Truth In Mathematics

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Truth in Mathematics

Author : Harold G. Dales
Publisher : Oxford University Press
ISBN 13 : 9780198514763
Total Pages : 396 pages
Book Rating : 4.5/5 (147 download)

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Book Synopsis Truth in Mathematics by : Harold G. Dales

Download or read book Truth in Mathematics written by Harold G. Dales and published by Oxford University Press. This book was released on 1998 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nature of truth in mathematics has exercised the minds of thinkers from at least the time of the ancient Greeks. The great advances in mathematics and philosophy in the twentieth century and in particular the work by G]odel and the development of the notion of independence in mathematics have led to new and complex views on this question. Collecting the work of a number of outstanding mathematicians and philosophers, including Yurii Manin, Vaughan Jones, and Per Martin-L]of, this volume provides an overview of the forefront of current thinking and a valuable introduction for researchers in the area.

Trick or Truth?

Author : Anthony Aguirre
Publisher : Springer
ISBN 13 : 3319274953
Total Pages : 253 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Trick or Truth? by : Anthony Aguirre

Download or read book Trick or Truth? written by Anthony Aguirre and published by Springer. This book was released on 2016-02-20 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: The prize-winning essays in this book address the fascinating but sometimes uncomfortable relationship between physics and mathematics. Is mathematics merely another natural science? Or is it the result of human creativity? Does physics simply wear mathematics like a costume, or is math the lifeblood of physical reality? The nineteen wide-ranging, highly imaginative and often entertaining essays are enhanced versions of the prize-winning entries to the FQXi essay competition “Trick or Truth”, which attracted over 200 submissions. The Foundational Questions Institute, FQXi, catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources.

Probability, Statistics, and Truth

Author : Richard Von Mises
Publisher : Courier Corporation
ISBN 13 : 0486242145
Total Pages : 273 pages
Book Rating : 4.4/5 (862 download)

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Book Synopsis Probability, Statistics, and Truth by : Richard Von Mises

Download or read book Probability, Statistics, and Truth written by Richard Von Mises and published by Courier Corporation. This book was released on 1981-01-01 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive study of probability considers the approaches of Pascal, Laplace, Poisson, and others. It also discusses Laws of Large Numbers, the theory of errors, and other relevant topics.

Truth Through Proof

Author : Alan Weir
Publisher : OUP Oxford
ISBN 13 : 9780199541492
Total Pages : 296 pages
Book Rating : 4.5/5 (414 download)

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Book Synopsis Truth Through Proof by : Alan Weir

Download or read book Truth Through Proof written by Alan Weir and published by OUP Oxford. This book was released on 2010-10-14 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Truth Through Proof defends an anti-platonist philosophy of mathematics derived from game formalism. Alan Weir aims to develop a more satisfactory successor to game formalism utilising a widely accepted, broadly neo-Fregean framework, in which the proposition expressed by an utterance is a function of both sense and background circumstance.

Kurt Gödel and the Foundations of Mathematics

Author : Matthias Baaz
Publisher : Cambridge University Press
ISBN 13 : 1139498436
Total Pages : 541 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Kurt Gödel and the Foundations of Mathematics by : Matthias Baaz

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.

Truth, Existence and Explanation

Author : Mario Piazza
Publisher : Springer
ISBN 13 : 3319933426
Total Pages : 278 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Truth, Existence and Explanation by : Mario Piazza

Download or read book Truth, Existence and Explanation written by Mario Piazza and published by Springer. This book was released on 2018-10-24 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains more than 15 essays that explore issues in truth, existence, and explanation. It features cutting-edge research in the philosophy of mathematics and logic. Renowned philosophers, mathematicians, and younger scholars provide an insightful contribution to the lively debate in this interdisciplinary field of inquiry. The essays look at realism vs. anti-realism as well as inflationary vs. deflationary theories of truth. The contributors also consider mathematical fictionalism, structuralism, the nature and role of axioms, constructive existence, and generality. In addition, coverage also looks at the explanatory role of mathematics and the philosophical relevance of mathematical explanation. The book will appeal to a broad mathematical and philosophical audience. It contains work from FilMat, the Italian Network for the Philosophy of Mathematics. These papers collected here were also presented at their second international conference, held at the University of Chieti-Pescara, May 2016.

Slicing The Truth: On The Computable And Reverse Mathematics Of Combinatorial Principles

Author : Denis R Hirschfeldt
Publisher : World Scientific
ISBN 13 : 9814612634
Total Pages : 231 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Slicing The Truth: On The Computable And Reverse Mathematics Of Combinatorial Principles by : Denis R Hirschfeldt

Download or read book Slicing The Truth: On The Computable And Reverse Mathematics Of Combinatorial Principles written by Denis R Hirschfeldt and published by World Scientific. This book was released on 2014-07-18 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions.

Roads to Infinity

Author : John Stillwell
Publisher : CRC Press
ISBN 13 : 1439865507
Total Pages : 202 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Roads to Infinity by : John Stillwell

Download or read book Roads to Infinity written by John Stillwell and published by CRC Press. This book was released on 2010-07-13 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of a CHOICE Outstanding Academic Title Award for 2011!This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is h

Principia Mathematica

Author : Alfred North Whitehead
Publisher :
ISBN 13 :
Total Pages : 688 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Principia Mathematica by : Alfred North Whitehead

Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematics for Human Flourishing

Author : Francis Su
Publisher : Yale University Press
ISBN 13 : 0300237138
Total Pages : 287 pages
Book Rating : 4.3/5 (2 download)

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Book Synopsis Mathematics for Human Flourishing by : Francis Su

Download or read book Mathematics for Human Flourishing written by Francis Su and published by Yale University Press. This book was released on 2020-01-07 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.

An Introduction to Mathematical Logic and Type Theory

Author : Peter B. Andrews
Publisher : Springer Science & Business Media
ISBN 13 : 9401599343
Total Pages : 404 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis An Introduction to Mathematical Logic and Type Theory by : Peter B. Andrews

Download or read book An Introduction to Mathematical Logic and Type Theory written by Peter B. Andrews and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Infinity And Truth

Author : Chi Tat Chong
Publisher : World Scientific
ISBN 13 : 9814571059
Total Pages : 245 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Infinity And Truth by : Chi Tat Chong

Download or read book Infinity And Truth written by Chi Tat Chong and published by World Scientific. This book was released on 2013-11-28 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the talks given at the Workshop on Infinity and Truth held at the Institute for Mathematical Sciences, National University of Singapore, from 25 to 29 July 2011. The chapters cover topics in mathematical and philosophical logic that examine various aspects of the foundations of mathematics. The theme of the volume focuses on two basic foundational questions: (i) What is the nature of mathematical truth and how does one resolve questions that are formally unsolvable within the Zermelo-Fraenkel Set Theory with the Axiom of Choice, and (ii) Do the discoveries in mathematics provide evidence favoring one philosophical view over others? These issues are discussed from the vantage point of recent progress in foundational studies.The final chapter features questions proposed by the participants of the Workshop that will drive foundational research. The wide range of topics covered here will be of interest to students, researchers and mathematicians concerned with issues in the foundations of mathematics.

Intuitionistic Proof Versus Classical Truth

Author : Enrico Martino
Publisher : Springer
ISBN 13 : 3319743570
Total Pages : 173 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Intuitionistic Proof Versus Classical Truth by : Enrico Martino

Download or read book Intuitionistic Proof Versus Classical Truth written by Enrico Martino and published by Springer. This book was released on 2018-02-23 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the role of acts of choice in classical and intuitionistic mathematics. Featuring fifteen papers – both new and previously published – it offers a fresh analysis of concepts developed by the mathematician and philosopher L.E.J. Brouwer, the founder of intuitionism. The author explores Brouwer’s idealization of the creative subject as the basis for intuitionistic truth, and in the process he also discusses an important, related question: to what extent does the intuitionistic perspective succeed in avoiding the classical realistic notion of truth? The papers detail realistic aspects in the idealization of the creative subject and investigate the hidden role of choice even in classical logic and mathematics, covering such topics as bar theorem, type theory, inductive evidence, Beth models, fallible models, and more. In addition, the author offers a critical analysis of the response of key mathematicians and philosophers to Brouwer’s work. These figures include Michael Dummett, Saul Kripke, Per Martin-Löf, and Arend Heyting. This book appeals to researchers and graduate students with an interest in philosophy of mathematics, linguistics, and mathematics.

Our Mathematical Universe

Author : Max Tegmark
Publisher : Vintage
ISBN 13 : 0307744256
Total Pages : 434 pages
Book Rating : 4.3/5 (77 download)

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Book Synopsis Our Mathematical Universe by : Max Tegmark

Download or read book Our Mathematical Universe written by Max Tegmark and published by Vintage. This book was released on 2015-02-03 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.

Math Art

Author : Stephen Ornes
Publisher : Sterling New York
ISBN 13 : 9781454930440
Total Pages : 0 pages
Book Rating : 4.9/5 (34 download)

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Book Synopsis Math Art by : Stephen Ornes

Download or read book Math Art written by Stephen Ornes and published by Sterling New York. This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The worlds of visual art and mathematics beautifully unite in this spectacular volume by award-winning writer Stephen Ornes. He explores the growing sensation of math art, presenting such pieces as a colorful crocheted representation of non-Euclidian geometry that looks like sea coral and a 65-ton, 28-foot-tall bronze sculpture covered in a space-filling curve. We learn the artist's story for every work, plus the mathematical concepts and equations behind the art.

Tracking the Automatic ANT

Author : David Gale
Publisher : Springer Science & Business Media
ISBN 13 : 1461221927
Total Pages : 239 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Tracking the Automatic ANT by : David Gale

Download or read book Tracking the Automatic ANT written by David Gale and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: For those fascinated by the abstract universe of mathematics, David Gale's columns in "The Mathematical Intelligencer" have been a prime source of entertainment, and here his columns are collected for the first time in book form. Encouraged by the magazine's editor, Sheldon Axler, to write on whatever pleased him, Gale ranged far and wide across the field of mathematics, frequently returning to favorite themes: triangles, tilings, games and paradoxes, as well as the particular automaton that gives this collection its title, the "automatic ant." Suitable for everyone having some familiarity with mathematical ideas.

Islands of Truth

Author : Ivars Peterson
Publisher : W H Freeman & Company
ISBN 13 : 9780716721482
Total Pages : 325 pages
Book Rating : 4.7/5 (214 download)

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Book Synopsis Islands of Truth by : Ivars Peterson

Download or read book Islands of Truth written by Ivars Peterson and published by W H Freeman & Company. This book was released on 1991-05-01 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ivars Peterson has come up with another itinerary of Mathland - where the habitat is mysterious and the inhabitants fascinating. He explores uncharted islands, introducing strange vibrations in the shadows of chaos, new twists in knot physics, and the straight side of circles. The tour is enjoyable to experienced travellers and first-time tourists alike. Peterson, a journalist with Science News, makes the arcane intelligible by interpreting mathematics into engaging prose.