Truth In Mathematics
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Truth In Mathematics
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Author : Harold G. Dales
language : en
Publisher: Oxford University Press
Release Date : 1998
Truth In Mathematics written by Harold G. Dales and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
The nature of truth in mathematics is a problem which 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 centuryand in particular the proof of Gödel's theorem and the development of the notion of independence in mathematicshave led to new viewpoints on this question in our era. This book is the result of the interaction of a number of outstanding mathematicians and philosophersincluding Yurii Manin, Vaughan Jones, and Per Martin-Löfand their discussions of this problem. It provides an overview of the forefront of current thinking, and is a valuable introduction and reference for researchers in the area.
Trick Or Truth
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Author : Anthony Aguirre
language : en
Publisher: Springer
Release Date : 2016-02-20
Trick Or Truth written by Anthony Aguirre and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-20 with Science categories.
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.
Truth Existence And Explanation
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Author : Mario Piazza
language : en
Publisher: Springer
Release Date : 2018-10-24
Truth Existence And Explanation written by Mario Piazza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-24 with Mathematics categories.
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.
Kurt G Del And The Foundations Of Mathematics
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Author : Matthias Baaz
language : en
Publisher: Cambridge University Press
Release Date : 2011-06-06
Kurt G Del And The Foundations Of Mathematics written by Matthias Baaz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-06 with Mathematics categories.
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.
Slicing The Truth On The Computable And Reverse Mathematics Of Combinatorial Principles
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Author : Denis R Hirschfeldt
language : en
Publisher: World Scientific
Release Date : 2014-07-18
Slicing The Truth On The Computable And Reverse Mathematics Of Combinatorial Principles written by Denis R Hirschfeldt and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-18 with Mathematics categories.
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.
Truth Through Proof
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Author : Alan Weir
language : en
Publisher:
Release Date : 2010
Truth Through Proof written by Alan Weir and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
Principia Mathematica
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Author : Alfred North Whitehead
language : en
Publisher: Cambridge University Press
Release Date : 1927
Principia Mathematica written by Alfred North Whitehead and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1927 with Mathematics categories.
The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.
Truth Objects Infinity
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Author : Fabrice Pataut
language : en
Publisher: Springer
Release Date : 2017-01-27
Truth Objects Infinity written by Fabrice Pataut and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-27 with Philosophy categories.
This volume features essays about and by Paul Benacerraf, whose ideas have circulated in the philosophical community since the early nineteen sixties, shaping key areas in the philosophy of mathematics, the philosophy of language, the philosophy of logic, and epistemology. The book started as a workshop held in Paris at the Collège de France in May 2012 with the participation of Paul Benacerraf. The introduction addresses the methodological point of the legitimate use of so-called “Princess Margaret Premises” in drawing philosophical conclusions from Gödel’s first incompleteness theorem. The book is then divided into three sections. The first is devoted to an assessment of the improved version of the original dilemma of “Mathematical Truth” due to Hartry Field: the challenge to the platonist is now to explain the reliability of our mathematical beliefs given the very subject matter of mathematics, either pure or applied. The second addresses the issue of the ontological status of numbers: Frege’s logicism, fictionalism, structuralism, and Bourbaki’s theory of structures are called up for an appraisal of Benacerraf’s negative conclusions of “What Numbers Could Not Be.” The third is devoted to supertasks and bears witness to the unique standing of Benacerraf’s first publication: “Tasks, Super-Tasks, and Modern Eleatics” in debates on Zeno’s paradox and associated paradoxes, infinitary mathematics, and constructivism and finitism in the philosophy of mathematics. Two yet unpublished essays by Benacerraf have been included in the volume: an early version of “Mathematical Truth” from 1968 and an essay on “What Numbers Could Not Be” from the mid 1970’s. A complete chronological bibliography of Benacerraf’s work to 2016 is provided.Essays by Jody Azzouni, Paul Benacerraf, Justin Clarke-Doane, Sébastien Gandon, Brice Halimi, Jon Pérez Laraudogoitia, Mary Leng, Antonio León-Sánchez and Ana C. León-Mejía, Marco Panza, Fabrice Pataut, Philippe de Rouilhan, Andrea Sereni, and Stewart Shapiro.
Proof And The Art Of Mathematics
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Author : Joel David Hamkins
language : en
Publisher: MIT Press
Release Date : 2021-02-23
Proof And The Art Of Mathematics written by Joel David Hamkins and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-23 with Mathematics categories.
How to write mathematical proofs, shown in fully-worked out examples. This is a companion volume Joel Hamkins's Proof and the Art of Mathematics, providing fully worked-out solutions to all of the odd-numbered exercises as well as a few of the even-numbered exercises. In many cases, the solutions go beyond the exercise question itself to the natural extensions of the ideas, helping readers learn how to approach a mathematical investigation. As Hamkins asks, "Once you have solved a problem, why not push the ideas harder to see what further you can prove with them?" These solutions offer readers examples of how to write a mathematical proofs. The mathematical development of this text follows the main book, with the same chapter topics in the same order, and all theorem and exercise numbers in this text refer to the corresponding statements of the main text.
Why Beauty Is Truth
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Author : Ian Stewart
language : en
Publisher: Hachette UK
Release Date : 2007-08-02
Why Beauty Is Truth written by Ian Stewart and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-02 with Science categories.
At the heart of relativity theory, quantum mechanics, string theory, and much of modern cosmology lies one concept: symmetry. In Why Beauty Is Truth, world-famous mathematician Ian Stewart narrates the history of the emergence of this remarkable area of study. Stewart introduces us to such characters as the Renaissance Italian genius, rogue, scholar, and gambler Girolamo Cardano, who stole the modern method of solving cubic equations and published it in the first important book on algebra, and the young revolutionary Evariste Galois, who refashioned the whole of mathematics and founded the field of group theory only to die in a pointless duel over a woman before his work was published. Stewart also explores the strange numerology of real mathematics, in which particular numbers have unique and unpredictable properties related to symmetry. He shows how Wilhelm Killing discovered "Lie groups" with 14, 52, 78, 133, and 248 dimensions-groups whose very existence is a profound puzzle. Finally, Stewart describes the world beyond superstrings: the "octonionic" symmetries that may explain the very existence of the universe.