Hilberts Programs And Beyond

Author : Wilfried Sieg
Publisher : Oxford University Press
ISBN 13 : 0195372220
Total Pages : 452 pages
Book Rating : 4.29/5 ( download)

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Download or read book Hilbert's Programs and Beyond written by Wilfried Sieg and published by Oxford University Press. This book was released on 2013-03-07 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: David Hilbert was one of the great mathematicians who expounded the centrality of their subject in human thought. In this collection of essays, Wilfried Sieg frames Hilbert's foundational work, from 1890 to 1939, in a comprehensive way and integrates it with modern proof theoretic investigations.

Author : Curtis Franks
Publisher : Cambridge University Press
ISBN 13 : 0521514371
Total Pages : 229 pages
Book Rating : 4.78/5 ( download)

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Download or read book The Autonomy of Mathematical Knowledge written by Curtis Franks and published by Cambridge University Press. This book was released on 2009-10-08 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study reconstructs, analyses and re-evaluates the programme of influential mathematical thinker David Hilbert, presenting it in a different light.

Author : Alfred North Whitehead
Publisher :
ISBN 13 :
Total Pages : 696 pages
Book Rating : 4.01/5 ( download)

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Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Matthias Baaz
Publisher : Cambridge University Press
ISBN 13 : 1139498436
Total Pages : 541 pages
Book Rating : 4.32/5 ( download)

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Download or read book Kurt Gödel and the Foundations of Mathematics written by Matthias Baaz and published by Cambridge University Press. This book was released on 2011-06-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
ISBN 13 : 0387226761
Total Pages : 535 pages
Book Rating : 4.67/5 ( download)

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Download or read book Geometry: Euclid and Beyond written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.

Author :
Publisher : Elsevier
ISBN 13 : 9780080466637
Total Pages : 1218 pages
Book Rating : 4.3X/5 ( download)

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Download or read book Philosophy of Logic written by and published by Elsevier. This book was released on 2006-11-29 with total page 1218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert’s program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights. - Written by leading logicians and philosophers - Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic - Clear, in-depth expositions of technical detail - Progressive organization from general considerations to informal to symbolic logic to nonclassical logics - Presents current work in symbolic logic within a unified framework - Accessible to students, engaging for experts and professionals - Insightful philosophical discussions of all aspects of logic - Useful bibliographies in every chapter

Author : Joel David Hamkins
Publisher : MIT Press
ISBN 13 : 0262542234
Total Pages : 350 pages
Book Rating : 4.34/5 ( download)

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Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Author : Eugenia Cheng
Publisher : Profile Books
ISBN 13 : 1782830812
Total Pages : 204 pages
Book Rating : 4.18/5 ( download)

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Download or read book Beyond Infinity written by Eugenia Cheng and published by Profile Books. This book was released on 2017-03-09 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.

Author : Constance Reid
Publisher : Springer Science & Business Media
ISBN 13 : 9780387962566
Total Pages : 620 pages
Book Rating : 4.65/5 ( download)

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Download or read book Hilbert-Courant written by Constance Reid and published by Springer Science & Business Media. This book was released on 1986-05-22 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: I am very pleased that my books about David Hilbert, published in 1970, and Richard Courant, published in 1976, are now being issued by Springer Verlag in a single volume. I have always felt that they belonged together, Courant being, as I have written, the natural and necessary sequel to Hilbert the rest of the story. To make the two volumes more compatible when published as one, we have combined and brought up to date the indexes of names and dates. U nfortu nately we have had to omit Hermann Weyl's article on "David Hilbert and his mathematical work," but the interested reader can always find it in the hard back edition of Hilbert and in Weyl's collected papers. At the request of a number of readers we have included a listing of all of Hilbert's famous Paris problems. It was, of course, inevitable that we would give the resulting joint volume the title Hilbert-Courant.

Author : Hao Wang
Publisher : Courier Corporation
ISBN 13 : 0486171043
Total Pages : 292 pages
Book Rating : 4.43/5 ( download)

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Download or read book Popular Lectures on Mathematical Logic written by Hao Wang and published by Courier Corporation. This book was released on 2014-09-22 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noted logician discusses both theoretical underpinnings and practical applications, exploring set theory, model theory, recursion theory and constructivism, proof theory, logic's relation to computer science, and other subjects. 1981 edition, reissued by Dover in 1993 with a new Postscript by the author.