Direct and Converse Theorems

The Elements of Symbolic Logic

Author: I. S. Gradshtein

Publisher: Elsevier

ISBN: 1483155072

Category: Mathematics

Page: 192

View: 2224

Direct and Converse Theorems: The Elements of Symbolic Logic, Third Edition explains the logical relations between direct, converse, inverse, and inverse converse theorems, as well as the concept of necessary and sufficient conditions. This book consists of two chapters. The first chapter is devoted to the question of negation. Connected with the question of the negation of a proposition are interrelations of the direct and converse and also of the direct and inverse theorems; the interrelations of necessary and sufficient conditions; and the definition of the locus of a point. The second chapter explains several questions of mathematical logic–a science that is being developed in connection with the theory of mathematical proof. This edition is provided with a large number of problems and questions to help easily understand the material. The book is intended for students studying mathematics, specifically at intermediate colleges of various types. The text is also a useful reference for university students and teachers.

Premises and Conclusions

Symbolic Logic for Legal Analysis

Author: Robert E. Rodes

Publisher: Pearson College Division


Category: Law

Page: 387

View: 2159

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.

Elements of Intuitionism

Author: Michael A. E. Dummett

Publisher: Oxford University Press

ISBN: 9780198505242

Category: Mathematics

Page: 331

View: 8093

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.

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: 3994

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.

Introducing Symbolic Logic

Author: Robert M. Martin

Publisher: Broadview Press

ISBN: 1770481559

Category: Philosophy

Page: 253

View: 3414

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.

The Elements of Mathematical Logic

Author: Paul C. Rosenbloom

Publisher: Courier Corporation

ISBN: 0486446174

Category: Mathematics

Page: 214

View: 5589

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.

The Concept of Probability in the Mathematical Representation of Reality

Author: Hans Reichenbach

Publisher: Open Court Publishing Company

ISBN: 9780812696097

Category: Mathematics

Page: 154

View: 2246

The first English translation of Hans Reichenbach's lucid doctoral thesis sheds new light on how Kant’s Critique of Pure Reason was understood in some quarters at the time. The source of several themes in his still influential The Direction of Time, the thesis shows Reichenbach's early focus on the interdependence of physics, probability, and epistemology.

Essentials of Symbolic Logic - Third Edition

Author: R.L. Simpson

Publisher: Broadview Press

ISBN: 1770484957

Category: Philosophy

Page: 296

View: 6021

The third edition of Essentials of Symbolic Logic is a concise and clearly written introduction to the topic. Based on years of use in colleges and universities, the book provides an accessible and thorough grounding in sentence logic and predicate logic. While technical jargon is kept to a minimum, all necessary logical concepts and vocabulary are explained clearly. A standard system of natural deduction is developed, and readers are given suggestions for developing strategies for creating derivations (proofs) in this system. An instructor’s website is available with solutions to all the exercises in the text, including the many new exercises which have been added to this new edition.

An Introduction to Symbolic Logic

Author: Langer

Publisher: Courier Corporation

ISBN: 9780486601649

Category: Mathematics

Page: 384

View: 3626

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.


The Laws of Truth

Author: Nicholas Jeremy Josef Smith

Publisher: Princeton University Press

ISBN: 0691151636

Category: Philosophy

Page: 528

View: 5788

Provides an essential introduction to classical logic.

Principles of Mathematical Logic

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

Publisher: American Mathematical Soc.

ISBN: 0821820249

Category: Mathematics

Page: 172

View: 9831

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.

The Rise of Scientific Philosophy

Author: Hans Reichenbach

Publisher: Univ of California Press

ISBN: 9780520010550

Category: Philosophy

Page: 333

View: 8574

This book represents a new approach to philosophy. It treats philosophy as not a collection of systems, but as a study of problems. It recognizes in traditional philosophical systems the historical function of having asked questions rather than having given solutions. Professor Reichenbach traces the failures of the systems to psychological causes. Speculative philosophers offered answers at a time when science had not yet provided the means to give true answers. Their search for certainty and for moral directives led them to accept pseudo-solutions. Plato, Descartes, Spinoza, Kant, and many others are cited to illustrate the rationalist fallacy: reason, unaided by observation, was regarded as a source of knowledge, revealing the physical world and "moral truth." The empiricists could not disprove this thesis, for they could not give a valid account of mathematical knowledge. Mathematical discoveries in the early nineteenth century cleared the way for modern scientific philosophy. Its advance was furthered by discoveries in modern physics, chemistry, biology, and psychology. These findings have made possible a new conception of the universe and of the atom. The work of scientists thus altered philosophy completely and brought into being a philosopher with a new attitude and training. Instead of dictating so-called laws of reason to the scientist, this modern philosopher proceeds by analyzing scientific methods and results. He finds answers to the age-old questions of space, time, causality, and life; of the human observer and the external world. He tells us how to find our way through this world without resorting to unjustifiable beliefs or assuming a supernatural origin for moral standards. Philosophy thus is no longer a battleground of contradictory opinions, but a science discovering truth step by step. Professor Reichenbach, known for his many contributions to logic and the philosophy of science, addresses this book to a wider audience. He writes for those who do not have the leisure or preparation to read in the fields of mathematics, symbolic logic, or physics. Besides showing the principal foundations of the new philosophy, he has been careful to provide the necessary factual background. He has written a philosophical study, not a mere popularization. It contains within its chapters all the necessary scientific material in an understandable form--and, therefore, conveys all the information indispensable to a modern world-view. The late Hans Reichenbach was Professor of Philosophy at the University of California, Los Angeles. His previous books include

Symbolic Logic

Classical and Advanced Systems

Author: Harry J. Gensler

Publisher: N.A

ISBN: 9780138799410

Category: Logic, Symbolic and mathematical.

Page: 329

View: 9274

Elementary Symbolic Logic

Second Edition

Author: William Gustason,Dolph E. Ulrich

Publisher: Waveland Press

ISBN: 1478608889

Category: Mathematics

Page: 353

View: 1377

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.

Elements of Sentence Logic

Author: Wayne A. Patterson

Publisher: Marshall Cavendish International


Category: Language Arts & Disciplines

Page: 216

View: 5652

This book provides a lucid and comprehensive account of all aspects of sentence logic, and is fundamental to the study of modern symbolic logic. The close relationship between logic and language is emphasized throughout and the reader is shown how logical concepts are ultimately derived from our common sense understanding of how our language works. A variety of exercises at the end of each chapter reinforces the reader's grasp of these concepts.

Elements of Logical Reasoning

Author: Jan von Plato

Publisher: Cambridge University Press

ISBN: 1139867768

Category: Mathematics

Page: N.A

View: 2695

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.

Introduction to Mathematical Logic

Extended Edition

Author: Michał Walicki

Publisher: World Scientific Publishing Company

ISBN: 9814719986

Category: Mathematics

Page: 304

View: 3707

This is a systematic and well-paced introduction to mathematical logic. Excellent as a course text, the book presupposes only elementary background and can be used also for self-study by more ambitious students. Starting with the basics of set theory, induction and computability, it covers propositional and first order logic — their syntax, reasoning systems and semantics. Soundness and completeness results for Hilbert's and Gentzen's systems are presented, along with simple decidability arguments. The general applicability of various concepts and techniques is demonstrated by highlighting their consistent reuse in different contexts. Unlike in most comparable texts, presentation of syntactic reasoning systems precedes the semantic explanations. The simplicity of syntactic constructions and rules — of a high, though often neglected, pedagogical value — aids students in approaching more complex semantic issues. This order of presentation also brings forth the relative independence of syntax from the semantics, helping to appreciate the importance of the purely symbolic systems, like those underlying computers. An overview of the history of logic precedes the main text, while informal analogies precede introduction of most central concepts. These informal aspects are kept clearly apart from the technical ones. Together, they form a unique text which may be appreciated equally by lecturers and students occupied with mathematical precision, as well as those interested in the relations of logical formalisms to the problems of computability and the philosophy of logic. This revised edition contains also, besides many new exercises, a new chapter on semantic paradoxes. An equivalence of logical and graphical representations allows us to see vicious circularity as the odd cycles in the graphical representation and can be used as a simple tool for diagnosing paradoxes in natural discourse.

Mathematical Logic

Author: Willard QUINE

Publisher: Harvard University Press

ISBN: 9780674554511

Category: Philosophy

Page: 346

View: 8910

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