Direct and Converse Theorems

The Elements of Symbolic Logic

Author: I. S. Gradshtein

Publisher: Elsevier

ISBN: 1483155072

Category: Mathematics

Page: 192

View: 7573

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.

Elements of Sentence Logic

Author: Wayne A. Patterson

Publisher: Marshall Cavendish International


Category: Language Arts & Disciplines

Page: 216

View: 7897

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 Intuitionism

Author: Michael A. E. Dummett

Publisher: Oxford University Press

ISBN: 9780198505242

Category: Mathematics

Page: 331

View: 4836

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.

Introducing Symbolic Logic

Author: Robert M. Martin

Publisher: Broadview Press

ISBN: 9781551116358

Category: Philosophy

Page: 272

View: 517

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.

Premises and Conclusions

Symbolic Logic for Legal Analysis

Author: Robert E. Rodes

Publisher: Pearson College Division


Category: Law

Page: 387

View: 487

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.

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: 3798

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.

Mathematical Logic

Author: Willard QUINE

Publisher: Harvard University Press

ISBN: 9780674554511

Category: Philosophy

Page: 346

View: 3454

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

Handbook of Mathematical Logic

Author: J. Barwise

Publisher: Elsevier

ISBN: 9780080933641

Category: Mathematics

Page: 1164

View: 4062

The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.

Kausalität als linguistische Kategorie

Mittel und Möglichkeiten für Begründungen

Author: Beda Schmidhauser

Publisher: Walter de Gruyter

ISBN: 3110926857

Category: Language Arts & Disciplines

Page: 261

View: 2908

In dieser rein linguistisch orientierten Arbeit wird der Versuch unternommen, die Kausalität als eine linguistische Gesamtkategorie zu erfassen. Hauptsächliches Ziel der Untersuchung ist dabei die Beschreibung sprachlicher Mittel und Möglichkeiten für die Darstellung kausaler Zusammenhänge in Texten. Anhand einer ausführlichen Darlegung der verschiedenen methodischen Zugänge zum Problemkreis ergibt sich als ein zentrales Resultat der Untersuchung, daß die Kausalität nur ausgehend von einer Sprachhandlung BEGRÜNDEN als eine Gesamtkategorie erfaßt werden kann. Auf der Grundlage dieses Konzepts werden anschließend die sprachlichen Mittel zum Ausdruck von Begründungen (da, denn, weil, deshalb, -halber, O/, etc.) unter Berücksichtigung ihrer spezifischen Rahmenbedingungen aufgeführt und eingehend beschrieben. Besonders nützlich dürfte dabei das reichhaltige Beispielmaterial sein. Als theoretische Schwerpunkte ergeben sich u.a. Fragestellungen zur Kasusgrammatik, zur Behandlung des Symptombezugs (verkehrte Darstellung des Ursache-Wirkungs-Verhältnisses) sowie zum Verhältnis von Kausalität und Temporalität (d.h. des temporal-kausalen Fehlschlusses post hoc, ergo propter hoc). Aufgrund ihrer thematischen Orientierung leistet die Untersuchung gleichzeitig einen Beitrag zu der von Wissenschaftlern und Sprachpädagogen geführten Diskussion über die angeblich abnehmenden Fähigkeiten von Muttersprachlern, Texte als in sich kohärentes Geflecht von logischen Bezügen zu erkennen und zu gestalten. Dementsprechend richtet sich dieses Buch nicht nur an spezialisierte Linguisten, sondern z.B. auch an Deutschlehrerinnen und -lehrer der gymnasialen Oberstufe.

Elements of Logic via Numbers and Sets

Author: D.L. Johnson

Publisher: Springer Science & Business Media

ISBN: 1447106032

Category: Mathematics

Page: 188

View: 381

In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs. Dave Johnson has drawn from his considerable experience to provide a text that concentrates on the most important elements of the subject using clear, simple explanations that require no background knowledge of logic. It gives many useful examples and problems, many with fully-worked solutions at the end of the book. In addition to a comprehensive index, there is also a useful `Dramatis Personae` an index to the many symbols introduced in the text, most of which will be new to students and which will be used throughout their degree programme.

Experience and Prediction

An Analysis of the Foundations and the Structure of Knowledge

Author: Hans Reichenbach

Publisher: N.A

ISBN: 9781258214906


Page: 416

View: 9849

First published in 1949 expressly to introduce logical positivism to English speakers. Reichenbach, with Rudolph Carnap, founded logical positivism, a form of epistemofogy that privileged scientific over metaphysical truths.

Philosophy of Language

Author: F. Von Kutschera

Publisher: Springer Science & Business Media

ISBN: 9401018200

Category: Philosophy

Page: 311

View: 9120

This book has arisen out of lectures I gave in recent years at the Uni versities of Munich and Regensburg, and it is intended to serve as a textbook for courses in the Philosophy of Language. In my lectures I was able to presuppose that the students had taken an introductory course in logic. Some knowledge of logic will also be helpful in studying this book - as it is almost everywhere else in philosophy -, especially in Section 3. 2, but it is no prerequisite. I would like to give my sincere thanks to Prof. Terrell for his excellent translation of the book, which is based on the second, revised and en larged German edition. Regensburg, May 1975 FRANZ VON KUTSCHERA INTRODUCTION Language has become one of philosophy's most important and pressing themes during this century. This preoccupation with language has its ori gins in the most diverse areas of philosophical inquiry.

Key Writers on Art: The Twentieth Century

Author: Chris Murray

Publisher: Routledge

ISBN: 1134597207

Category: Art

Page: 336

View: 7454

Key Writers on Art: The Twentieth Century offers a unique and authoritative guide to modern responses to art. Featuring 48 essays on the most important twentieth century writers and thinkers and written by an international panel of expert contributors, it introduces readers to key approaches and analytical tools used in the study of contemporary art. It discusses writers such as Adorno, Barthes, Benjamin, Freud, Greenberg, Heuser, Kristeva, Merleau-Ponty, Pollock, Read and Sontag.

Correspondence, Invariance and Heuristics

Essays in Honour of Heinz Post

Author: S. French,H. Kamminga

Publisher: Springer Science & Business Media

ISBN: 9401711852

Category: Science

Page: 364

View: 9432

This volume is presented in honour of Heinz Post, who founded a distinc tive and distinguished school of philosophy of science at Chelsea College, University of London. The 'Chelsea tradition' in philosophy of science takes the content of science seriously, as exemplified by the papers presented here. The unifying theme of this work is that of 'Correspondence, Invariance and Heuristics', after the title of a classic and seminal paper by Heinz Post, published in 1971, which is reproduced in this volume with the kind permission of the editors and publishers of Studies in History and Philosophy of Science. Described by Paul Feyerabend in Against Method as "brilliant" and " . . . a partial antidote against the view which I try to defend" (1975, p. 61, fn. 17), this paper, peppered with illustrative examples from the history of science, brings to the fore some of Heinz Post's central concerns: the heuristic criteria used by scientists in constructing their theories, the intertheoretic relationships which these criteria reflect and, in particular, the nature of the correspondence that holds between a theory and its predecessors (and its suc cessors). The appearance of this volume more than twenty years later is an indica tion of the fruitfulness of Post's contribution: philosophers of science continue to explore the issues raised in his 1971 paper.