Set Theory, Logic and Their Limitations

Author: Moshe Machover

Publisher: Cambridge University Press

ISBN: 9780521479981

Category: Mathematics

Page: 288

View: 9188

Rigorous coverage of logic and set theory for students of mathematics and philosophy.
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Logik

Grund- und Aufbaukurs in Aussagen- und Prädikatenlogik

Author: Gerhard Schurz

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110590689

Category: Philosophy

Page: 447

View: 2579

Diese Einführung in die Logik umfaßt einen Grundkurs und einen Aufbaukurs. Der Grundkurs ist voraussetzungsfrei geschrieben und führt in die Semantik und Beweistheorie der Aussagenlogik und elementaren Prädikatenlogik ein, eingebettet in die allgemeine Theorie des rationalen Schließens. Logische Zusammenhänge werden in Verbindung mit sorgfältig ausgewählten Übungsbeispielen – inklusive Lösungen – einsichtig gemacht. Auf die philosophische Anwendung der Logik in der logischen Rekonstruktion natursprachlicher Texte und Argumente liegt besonderes Augenmerk. Zusammenhänge zwischen alternativen logischen Notationen und Techniken, die anfangs oft Schwierigkeiten bereiten, werden sorgfältig erklärt. Der anschließende Aufbaukurs schlägt die Brücke zwischen einer philosophischen Logikeinführung und dem fortgeschrittenen Niveau moderner formaler Logik. Nach einer gründlichen Einführung in die volle Prädikatenlogik und ihrer mengentheoretischen Semantik wendet sich der Band metalogischen Methoden zu. Prominente Resultate zur Korrektheit und Vollständigkeit der Prädikatenlogik, zur Entscheidbarkeit der monadischen und Unentscheidbarkeit der vollen Prädikatenlogik sowie zur Unvollständigkeit der Arithmetik 1. Stufe werden Schritt um Schritt erklärt. Abgerundet wird der Band durch zahlreiche Exkurse zur philosophischen Vertiefung logischer Grundlagenfragen. Zahlreiche Übungsbeispiele mit Lösungen zum Download vertiefen den Stoff. Die Lösungen werden ab Oktober 2018 verfügbar sein.
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Enzyklopädie Philosophie und Wissenschaftstheorie

Bd. 5: Log–N

Author: Jürgen Mittelstraß

Publisher: Springer-Verlag

ISBN: 3476001407

Category: Philosophy

Page: 629

View: 8946

Das gesamte Wissen der Philosophie und Wissenschaftstheorie. Die Sach- und Personenartikel des Nachschlagewerks erfassen nicht nur den klassischen Bestand des philosophischen Wissens, sondern werden auch den neueren Entwicklungen in der Philosophie gerecht. Insbesondere in den Bereichen Logik, Erkenntnis- und Wissenschaftstheorie sowie Sprachphilosophie. Jetzt erscheint der fünfte Band der Neuauflage mit über 70 neuen Artikeln u. a. zu diesen Begriffen: antike Logik, Lüge, Macht, Medizin, Nano und Neurowissenschaften. Mit neuen Personenartikeln, darunter Luhmann, Lyotard, Maturana.
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Introduction to Model Theory

Author: Philipp Rothmaler

Publisher: CRC Press

ISBN: 9789056993139

Category: Mathematics

Page: 324

View: 3666

Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory. In this spirit, the compactness theorem is proved via the algebraically useful ultrsproduct technique (rather than via the completeness theorem of first-order logic). This leads fairly quickly to algebraic applications, like Malcev's local theorems of group theory and, after a little more preparation, to Hilbert's Nullstellensatz of field theory. Steinitz dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal theories. There is a final chapter on the models of the first-order theory of the integers as an abelian group. Both these topics appear here for the first time in a textbook at the introductory level, and are used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory.
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Principia Mathematica.

Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: 167

View: 1679

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Internationale mathematische Nachrichten

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 3212

Issues for Dec. 1952- include section: Nachrichten der Österreichischen Mathematischen Gesellschaft.
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Beweise und Widerlegungen

Die Logik mathematischer Entdeckungen

Author: Imre Lakatos

Publisher: Springer-Verlag

ISBN: 3663001962

Category: Mathematics

Page: 163

View: 2916

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Cantorian Set Theory and Limitation of Size

Author: Michael Hallett

Publisher: Oxford University Press

ISBN: 9780198532835

Category: Mathematics

Page: 343

View: 3415

Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.
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Mathematical Logic

Author: H.-D. Ebbinghaus,J. Flum,Wolfgang Thomas

Publisher: Springer Science & Business Media

ISBN: 9780387942582

Category: Mathematics

Page: 291

View: 930

This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.
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Numbers, Sets and Axioms

The Apparatus of Mathematics

Author: A. G. Hamilton

Publisher: Cambridge University Press

ISBN: 9780521287616

Category: Mathematics

Page: 255

View: 3040

Following the success of Logic for Mathematicians, Dr Hamilton has written a text for mathematicians and students of mathematics that contains a description and discussion of the fundamental conceptual and formal apparatus upon which modern pure mathematics relies. The author's intention is to remove some of the mystery that surrounds the foundations of mathematics. He emphasises the intuitive basis of mathematics; the basic notions are numbers and sets and they are considered both informally and formally. The role of axiom systems is part of the discussion but their limitations are pointed out. Formal set theory has its place in the book but Dr Hamilton recognises that this is a part of mathematics and not the basis on which it rests. Throughout, the abstract ideas are liberally illustrated by examples so this account should be well-suited, both specifically as a course text and, more broadly, as background reading. The reader is presumed to have some mathematical experience but no knowledge of mathematical logic is required.
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Die Grenzen des Wachstums

Bericht des Club of Rome zur Lage der Menschheit

Author: Dennis Meadows,Donella H. Meadows

Publisher: N.A

ISBN: N.A

Category: Economic history

Page: 183

View: 2630

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The Design of Everyday Things

Psychologie und Design der alltäglichen Dinge

Author: Norman Don

Publisher: Vahlen

ISBN: 3800648105

Category: Business & Economics

Page: 320

View: 8247

Apple, Audi, Braun oder Samsung machen es vor: Gutes Design ist heute eine kritische Voraussetzung für erfolgreiche Produkte. Dieser Klassiker beschreibt die fundamentalen Prinzipien, um Dinge des täglichen Gebrauchs umzuwandeln in unterhaltsame und zufriedenstellende Produkte. Don Norman fordert ein Zusammenspiel von Mensch und Technologie mit dem Ziel, dass Designer und Produktentwickler die Bedürfnisse, Fähigkeiten und Handlungsweisen der Nutzer in den Vordergrund stellen und Designs an diesen angepasst werden. The Design of Everyday Things ist eine informative und spannende Einführung für Designer, Marketer, Produktentwickler und für alle an gutem Design interessierten Menschen. Zum Autor Don Norman ist emeritierter Professor für Kognitionswissenschaften. Er lehrte an der University of California in San Diego und der Northwest University in Illinois. Mitte der Neunzigerjahre leitete Don Norman die Advanced Technology Group bei Apple. Dort prägte er den Begriff der User Experience, um über die reine Benutzbarkeit hinaus eine ganzheitliche Erfahrung der Anwender im Umgang mit Technik in den Vordergrund zu stellen. Norman ist Mitbegründer der Beratungsfirma Nielsen Norman Group und hat unter anderem Autohersteller von BMW bis Toyota beraten. „Keiner kommt an Don Norman vorbei, wenn es um Fragen zu einem Design geht, das sich am Menschen orientiert.“ Brand Eins 7/2013 „Design ist einer der wichtigsten Wettbewerbsvorteile. Dieses Buch macht Spaß zu lesen und ist von größter Bedeutung.” Tom Peters, Co-Autor von „Auf der Suche nach Spitzenleistungen“
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Einführung in die Modelltheorie

Vorlesungen

Author: Philipp Rothmaler

Publisher: Spektrum Akademischer Verlag

ISBN: 9783860254615

Category: Model theory

Page: 331

View: 4967

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Mathematical Logic

Author: George Tourlakis

Publisher: John Wiley & Sons

ISBN: 1118030699

Category: Mathematics

Page: 294

View: 6270

A comprehensive and user-friendly guide to the use of logic inmathematical reasoning Mathematical Logic presents a comprehensive introductionto formal methods of logic and their use as a reliable tool fordeductive reasoning. With its user-friendly approach, this booksuccessfully equips readers with the key concepts and methods forformulating valid mathematical arguments that can be used touncover truths across diverse areas of study such as mathematics,computer science, and philosophy. The book develops the logical tools for writing proofs byguiding readers through both the established "Hilbert" style ofproof writing, as well as the "equational" style that is emergingin computer science and engineering applications. Chapters havebeen organized into the two topical areas of Boolean logic andpredicate logic. Techniques situated outside formal logic areapplied to illustrate and demonstrate significant facts regardingthe power and limitations of logic, such as: Logic can certify truths and only truths. Logic can certify all absolute truths (completeness theorems ofPost and Gödel). Logic cannot certify all "conditional" truths, such as thosethat are specific to the Peano arithmetic. Therefore, logic hassome serious limitations, as shown through Gödel'sincompleteness theorem. Numerous examples and problem sets are provided throughout thetext, further facilitating readers' understanding of thecapabilities of logic to discover mathematical truths. In addition,an extensive appendix introduces Tarski semantics and proceeds withdetailed proofs of completeness and first incompleteness theorems,while also providing a self-contained introduction to the theory ofcomputability. With its thorough scope of coverage and accessible style,Mathematical Logic is an ideal book for courses inmathematics, computer science, and philosophy at theupper-undergraduate and graduate levels. It is also a valuablereference for researchers and practitioners who wish to learn howto use logic in their everyday work.
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Naive Mengenlehre

Author: Paul R. Halmos

Publisher: Vandenhoeck & Ruprecht

ISBN: 9783525405277

Category: Arithmetic

Page: 132

View: 3362

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Rough Sets and Current Trends in Computing

Second International Conference, RSCTC 2000 Banff, Canada, October 16-19, 2000 Revised Papers

Author: Wojciech Ziarko,Yiyu Yao

Publisher: Springer Science & Business Media

ISBN: 3540430741

Category: Computers

Page: 676

View: 4459

This book constitutes the thoroughly refereed post-proceedings of the Second International Conference on Rough Sets and Current Trends in Computing, RSCTC 2000, held in Banff, Canada in October 2000. The 80 revised papers presented together with an introduction and three keynote presentations have gone through two rounds of reviewing and revision. The papers are organized in topical sections on granual computing, rough sets and systems, fuzzy sets and systems, rough sets and data mining, nonclassical logics and reasoning, pattern recognition and image processing, neural networks and genetic algorithms, and current trends in computing.
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Handbook of Philosophical Logic

Author: Dov M. Gabbay,Franz Guenthner

Publisher: Springer Science & Business Media

ISBN: 9781402019661

Category: Philosophy

Page: 323

View: 8925

It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.
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Das Ziel

Ein Roman über Prozessoptimierung

Author: Eliyahu M. Goldratt,Jeff Cox

Publisher: Campus Verlag

ISBN: 3593423596

Category: Business & Economics

Page: 406

View: 3784

Ein Roman über Prozessoptimierung? Geht das? Das geht nicht nur – das liest sich auch spannend von der ersten bis zur letzten Seite. Eliyahu M. Goldratts "Das Ziel" ist die Geschichte des Managers Alex Rogo, der mit ungewöhnlichen und schlagkräftigen neuen Methoden in seinem Unternehmen für Aufsehen sorgt. Der Klassiker unter den Wirtschaftsbüchern, der das Managementdenken weltweit umkrempelt, wurde jetzt erweitert um den wichtigsten Aufsatz des Autors, "Standing on the Shoulders of Giants": Pflichtlektüre für Manager – und fesselnder Lesestoff.
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Verification, Model Checking, and Abstract Interpretation

12th International Conference, VMCAI 2011, Austin, TX, USA, January 23-25, 2011 Proceedings

Author: Ranjit Jhala,David Schmidt

Publisher: Springer Science & Business Media

ISBN: 3642182747

Category: Computers

Page: 419

View: 7447

This book constitutes the refereed proceedings of the 12th International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2011, held in Austin, TX, USA, in January 2011, co-located with the Symposium on Principles of Programming Languages, POPL 2011. The 24 revised full papers presented together with 4 invited talks were carefully reviewed and selected from 71 initial submissions. The papers showcases state-of-the-art research in areas such as verification, model checking, abstract interpretation and address any programming paradigm, including concurrent, constraint, functional, imperative, logic and object-oriented programming. Further topics covered are static analysis, deductive methods, program certification, debugging techniques, abstract domains, type systems, and optimization.
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