
| tarski logic semantics metamathematics: What is a Logical System? Dov M. Gabbay, 1994 This extraordinary collection of papers addresses a fundamental question of logic and computation. What is a logical system?. With contributions from many world famous researchers, it presents a wide spectrum of views on the problem, reflecting mainstream current approaches to logic and how it is applied. |
| tarski logic semantics metamathematics: Sets, Logic, Computation Richard Zach, 2021-07-13 A textbook on the semantics, proof theory, and metatheory of first-order logic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. It is based on the Open Logic project, and available for free download at slc.openlogicproject.org. |
| tarski logic semantics metamathematics: Problems of Semantics L. Tondl, 2012-12-06 Ladislav Tondl's insightful investigations into the language of the sciences bear directly upon some decisive points of confrontation in modern philos ophy of science and of language itself. In the decade since his Scientific Procedures was published in English (Boston Studies 11), Dr Tondl has enlarged his original monograph of 1966 on the promise, problems and achievements of modern semantics: the main topic of his later work has been semantic information theory. A Russian translation, considerably expanded as a second edition, was published in 1975 (Moscow, Progress Publishers) with an appreciative critical commentary, in the form of a conclusion, by Professor Avenir I. Uemov of Odessa. Indeed many Soviet studies in the problems of the semantics of science show the same sort of philosophical curiosity about the relationship of meanings in scientific language to pro cedures in scientific epistemology that characterizes Tondl's work, as in the work of Mirislav Popovich (Kiev) and Vadirn Sadovsky (Moscow) and their colleagues. But we know that interest in these matters is world-wide, ranging from such classical topics as sense and denotation, empiricist reduction, vagueness and denotational opacity, to the new and equally exciting topics of the semantics of non-unique preference choices, the nuances of informational synonymity, and the semantics of a picture shape (so briefly but beautifully sketched in Tondl's dense and promising last chapter). We are pleased to have had Tondl's kind cooperation in producing this English edition, actually a third edition, of his research about semantics. |
| tarski logic semantics metamathematics: Type-Logical Semantics Bob Carpenter, 1998-07-24 Based on an introductory course on natural-language semantics, this book provides an introduction to type-logical grammar and the range of linguistic phenomena that can be handled in categorial grammar. It also contains a great deal of original work on categorial grammar and its application to natural-language semantics. The author chose the type-logical categorial grammar as his grammatical basis because of its broad syntactic coverage and its strong linkage of syntax and semantics. Although its basic orientation is linguistic, the book should also be of interest to logicians and computer scientists seeking connections between logical systems and natural language. The book, which stepwise develops successively more powerful logical and grammatical systems, covers an unusually broad range of material. Topics covered include higher-order logic, applicative categorial grammar, the Lambek calculus, coordination and unbounded dependencies, quantifiers and scope, plurals, pronouns and dependency, modal logic, intensionality, and tense and aspect. The book contains more mathematical development than is usually found in texts on natural language; an appendix includes the basic mathematical concepts used throughout the book. |
| tarski logic semantics metamathematics: Knowledge Contributors Vincent F. Hendricks, Klaus Frovin Jørgensen, Stig Andur Pedersen, 2013-11-27 The aim of this thematically unified anthology is to track the history of epistemic logic, to consider some important applications of these logics of knowledge and belief in a variety of fields, and finally to discuss future directions of research with particular emphasis on 'active agenthood' and multi-modal systems. It is accessible to researchers and graduate students in philosophy, computer science, game theory, economics and related disciplines utilizing the means and methods of epistemic logic. |
| tarski logic semantics metamathematics: Logic, Epistemology, and the Unity of Science Shahid Rahman, John Symons, Dov M. Gabbay, jean paul van bendegem, 2009-03-15 The first volume in this new series explores, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The book offers essays from important and influential philosophers in contemporary philosophy, discussing a range of topics from philosophy of science to epistemology, philosophy of logic and game theoretical approaches. It will be of interest to philosophers, computer scientists and all others interested in the scientific rationality. |
| tarski logic semantics metamathematics: Biology and Language Joseph Henry Woodger, 2021-09-09 This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. |
| tarski logic semantics metamathematics: Algebraic Foundations of Many-Valued Reasoning R.L. Cignoli, Itala M. d'Ottaviano, Daniele Mundici, 2013-03-09 This unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material never before published, such as a simple proof of the completeness theorem and of the equivalence between Chang's MV algebras and Abelian lattice-ordered groups with unit - a necessary prerequisite for the incorporation of a genuine addition operation into fuzzy logic. Readers interested in fuzzy control are provided with a rich deductive system in which one can define fuzzy partitions, just as Boolean partitions can be defined and computed in classical logic. Detailed bibliographic remarks at the end of each chapter and an extensive bibliography lead the reader on to further specialised topics. |
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