The Foundations Of Mathematics A Contribution To The Philosophy Of Geometry
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The Foundations Of Mathematics
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Author : Paul Carus
language : en
Publisher: Cosimo, Inc.
Release Date : 2004-01-01
The Foundations Of Mathematics written by Paul Carus and has been published by Cosimo, Inc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
In this brief treatise, Carus traces the roots of his belief in the philosophical basis for mathematics and analyzes that basis after a historical overview of Euclid and his successors. He then examines his base argument and proceeds to a study of different geometrical systems, all pulled together in his epilogue, which examines matter, mathematics, and, ultimately, the nature of God.
The Foundations Of Mathematics A Contribution To The Philosophy Of Geometry
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Author : Paul Carus
language : en
Publisher:
Release Date : 1908
The Foundations Of Mathematics A Contribution To The Philosophy Of Geometry written by Paul Carus and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1908 with Geometry categories.
The Foundations Of Mathematics A Contribution To The Philosophy Of Geometry
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Author : Carus Paul
language : en
Publisher: Wentworth Press
Release Date : 2019-02-28
The Foundations Of Mathematics A Contribution To The Philosophy Of Geometry written by Carus Paul and has been published by Wentworth Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-28 with History categories.
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Foundations Of Mathematics
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Author : Paul Carus
language : en
Publisher: Forgotten Books
Release Date : 2015-06-02
The Foundations Of Mathematics written by Paul Carus and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-02 with Philosophy categories.
Excerpt from The Foundations of Mathematics: A Contribution to the Philosophy of Geometry Finally, he adds what he calls Common Notions which embody some general principles of logic (of pure reason) specially needed in geometry, such as that things which are equal to the same thing are equal to one another; that if equals be added to equals, the wholes are equal, etc. I need not mention here perhaps, since it is a fact of no consequence, that the readings of the several manuscripts vary, and that some propositions (e. g., that all right angles are equal to one another) are now missing, now counted among the postulates, and now adduced as common notions. The commentators of Euclid who did not understand the difference between Postulates and Common Notions, spoke of both as axioms, and even to-day the term Common Notion is mostly so translated. In our modern editions of Euclid we find a statement concerning parallel lines added to either the Postulates or Common Notions. Originally it appeared in Proposition 29 where it is needed to prop up the argument that would prove the equality of alternate angles in case a third straight line falls upon parallel straight lines. 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.
Foundations Of Mathematics
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Author : Carus Paul
language : en
Publisher:
Release Date : 1901
Foundations Of Mathematics written by Carus Paul and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1901 with categories.
The Foundations Of Mathematics A Contribution To The Philosophy Of Geometry Scholar S Choice Edition
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Author : Carus Paul
language : en
Publisher: Scholar's Choice
Release Date : 2015-02-19
The Foundations Of Mathematics A Contribution To The Philosophy Of Geometry Scholar S Choice Edition written by Carus Paul and has been published by Scholar's Choice this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-19 with categories.
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Philosophy And Foundations Of Mathematics
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Author : A. Heyting
language : en
Publisher: Elsevier
Release Date : 2014-05-12
Philosophy And Foundations Of Mathematics written by A. Heyting and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
L.E.J. Brouwer: Collected Works, Volume 1: Philosophy and Foundations of Mathematics focuses on the principles, operations, and approaches promoted by Brouwer in studying the philosophy and foundations of mathematics. The publication first ponders on the construction of mathematics. Topics include arithmetic of integers, negative numbers, measurable continuum, irrational numbers, Cartesian geometry, similarity group, characterization of the linear system of the Cartesian or Euclidean and hyperbolic space, and non-Archimedean uniform groups on the one-dimensional continuum. The book then examines mathematics and experience and mathematics and logic. Topics include denumerably unfinished sets, continuum problem, logic of relations, consistency proofs for formal systems independent of their interpretation, infinite numbers, and problems of space and time. The text is a valuable reference for students, mathematicians, and researchers interested in the contributions of Brouwer in the studies on the philosophy and foundations of mathematics.
An Essay On The Foundations Of Geometry
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Author : Bertrand Russell
language : en
Publisher: Prabhat Prakashan
Release Date : 1956-01-01
An Essay On The Foundations Of Geometry written by Bertrand Russell and has been published by Prabhat Prakashan this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956-01-01 with Fiction categories.
Essays On The Foundations Of Mathematics By Moritz Pasch
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Author : Stephen Pollard
language : en
Publisher: Springer
Release Date : 2010-09-03
Essays On The Foundations Of Mathematics By Moritz Pasch written by Stephen Pollard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-03 with Mathematics categories.
Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science; he provides axioms for the combinatorial reasoning essential to Hilbert’s program of consistency proofs; he explores "implicit definition" (a generalization of definition by abstraction) and indicates how this technique yields an "empiricist" reconstruction of set theory; he argues that we cannot fully understand the logical structure of mathematics without clearly distinguishing between decidable and undecidable properties; he offers a rare glimpse into the mind of a master of axiomatics, surveying in detail the thought experiments he employed as he struggled to identify fundamental mathematical principles; and much more. This volume will: Give English speakers access to an important body of work from a turbulent and pivotal period in the history of mathematics, help us look beyond the familiar triad of formalism, intuitionism, and logicism, show how deeply we can see with the help of a guide determined to present fundamental mathematical ideas in ways that match our human capacities, will be of interest to graduate students and researchers in logic and the foundations of mathematics.
Essays On The Foundations Of Mathematics By Moritz Pasch
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Author : Stephen Pollard
language : en
Publisher: Springer
Release Date : 2012-11-06
Essays On The Foundations Of Mathematics By Moritz Pasch written by Stephen Pollard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-06 with Mathematics categories.
Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science; he provides axioms for the combinatorial reasoning essential to Hilbert’s program of consistency proofs; he explores "implicit definition" (a generalization of definition by abstraction) and indicates how this technique yields an "empiricist" reconstruction of set theory; he argues that we cannot fully understand the logical structure of mathematics without clearly distinguishing between decidable and undecidable properties; he offers a rare glimpse into the mind of a master of axiomatics, surveying in detail the thought experiments he employed as he struggled to identify fundamental mathematical principles; and much more. This volume will: Give English speakers access to an important body of work from a turbulent and pivotal period in the history of mathematics, help us look beyond the familiar triad of formalism, intuitionism, and logicism, show how deeply we can see with the help of a guide determined to present fundamental mathematical ideas in ways that match our human capacities, will be of interest to graduate students and researchers in logic and the foundations of mathematics.