Download or read book Philosophy and Geometry written by Lorenzo Magnani and published by Springer Science & Business Media. This book was released on 2001-05-31 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book also ties together the concerns of philosophers of science and cognitive science researchers, showing, for example, the connections between geometrical reasoning and cognition as well as the results of recent logical and computational models of geometrical reasoning. All the topics are covered from a novel combination of both historical and contemporary perspectives."--Jacket.
Download or read book Philosophy of Geometry from Riemann to Poincar written by R. Torretti and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry has fascinated philosophers since the days of Thales and Pythagoras. In the 17th and 18th centuries it provided a paradigm of knowledge after which some thinkers tried to pattern their own metaphysical systems. But after the discovery of non-Euclidean geometries in the 19th century, the nature and scope of geometry became a bone of contention. Philosophical concern with geometry increased in the 1920's after Einstein used Riemannian geometry in his theory of gravitation. During the last fifteen or twenty years, renewed interest in the latter theory -prompted by advances in cosmology -has brought geometry once again to the forefront of philosophical discussion. The issues at stake in the current epistemological debate about geometry can only be understood in the light of history, and, in fact, most recent works on the subject include historical material. In this book, I try to give a selective critical survey of modern philosophy of geometry during its seminal period, which can be said to have begun shortly after 1850 with Riemann's generalized conception of space and to achieve some sort of completion at the turn of the century with Hilbert's axiomatics and Poincare's conventionalism. The philosophy of geometry of Einstein and his contemporaries will be the subject of another book. The book is divided into four chapters. Chapter 1 provides back ground information about the history of science and philosophy.
Download or read book Philosophical Geometry written by André VandenBroeck and published by Inner Traditions. This book was released on 1987-06-01 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ancient Egyptians and Greeks (up to Euclid) saw in plane geometry much more than land-surveying. For the Greeks, Gaia or Ge (from which our word “geometry” derives) was a universe rather than a planet. Man was the measure of the cosmos and geometry was the expression of this faculty, the discipline through which one studied the unity of cosmic necessity and human thought. For this reason tradition has it that Plato inscribed on the gates of his Academy: “Only geometers enter here.” This aspect of the discipline was lost in modern times until studies such as those of Matila Ghyka rekindled an interest that culminated in R. A. Schwaller de Lubicz’s Pythagorean synthesis. Since it was essentially a rediscovery of unselfconscious modes of thinking, this synthesis did not pose the problem of foundations. Philosophical Geometry originated in the author’s perception of this problem while working with de Lubicz in Grasse, France, in 1960-61. Written in 1972, Philosophical Geometry was conceived as a textbook and took shape in a teaching situation, individual elaboration of theory being the declared aim. Defined as “the activity of establishing a necessary conduct for mind through a set of signs denoting a necessary conduct of facts,” Philosophical Geometry approaches a universal theme to which the existence of every human being contributes a chapter. Philosophical Geometry is, and has been, an avenue toward inscription of such fundamental experience.
Download or read book The Foundations of Mathematics written by Paul Carus and published by . This book was released on 1908 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Philosophy and Geometry written by L. Magnani and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Philosophers have studied geometry since ancient times. Geometrical knowledge has often played the role of a laboratory for the philosopher's conceptual experiments dedicated to the ideation of powerful theories of knowledge. Lorenzo Magnani's new book Philosophy and Geometry illustrates the rich intrigue of this fascinating story of human knowledge, providing a new analysis of the ideas of many scholars (including Plato, Proclus, Kant, and Poincaré), and discussing conventionalist and neopositivist perspectives and the problem of the origins of geometry. The book also ties together the concerns of philosophers of science and cognitive scientists, showing, for example, the connections between geometrical reasoning and cognition as well as the results of recent logical and computational models of geometrical reasoning. All the topics are dealt with using a novel combination of both historical and contemporary perspectives. Philosophy and Geometry is a valuable contribution to the renaissance of research in the field.
Download or read book Geometry and Monadology written by Vincenzo de Risi and published by Springer Science & Business Media. This book was released on 2007-08-08 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reconstructs, from both historical and theoretical points of view, Leibniz’s geometrical studies, focusing in particular on the research Leibniz carried out in his final years. The work’s main purpose is to offer a better understanding of the philosophy of space and in general of the mature Leibnizean metaphysics. This is the first ever, comprehensive historical reconstruction of Leibniz’s geometry.
Download or read book New Foundations for Physical Geometry written by Tim Maudlin and published by . This book was released on 2014-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
Download or read book Mathesis of the Mind written by David W. Wood and published by Brill Rodopi. This book was released on 2012 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first major study in any language on J.G. Fichte's philosophy of mathematics and theory of geometry. It investigates both the external formal and internal cognitive parallels between the axioms, intuitions and constructions of geometry and the scientific methodology of the Fichtean system of philosophy. In contrast to "ordinary" Euclidean geometry, in his "Erlanger Logik "of 1805 Fichte posits a model of an "ursprungliche" or original geometry - that is to say, a synthetic and constructivistic conception grounded in ideal archetypal elements that are grasped through geometrical or intelligible intuition. Accordingly, this study classifies Fichte's philosophy of mathematics as a whole as a species of mathematical Platonism or neo-Platonism, and concludes that the "Wissenschaftslehre "itself may be read as an attempt at a new philosophical mathesis, or "mathesis of the mind." "This work testifies to the author's exact and extensive knowledge of the Fichtean texts, as well as of the philosophical, scientific and historical contexts. Wood has opened up completely new paths for Fichte research, and examines with clarity and precision a domain that up to now has hardly been researched." Professor Dr. Marco Ivaldo (University of Naples) "This study, written in a language distinguished by its limpidity and precision, and constantly supported by a close reading of the Fichtean texts and secondary literature, furnishes highly detailed and convincing demonstrations. In directly confronting the difficult historical relationship between the "Wissenschaftslehre "and mathematics, the author has broken new ground that is at once stimulating, decidedly innovative, and elegantly audacious." Professor Dr. Emmanuel Cattin (Universite Blaise-Pascal, Clermont-Ferrand)
Download or read book Sacred Geometry written by Robert Lawlor and published by . This book was released on 1994 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Relativity and Geometry written by Roberto Torretti and published by Elsevier. This book was released on 2014-05-20 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relativity and Geometry aims to elucidate the motivation and significance of the changes in physical geometry brought about by Einstein, in both the first and the second phases of relativity. The book contains seven chapters and a mathematical appendix. The first two chapters review a historical background of relativity. Chapter 3 centers on Einstein's first Relativity paper of 1905. Subsequent chapter presents the Minkowskian formulation of special relativity. Chapters 5 and 6 deal with Einstein's search for general relativity from 1907 to 1915, as well as some aspects and subsequent developments of the theory. The last chapter explores the concept of simultaneity, geometric conventionalism, and a few other questions concerning space time structure, causality, and time.
Download or read book Spinoza s Geometry of Power written by Valtteri Viljanen and published by Cambridge University Press. This book was released on 2011-09-29 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This work examines the unique way in which Benedict de Spinoza (1632–77) combines two significant philosophical principles: that real existence requires causal power and that geometrical objects display exceptionally clearly how things have properties in virtue of their essences. Valtteri Viljanen argues that underlying Spinoza's psychology and ethics is a compelling metaphysical theory according to which each and every genuine thing is an entity of power endowed with an internal structure akin to that of geometrical objects. This allows Spinoza to offer a theory of existence and of action - human and non-human alike - as dynamic striving that takes place with the same kind of necessity and intelligibility that pertain to geometry. Viljanen's fresh and original study will interest a wide range of readers in Spinoza studies and early modern philosophy more generally.
Download or read book Philosophy of Mathematics and Deductive Structure in Euclid s Elements written by Ian Mueller and published by Courier Dover Publications. This book was released on 2006 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics and its similarities to modern views as well as its differences. It focuses on philosophical, foundational, and logical questions -- rather than focusing strictly on historical and mathematical issues -- and features several helpful appendixes.
Download or read book Euclid written by Josette Campbell and published by The Rosen Publishing Group, Inc. This book was released on 2015-07-15 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Euclid, a Greek mathematician, flourished around 300 BCE. It was he who shaped geometry into what it is today. As a result, he became known as the father of geometry. Euclid founded his own school in Alexandria, Egypt, and gained a reputation as an exceptional geometry teacher. The Elements, his thirteen-volume treatise on mathematics and geometry, was considered to be one of the most influential mathematical works in history. Readers consider some of the definitions and postulates from this great work. They also learn about ancient Greek civilization and the renowned Greek mathematicians and philosophers who influenced Euclid's thinking.
Download or read book The Geometry of Desert written by Shelly Kagan and published by Oxford University Press. This book was released on 2014-12-04 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Geometry of Desert explores the hidden complexity of moral desert. Using graphs to illustrate and contrast alternative views, it carefully investigates the various ways in which the value of an outcome varies when people get (or fail to get) what they deserve.
Download or read book From a Geometrical Point of View written by Jean-Pierre Marquis and published by Springer Science & Business Media. This book was released on 2008-11-20 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein’s Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane’s work in the early 1940’s and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation of categorical logic, some of its results and its significance in the foundations of mathematics. From a Geometrical Point of View aims to provide its readers with a conceptual perspective on category theory and categorical logic, in order to gain insight into their role and nature in contemporary mathematics. It should be of interest to mathematicians, logicians, philosophers of mathematics and science in general, historians of contemporary mathematics, physicists and computer scientists.
Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
Download or read book Geometry of the Passions written by Remo Bodei and published by University of Toronto Press. This book was released on 2018-08-08 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The passions have long been condemned as a creator of disturbance and purveyor of the temporary loss of reason, but as Remo Bodei argues in Geometry of the Passions, we must abandon the perception that order and disorder are in a constant state of collision. By means of a theoretical and historical analysis, Bodei interprets the relationship between passion and reason as a conflict between two complementary logics. Geometry of the Passions investigates the paradoxical conflict-collaboration between passions and reason, and between individual and political projects. Tracing the roles passion and reason have played throughout history, including in the political agendas of Descartes, Hobbes, and the French Jacobins, Geometry of the Passions reveals how passion and reason may be used as a vehicle for affirmation rather than self-enslavement.
