Truth, Proof and Infinity PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Truth, Proof and Infinity PDF full book. Access full book title Truth, Proof and Infinity by P. Fletcher. Download full books in PDF and EPUB format.
Author: P. Fletcher
Publisher: Springer Science & Business Media
ISBN: 9401736162
Category : Philosophy
Languages : en
Pages : 477
Get Book
Book Description
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: P. Fletcher
Publisher: Springer Science & Business Media
ISBN: 9401736162
Category : Philosophy
Languages : en
Pages : 477
Get Book
Book Description
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
ISBN: 1439865507
Category : Mathematics
Languages : en
Pages : 202
Get Book
Book Description
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: David Deutsch
Publisher: Penguin UK
ISBN: 0141969695
Category : Science
Languages : en
Pages : 571
Get Book
Book Description
'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: Paul Sinclair
Publisher:
ISBN: 9780957500785
Category :
Languages : en
Pages :
Get Book
Book Description
Author: Glenn F. Chesnut
Publisher: iUniverse
ISBN: 1532070349
Category : Philosophy
Languages : en
Pages : 371
Get Book
Book Description
This book is more than just a set of logical proofs. It shows us who and what God is, and explains how our universe exploded into existence in the Big Bang, some 13.799 billion years ago, in such a way that all other Being in the universe derives its existence and nature — and its capacities for growth, power, moral character, change, and novelty — from God as the Ground of Being. This is a book for people who are interested in philosophy. It begins with a discussion of some of the fallacies into which the concept of infinity has led careless thinkers over the centuries. In particular, Chesnut demonstrates how often the modern defenses of atheism have been based on what are no more than pseudo-infinite regresses. This includes in particular self-delusive attempts to get rid of God by constructing what would be no more than imaginary universe-sized perpetual motion machines. The last half of the book then has as its central focus the set of Five Proofs for the Existence of God formulated by the great medieval thinker St. Thomas Aquinas, where Chesnut begins by showing how each of the proofs was interpreted in the middle ages. But the development of modern science requires that the Five Proofs be reworked for today, so he shows, for example, how the Proof from Motion can be reworded as an Argument from Energy, subject to the laws of thermodynamics, and how the Proof from Gradations in Truth and Value forces us to decide whether we will accept that at least some moral values are real, or instead will become what modern psychologists call psychopaths. This present book, combined with the work Chesnut authored nine years ago — God and Spirituality: Philosophical Essays — sets out an architectonic philosophical system for the twenty-first century, grounded on one side in the classics of the ancient Greco-Roman world and the medieval period, but on the other hand taking seriously the revolutionary changes in western thought produced by the development of twentieth-century science, including relativity, quantum theory, the uncertainty principle, and Gödel’s proof.
Author: Rudy Rucker
Publisher: Princeton University Press
ISBN: 0691191255
Category : Mathematics
Languages : en
Pages :
Get Book
Book Description
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: Martin Aigner
Publisher: Springer Science & Business Media
ISBN: 3662223430
Category : Mathematics
Languages : en
Pages : 194
Get Book
Book Description
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: Hermann Weyl
Publisher: Courier Corporation
ISBN: 0486266931
Category : Mathematics
Languages : en
Pages : 208
Get Book
Book Description
Original anthology features less-technical essays discussing logic, topology, abstract algebra, relativity theory, and the works of David Hilbert. Most have been long unavailable or previously unpublished in book form. 2012 edition.
Author: Thomas Piecha
Publisher: Springer
ISBN: 331922686X
Category : Philosophy
Languages : en
Pages : 283
Get Book
Book Description
This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory. The field of proof-theoretic semantics has existed for almost 50 years, but the term itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from presentations at the Second International Conference on Proof-Theoretic Semantics in Tübingen in 2013, where contributing authors were asked to provide a self-contained description and analysis of a significant research question in this area. The contributions are representative of the field and should be of interest to logicians, philosophers, and mathematicians alike.
Author: Loren Graham
Publisher: Harvard University Press
ISBN: 0674032934
Category : History
Languages : en
Pages : 252
Get Book
Book Description
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.
