Cultures of Mathematics and Logic

Cultures of Mathematics and Logic PDF Author: Shier Ju
Publisher: Birkhäuser
ISBN: 3319315021
Category : Mathematics
Languages : en
Pages : 130

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Book Description
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.

Cultures of Mathematics and Logic

Cultures of Mathematics and Logic PDF Author: Shier Ju
Publisher: Birkhäuser
ISBN: 3319315021
Category : Mathematics
Languages : en
Pages : 130

Get Book Here

Book Description
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.

Science and an African Logic

Science and an African Logic PDF Author: Helen Verran
Publisher: University of Chicago Press
ISBN: 0226853918
Category : Philosophy
Languages : en
Pages : 289

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Book Description
Does two and two equal four? Ask someone and they should answer yes. An equation such as this seems the very definition of certainty, but is it? In this book, Helen Verran addresses precisely that question.

Mathematical Logic

Mathematical Logic PDF Author: Joseph R. Shoenfield
Publisher: CRC Press
ISBN: 135143330X
Category : Mathematics
Languages : en
Pages : 351

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Book Description
This classic introduction to the main areas of mathematical logic provides the basis for a first graduate course in the subject. It embodies the viewpoint that mathematical logic is not a collection of vaguely related results, but a coherent method of attacking some of the most interesting problems, which face the mathematician. The author presents the basic concepts in an unusually clear and accessible fashion, concentrating on what he views as the central topics of mathematical logic: proof theory, model theory, recursion theory, axiomatic number theory, and set theory. There are many exercises, and they provide the outline of what amounts to a second book that goes into all topics in more depth. This book has played a role in the education of many mature and accomplished researchers.

Mathematics in Western Culture

Mathematics in Western Culture PDF Author: Morris Kline
Publisher: Oxford University Press
ISBN: 0195345452
Category : Mathematics
Languages : en
Pages : 513

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Book Description
This book gives a remarkably fine account of the influences mathematics has exerted on the development of philosophy, the physical sciences, religion, and the arts in Western life.

Foundations of Mathematical Logic

Foundations of Mathematical Logic PDF Author: Haskell Brooks Curry
Publisher: Courier Corporation
ISBN: 9780486634623
Category : Mathematics
Languages : en
Pages : 420

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Book Description
Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods — including algorithms and epitheory — and offers a brief treatment of Markov's approach to algorithms. It also explains elementary facts about lattices and similar algebraic systems. 1963 edition.

Mathematics and Logic in History and in Contemporary Thought

Mathematics and Logic in History and in Contemporary Thought PDF Author: Ettore Carruccio
Publisher: Routledge
ISBN: 1351506617
Category : Mathematics
Languages : en
Pages : 400

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Book Description
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.

Truth

Truth PDF Author: Felipe Fernández-Armesto
Publisher: Macmillan
ISBN: 1466852399
Category : Philosophy
Languages : en
Pages : 275

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Book Description
Written by a renowned Oxford historian, this fascinating volume presents a global history of truth. Sharp and authoritative, Truth manages to touch every period of human experience; it leaps from truth-telling technologies of "primitive" societies to the private mental worlds of great philosophers; from spiritualism to science and from New York to New Guinea. In clear, lucid prose, this little book takes on an enormous subject and makes it understandable to anyone.

A Concise Introduction to Mathematical Logic

A Concise Introduction to Mathematical Logic PDF Author: Wolfgang Rautenberg
Publisher: Springer
ISBN: 1441912215
Category : Mathematics
Languages : en
Pages : 337

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Book Description
Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.

A Course in Mathematical Logic for Mathematicians

A Course in Mathematical Logic for Mathematicians PDF Author: Yu. I. Manin
Publisher: Springer Science & Business Media
ISBN: 1441906150
Category : Mathematics
Languages : en
Pages : 389

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Book Description
1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.

An Introduction to Mathematical Logic and Type Theory

An Introduction to Mathematical Logic and Type Theory PDF Author: Peter B. Andrews
Publisher: Springer Science & Business Media
ISBN: 9401599343
Category : Mathematics
Languages : en
Pages : 404

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Book Description
In case you are considering to adopt this book for courses with over 50 students, please contact [email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.