Truth Objects Infinity

Author : Fabrice Pataut
Publisher : Springer
Page : 309 pages
File Size : 40,7 Mb
Release : 2017-01-27
Category : Philosophy
ISBN : 9783319459806

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Truth, Objects, Infinity by Fabrice Pataut Pdf

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 Two yet unpublished essays by Benacerraf have been included in the volume: an early version of “Mathematical Truth” from 1968 and an essay on “What Numbers Could Not Be” from the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.

Author : David Deutsch
Publisher : Penguin UK
Page : 571 pages
File Size : 49,7 Mb
Release : 2011-03-31
Category : Science
ISBN : 9780141969695

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The Beginning of Infinity by David Deutsch Pdf

'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 : P. Fletcher
Publisher : Springer Science & Business Media
Page : 477 pages
File Size : 49,5 Mb
Release : 2013-06-29
Category : Philosophy
ISBN : 9789401736169

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Truth, Proof and Infinity by P. Fletcher Pdf

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 : Loren Graham,Jean-Michel Kantor
Publisher : Harvard University Press
Page : 252 pages
File Size : 45,6 Mb
Release : 2009-03-31
Category : History
ISBN : 9780674032934

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Naming Infinity by Loren Graham,Jean-Michel Kantor Pdf

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 : A. W. Moore
Publisher : Dartmouth Publishing Company
Page : 488 pages
File Size : 40,6 Mb
Release : 1993
Category : Mathematics
ISBN : UOM:39015029074484

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Infinity by A. W. Moore Pdf

Author : Chitat Chong,Qi Feng,Theodore A Slaman,W Hugh Woodin
Publisher : World Scientific
Page : 244 pages
File Size : 53,9 Mb
Release : 2013-11-28
Category : Mathematics
ISBN : 9789814571050

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Infinity and Truth by Chitat Chong,Qi Feng,Theodore A Slaman,W Hugh Woodin Pdf

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

Author : Rudy Rucker
Publisher : Princeton University Press
Page : 372 pages
File Size : 49,6 Mb
Release : 2019-07-23
Category : Computers
ISBN : 9780691191386

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Infinity and the Mind by Rudy Rucker Pdf

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 : James Dashner
Publisher : Scholastic Inc.
Page : 214 pages
File Size : 52,5 Mb
Release : 2012-08-28
Category : Juvenile Fiction
ISBN : 9780545473941

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A Mutiny in Time (Infinity Ring, Book 1) by James Dashner Pdf

Scholastic's next multi-platform mega-event begins here!History is broken, and three kids must travel back in time to set it right!When best friends Dak Smyth and Sera Froste stumble upon the secret of time travel -- a hand-held device known as the Infinity Ring -- they're swept up in a centuries-long secret war for the fate of mankind. Recruited by the Hystorians, a secret society that dates back to Aristotle, the kids learn that history has gone disastrously off course.Now it's up to Dak, Sera, and teenage Hystorian-in-training Riq to travel back in time to fix the Great Breaks . . . and to save Dak's missing parents while they're at it. First stop: Spain, 1492, where a sailor named Christopher Columbus is about to be thrown overboard in a deadly mutiny!

Author : Jus Accardo
Publisher : Entangled: Teen
Page : 255 pages
File Size : 55,8 Mb
Release : 2016-11-01
Category : Young Adult Fiction
ISBN : 9781633754966

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Infinity by Jus Accardo Pdf

There are three things Kori knows for sure about her life: One: Her army general dad is insanely overprotective. Two: The guy he sent to watch her, Cade, is way too good-looking. Three: Everything she knew was a lie. Now there are three things Kori never knew about her life: One: There’s a device that allows her to jump dimensions. Two: Cade’s got a lethal secret. Three: Someone wants her dead. The Infinity Division series is best enjoyed in order. Reading Order: Book #1 Infinity Book #2 Omega Book #3 Alpha

Author : Walter Russell
Publisher : David De Angelis
Page : 587 pages
File Size : 46,7 Mb
Release : 2022-05-04
Category : Science
ISBN : 9791221329421

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The Universal One by Walter Russell Pdf

THE UNIVERSAL ONE was originally published in 1927 and distributed to the top scientists in the country. It is being republished at this crucial period for the sole purpose of again releasing vital new scientific knowledge to this new age- of new comprehension. Today the whole world is in a state of chaos fighting against the forces of greed, envy, jealousy and fear. Disharmony is rife. All of our human relations are in a state of violent upheaval. Civilization is in reverse. Science is being used to destroy instead of to build. We talk of world peace, yet those who are to plan the new world do not know the answer, the solution. Present knowledge of man's relation to Nature and Natural Law which controls his human relations is, as yet, inadequate to meet the situation. Man is still too near his jungle to either know the law which inexorably governs his every action and that of everything in Nature or to comprehend that he must obey Nature or be self-destroyed. Still dominated by jungle habits, he settles his human relations by jungle methods. Wars and world chaos will continue until new knowledge applicable to the coming new cycle in man's evolution is acquired by him. What is this new knowledge? A consistent cosmogony is sorely needed for this newly dawning day of man's exaltation which is to come. Walter Russell spent a full seven years in writing this book. When it was first published in 1927, it won more condemnation than favor from a world which was not then as ready for it as now. The book mixed science and metaphysics in a manner which nullified its impression upon physicists. Gradually, however, many of its then radical statements have been verified by some of the world's greatest scientists and have won him many followers. The physicist draws a sharp line between things which he can in some way detect by the evidence of his senses and things which lie beyond that evidence. There is no denial of a "something" beyond the range of his senses and his sensed instruments, but what may be there is conjectural and, therefore, inadmissible as scientific data of a reliable nature. In other words, material evidence which lies within the narrow limits of man's sense-range is the only admissible evidence to science. But what about that vast range which will not respond to our sensed bodies and sensed instruments? Down the ages a rare few have been permitted to sever the senses which connect matter with its motivated Source in the consciousness of Universal Mind. These few have become conscious of the cosmos and have tried to tell the world of its simplicity. Each of these has faced an impossible task. The generalities and symbols which they did set down have been discounted and relegated to poetry or metaphysics or mysticism.

Author : Rhonda Byrne
Publisher : Simon and Schuster
Page : 224 pages
File Size : 51,9 Mb
Release : 2011-07-07
Category : Body, Mind & Spirit
ISBN : 9780731815296

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The Secret by Rhonda Byrne Pdf

The tenth-anniversary edition of the book that changed lives in profound ways, now with a new foreword and afterword. In 2006, a groundbreaking feature-length film revealed the great mystery of the universe—The Secret—and, later that year, Rhonda Byrne followed with a book that became a worldwide bestseller. Fragments of a Great Secret have been found in the oral traditions, in literature, in religions and philosophies throughout the centuries. For the first time, all the pieces of The Secret come together in an incredible revelation that will be life-transforming for all who experience it. In this book, you’ll learn how to use The Secret in every aspect of your life—money, health, relationships, happiness, and in every interaction you have in the world. You’ll begin to understand the hidden, untapped power that’s within you, and this revelation can bring joy to every aspect of your life. The Secret contains wisdom from modern-day teachers—men and women who have used it to achieve health, wealth, and happiness. By applying the knowledge of The Secret, they bring to light compelling stories of eradicating disease, acquiring massive wealth, overcoming obstacles, and achieving what many would regard as impossible.

Author : H. M. Hubey
Publisher : World Scientific
Page : 550 pages
File Size : 52,6 Mb
Release : 1998
Category : Mathematics
ISBN : 9810230818

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The Diagonal Infinity by H. M. Hubey Pdf

CD-ROM consists of four directories: parametric plots, fractals, etc; nonlinear differential equations; fuzzy logics; and graphics files.

Author : Marcus Chown
Publisher : Diversion Books
Page : 216 pages
File Size : 44,7 Mb
Release : 2019-04-23
Category : Science
ISBN : 9781635765939

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Infinity in the Palm of Your Hand by Marcus Chown Pdf

A mind-bending journey through some of the most weird and wonderful facts about our universe, vividly illuminating the hidden truths that govern our everyday lives. Fact: You could fit the whole human race in the volume of a sugar cube. Fact: The electrical energy in a single mosquito is enough to cause a global mass extinction. Fact: You age more quickly on the top floor than on the ground floor. So much of our world seems to make perfect sense, and scientific breakthroughs have helped us understand ourselves, our planet, and our place in the universe in fascinating detail. But our adventures in space, our deepening understanding of the quantum world, and our leaps in technology have also revealed a universe far stranger than we ever imagined. With brilliant clarity and wit, bestselling author Marcus Chown examines the profound science behind fifty remarkable scientific facts that help explain the vast complexities of our existence. “The tone is consistently light and breezy...An addictive, intriguing, and entertaining read...A handy guide for anyone yearning to spice up their conversational skills.”—Booklist “Heavy stuff lightly spun―just the thing for the science buff in the house.”―Kirkus Review

Author : Karsten Harries
Publisher : MIT Press
Page : 400 pages
File Size : 41,9 Mb
Release : 2001
Category : Architecture
ISBN : 026258218X

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Infinity and Perspective by Karsten Harries Pdf

A philosophical exploration of the origin and limits of the modern world.

Author : John Stillwell
Publisher : CRC Press
Page : 202 pages
File Size : 55,8 Mb
Release : 2010-07-13
Category : Mathematics
ISBN : 9781439865507

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Roads to Infinity by John Stillwell Pdf

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