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Author: David Booth
Publisher: Birkhäuser
ISBN: 3034890311
Category : Mathematics
Languages : en
Pages : 284
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Book Description
Finsler's papers on set theory are presented, here for the first time in English translation, in three parts, and each is preceded by an introduction to the field written by the editors. In the philosophical part of his work Finsler develops his approach to the paradoxes, his attitude toward formalized theories and his defense of Platonism in mathematics. He insisted on the existence of a conceptual realm within mathematics that transcends formal systems. From the foundational point of view, Finsler's set theory contains a strengthened criterion for set identity and a coinductive specification of the universe of sets. The notion of the class of circle free sets introduced by Finsler is potentially a very fertile one although not very widespread today. Combinatorially, Finsler considers sets as generalized numbers to which one may apply arithmetical techniques. The introduction to this third section of the book extends Finsler's theory to non-well-founded sets. The present volume makes Finsler's papers on set theory accessible at long last to a wider group of mathematicians, philosophers and historians of science. A technical background is not necessary to appreciate the satisfying interplay of philosophical and mathematical ideas that characterizes this work.
Author: David Booth
Publisher: Birkhäuser
ISBN: 3034890311
Category : Mathematics
Languages : en
Pages : 284
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Book Description
Finsler's papers on set theory are presented, here for the first time in English translation, in three parts, and each is preceded by an introduction to the field written by the editors. In the philosophical part of his work Finsler develops his approach to the paradoxes, his attitude toward formalized theories and his defense of Platonism in mathematics. He insisted on the existence of a conceptual realm within mathematics that transcends formal systems. From the foundational point of view, Finsler's set theory contains a strengthened criterion for set identity and a coinductive specification of the universe of sets. The notion of the class of circle free sets introduced by Finsler is potentially a very fertile one although not very widespread today. Combinatorially, Finsler considers sets as generalized numbers to which one may apply arithmetical techniques. The introduction to this third section of the book extends Finsler's theory to non-well-founded sets. The present volume makes Finsler's papers on set theory accessible at long last to a wider group of mathematicians, philosophers and historians of science. A technical background is not necessary to appreciate the satisfying interplay of philosophical and mathematical ideas that characterizes this work.
Author: Godehard Link
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 161451996X
Category : Philosophy
Languages : en
Pages : 382
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Book Description
The essays collected in this volume focus on the role of formalist aspects in mathematical theorizing and practice, examining issues such as infinity, finiteness, and proof procedures, as well as central historical figures in the field, including Frege, Russell, Hilbert and Wittgenstein. Using modern logico-philosophical tools and systematic conceptual and logical analyses, the volume provides a thorough, up-to-date account of the subject.
Author: Adam Rieger
Publisher: Springer Nature
ISBN: 3031545575
Category :
Languages : en
Pages : 386
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Book Description
Author: Luca Incurvati
Publisher: Cambridge University Press
ISBN: 1108758355
Category : Science
Languages : en
Pages : 255
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Book Description
Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics.
Author: Ross P. Cameron
Publisher: Oxford University Press
ISBN: 0198854277
Category : Chain of being (Philosophy)
Languages : en
Pages : 265
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Book Description
'Chains of Being' argues that there can be infinite chains of dependence or grounding. Cameron also defends the view that there can be circular relations of ontological dependence or grounding, and uses these claims to explore issues in logic and ontology.
Author: Daniel Parrochia
Publisher: John Wiley & Sons
ISBN: 1394209371
Category : Mathematics
Languages : en
Pages : 276
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Book Description
From Pythagoreans to Hegel, and beyond, this book gives a brief overview of the history of the notion of graphs and introduces the main concepts of graph theory in order to apply them to philosophy. In addition, this book presents how philosophers can use various mathematical notions of order. Throughout the book, philosophical operations and concepts are defined through examining questions relating the two kinds of known infinities – discrete and continuous – and how Woodin's approach can influence elements of philosophy. We also examine how mathematics can help a philosopher to discover the elements of stability which will help to build an image of the world, even if various approaches (for example, negative theology) generally cannot be valid. Finally, we briefly consider the possibilities of weakening formal thought represented by fuzziness and neutrosophic graphs. In a nutshell, this book expresses the importance of graphs when representing ideas and communicating them clearly with others.
Author: Alex Harvey
Publisher: Springer Science & Business Media
ISBN: 146121422X
Category : Science
Languages : en
Pages : 518
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Book Description
This collection of nearly forty essays in honor of the noted physicist and cosmologist Engelbert Schucking spans the gamut of research in Einsteins theory of general relativity and presents a lively and personal account of current work in the field. Indispensable for physicists involved in research in the field, the book includes important chapters by noted theorists such as A. Ashtekar, P.G. Bergmann, J. Ehlers, E.T. Newman, J.V. Narlikar, R. Penrose, D.W. Sciama, J. Stachel, and W. Rindler.
Author: Peter P. Chen
Publisher: Springer
ISBN: 3540488545
Category : Computers
Languages : en
Pages : 326
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Book Description
This volume contains a collection of selected papers presented at the Symposium on Conceptual Modeling, which was held in Los Angeles, California, on December 2, th 1997, immediately before the 16 International Conference on Conceptual Modeling (ER’97), which was held at UCLA. A total of eighteen papers were selected for inclusion in this volume. These papers are written by experts in the conceptual modeling area and represent the most current thinking of these experts. This volume also contains the summaries of three workshops that were held on 6 7 December 1997, immediately after the ER’97 conference at UCLA. The topics of these three workshops are: • Behavioral Modeling • Conceptual Modeling in Multimedia Information Seeking • What Is the Role of Cognition in Conceptual Modeling? Since these topics are not only very important but also very timely, we think it is appropriate to include the summary of these three workshops in this volume. Those readers interested in further investigating topics related to the three workshops can either look up the individual paper published on the Web or contact the authors directly. The summary paper by Chen at the beginning of this volume also includes the summary of several interesting speeches at the Symposium.
Author: Kurt Gödel
Publisher:
ISBN: 019968961X
Category : Computers
Languages : en
Pages : 685
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Book Description
Kurt Gödel (1906 - 1978) was the most outstanding logician of the twentieth century. These collected works form the only comprehensive edition of Gödel's work available and are designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy.
Author: Kurt Gödel
Publisher:
ISBN: 0199689628
Category : Computers
Languages : en
Pages : 691
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Book Description
Kurt Gödel (1906 - 1978) was the most outstanding logician of the twentieth century. These collected works form the only comprehensive edition of Gödel's work available and are designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy.
