Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Finsler Set Theory
Download Finsler Set Theory full books in PDF, epub, and Kindle. Read online Finsler Set Theory ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Finsler Set Theory: Platonism and Circularity by : David Booth
Download or read book Finsler Set Theory: Platonism and Circularity written by David Booth and published by Birkhäuser. This book was released on 2012-12-06 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Formalism and Beyond by : Godehard Link
Download or read book Formalism and Beyond written by Godehard Link and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-10-09 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Chains of Being by : Ross P. Cameron
Download or read book Chains of Being written by Ross P. Cameron and published by Oxford University Press. This book was released on 2022-03-10 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Chains of Being, Ross P. Cameron argues for both Metaphysical Infinitism, the view that there can be infinitely descending chains of ontological dependence or grounding, with no bottom level of fundamental things or facts, and Metaphysical Holism, the view that there can be circles of ontological dependence or grounding. Cameron argues against the widespread orthodoxy of Metaphysical Foundationalism: that everything in reality is ultimately accounted for by a base class of fundamental phenomena. In doing so, he makes the case against another widespread orthodoxy: that relations like grounding and ontological dependence are explanatory relations. Cameron provides an alternative account of metaphysical explanation that does not tie explanation to determination relations like grounding and ontological dependence, and he shows how explanation works in infinitist and holistic metaphysics. Embracing the possibility of infinite regress and circularity can be theoretically fruitful, as is shown by applying it to a number of cases across a wide range of philosophical areas, including: non-well-founded set theory, mathematical structuralism, the metaphysics of persons, the metaphysics of gender and sexuality, the semantic paradoxes, and others. In the course of exploring these applications, Cameron defends distinctive views concerning when an infinite regress is vicious, the nature of truth, non-classical logic and dialetheism, social construction, and more.
Book Synopsis Differential Geometry of Spray and Finsler Spaces by : Zhongmin Shen
Download or read book Differential Geometry of Spray and Finsler Spaces written by Zhongmin Shen and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we study sprays and Finsler metrics. Roughly speaking, a spray on a manifold consists of compatible systems of second-order ordinary differential equations. A Finsler metric on a manifold is a family of norms in tangent spaces, which vary smoothly with the base point. Every Finsler metric determines a spray by its systems of geodesic equations. Thus, Finsler spaces can be viewed as special spray spaces. On the other hand, every Finsler metric defines a distance function by the length of minimial curves. Thus Finsler spaces can be viewed as regular metric spaces. Riemannian spaces are special regular metric spaces. In 1854, B. Riemann introduced the Riemann curvature for Riemannian spaces in his ground-breaking Habilitationsvortrag. Thereafter the geometry of these special regular metric spaces is named after him. Riemann also mentioned general regular metric spaces, but he thought that there were nothing new in the general case. In fact, it is technically much more difficult to deal with general regular metric spaces. For more than half century, there had been no essential progress in this direction until P. Finsler did his pioneering work in 1918. Finsler studied the variational problems of curves and surfaces in general regular metric spaces. Some difficult problems were solved by him. Since then, such regular metric spaces are called Finsler spaces. Finsler, however, did not go any further to introduce curvatures for regular metric spaces. He switched his research direction to set theory shortly after his graduation.
Book Synopsis Conceptions of Set and the Foundations of Mathematics by : Luca Incurvati
Download or read book Conceptions of Set and the Foundations of Mathematics written by Luca Incurvati and published by Cambridge University Press. This book was released on 2020-01-23 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Book Synopsis Themes from Weir: A Celebration of the Philosophy of Alan Weir by : Adam Rieger
Download or read book Themes from Weir: A Celebration of the Philosophy of Alan Weir written by Adam Rieger and published by Springer Nature. This book was released on with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8) by : Herbert Busemann
Download or read book Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8) written by Herbert Busemann and published by Princeton University Press. This book was released on 2016-03-02 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8), will be forthcoming.
Book Synopsis Mathematics and Philosophy 2 by : Daniel Parrochia
Download or read book Mathematics and Philosophy 2 written by Daniel Parrochia and published by John Wiley & Sons. This book was released on 2023-04-14 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Kurt Gödel: Collected Works: Volume IV by : Kurt Gödel
Download or read book Kurt Gödel: Collected Works: Volume IV written by Kurt Gödel and published by Clarendon Press. This book was released on 2014-01-09 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kurt Gödel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein's equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought and accomplishment. The first two volumes were devoted to Gödel's publications in full (both in original and translation), and the third volume featured a wide selection of unpublished articles and lecture texts found in Gödel's Nachlass. These long-awaited final two volumes contain Gödel's correspondence of logical, philosophical, and scientific interest. Volume IV covers A to G, with H to Z in volume V; in addition, Volume V contains a full inventory of Gödel's Nachlass. All volumes include introductory notes that provide extensive explanatory and historical commentary on each body of work, English translations of material originally written in German (some transcribed from the Gabelsberger shorthand), and a complete bibliography of all works cited. Kurt Gödel: Collected Works is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy. The only comprehensive edition of Gödel's work available, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science and all others who wish to be acquainted with one of the great minds of the twentieth century.
Book Synopsis Quine, New Foundations, and the Philosophy of Set Theory by : Sean Morris
Download or read book Quine, New Foundations, and the Philosophy of Set Theory written by Sean Morris and published by Cambridge University Press. This book was released on 2018-12-13 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quine's set theory, New Foundations, has often been treated as an anomaly in the history and philosophy of set theory. In this book, Sean Morris shows that it is in fact well-motivated, emerging in a natural way from the early development of set theory. Morris introduces and explores the notion of set theory as explication: the view that there is no single correct axiomatization of set theory, but rather that the various axiomatizations all serve to explicate the notion of set and are judged largely according to pragmatic criteria. Morris also brings out the important interplay between New Foundations, Quine's philosophy of set theory, and his philosophy more generally. We see that his early technical work in logic foreshadows his later famed naturalism, with his philosophy of set theory playing a crucial role in his primary philosophical project of clarifying our conceptual scheme and specifically its logical and mathematical components.
Book Synopsis From Kant to Hilbert Volume 2 by : William Bragg Ewald
Download or read book From Kant to Hilbert Volume 2 written by William Bragg Ewald and published by Oxford University Press. This book was released on 1999 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work brings together a comprehensive selection of mathematical works from the period 1707-1930. During this time the foundations of modern mathematics were laid, and From Kant to Hilbert provides an overview of the foundational work in each of the main branches of mathmeatics with narratives showing how they were linked. Now available as a separate volume.
Book Synopsis The Search for Mathematical Roots, 1870-1940 by : Ivor Grattan-Guinness
Download or read book The Search for Mathematical Roots, 1870-1940 written by Ivor Grattan-Guinness and published by Princeton University Press. This book was released on 2011-02-11 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913). ? This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.
Download or read book On Einstein’s Path written by Alex Harvey and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Kurt Gödel: Collected Works: Volume V by : Kurt Gödel
Download or read book Kurt Gödel: Collected Works: Volume V written by Kurt Gödel and published by . This book was released on 2013-10 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Advanced Topics in Bisimulation and Coinduction by : Davide Sangiorgi
Download or read book Advanced Topics in Bisimulation and Coinduction written by Davide Sangiorgi and published by Cambridge University Press. This book was released on 2011-10-13 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coinduction is a method for specifying and reasoning about infinite data types and automata with infinite behaviour. In recent years, it has come to play an ever more important role in the theory of computing. It is studied in many disciplines, including process theory and concurrency, modal logic and automata theory. Typically, coinductive proofs demonstrate the equivalence of two objects by constructing a suitable bisimulation relation between them. This collection of surveys is aimed at both researchers and Master's students in computer science and mathematics and deals with various aspects of bisimulation and coinduction, with an emphasis on process theory. Seven chapters cover the following topics: history, algebra and coalgebra, algorithmics, logic, higher-order languages, enhancements of the bisimulation proof method, and probabilities. Exercises are also included to help the reader master new material.
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Book Synopsis Beyond Measure: A Guided Tour Through Nature, Myth And Number by : Jay Kappraff
Download or read book Beyond Measure: A Guided Tour Through Nature, Myth And Number written by Jay Kappraff and published by World Scientific. This book was released on 2002-12-16 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of essays that stand on their own but are also loosely connected. Part I documents how numbers and geometry arise in several cultural contexts and in nature: the ancient musical scale, proportion in architecture, ancient geometry, megalithic stone circles, the hidden pavements of the Laurentian library, the shapes of the Hebrew letters, and the shapes of biological forms. The focus is on how certain numbers, such as the golden and silver means, present themselves within these systems. Part II shows how many of the same numbers and number sequences are related to the modern mathematical study of numbers, dynamical systems, chaos, and fractals.
