Truth Proof And Infinity
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Author |
: P. Fletcher |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 477 |
Release |
: 2013-06-29 |
ISBN-10 |
: 9789401736169 |
ISBN-13 |
: 9401736162 |
Rating |
: 4/5 (69 Downloads) |
Synopsis Truth, Proof and Infinity by : P. Fletcher
Constructive mathematics is based on the thesis that the meaning of a mathematical formula is given, not by its truth-conditions, but in terms of what constructions count as a proof of it. However, the meaning of the terms `construction' and `proof' has never been adequately explained (although Kriesel, Goodman and Martin-Löf have attempted axiomatisations). This monograph develops precise (though not wholly formal) definitions of construction and proof, and describes the algorithmic substructure underlying intuitionistic logic. Interpretations of Heyting arithmetic and constructive analysis are given. The philosophical basis of constructivism is explored thoroughly in Part I. The author seeks to answer objections from platonists and to reconcile his position with the central insights of Hilbert's formalism and logic. Audience: Philosophers of mathematics and logicians, both academic and graduate students, particularly those interested in Brouwer and Hilbert; theoretical computer scientists interested in the foundations of functional programming languages and program correctness calculi.
Author |
: John Stillwell |
Publisher |
: CRC Press |
Total Pages |
: 202 |
Release |
: 2010-07-13 |
ISBN-10 |
: 9781439865507 |
ISBN-13 |
: 1439865507 |
Rating |
: 4/5 (07 Downloads) |
Synopsis Roads to Infinity by : John Stillwell
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
Author |
: Loren Graham |
Publisher |
: Harvard University Press |
Total Pages |
: 252 |
Release |
: 2009-03-31 |
ISBN-10 |
: 9780674032934 |
ISBN-13 |
: 0674032934 |
Rating |
: 4/5 (34 Downloads) |
Synopsis Naming Infinity by : Loren Graham
In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.
Author |
: P. Fletcher |
Publisher |
: |
Total Pages |
: |
Release |
: 1988 |
ISBN-10 |
: OCLC:59773326 |
ISBN-13 |
: |
Rating |
: 4/5 (26 Downloads) |
Synopsis Truth, Proof and Infinity by : P. Fletcher
Author |
: David Deutsch |
Publisher |
: Penguin UK |
Total Pages |
: 571 |
Release |
: 2011-03-31 |
ISBN-10 |
: 9780141969695 |
ISBN-13 |
: 0141969695 |
Rating |
: 4/5 (95 Downloads) |
Synopsis The Beginning of Infinity by : David Deutsch
'Science has never had an advocate quite like David Deutsch ... A computational physicist on a par with his touchstones Alan Turing and Richard Feynman, and a philosopher in the line of his greatest hero, Karl Popper. His arguments are so clear that to read him is to experience the thrill of the highest level of discourse available on this planet and to understand it' Peter Forbes, Independent In our search for truth, how far have we advanced? This uniquely human quest for good explanations has driven amazing improvements in everything from scientific understanding and technology to politics, moral values and human welfare. But will progress end, either in catastrophe or completion - or will it continue infinitely? In this profound and seminal book, David Deutsch explores the furthest reaches of our current understanding, taking in the Infinity Hotel, supernovae and the nature of optimism, to instill in all of us a wonder at what we have achieved - and the fact that this is only the beginning of humanity's infinite possibility. 'This is Deutsch at his most ambitious, seeking to understand the implications of our scientific explanations of the world ... I enthusiastically recommend this rich, wide-ranging and elegantly written exposition of the unique insights of one of our most original intellectuals' Michael Berry, Times Higher Education Supplement 'Bold ... profound ... provocative and persuasive' Economist 'David Deutsch may well go down in history as one of the great scientists of our age' Scotsman
Author |
: Martin Aigner |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 194 |
Release |
: 2013-06-29 |
ISBN-10 |
: 9783662223437 |
ISBN-13 |
: 3662223430 |
Rating |
: 4/5 (37 Downloads) |
Synopsis Proofs from THE BOOK by : Martin Aigner
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Author |
: Paul Sinclair |
Publisher |
: |
Total Pages |
: |
Release |
: 2016 |
ISBN-10 |
: 0957500785 |
ISBN-13 |
: 9780957500785 |
Rating |
: 4/5 (85 Downloads) |
Synopsis Truth-proof by : Paul Sinclair
Author |
: Richard H. Hammack |
Publisher |
: |
Total Pages |
: 314 |
Release |
: 2016-01-01 |
ISBN-10 |
: 0989472116 |
ISBN-13 |
: 9780989472111 |
Rating |
: 4/5 (16 Downloads) |
Synopsis Book of Proof by : Richard H. Hammack
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
Author |
: Rudolf V Rucker |
Publisher |
: Princeton University Press |
Total Pages |
: 373 |
Release |
: 2019-07-23 |
ISBN-10 |
: 9780691191256 |
ISBN-13 |
: 0691191255 |
Rating |
: 4/5 (56 Downloads) |
Synopsis Infinity and the Mind by : Rudolf V Rucker
A dynamic exploration of infinity In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the “Mindscape,” where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Using cartoons, puzzles, and quotations to enliven his text, Rucker acquaints us with staggeringly advanced levels of infinity, delves into the depths beneath daily awareness, and explains Kurt Gödel’s belief in the possibility of robot consciousness. In the realm of infinity, mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise, we gain profound insights into the human mind, its powers, and its limitations. This Princeton Science Library edition includes a new preface by the author.
Author |
: Joel David Hamkins |
Publisher |
: MIT Press |
Total Pages |
: 350 |
Release |
: 2021-03-09 |
ISBN-10 |
: 9780262542234 |
ISBN-13 |
: 0262542234 |
Rating |
: 4/5 (34 Downloads) |
Synopsis Lectures on the Philosophy of Mathematics by : Joel David Hamkins
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.