Direct and Converse Theorems

The Elements of Symbolic Logic

Author: I. S. Gradshtein

Publisher: Elsevier

ISBN: 1483155072

Category: Mathematics

Page: 192

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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 Deductive Inference

An Introduction to Symbolic Logic

Author: Joseph Bessie,Stuart Glennan

Publisher: Wadsworth Publishing Company

ISBN: 9780534551216

Category: Mathematics

Page: 479

View: 8728

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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.

Elements of Intuitionism

Author: Michael A. E. Dummett

Publisher: Oxford University Press

ISBN: 9780198505242

Category: Mathematics

Page: 331

View: 7529

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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 Sentence Logic

Author: Wayne A. Patterson

Publisher: Marshall Cavendish International

ISBN: N.A

Category: Language Arts & Disciplines

Page: 216

View: 8642

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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.

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: 9740

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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.

The Rise of Scientific Philosophy

Author: Hans Reichenbach

Publisher: Univ of California Press

ISBN: 0520010558

Category: Philosophy

Page: 348

View: 3660

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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

The Philosophy of Space and Time

Author: Hans Reichenbach

Publisher: Courier Corporation

ISBN: 0486138038

Category: Science

Page: 336

View: 8569

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A clear, penetrating exposition of developments in physical science and mathematics brought about by non-Euclidean geometries, including in-depth coverage of the foundations of geometry, theory of time, other topics.

Philosophic Foundations of Quantum Mechanics

Author: Hans Reichenbach

Publisher: Courier Corporation

ISBN: 0486150100

Category: Science

Page: 208

View: 5220

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Noted philosopher offers a philosophical interpretation of quantum physics that reviews the basics of quantum mechanics and outlines their mathematical methods, blending philosophical ideas and mathematical formulations to develop a variety of concrete interpretations. 1944 edition.

The Logic of Time

A Model-Theoretic Investigation into the Varieties of Temporal Ontology and Temporal Discourse

Author: Johan van Benthem

Publisher: Springer Science & Business Media

ISBN: 9401098689

Category: Philosophy

Page: 276

View: 7784

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That philosophical themes could be studied in an exact manner by logical meanS was a delightful discovery to make. Until then, the only outlet for a philosophical interest known to me was the production of poetry or essays. These means of expression remain inconclusive, however, with a tendency towards profuseness. The logical discipline provides so me intellectual backbone, without excluding the literary modes. A master's thesis by Erik Krabbe introduced me to the subject of tense logic. The doctoral dissertation of Paul N eedham awaked me (as so many others) from my dogmatic slumbers concerning the latter's mono poly on the logical study of Time. Finally, a set of lecture notes by Frank Veltman showed me how classical model theory is just as relevant to that study as more exotic intensional techniques. Of the authors whose work inspired me most, I would mention Arthur Prior, for his irresistible blend of logic and philosophy, Krister Segerberg, for his technical opening up of a systematic theory, and Hans Kamp, for his mastery of all these things at once. Many colleagues have made helpful comments on the two previous versions of this text. I would like to thank especially my students Ed Brinksma, Jan van Eyck and Wilfried Meyer-Viol for their logical and cultural criticism. The drawings were contributed by the versatile Bauke Mulder. Finally, Professor H intikka's kind appreciation provided the stimulus to write this book.

Philosophical Logic

Author: Robert L. Arrington,Peter M. Burkholder,Shannon Dubose,James W. Dye,James K. Feibleman,Bertrand P. Helm,Max Hocutt,Harold N. Lee,Louise N. Roberts,John C. Sallis,Donald H. Weiss

Publisher: Springer Science & Business Media

ISBN: 9401034974

Category: Philosophy

Page: 162

View: 1189

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With this issue we initiate the policy of expanding the scope of Tulane Studies in Philosophy to include, in addition to the work of members of the department, contributions from philosophers who have earned advanced degrees from Tulane and who are now teaching in other colleges and universities. The Editor THE LOGIC OF OUR LANGUAGE ROBERT L. ARRINGTON Wittgenstein wrote in the Tractatus that "logic is not a body of doctrine, but a mirror-image of the world. " 1 In line with his suggestion that a proposition is a 'picture', Wittgenstein argued that propositions 'show' the logical structure of the real. He was insistent, however, that "the apparent logical form of a proposition need not be its real one. " 2 As a result of this we can misunderstand the structure of fact. Philosophical problems arise just when "the logic of our language is mis understood. " 3 It is common knowledge that much of this view of logic was rejected by Wittgenstein himself in the Philosophical Investi gations. There we are told that language has no ideal or sublime 4 logic which mirrors the structure of the extra-linguistic world. Consequently, inferences from the structure of language to the structure of that extra-linguistic world are invalid. Reality can be 'cut up' in any of a number of ways by language. Wittgenstein adopted a view of philosophy which would render that discipline a non-explanatory, non-critical study of the multiple ways in which language can be used.

Principia Mathematica.

Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: 167

View: 6711

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Die slavischen Sprachen

ein internationales Handbuch zu ihrer Struktur, ihrer Geschichte und ihrer Erforschung

Author: Sebastian Kempgen

Publisher: Walter de Gruyter

ISBN: 3110156601

Category: Foreign Language Study

Page: 1116

View: 2498

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The handbook is intended to present a well balanced general view of the current state of Slavic linguistics and the Slavic languages with regard to their synchronic and diachronic description. In contrast to previous undertakings of a similar nature, this handbook is not intended to be a grammar with chapters on individual languages. Its length, the extensive scope of its subject matter, the systematic approach and the method of description which reflect the current state of Slavic Linguistics set this handbook apart from others.

Mathematical Logic

Author: Willard QUINE

Publisher: Harvard University Press

ISBN: 9780674554511

Category: Philosophy

Page: 346

View: 483

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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

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: 1841

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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: 7327

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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.

Scientific Procedures

A Contribution Concerning the Methodological Problems of Scientific Concepts and Scientific Explanation

Author: L. Tondl

Publisher: Springer Science & Business Media

ISBN: 9401029164

Category: Science

Page: 271

View: 2465

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For a decade, we have admired the incisive and broadly informed works of Ladislav Tondl on the foundations of science. Now it is indeed a pleasure to include this book among the Boston Studies in the Philosophy of Science. We hope that it will help to deepen the collaborative scholar ship of scientists and philosophers in Czechoslovakia with the English reading scholars of the world. Professor Ladislav Tondl was born in 1924, and completed his higher education at the Charles University iIi Prague. His doctorate was granted by the Institute of Information Theory and Automation. He was a professor and scientific research worker at the Institute for the Theory and Methodology of Science, which was a component part of the Czechoslovak Academy of Sciences. Tondl's principal fields of interest are the methodology of the empirical and experimental sciences, logical semantics, and cybernetics. For many years, he collaborated with Professor Albert Perez and others at the Institute of Information Theory and Automation in Prague, and he has undertaken fruitful collaboration with logicians in the Soviet and Polish schools, and been influenced by the Finnish logicians as well, among them Jaakko Hintikka. We list below a selection of his main publications. Perhaps the most accessible in presenting his central conception of the relationship between modem information theory and the methodology of the sciences is his 1965 paper with Perez, 'On the Role of Information Theory in Certain Scientific Procedures'.