Infinity And Truth
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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
Roads To Infinity
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Author : John Stillwell
language : en
Publisher: CRC Press
Release Date : 2010-07-13
Roads To Infinity written by John Stillwell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-13 with Mathematics categories.
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
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.
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.
The Beauty Of The Infinite
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Author : David Bentley Hart
language : en
Publisher: Wm. B. Eerdmans Publishing
Release Date : 2004-10-29
The Beauty Of The Infinite written by David Bentley Hart and has been published by Wm. B. Eerdmans Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-29 with Religion categories.
The Beauty of the Infinite is a splendid extended essay in "theological aesthetics." David Bentley Hart here meditates on the power of a Christian understanding of beauty and sublimity to rise above the violence -- both philosophical and literal -- characteristic of the postmodern world. The book begins by tracing the shifting use and nature of metaphysics in the thought of Kant, Hegel, Nietzsche, Heidegger, Lyotard, Derrida, Deleuze, Nancy, Levinas, and others. Hart pays special attention to Nietzsche's famous narrative of the "will to power" -- a narrative largely adopted by the world today -- and he offers an engaging revision (though not rejection) of the genealogy of nihilism, thereby highlighting the significant "interruption" that Christian thought introduced into the history of metaphysics. This discussion sets the stage for a retrieval of the classic Christian account of beauty and sublimity, and of the relation of both to the question of being. Written in the form of a dogmatica minora, this main section of the book offers a pointed reading of the Christian story in four moments, or parts: Trinity, creation, salvation, and eschaton. Through a combination of narrative and argument throughout, Hart ends up demonstrating the power of Christian metaphysics not only to withstand the critiques of modern and postmodern thought but also to move well beyond them. Strikingly original and deeply rewarding, The Beauty of the Infinite is both a constructively critical account of the history of metaphysics and a compelling contribution to it.
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.
Truth Infinite Absolute
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Author : Benjamin Livell
language : en
Publisher: Page Publishing Inc
Release Date : 2020-11-15
Truth Infinite Absolute written by Benjamin Livell and has been published by Page Publishing Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-15 with Philosophy categories.
The key unlocking the mind. Some seek a freedom from restraint yet need only to stop restraining themselves. Some seek to become that of greater good yet confuse that which is good from bad and bad from good. Some seek that of change about themselves yet not a moment is spent to change that within the self. Some seek God by searching yet are forever kept away by their very searching. All keys are relative to their lock as all locks are relative to their keys. With this being said, if we wish to unlock the mind, we must use mind upon itself as a key. Mind is a great mover, and in life we find ourselves carried along in its power. This is the birth of the chain and lock. For only the mind may set restraint against itself. So only the mind may set itself to freedom. Within these pages is everything and nothing. For the seeker living a life of true vision, everything. For those without courage to open their eyes, near nothing. But there is always a chance at new discovery of self. May we not all share in this self-discovery? Because the greatness we find rests in us all. This book is a work of understanding that greatness found, the truth residing within everything.
Infinity
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Author : Michael Heller
language : en
Publisher: Cambridge University Press
Release Date : 2011-02-07
Infinity written by Michael Heller 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 2011-02-07 with Mathematics categories.
This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen world-renowned researchers in the fields of mathematics, physics, cosmology, philosophy and theology offer a rich intellectual exchange among various current viewpoints, rather than displaying a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity.
Badiou Infinity And Subjectivity
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Author : Mohammad Reza Naderi
language : en
Publisher: Lexington Books
Release Date : 2023-12-20
Badiou Infinity And Subjectivity written by Mohammad Reza Naderi and has been published by Lexington Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-20 with Mathematics categories.
In Badiou, Infinity, and Subjectivity: Reading Hegel and Lacan after Badiou, Mohammad Reza Naderi elaborates on the trajectory of Alain Badiou’s philosophy by following a leading thread: the dominance of axiomatic thought and the category of mathematical infinity. According to this primary proposition, axiomatic thought is the only form of thinking adequate to the infinity of being. Using both primary and secondary literature, the author demonstrates two other major propositions: 1) The coherence of Badiou’s intellectual development from the early interventions to the publication of Being and Event, and 2) The formation of a theory Naderi calls “discipline.” By working through three dimensions of disciplinary thinking—interiority, novelty, and beginning—Naderi provides a new framework for understanding the inner structure of what Badiou calls “procedures of truths” and develops a new interpretation that ultimately reveals the inner logic of Badiou’s method.
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.