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Author: John W Schutz
Publisher: CRC Press
ISBN: 9780582317604
Category : Science
Languages : en
Pages : 260
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Book Description
The primary aim of this monograph is to clarify the undefined primitive concepts and the axioms which form the basis of Einstein's theory of special relativity. Minkowski space-time is developed from a set of independent axioms, stated in terms of a single relation of betweenness. It is shown that all models are isomorphic to the usual coordinate model, and the axioms are consistent relative to the reals.
Author: John W Schutz
Publisher: CRC Press
ISBN: 9780582317604
Category : Science
Languages : en
Pages : 260
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Book Description
The primary aim of this monograph is to clarify the undefined primitive concepts and the axioms which form the basis of Einstein's theory of special relativity. Minkowski space-time is developed from a set of independent axioms, stated in terms of a single relation of betweenness. It is shown that all models are isomorphic to the usual coordinate model, and the axioms are consistent relative to the reals.
Author:
Publisher: PediaPress
ISBN:
Category :
Languages : en
Pages : 313
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Book Description
Author: Marco Aiello
Publisher: Springer Science & Business Media
ISBN: 1402055870
Category : Science
Languages : en
Pages : 1072
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Book Description
The aim of this handbook is to create, for the first time, a systematic account of the field of spatial logic. The book comprises a general introduction, followed by fourteen chapters by invited authors. Each chapter provides a self-contained overview of its topic, describing the principal results obtained to date, explaining the methods used to obtain them, and listing the most important open problems. Jointly, these contributions constitute a comprehensive survey of this rapidly expanding subject.
Author: András Prékopa
Publisher: Springer Science & Business Media
ISBN: 0387295550
Category : Mathematics
Languages : en
Pages : 497
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Book Description
"From nothing I have created a new different world," wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.
Author: Fernando Ferreira
Publisher: Springer Nature
ISBN: 3030777995
Category : Mathematics
Languages : en
Pages : 293
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Book Description
In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere. The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Göttingen as his main collaborator in foundational studies in the years to come. The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations.
Author:
Publisher: PediaPress
ISBN:
Category :
Languages : en
Pages : 1121
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Book Description
Author: Craig Callender
Publisher: Oxford University Press
ISBN: 0192517856
Category : Science
Languages : en
Pages : 358
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Book Description
As we navigate through life we instinctively model time as having a flowing present that divides a fixed past from open future. This model develops in childhood and is deeply saturated within our language, thought and behavior, affecting our conceptions of the universe, freedom and the self. Yet as central as it is to our lives, physics seems to have no room for this flowing present. What Makes Time Special? demonstrates this claim in detail and then turns to two novel positive tasks. First, by looking at the world "sideways" - in the spatial directions -- it shows that physics is not "spatializing time" as is commonly alleged. Even relativity theory makes significant distinctions between the spacelike and timelike directions, often with surprising consequences. Second, if the flowing present is an illusion, it is a deep one worthy of explanation. The author develops a picture whereby the temporal flow arises as an interaction effect between an observer and the physics of the world. Using insights from philosophy, cognitive science, biology, psychology and physics, the theory claims that the flowing present model of time is the natural reaction to the perceptual and evolutionary challenges thrown at us. Modeling time as flowing makes sense even if it misrepresents it.
Author: Alexandru Baltag
Publisher: Springer
ISBN: 3319060252
Category : Philosophy
Languages : en
Pages : 1072
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Book Description
This book illustrates the program of Logical-Informational Dynamics. Rational agents exploit the information available in the world in delicate ways, adopt a wide range of epistemic attitudes, and in that process, constantly change the world itself. Logical-Informational Dynamics is about logical systems putting such activities at center stage, focusing on the events by which we acquire information and change attitudes. Its contributions show many current logics of information and change at work, often in multi-agent settings where social behavior is essential, and often stressing Johan van Benthem's pioneering work in establishing this program. However, this is not a Festschrift, but a rich tapestry for a field with a wealth of strands of its own. The reader will see the state of the art in such topics as information update, belief change, preference, learning over time, and strategic interaction in games. Moreover, no tight boundary has been enforced, and some chapters add more general mathematical or philosophical foundations or links to current trends in computer science. The theme of this book lies at the interface of many disciplines. Logic is the main methodology, but the various chapters cross easily between mathematics, computer science, philosophy, linguistics, cognitive and social sciences, while also ranging from pure theory to empirical work. Accordingly, the authors of this book represent a wide variety of original thinkers from different research communities. And their interconnected themes challenge at the same time how we think of logic, philosophy and computation. Thus, very much in line with van Benthem's work over many decades, the volume shows how all these disciplines form a natural unity in the perspective of dynamic logicians (broadly conceived) exploring their new themes today. And at the same time, in doing so, it offers a broader conception of logic with a certain grandeur, moving its horizons beyond the traditional study of consequence relations.
Author: John W. Schutz
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 352
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Book Description
The aim of this monograph is to give an axiomatic development of Einstein's theory of special relativity from axioms which describe intuitive concepts concerning the kinematic behavior of inertial particles and light signals.
Author: Hans Jürgen Borchers
Publisher: Springer
ISBN: 354037681X
Category : Science
Languages : en
Pages : 196
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Book Description
Here is a systematic approach to such fundamental questions as: What mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it? The author proposes an axiomatization of the physics inspired notion of Einstein-Weyl causality and investigating the consequences in terms of possible topological spaces. One significant result is that the notion of causality can effectively be extended to discontinuum.
