Mathematics

The Elements of Mathematical Logic

Author: Paul C. Rosenbloom

Publisher: Courier Corporation

ISBN: 0486446174

Category: Mathematics

Page: 214

View: 953

This introduction to mathematical logic stresses the use of logical methods in attacking nontrivial problems. It covers the logic of classes, of propositions, of propositional functions, and the general syntax of language, with a brief introduction to so-called undecidability and incompleteness theorems; and much more. 1950 edition.
Mathematics

Elements of Intuitionism

Author: Michael A. E. Dummett

Publisher: Oxford University Press

ISBN: 9780198505242

Category: Mathematics

Page: 331

View: 8966

This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.
Law

Premises and Conclusions

Symbolic Logic for Legal Analysis

Author: Robert E. Rodes

Publisher: Pearson College Division

ISBN: N.A

Category: Law

Page: 387

View: 3476

This solidly written book explains the elements of contemporary symbolic logic, and examines the ways in which it illuminates the structure of legal reasoning and clarifies various legal problems. Offering a clear and succinct presentation of standard propositional and predicate logic, it presents the elements of standard logic and applies those techniques to legal materials. It covers the use of standard logic in legal argument, including the denial or distinguishing of premises and the rules of pleading, and makes extensive use of legal materials, cases and statutes, in both examples and exercises. Readers are also given strategies for handling major legal problems in standard logic, including ways for treating conditions contrary to fact, necessary and sufficient conditions, result within the risk, and intent. For logicians and philosophers of law.
Philosophy

Logic

The Laws of Truth

Author: Nicholas Jeremy Josef Smith

Publisher: Princeton University Press

ISBN: 0691151636

Category: Philosophy

Page: 528

View: 3915

Provides an essential introduction to classical logic.
Philosophy

Introducing Symbolic Logic

Author: Robert M. Martin

Publisher: Broadview Press

ISBN: 1460401158

Category: Philosophy

Page: 253

View: 3922

This accessible, SHORT introduction to symbolic logic includes coverage of sentential and predicate logic, translations, truth tables, and derivations. The author's engaging style makes this the most informal of introductions to formal logic. Topics are explained in a conversational, easy-to-understand way for readers not familiar with mathematics or formal systems, and the author provides patient, reader-friendly explanations—even with the occasional bit of humour. The first half of the book deals with all the basic elements of Sentential Logic: the five truth-functional connectives, formation rules and translation into this language, truth-tables for validity, logical truth/falsity, equivalency, consistency and derivations. The second half deals with Quantifier Logic: the two quantifiers, formation rules and translation, demonstrating certain logical characteristics by “Finding an Interpretation” and derivations. There are plenty of exercises scattered throughout, more than in many texts, arranged in order of increasing difficulty and including separate answer keys.
Mathematics

Beginning Logic

Author: E.J. Lemmon

Publisher: CRC Press

ISBN: 9780412380907

Category: Mathematics

Page: 240

View: 9649

The aim of this book is to provide an exposition of elementary formal logic. The course, which is primarily intended for first-year students who have no previous knowledge of the subject, forms a working basis for more advanced reading and is presented in such a way as to be intelligible to the layman. The nature of logic is examined with the gradual introduction of worked samples showing how to distinguish the sound statement from the unsound. Arguments whose soundness cannot be proved by propositional calculus are discussed, and it is shown how formalization can reveal the logical form of arguments. The final section of the book deals with the application of the predicate calculus as applied in various other fields of logic.
Mathematics

Introduction to Logic

and to the Methodology of Deductive Sciences

Author: Alfred Tarski

Publisher: Courier Corporation

ISBN: 0486318893

Category: Mathematics

Page: 272

View: 7753

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.
Mathematics

An Introduction to Symbolic Logic

Author: Langer

Publisher: Courier Corporation

ISBN: 9780486601649

Category: Mathematics

Page: 384

View: 9786

Famous classic has introduced countless readers to symbolic logic with its thorough and precise exposition. Starts with simple symbols and conventions and concludes with the Boole-Schroeder and Russell-Whitehead systems. No special knowledge of mathematics necessary. "One of the clearest and simplest introductions to a subject which is very much alive." — Mathematics Gazette.
Philosophy

The Logic of Our Language

An Introduction to Symbolic Logic

Author: Rodger L. Jackson,Melanie L. McLeod

Publisher: Broadview Press

ISBN: 1460402782

Category: Philosophy

Page: 352

View: 373

The Logic of Our Language teaches the practical and everyday application of formal logic. Rather than overwhelming the reader with abstract theory, Jackson and McLeod show how the skills developed through the practice of logic can help us to better understand our own language and reasoning processes. The authors’ goal is to draw attention to the patterns and logical structures inherent in our spoken and written language by teaching the reader how to translate English sentences into formal symbols. Other logical tools, including truth tables, truth trees, and natural deduction, are then introduced as techniques for examining the properties of symbolized sentences and assessing the validity of arguments. A substantial number of practice questions are offered both within the book itself and as interactive activities on a companion website.
Mathematics

Elements of Deductive Inference

An Introduction to Symbolic Logic

Author: Joseph Bessie,Stuart Glennan

Publisher: Wadsworth Publishing Company

ISBN: 9780534551216

Category: Mathematics

Page: 479

View: 2112

The text covers elementary logic, from statement logic through relational logic with identity and function symbols. The authors acquaint students with formal techniques at a level appropriate for undergraduates, but extends far enough and deep enough into the subject that it is suitable for a brief first-year graduate course. The text covers full and brief truth tables, and presents the method of truth (consistency) trees and natural deduction for the whole of elementary logic. The text's organization allows instructors to cover just statement logic, or statement logic combined with various extensions into predicate logic: monadic logic with or without identity, or the preceding plus relational logic with or without identity and with or without function symbols. At each stage, the instructor may elect to pursue truth trees and/or natural deduction. A final chapter provides a perspective for further study and applications of logic. The text may be used with or without the accompanying software.
Mathematics

Elementary Symbolic Logic

Second Edition

Author: William Gustason,Dolph E. Ulrich

Publisher: Waveland Press

ISBN: 1478608889

Category: Mathematics

Page: 353

View: 387

This volume offers a serious study of the fundamentals of symbolic logic that will neither frustrate nor bore the reader. The emphasis is on developing the students grasp of standard techniques and concepts rather than on achieving a high degree of sophistication. Coverage embraces all of the standard topics in sentential and quantificational logic, including multiple quantification, relations, and identity. Semantic and deductive topics are carefully distinguished, and appendices include an optional discussion of metatheory for sentential logic and truth trees.
Mathematics

Principles of Mathematical Logic

Author: David Hilbert,Wilhelm Ackermann,Robert E. Luce

Publisher: American Mathematical Soc.

ISBN: 0821820249

Category: Mathematics

Page: 172

View: 986

David Hilbert was particularly interested in the foundations of mathematics. Among many other things, he is famous for his attempt to axiomatize mathematics. This now classic text is his treatment of symbolic logic. This translation is based on the second German edition and has been modified according to the criticisms of Church and Quine. In particular, the authors' original formulation of Godel's completeness proof for the predicate calculus has been updated. In the first half of the twentieth century, an important debate on the foundations of mathematics took place. Principles of Mathematical Logic represents one of Hilbert's important contributions to that debate. Although symbolic logic has grown considerably in the subsequent decades, this book remains a classic.
Logic, Symbolic and mathematical.

Symbolic Logic

Classical and Advanced Systems

Author: Harry J. Gensler

Publisher: N.A

ISBN: 9780138799410

Category: Logic, Symbolic and mathematical.

Page: 329

View: 5778

Mathematics

Elements of Logical Reasoning

Author: Jan von Plato

Publisher: Cambridge University Press

ISBN: 1139867768

Category: Mathematics

Page: N.A

View: 589

Some of our earliest experiences of the conclusive force of an argument come from school mathematics: faced with a mathematical proof, we cannot deny the conclusion once the premises have been accepted. Behind such arguments lies a more general pattern of 'demonstrative arguments' that is studied in the science of logic. Logical reasoning is applied at all levels, from everyday life to advanced sciences, and a remarkable level of complexity is achieved in everyday logical reasoning, even if the principles behind it remain intuitive. Jan von Plato provides an accessible but rigorous introduction to an important aspect of contemporary logic: its deductive machinery. He shows that when the forms of logical reasoning are analysed, it turns out that a limited set of first principles can represent any logical argument. His book will be valuable for students of logic, mathematics and computer science.
Philosophy

Methods of Logic

Author: Willard Van Orman Quine

Publisher: Harvard University Press

ISBN: 9780674571761

Category: Philosophy

Page: 333

View: 2761

Provides comprehensive coverage of logical structure as well as the techniques of formal reasoning
Philosophy

Mathematical Logic

Author: Willard QUINE

Publisher: Harvard University Press

ISBN: 9780674554511

Category: Philosophy

Page: 346

View: 4296

W. V. Quineâe(tm)s systematic development of mathematical logic has been widely praised for the new material presented and for the clarity of its exposition. This revised edition, in which the minor inconsistencies observed since its first publication have been eliminated, will be welcomed by all students and teachers in mathematics and philosophy who are seriously concerned with modern logic. Max Black, in Mind, has said of this book, âeoeIt will serve the purpose of inculcating, by precept and example, standards of clarity and precision which are, even in formal logic, more often pursued than achieved.âe
Mathematics

An Introduction to Formal Logic

Author: Peter Smith

Publisher: Cambridge University Press

ISBN: 9780521008044

Category: Mathematics

Page: 357

View: 7017

Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.
Science

Can Theories be Refuted?

Essays on the Duhem-Quine Thesis

Author: Sandra Harding

Publisher: Springer Science & Business Media

ISBN: 9401018634

Category: Science

Page: 323

View: 5846

According to a view assumed by many scientists and philosophers of science and standardly found in science textbooks, it is controlled ex perience which provides the basis for distinguishing between acceptable and unacceptable theories in science: acceptable theories are those which can pass empirical tests. It has often been thought that a certain sort of test is particularly significant: 'crucial experiments' provide supporting empiri cal evidence for one theory while providing conclusive evidence against another. However, in 1906 Pierre Duhem argued that the falsification of a theory is necessarily ambiguous and therefore that there are no crucial experiments; one can never be sure that it is a given theory rather than auxiliary or background hypotheses which experiment has falsified. w. V. Quine has concurred in this judgment, arguing that "our statements about the external world face the tribunal of sense experience not indi vidually but only as a corporate body". Some philosophers have thought that the Duhem-Quine thesis gra tuitously raises perplexities. Others see it as doubly significant; these philosophers think that it provides a base for criticism of the foundational view of knowledge which has dominated much of western thought since Descartes, and they think that it opens the door to a new and fruitful way to conceive of scientific progress in particular and of the nature and growth of knowledge in general.
Logic, Symbolic and mathematical

Principia Mathematica

Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: N.A

View: 8965