Truth Objects Infinity
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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 Two yet unpublished essays by Benacerraf have been included in the volume: an early version of “Mathematical Truth” from 1968 and an essay on “What Numbers Could Not Be” from the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.
Infinity And The Mind
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Author : Rudy Rucker
language : en
Publisher: Princeton University Press
Release Date : 2019-07-23
Infinity And The Mind written by Rudy Rucker and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-23 with Computers categories.
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.
The Beginning Of Infinity
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Author : David Deutsch
language : en
Publisher: Penguin UK
Release Date : 2011-03-31
The Beginning Of Infinity written by David Deutsch and has been published by Penguin UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-31 with Science categories.
'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
Infinity
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Author : A. W. Moore
language : en
Publisher: Dartmouth Publishing Company
Release Date : 1993
Infinity written by A. W. Moore and has been published by Dartmouth Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
The Beginning Of Infinity
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Author : David Deutsch
language : en
Publisher: Penguin
Release Date : 2011-07-21
The Beginning Of Infinity written by David Deutsch and has been published by Penguin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-21 with Science categories.
The New York Times bestseller: A provocative, imaginative exploration of the nature and progress of knowledge “Dazzling.” – Steven Pinker, The Guardian In this groundbreaking book, award-winning physicist David Deutsch argues that explanations have a fundamental place in the universe—and that improving them is the basic regulating principle of all successful human endeavor. Taking us on a journey through every fundamental field of science, as well as the history of civilization, art, moral values, and the theory of political institutions, Deutsch tracks how we form new explanations and drop bad ones, explaining the conditions under which progress—which he argues is potentially boundless—can and cannot happen. Hugely ambitious and highly original, The Beginning of Infinity explores and establishes deep connections between the laws of nature, the human condition, knowledge, and the possibility for progress.
Truth Proof And Infinity
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Author : P. Fletcher
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Truth Proof And Infinity written by P. Fletcher and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Philosophy categories.
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.
The Infinite
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Author : A.W. Moore
language : en
Publisher: Routledge
Release Date : 2012-08-06
The Infinite written by A.W. Moore and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-06 with Mathematics categories.
Anyone who has pondered the limitlessness of space and time, or the endlessness of numbers, or the perfection of God will recognize the special fascination of this question. Adrian Moore's historical study of the infinite covers all its aspects, from the mathematical to the mystical.
Infinity And Perspective
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Author : Karsten Harries
language : en
Publisher: MIT Press
Release Date : 2001
Infinity And Perspective written by Karsten Harries and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Architecture categories.
A philosophical exploration of the origin and limits of the modern world.
Truth And Symbol
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Author : Karl Jaspers
language : en
Publisher: Rowman & Littlefield
Release Date : 1959
Truth And Symbol written by Karl Jaspers and has been published by Rowman & Littlefield this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with Literary Criticism categories.
To find more information about Rowman and Littlefield titles, please visit www.rowmanlittlefield.com.
Infinity And Truth
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Author : Chitat Chong
language : en
Publisher: World Scientific
Release Date : 2013-11-28
Infinity And Truth written by Chitat Chong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-28 with Mathematics categories.
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. Contents:Invited Lectures:Absoluteness, Truth, and Quotients (Ilijas Farah)A Multiverse Perspective on the Axiom of Constructiblity (Joel David Hamkins)Hilbert, Bourbaki and the Scorning of Logic (A R D Mathias)Toward Objectivity in Mathematics (Stephen G Simpson)Sort Logic and Foundations of Mathematics (Jouko Väänänen)Reasoning about Constructive Concepts (Nik Weaver)Perfect Infinites and Finite Approximation (Boris Zilber)Special Session:An Objective Justification for Actual Infinity? (Stephen G Simpson)Oracle Questions (Theodore A Slaman and W Hugh Woodin) Readership: Mathematicians, philosophers, scientists, graduate students, academic institutions, and research organizations interested in logic and the philosophy of mathematics. Keywords:Mathematical Logic;Foundations of Mathematics;Philosophy of Mathematics;Mathematical Truth;Infinity;Set Theory;Proof Theory;MultiverseKey Features:All the contributors are world-renownedThe final chapter is written by Theodore A Slaman and W Hugh Woodin, who are two of the leading logicians in the world. They are also the volume editors