Mathematics and Logic

Author: Mark Kac,Stanislaw M. Ulam

Publisher: Courier Corporation

ISBN: 0486670856

Category: Philosophy

Page: 170

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Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."

Basic Concepts of Mathematics and Logic

Author: Michael C. Gemignani

Publisher: Courier Corporation

ISBN: 0486435067

Category: Mathematics

Page: 280

View: 1473

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This text emphasizes logic and the theory of sets. Students who take no further courses in the field will find it an excellent resource for developing an appreciation for the nature of mathematics. Others will discover the foundations for future studies — set theory, logic, counting, numbers, functions, and more. 1968 edition. 43 figures. 25 tables.

The Oxford Handbook of Philosophy of Mathematics and Logic

Author: Stewart Shapiro

Publisher: OUP USA

ISBN: 0195148770

Category: Mathematics

Page: 833

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Covers the state of the art in the philosophy of maths and logic, giving the reader an overview of the major problems, positions, and battle lines. The chapters in this book contain both exposition and criticism as well as substantial development of their own positions. It also includes a bibliography.

My Best Mathematical and Logic Puzzles

Author: Martin Gardner

Publisher: Courier Corporation

ISBN: 0486281523

Category: Games

Page: 82

View: 1982

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The noted expert and longtime author of Scientific American's Mathematical Games column selects 70 of his favorite "short" puzzles. Enthusiasts can challenge their skills with such mind-bogglers as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, Bronx vs. Brooklyn, and dozens more involving logic and basic math. Complete solutions included.

The Philosophy of Mathematics and Logic in the 1920s and 1930s in Poland

Author: Roman Murawski

Publisher: Springer

ISBN: 3034808313

Category: Mathematics

Page: 228

View: 5248

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The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s. It was a remarkable period in the history of Polish science, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent the development of logic and mathematics was accompanied by a philosophical reflection. We try to answer those questions by analyzing both works of Polish logicians and mathematicians who have a philosophical temperament as well as their research practice. Works and philosophical views of the following Polish scientists will be analyzed: Wacław Sierpiński, Zygmunt Janiszewski, Stefan Mazurkiewicz, Stefan Banach Hugo Steinhaus, Eustachy Żylińsk and Leon Chwistek, Jan Łukasiewicz, Zygmunt Zawirski, Stanisław Leśniewski, Tadeusz Kotarbiński, Kazimierz Ajdukiewicz, Alfred Tarski, Andrzej Mostowski and Henryk Mehlberg, Jan Sleszyński, Stanisław Zaremba and Witold Wilkosz. To indicate the background of scientists being active in the 1920s and 1930s we consider in Chapter 1 some predecessors, in particular: Jan Śniadecki, Józef Maria Hoene-Wroński, Samuel Dickstein and Edward Stamm.

Mathematics and Logic in History and in Contemporary Thought

Author: Ettore Carruccio,Isabel Quigly

Publisher: Routledge

ISBN: 1351506617

Category: Mathematics

Page: 400

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This book is not a conventional history of mathematics as such, a museum of documents and scientific curiosities. Instead, it identifies this vital science with the thought of those who constructed it and in its relation to the changing cultural context in which it evolved. Particular emphasis is placed on the philosophic and logical systems, from Aristotle onward, that provide the basis for the fusion of mathematics and logic in contemporary thought.

Giuseppe Peano between Mathematics and Logic

Proceeding of the International Conference in honour of Giuseppe Peano on the 150th anniversary of his birth and the centennial of the Formulario Mathematico Torino (Italy) October 2-3, 2008

Author: Fulvia Skof

Publisher: Springer Science & Business Media

ISBN: 9788847018365

Category: Mathematics

Page: 190

View: 8217

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This book contains the papers developing out the presentations given at the International Conference organized by the Torino Academy of Sciences and the Department of Mathematics Giuseppe Peano of the Torino University to celebrate the 150th anniversary of G. Peano's birth - one of the greatest figures in modern mathematics and logic and the most important mathematical logician in Italy - a century after the publication of Formulario Mathematico, a great attempt to systematise Mathematics in symbolic form.

After Gödel

Platonism and Rationalism in Mathematics and Logic

Author: Richard L. Tieszen

Publisher: Oxford University Press

ISBN: 019960620X

Category: Mathematics

Page: 245

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Richard Tieszen analyzes, develops, and defends the writings of Kurt Gödel (1906-1978) on the philosophy and foundations of mathematics and logic. Gödel's relation to the work of Plato, Leibniz, Husserl, and Kant is examined, and a new type of platonic rationalism that requires rational intuition, called 'constituted platonism', is proposed.

Mathematical Logic

Author: Stephen Cole Kleene

Publisher: Courier Corporation

ISBN: 0486317072

Category: Mathematics

Page: 416

View: 4071

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Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.

The Outer Limits of Reason

What Science, Mathematics, and Logic Cannot Tell Us

Author: Noson S. Yanofsky

Publisher: MIT Press

ISBN: 0262316781

Category: Science

Page: 424

View: 325

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Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

Cultures of Mathematics and Logic

Selected Papers from the Conference in Guangzhou, China, November 9-12, 2012

Author: Shier Ju,Benedikt Löwe,Thomas Müller,Yun Xie

Publisher: Birkhäuser

ISBN: 3319315021

Category: Mathematics

Page: 123

View: 8397

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This book gathers the proceedings of the conference "Cultures of Mathematics and Logic," held in Guangzhou, China. The event was the third in a series of interdisciplinary, international conferences emphasizing the cultural components of philosophy of mathematics and logic. It brought together researchers from many disciplines whose work sheds new light on the diversity of mathematical and logical cultures and practices. In this context, the cultural diversity can be diachronical (different cultures in different historical periods), geographical (different cultures in different regions), or sociological in nature.

Math and logic games

Author: Franco Agostini

Publisher: Harper Perennial

ISBN: 9780060970215

Category: Games

Page: 181

View: 2308

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Discusses games with numbers, geometrical figures, logic, probability, and paradoxes, and looks at their mathematical basis

Algebraic Methods of Mathematical Logic

Author: Ladislav Rieger

Publisher: Elsevier

ISBN: 1483270521

Category: Mathematics

Page: 210

View: 9787

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Algebraic Methods of Mathematical Logic focuses on the algebraic methods of mathematical logic, including Boolean algebra, mathematical language, and arithmetization. The book first offers information on the dialectic of the relation between mathematical and metamathematical aspects; metamathematico-mathematical parallelism and its natural limits; practical applications of methods of mathematical logic; and principal mathematical tools of mathematical logic. The text then elaborates on the language of mathematics and its symbolization and recursive construction of the relation of consequence. Discussions focus on recursive construction of the relation of consequence, fundamental descriptively-semantic rules, mathematical logic and mathematical language as a material system of signs, and the substance and purpose of symbolization of mathematical language. The publication examines expressive possibilities of symbolization; intuitive and mathematical notions of an idealized axiomatic mathematical theory; and the algebraic theory of elementary predicate logic. Topics include the notion of Boolean algebra based on joins, meets, and complementation, logical frame of a language and mathematical theory, and arithmetization and algebraization. The manuscript is a valuable reference for mathematicians and researchers interested in the algebraic methods of mathematical logic.

Mathematics and Humor

A Study of the Logic of Humor

Author: John Allen Paulos

Publisher: University of Chicago Press

ISBN: 9780226650234

Category: Mathematics

Page: 124

View: 4768

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John Allen Paulos cleverly scrutinizes the mathematical structures of jokes, puns, paradoxes, spoonerisms, riddles, and other forms of humor, drawing examples from such sources as Rabelais, Shakespeare, James Beattie, René Thom, Lewis Carroll, Arthur Koestler, W. C. Fields, and Woody Allen. "Jokes, paradoxes, riddles, and the art of non-sequitur are revealed with great perception and insight in this illuminating account of the relationship between humor and mathematics."—Joseph Williams, New York Times "'Leave your mind alone,' said a Thurber cartoon, and a really complete and convincing analysis of what humour is might spoil all jokes forever. This book avoids that danger. What it does. . .is describe broadly several kinds of mathematical theory and apply them to throw sidelights on how many kinds of jokes work."—New Scientist "Many scholars nowadays write seriously about the ludicrous. Some merely manage to be dull. A few—like Paulos—are brilliant in an odd endeavor."—Los Angeles Times Book Review

Math and Logic Puzzles That Make Kids Think

Author: Jeffrey J. Wanko

Publisher: N.A

ISBN: 9781593634162

Category: Education

Page: 89

View: 8784

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The Social Studies book includes units that ask students to explore the struggles of America's first permanent English settlement in Jamestown, hold an African economic summit, study various Supreme Court cases and primary source documents, and create a Civil War documentary that views the war from the aspect of a person living in a particular state.

Puzzles in Math and Logic

100 New Recreations

Author: Aaron J. Friedland

Publisher: Courier Corporation

ISBN: 9780486222561

Category: Games

Page: 66

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Selected brain teasers requiring geometric, algebraic, and logical solutions