The Infinite Counted By God A Dedekindian Interpretation Of Cantor S Transfinite Ordinal Number Concept
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The Infinite Counted By God A Dedekindian Interpretation Of Cantor S Transfinite Ordinal Number Concept
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Author :
language : pt-BR
Publisher:
Release Date : 2003
The Infinite Counted By God A Dedekindian Interpretation Of Cantor S Transfinite Ordinal Number Concept written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
Subjacente à teoria dos números ordinais transfinitos de Cantor, há umaperspectiva finitista. Segundo tal perspectiva, Deus pode bem ordenar o infinitousando, para tanto, de procedimentos similares ao ato de contar, entendido como oato de bem ordenar o finito. Desta maneira, um diálogo natural entre Cantor eDedekind torna-se possível, dado que Dedekind foi o primeiro a tratar o ato decontar como sendo, em sua essência, uma forma de bem ordenar o mundo espáciotemporalpelos números naturais. Nesta tese, o conceito de número ordinaltransfinito, de Cantor, é entendido como uma extensão do conceito dedekindiano denúmero natural.
Introduction To Mathematical Philosophy
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Author : Bertrand Russell
language : en
Publisher: Courier Corporation
Release Date : 1993-01-01
Introduction To Mathematical Philosophy written by Bertrand Russell and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Mathematics categories.
In the words of Bertrand Russell, "Because language is misleading, as well as because it is diffuse and inexact when applied to logic (for which it was never intended), logical symbolism is absolutely necessary to any exact or thorough treatment of mathematical philosophy." That assertion underlies this book, a seminal work in the field for more than 70 years. In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy. In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.
Principia Mathematica
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Author : Alfred North Whitehead
language : en
Publisher: Cambridge University Press
Release Date : 1927
Principia Mathematica written by Alfred North Whitehead 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 1927 with Mathematics categories.
The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.
Philosophy Of Mathematics
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Author : Charles S. Peirce
language : en
Publisher: Indiana University Press
Release Date : 2010-08-19
Philosophy Of Mathematics written by Charles S. Peirce and has been published by Indiana University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-19 with Philosophy categories.
The philosophy of mathematics plays a vital role in the mature philosophy of Charles S. Peirce. Peirce received rigorous mathematical training from his father and his philosophy carries on in decidedly mathematical and symbolic veins. For Peirce, math was a philosophical tool and many of his most productive ideas rest firmly on the foundation of mathematical principles. This volume collects Peirce's most important writings on the subject, many appearing in print for the first time. Peirce's determination to understand matter, the cosmos, and "the grand design" of the universe remain relevant for contemporary students of science, technology, and symbolic logic.
My Philosophical Development
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Author : Bertrand Russell
language : en
Publisher:
Release Date : 1956
My Philosophical Development written by Bertrand Russell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956 with categories.
Visualization Explanation And Reasoning Styles In Mathematics
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Author : P. Mancosu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Visualization Explanation And Reasoning Styles In Mathematics written by P. Mancosu 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 2006-03-30 with Mathematics categories.
In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.
The Foundations Of Arithmetic
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Author : Gottlob Frege
language : en
Publisher: John Wiley & Sons
Release Date : 1980
The Foundations Of Arithmetic written by Gottlob Frege and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
A philosophical discussion of the concept of number In the book, The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, Gottlob Frege explains the central notions of his philosophy and analyzes the perspectives of predecessors and contemporaries. The book is the first philosophically relevant discussion of the concept of number in Western civilization. The work went on to significantly influence philosophy and mathematics. Frege was a German mathematician and philosopher who published the text in 1884, which seeks to define the concept of a number. It was later translated into English. This is the revised second edition.
Foundational Theories Of Classical And Constructive Mathematics
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Author : Giovanni Sommaruga
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-24
Foundational Theories Of Classical And Constructive Mathematics written by Giovanni Sommaruga 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 2011-03-24 with Mathematics categories.
The book "Foundational Theories of Classical and Constructive Mathematics" is a book on the classical topic of foundations of mathematics. Its originality resides mainly in its treating at the same time foundations of classical and foundations of constructive mathematics. This confrontation of two kinds of foundations contributes to answering questions such as: Are foundations/foundational theories of classical mathematics of a different nature compared to those of constructive mathematics? Do they play the same role for the resp. mathematics? Are there connections between the two kinds of foundational theories? etc. The confrontation and comparison is often implicit and sometimes explicit. Its great advantage is to extend the traditional discussion of the foundations of mathematics and to render it at the same time more subtle and more differentiated. Another important aspect of the book is that some of its contributions are of a more philosophical, others of a more technical nature. This double face is emphasized, since foundations of mathematics is an eminent topic in the philosophy of mathematics: hence both sides of this discipline ought to be and are being paid due to.
The Origins Of Cauchy S Rigorous Calculus
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Author : Judith V. Grabiner
language : en
Publisher: Courier Corporation
Release Date : 2012-05-11
The Origins Of Cauchy S Rigorous Calculus written by Judith V. Grabiner and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-11 with Mathematics categories.
This text examines the reinterpretation of calculus by Augustin-Louis Cauchy and his peers in the 19th century. These intellectuals created a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. 1981 edition.
Theoretical Writings
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Author : Alain Badiou
language : en
Publisher: Bloomsbury Publishing
Release Date : 2015-10-29
Theoretical Writings written by Alain Badiou and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-29 with Philosophy categories.
Alain Badiou is arguably the most original and influential philosopher working in France today. Working against the tide of postmodern orthodoxy, Badiou revitalizes philosophy's perennial attempt to provide a systematic theory of truth. Theoretical Writings presents, in Badiou's own words, 'the theoretical core of [his] Philosophy'. Beginning with the controversial assertion that ontology is mathematics, the chapters step the reader through his key concepts of being, subject and truth via startling re-readings of canonical figures including Spinoza, Kant and Hegel and engagements with poetry, psychoanalysis and radical politics. Theoretical Writings is an indispensable introduction to one of the great thinkers of our time.