Direct and Converse Theorems

The Elements of Symbolic Logic

Author: I. S. Gradshtein

Publisher: Elsevier

ISBN: 1483155072

Category: Mathematics

Page: 192

View: 3517

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: 6348

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.

Philosophic Foundations of Quantum Mechanics

Author: Hans Reichenbach

Publisher: Courier Corporation

ISBN: 0486150100

Category: Science

Page: 208

View: 6247

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 Philosophy of Space and Time

Author: Hans Reichenbach

Publisher: Courier Corporation

ISBN: 0486138038

Category: Science

Page: 336

View: 8779

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.

Elements of Intuitionism

Author: Michael A. E. Dummett

Publisher: Oxford University Press

ISBN: 9780198505242

Category: Mathematics

Page: 331

View: 4032

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.

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: 6814

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.

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: 7036

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: 9780520010550

Category: Philosophy

Page: 333

View: 2545

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 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: 6207

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.

Introducing Symbolic Logic

Author: Robert M. Martin

Publisher: Broadview Press

ISBN: 9781551116358

Category: Philosophy

Page: 272

View: 2184

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.

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: 3125

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.

Mathematical Logic

Author: Willard QUINE

Publisher: Harvard University Press

ISBN: 9780674554511

Category: Philosophy

Page: 346

View: 6339

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

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: 8317

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.

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: 2930

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.

The Direction of Time

Author: Hans Reichenbach

Publisher: Courier Corporation

ISBN: 0486137252

Category: Science

Page: 304

View: 6120

Distinguished physicist examines emotive significance of time, time order of mechanics, time direction of thermodynamics and microstatistics, time direction of macrostatistics, time of quantum physics, more. 1971 edition.

Hans Reichenbach: Logical Empiricist

Author: M.H. Salmon

Publisher: Springer Science & Business Media

ISBN: 9789027709585

Category: Science

Page: 793

View: 7574

Logical empiricism - not to be confused with logical positivism (see pp. 40-44) - is a movement which has left an indelible mark on twentieth century philosophy; Hans Reichenbach (1891-1953) was one of its found ers and one of its most productive advocates. His sudden and untimely death in 1953 halted his work when he was at the height of his intellectual powers; nevertheless, he bequeathed to us a handsome philosophical inheritance. At the present time, twenty-five years later, we can survey our heritage and see to what extent we have been enriched. The present collection of essays constitutes an effort to do just that - to exhibit the scope and unity of Reichenbach's philosophy, and its relevance to current philosophical issues. There is no Nobel Prize in philosophy - the closest analogue is a volume in The Library of Living Philosophers, an honor which, like the Nobel Prize, cannot be awarded posthumously. Among 'scientific philosophers,' Rudolf Carnap, Albert Einstein, Karl Popper, and Bertrand Russell have been so honored. Had Reichenbach lived longer, he would have shared the honor with Carnap, for at the time of his death a volume on Logical Empiricism, treating the works of Carnap and Reichenbach, was in its early stages of preparation. In the volume which emerged, Carnap wrote, "In 1953, when Reichenbach's creative activity was suddenly ended by his premature death, our movement lost one of its most active leaders.