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Time and Space in Formal Logic

Author: Richard L. Epstein

Publisher: Advanced Reasoning Forum

Published: 2022-09-13

Total Pages: 303

ISBN-13: 1938421698

Time and Space in Formal Logic begins with an analysis of assumptions about how logic and language relate. Then in the first section, times are taken to be established by true propositions, and those are related as before and after with temporal propositional connectives. In the second section, times are treated as things that can be picked out and counted, leading to a predicate logic that allows for quantification over times. In the third section, locations in space are also treated as things that can be picked out and counted, leading to a predicate logic that allows for quantification over both times and locations. Many applications of the formal systems to formalizing ordinary language propositions and inferences clarify better the assumptions we make in reasoning taking account of time and space by making those precise in the formal systems. Appendices on events, branching times, intentions, and descriptive names add to the scope of the work.

The Philosophy of Space and Time

Author: Hans Reichenbach

Publisher: Courier Corporation

Published: 2012-03-13

Total Pages: 340

ISBN-13: 0486138038

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A clear, penetrating exposition of developments in physical science and mathematics brought about by non-Euclidean geometries, including in-depth coverage of the foundations of geometry, theory of time, other topics.

A Treatise on Time and Space

Author: J. R. Lucas

Publisher: Routledge

Published: 2018-10-10

Total Pages: 328

ISBN-13: 0429685173

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Originally published in 1976. This comprehensive study discusses in detail the philosophical, mathematical, physical, logical and theological aspects of our understanding of time and space. The text examines first the many different definitions of time that have been offered, beginning with some of the puzzles arising from our awareness of the passage of time and shows how time can be understood as the concomitant of consciousness. In considering time as the dimension of change, the author obtains a transcendental derivation of the concept of space, and shows why there has to be only one dimension of time and three of space, and why Kant was not altogether misguided in believing the space of our ordinary experience to be Euclidean. The concept of space-time is then discussed, including Lorentz transformations, and in an examination of the applications of tense logic the author discusses the traditional difficulties encountered in arguments for fatalism. In the final sections he discusses eternity and the beginning and end of the universe. The book includes sections on the continuity of space and time, on the directedness of time, on the differences between classical mechanics and the Special and General theories of relativity, on the measurement of time, on the apparent slowing down of moving clocks, and on time and probability.

Space, Time and the Limits of Human Understanding

Author: Shyam Wuppuluri

Publisher: Springer

Published: 2016-12-01

Total Pages: 524

ISBN-13: 3319444182

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In this compendium of essays, some of the world’s leading thinkers discuss their conceptions of space and time, as viewed through the lens of their own discipline. With an epilogue on the limits of human understanding, this volume hosts contributions from six or more diverse fields. It presumes only rudimentary background knowledge on the part of the reader. Time and again, through the prism of intellect, humans have tried to diffract reality into various distinct, yet seamless, atomic, yet holistic, independent, yet interrelated disciplines and have attempted to study it contextually. Philosophers debate the paradoxes, or engage in meditations, dialogues and reflections on the content and nature of space and time. Physicists, too, have been trying to mold space and time to fit their notions concerning micro- and macro-worlds. Mathematicians focus on the abstract aspects of space, time and measurement. While cognitive scientists ponder over the perceptual and experiential facets of our consciousness of space and time, computer scientists theoretically and practically try to optimize the space-time complexities in storing and retrieving data/information. The list is never-ending. Linguists, logicians, artists, evolutionary biologists, geographers etc., all are trying to weave a web of understanding around the same duo. However, our endeavour into a world of such endless imagination is restrained by intellectual dilemmas such as: Can humans comprehend everything? Are there any limits? Can finite thought fathom infinity? We have sought far and wide among the best minds to furnish articles that provide an overview of the above topics. We hope that, through this journey, a symphony of patterns and tapestry of intuitions will emerge, providing the reader with insights into the questions: What is Space? What is Time? Chapter [15] of this book is available open access under a CC BY 4.0 license.

Philosophy of Physics

Author: Tim Maudlin

Publisher: Princeton University Press

Published: 2015-05-26

Total Pages: 199

ISBN-13: 0691165718

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Philosophical foundations of the physics of space-time This concise book introduces nonphysicists to the core philosophical issues surrounding the nature and structure of space and time, and is also an ideal resource for physicists interested in the conceptual foundations of space-time theory. Tim Maudlin's broad historical overview examines Aristotelian and Newtonian accounts of space and time, and traces how Galileo's conceptions of relativity and space-time led to Einstein's special and general theories of relativity. Maudlin explains special relativity with enough detail to solve concrete physical problems while presenting general relativity in more qualitative terms. Additional topics include the Twins Paradox, the physical aspects of the Lorentz-FitzGerald contraction, the constancy of the speed of light, time travel, the direction of time, and more. Introduces nonphysicists to the philosophical foundations of space-time theory Provides a broad historical overview, from Aristotle to Einstein Explains special relativity geometrically, emphasizing the intrinsic structure of space-time Covers the Twins Paradox, Galilean relativity, time travel, and more Requires only basic algebra and no formal knowledge of physics

Space, Time and Einstein

Author: J.B. Kennedy

Publisher: Routledge

Published: 2014-12-18

Total Pages: 255

ISBN-13: 1317489446

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This introduction to one of the liveliest and most popular fields in philosophy is written specifically for a beginning readership with no background in philosophy or science. Step-by-step analyses of the key arguments are provided and the philosophical heart of the issues is revealed without recourse to jargon, maths, or logical formulas. The book introduces Einstein's revolutionary ideas in a clear and simple way, along with the concepts and arguments of philosophers, both ancient and modern that have proved of lasting value. Specifically, the theories of the ancient Greek philosophers, Zeno, Euclid and Parmenides are considered alongside the ideas of Newton, Leibniz and Kant as well as the giants of twentieth-century physics, Einstein and Lorentz. The problems at the heart of the philosophy of space and time, such as change, motion, infinity, shape, and inflation, are examined and the seismic impact made by relativity theory and quantum theory is assessed in the light of the latest research. The writing is lucid and entertaining, allowing a beginning readership to grasp some difficult concepts while offering the more experienced reader a succinct and illuminating presentation of the state of the debate. "Space, Time and Einstein" shows the reader the excitement of scientific discovery and the beauty of theory in the search for answers to these fundamental questions.

Understanding Space-Time

Author: Robert DiSalle

Publisher: Cambridge University Press

Published: 2006-04-27

Total Pages: 204

ISBN-13: 9781139452663

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Presenting the history of space-time physics, from Newton to Einstein, as a philosophical development DiSalle reflects our increasing understanding of the connections between ideas of space and time and our physical knowledge. He suggests that philosophy's greatest impact on physics has come about, less by the influence of philosophical hypotheses, than by the philosophical analysis of concepts of space, time and motion, and the roles they play in our assumptions about physical objects and physical measurements. This way of thinking leads to interpretations of the work of Newton and Einstein and the connections between them. It also offers ways of looking at old questions about a priori knowledge, the physical interpretation of mathematics, and the nature of conceptual change. Understanding Space-Time will interest readers in philosophy, history and philosophy of science, and physics, as well as readers interested in the relations between physics and philosophy.

The Concepts of Space and Time

Author: M. Capek

Publisher: Springer

Published: 2014-11-14

Total Pages: 593

ISBN-13: 9401017271

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Time, Space and Philosophy

Author: Christopher Ray

Publisher: Routledge

Published: 2002-09-11

Total Pages: 281

ISBN-13: 1134968493

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This book provides a comprehensive, up-to-date and accessible introduction to the philosophy of space and time. Ray considers in detail the central questions of space and time which arizse from the ideas of Zeno, Newton, Mach, Leibniz and Einstein. Time, Space and Philosophy extends the debate in many areas:absolute simultaneity is examined as well as black holes, the big bang and even time travel. Time, Space and Philosophy will be invaluable to the student of philosophy and science and will be of considerable interest to mathematics students. The clear, non-technical approach should also make it suitable to for the general reader.

Time and Space

Author: Barry Dainton

Publisher: Routledge

Published: 2016-04-15

Total Pages: 632

ISBN-13: 1134944047

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The first edition (2001) of this title quickly established itself on courses on the philosophy of time and space. This fully revised and expanded new edition sees the addition of chapters on Zeno's paradoxes, speculative contemporary developments in physics, and dynamic time, making the second edition, once again, unrivalled in its breadth of coverage. Surveying both historical debates and the ideas of modern physics, Barry Dainton evaluates the central arguments in a clear and unintimidating way and is careful to keep the conceptual issues throughout comprehensible to students with little scientific or mathematical training. The book makes the philosophy of space and time accessible for anyone trying to come to grips with the complexities of this challenging subject. With over 100 original line illustrations and a full glossary of terms, the book has the requirements of students firmly in sight and will continue to serve as an essential textbook for philosophy of time and space courses.