Reasoning With The Infinite
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Reasoning With The Infinite
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Author : Michel Blay
language : en
Publisher: University of Chicago Press
Release Date : 1998
Reasoning With The Infinite written by Michel Blay and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with History categories.
Until the Scientific Revolution, the nature and motions of heavenly objects were mysterious and unpredictable. The Scientific Revolution was revolutionary in part because it saw the advent of many mathematical tools—chief among them the calculus—that natural philosophers could use to explain and predict these cosmic motions. Michel Blay traces the origins of this mathematization of the world, from Galileo to Newton and Laplace, and considers the profound philosophical consequences of submitting the infinite to rational analysis. "One of Michael Blay's many fine achievements in Reasoning with the Infinite is to make us realize how velocity, and later instantaneous velocity, came to play a vital part in the development of a rigorous mathematical science of motion."—Margaret Wertheim, New Scientist
Reasoning With The Infinite
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Author : Michel Blay
language : en
Publisher: University of Chicago Press
Release Date : 1999-11-10
Reasoning With The Infinite written by Michel Blay and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-10 with Science categories.
Until the Scientific Revolution, the nature and motions of heavenly objects were mysterious and unpredictable. The Scientific Revolution was revolutionary in part because it saw the advent of many mathematical tools—chief among them the calculus—that natural philosophers could use to explain and predict these cosmic motions. Michel Blay traces the origins of this mathematization of the world, from Galileo to Newton and Laplace, and considers the profound philosophical consequences of submitting the infinite to rational analysis. "One of Michael Blay's many fine achievements in Reasoning with the Infinite is to make us realize how velocity, and later instantaneous velocity, came to play a vital part in the development of a rigorous mathematical science of motion."—Margaret Wertheim, New Scientist
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.
Zeno Cantor And Infinity
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Author : David Holland
language : en
Publisher:
Release Date : 1990
Zeno Cantor And Infinity written by David Holland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Infinite categories.
On Reasoning About Infinite State Systems In The Modal My Calculus
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Author : H. Andersen
language : en
Publisher:
Release Date : 1993
On Reasoning About Infinite State Systems In The Modal My Calculus written by H. Andersen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Reasoning About Infinite Computation Paths
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Author : M. Y. Vardi
language : en
Publisher:
Release Date : 1988
Reasoning About Infinite Computation Paths written by M. Y. Vardi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
The Thinking Universe
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Author : Edmund E. Sheppard
language : en
Publisher: Forgotten Books
Release Date : 2015-06-27
The Thinking Universe written by Edmund E. Sheppard and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-27 with Self-Help categories.
Excerpt from The Thinking Universe: Reason as Applied to the Manifestations of the Infinite The aim of this work is to make comprehensible the Grandeur of the Immobile, Intangible Infinite, reposing Majestically in its Eternal, Unchanging Stillness, in Everything, as Everything, propelling Everything. Its Method is by a proper classification and description of the processes of the human mind to make clear that Right Reasoning must precede Right Thinking, which is synonymous with Right Acting. Its Development shows that human beings, always eager for health, happiness and prosperity, finding these things dependent upon the Rightness of their thoughts, will become more careful in their Reasoning and thus live cleaner and more reasonable lives. Its Iconoclasm is only that of removing obstacles delaying Man in his progress to Perfection. Its Constructiveness is the convincing of Man of his sufficient equipment to overcome all impediments to his arrival at Positive Rightness. Its Effect, by divesting Death of its terrors and the Future Life of its unreasonable dulness, must be to cause Man to regard Life Here and Now as a pleasing and profitable incident preparatory to still more pleasing and profitable experiences There and Then. Its Hope is that it may find its way into every home and every life. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Lapses In Mathematical Reasoning
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Author : V. M. Bradis
language : en
Publisher: Courier Dover Publications
Release Date : 2016-10-28
Lapses In Mathematical Reasoning written by V. M. Bradis and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-28 with Mathematics categories.
Designed as a method for teaching correct mathematical thinking to high school students, this book contains a brilliantly constructed series of what the authors call "lapses," erroneous statements that are part of a larger mathematical argument. These lapses lead to sophism or mathematical absurdities. The ingenious idea behind this technique is to lead the student deliberately toward a clearly false conclusion. The teacher and student then go back and analyze the lapse as a way to correct the problem. The authors begin by focusing on exercises in refuting erroneous mathematical arguments and their classification. The remaining chapters discuss examples of false arguments in arithmetic, algebra, geometry, trigonometry, and approximate computations. Ideally, students will come to the correct insights and conclusions on their own; however, each argument is followed by a detailed analysis of the false reasoning. Stimulating and unique, this book is an intriguing and enjoyable way to teach students critical mathematical reasoning skills.
The New Infinite And The Old Theology
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Author : Cassius J. Keyser
language : en
Publisher:
Release Date : 2016-06-22
The New Infinite And The Old Theology written by Cassius J. Keyser and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-22 with categories.
"The New Infinite and the Old Theology" is the title Professor Keyser gives to his study of the infinite from the viewpoint of the mathematician. Reason comes to the relief of theology. It is an apologetic presentation, in a way, since he aims to make the acceptance of the infinite both possible and easy from a mathematical viewpoint. The author regards theology as suffering a merely temporary decline-she has not availed herself of advancing knowledge. Mathematics is "especially qualified to assist her." Theology as an attempt to reach ideas, to reduce life to a formula is an absurd failure -not ideas but ideals, should be the goal, and the infinites exist as ideals rather than as ideas. Theology is not the science of religion (pp. 14, 15). "Theology is not a branch of analytical psychology, nor a branch of anthropology." Nor is "religion" the subject-matter of theology. "Religion is essentially emotion; theology is doctrine; the former feels, the latter thinks; theology is a structure, an edifice of thought; religion is a flow-a stream of sentiment," and so on. The subject matter of theology "consists of rational phenomena." "It is the task of theology to study these implications of logical thought which are hyperlogical and to interpret them in rational terms." There is a "supernalizing power;" this presents theology its task. "Theology is the science of idealization. The phenomena of idealization spring from foundations deeper than the will; their credentials are cosmic. Theology thus deals not with ideas, but ideals. Ideals are not to be grasped; they are things to be reached for. Theology must study the grounds and source of these ideals. God is, for example, not an idea, but an ideal. Theology cannot be a science of the overworld as astronomy is a science of the heavenly bodies. The overwork! faces downward and presents itself to reason as ideals. Of these theology speaks. While science is, as commonly defined, essentially atheistic, scientific man is not. Man is infinitely greater than science. Thus our author indicates a field for theology apart from science, and he proceeds to bring the Infinite, as it were, within reach by a course of mathematical reasoning. Some mathematical wonders are unfolded. The outcome of his search and reasoning is that the whole and the part may both be infinite. There is no absurdity in this thought. It is a mathematical commonplace. Infinites are not all alike. "There are countless mathematical infinities or infinitudes or infinites." The Infinite of theology is the envelope, enfolding them all. Thus Dr. Keyser leads to the Infinite of theology by way of the infinites within it. The infinite is in the finite, as mathematics shows. There is much interesting, and occasionally intricate reasoning, whereby mathematics justifies both the Dignity of Omniscience and Freedom; the fact of omnipresence as one of the "intelligible ideals." An illustration is found in the concept of "hyperspace." There results the "conceivability of the infinite Being being everywhere present in an infinite region without being contained in it." Mathematics contains the wonders which are found in theology, and theology can profit by the belief which mathematicians bestow on their wonders and seeming incredibilities. -Auburn Seminary Record, Vol. 12
On Reasoning About Infinite State Systems In The Modal Calculus
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Author : Henrik Reif Andersen
language : en
Publisher:
Release Date : 1993
On Reasoning About Infinite State Systems In The Modal Calculus written by Henrik Reif Andersen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.