Language Logic And Mathematics

Author : Jens Lemanski
Publisher : Springer Nature
Page : 318 pages
File Size : 52,9 Mb
Release : 2020-06-08
Category : Mathematics
ISBN : 9783030330903

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Language, Logic, and Mathematics in Schopenhauer by Jens Lemanski Pdf

The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse on logic. Beginning with Schopenhauer’s philosophy of language, the chapters examine the individual aspects of his semantics, semiotics, translation theory, language criticism, and communication theory. Additionally, Schopenhauer’s anticipation of modern contextualism is analyzed. The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. Special focus is given to the role of the Euler diagrams used frequently in his lectures and their significance to broader context of his logic. In the final section, chapters discuss Schopenhauer’s philosophy of mathematics while synthesizing all topics from the previous sections, emphasizing the relationship between intuition and concept. Aimed at a variety of academics, including researchers of Schopenhauer, philosophers, historians, logicians, mathematicians, and linguists, this title serves as a unique and vital resource for those interested in expanding their knowledge of Schopenhauer’s work as it relates to modern mathematical and logical study.

Author : C. W. Kilmister
Publisher : Unknown
Page : 128 pages
File Size : 45,6 Mb
Release : 1973
Category : Electronic
ISBN : OCLC:473942670

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Language Logic and Mathematics by C. W. Kilmister Pdf

Author : Alexander Miller
Publisher : Oxford University Press, USA
Page : 465 pages
File Size : 41,5 Mb
Release : 2020-03-19
Category : Mathematics
ISBN : 9780199278343

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Logic, Language, and Mathematics by Alexander Miller Pdf

Crispin Wright is widely recognised as one of the most important and influential analytic philosophers of the twentieth and twenty-first centuries. This volume is a collective exploration of the major themes of his work in philosophy of language, philosophical logic, and philosophy of mathematics. It comprises specially written chapters by a group of internationally renowned thinkers, as well as four substantial responses from Wright. In these thematically organized replies, Wright summarizes his life's work and responds to the contributory essays collected in this book. In bringing together such scholarship, the present volume testifies to both the enormous interest in Wright's thought and the continued relevance of Wright's seminal contributions in analytic philosophy for present-day debates;

Author : J. van Benthem,Alice G. B. ter Meulen
Publisher : Elsevier
Page : 1274 pages
File Size : 47,8 Mb
Release : 1997
Category : Computers
ISBN : 9780444817143

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Handbook of Logic and Language by J. van Benthem,Alice G. B. ter Meulen Pdf

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.

Author : Clive William Kilmister
Publisher : Unknown
Page : 144 pages
File Size : 40,9 Mb
Release : 1967
Category : Logic, Symbolic and mathematical
ISBN : STANFORD:36105031209823

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Language, Logic, and Mathematics by Clive William Kilmister Pdf

Author : Mohan Ganesalingam
Publisher : Springer
Page : 273 pages
File Size : 50,8 Mb
Release : 2013-03-14
Category : Computers
ISBN : 9783642370120

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The Language of Mathematics by Mohan Ganesalingam Pdf

The Language of Mathematics was awarded the E.W. Beth Dissertation Prize for outstanding dissertations in the fields of logic, language, and information. It innovatively combines techniques from linguistics, philosophy of mathematics, and computation to give the first wide-ranging analysis of mathematical language. It focuses particularly on a method for determining the complete meaning of mathematical texts and on resolving technical deficiencies in all standard accounts of the foundations of mathematics. "The thesis does far more than is required for a PhD: it is more like a lifetime's work packed into three years, and is a truly exceptional achievement." Timothy Gowers

Author : Zofia Adamowicz,Pawel Zbierski
Publisher : John Wiley & Sons
Page : 276 pages
File Size : 52,7 Mb
Release : 2011-09-26
Category : Mathematics
ISBN : 9781118030790

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Logic of Mathematics by Zofia Adamowicz,Pawel Zbierski Pdf

A thorough, accessible, and rigorous presentation of the central theorems of mathematical logic . . . ideal for advanced students of mathematics, computer science, and logic Logic of Mathematics combines a full-scale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems. Using a strict mathematical approach, this is the only book available that contains complete and precise proofs of all of these important theorems: * Gödel's theorems of completeness and incompleteness * The independence of Goodstein's theorem from Peano arithmetic * Tarski's theorem on real closed fields * Matiyasevich's theorem on diophantine formulas Logic of Mathematics also features: * Full coverage of model theoretical topics such as definability, compactness, ultraproducts, realization, and omission of types * Clear, concise explanations of all key concepts, from Boolean algebras to Skolem-Löwenheim constructions and other topics * Carefully chosen exercises for each chapter, plus helpful solution hints At last, here is a refreshingly clear, concise, and mathematically rigorous presentation of the basic concepts of mathematical logic-requiring only a standard familiarity with abstract algebra. Employing a strict mathematical approach that emphasizes relational structures over logical language, this carefully organized text is divided into two parts, which explain the essentials of the subject in specific and straightforward terms. Part I contains a thorough introduction to mathematical logic and model theory-including a full discussion of terms, formulas, and other fundamentals, plus detailed coverage of relational structures and Boolean algebras, Gödel's completeness theorem, models of Peano arithmetic, and much more. Part II focuses on a number of advanced theorems that are central to the field, such as Gödel's first and second theorems of incompleteness, the independence proof of Goodstein's theorem from Peano arithmetic, Tarski's theorem on real closed fields, and others. No other text contains complete and precise proofs of all of these theorems. With a solid and comprehensive program of exercises and selected solution hints, Logic of Mathematics is ideal for classroom use-the perfect textbook for advanced students of mathematics, computer science, and logic.

Author : Richard E. Hodel
Publisher : Courier Corporation
Page : 514 pages
File Size : 48,9 Mb
Release : 2013-01-01
Category : Mathematics
ISBN : 9780486497853

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An Introduction to Mathematical Logic by Richard E. Hodel Pdf

This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.

Author : Jaakko Hintikka
Publisher : Springer Science & Business Media
Page : 339 pages
File Size : 43,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401720458

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Language, Truth and Logic in Mathematics by Jaakko Hintikka Pdf

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.

Author : David Makinson
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 51,9 Mb
Release : 2012-02-27
Category : Computers
ISBN : 9781447125006

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Sets, Logic and Maths for Computing by David Makinson Pdf

This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions.

Author : Mark Kac,Stanislaw M. Ulam
Publisher : Courier Corporation
Page : 189 pages
File Size : 43,5 Mb
Release : 1992-01-01
Category : Philosophy
ISBN : 9780486670850

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Mathematics and Logic by Mark Kac,Stanislaw M. Ulam Pdf

Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."

Author : George Tourlakis
Publisher : John Wiley & Sons
Page : 314 pages
File Size : 41,5 Mb
Release : 2011-03-01
Category : Mathematics
ISBN : 9781118030691

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Mathematical Logic by George Tourlakis Pdf

A comprehensive and user-friendly guide to the use of logic in mathematical reasoning Mathematical Logic presents a comprehensive introduction to formal methods of logic and their use as a reliable tool for deductive reasoning. With its user-friendly approach, this book successfully equips readers with the key concepts and methods for formulating valid mathematical arguments that can be used to uncover truths across diverse areas of study such as mathematics, computer science, and philosophy. The book develops the logical tools for writing proofs by guiding readers through both the established "Hilbert" style of proof writing, as well as the "equational" style that is emerging in computer science and engineering applications. Chapters have been organized into the two topical areas of Boolean logic and predicate logic. Techniques situated outside formal logic are applied to illustrate and demonstrate significant facts regarding the power and limitations of logic, such as: Logic can certify truths and only truths. Logic can certify all absolute truths (completeness theorems of Post and Gödel). Logic cannot certify all "conditional" truths, such as those that are specific to the Peano arithmetic. Therefore, logic has some serious limitations, as shown through Gödel's incompleteness theorem. Numerous examples and problem sets are provided throughout the text, further facilitating readers' understanding of the capabilities of logic to discover mathematical truths. In addition, an extensive appendix introduces Tarski semantics and proceeds with detailed proofs of completeness and first incompleteness theorems, while also providing a self-contained introduction to the theory of computability. With its thorough scope of coverage and accessible style, Mathematical Logic is an ideal book for courses in mathematics, computer science, and philosophy at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who wish to learn how to use logic in their everyday work.

Author : H.-D. Ebbinghaus,J. Flum,Wolfgang Thomas
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 42,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475723557

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Mathematical Logic by H.-D. Ebbinghaus,J. Flum,Wolfgang Thomas Pdf

This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

Author : Rudolf Carnap
Publisher : Routledge
Page : 376 pages
File Size : 46,8 Mb
Release : 2014-06-23
Category : Philosophy
ISBN : 9781317830597

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Logical Syntax of Language by Rudolf Carnap Pdf

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".

Author : Christopher C. Leary,Lars Kristiansen
Publisher : Lulu.com
Page : 382 pages
File Size : 53,5 Mb
Release : 2015
Category : Education
ISBN : 9781942341079

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A Friendly Introduction to Mathematical Logic by Christopher C. Leary,Lars Kristiansen Pdf

At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.