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Phenomenology And Mathematics
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Book Synopsis Phenomenology, Logic, and the Philosophy of Mathematics by : Richard L. Tieszen
Download or read book Phenomenology, Logic, and the Philosophy of Mathematics written by Richard L. Tieszen and published by Cambridge University Press. This book was released on 2005-06-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this 2005 book, logic, mathematical knowledge and objects are explored alongside reason and intuition in the exact sciences.
Book Synopsis Phenomenology and Mathematics by : Mirja Hartimo
Download or read book Phenomenology and Mathematics written by Mirja Hartimo and published by Springer Science & Business Media. This book was released on 2010-03-11 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: During Edmund Husserl’s lifetime, modern logic and mathematics rapidly developed toward their current outlook and Husserl’s writings can be fruitfully compared and contrasted with both 19th century figures (Boole, Schröder, Weierstrass) as well as the 20th century characters (Heyting, Zermelo, Gödel). Besides the more historical studies, the internal ones on Husserl alone and the external ones attempting to clarify his role in the more general context of the developing mathematics and logic, Husserl’s phenomenology offers also a systematically rich but little researched area of investigation. This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics. It gathers the contributions of the main scholars of this emerging field into one publication for the first time. Combining both historical and systematic studies from various angles, the volume charts answers to the question "What kind of philosophy of mathematics is phenomenology?"
Book Synopsis Didactical Phenomenology of Mathematical Structures by : Hans Freudenthal
Download or read book Didactical Phenomenology of Mathematical Structures written by Hans Freudenthal and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: The launch ofa new book series is always a challenging eventn ot only for the Editorial Board and the Publisher, but also, and more particularly, for the first author. Both the Editorial Board and the Publisher are delightedt hat the first author in this series isw ell able to meet the challenge. Professor Freudenthal needs no introduction toanyone in the Mathematics Education field and it is particularly fitting that his book should be the first in this new series because it was in 1968 that he, and Reidel, produced the first issue oft he journal Edu cational Studies in Mathematics. Breakingfresh ground is therefore nothing new to Professor Freudenthal and this book illustrates well his pleasure at such a task. To be strictly correct the ‘ground’ which he has broken here is not new, but aswith Mathematics as an Educational Task and Weeding and Sowing, it is rather the novelty oft he manner in which he has carried out his analysis which provides us with so many fresh perspectives. It is our intention that this new book series should provide those who work int he emerging discipline of mathematicseducation with an essential resource, and at a time of considerable concern about the whole mathematics cu rriculum this book represents just such resource. ALAN J. BISHOP Managing Editor vii A LOOK BACKWARD AND A LOOK FORWARD Men die, systems last.
Book Synopsis Husserl and Mathematics by : Mirja Hartimo
Download or read book Husserl and Mathematics written by Mirja Hartimo and published by Cambridge University Press. This book was released on 2021-08-05 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Husserl and Mathematics explains the development of Husserl's phenomenological method in the context of his engagement in modern mathematics and its foundations. Drawing on his correspondence and other written sources, Mirja Hartimo details Husserl's knowledge of a wide range of perspectives on the foundations of mathematics, including those of Hilbert, Brouwer and Weyl, as well as his awareness of the new developments in the subject during the 1930s. Hartimo examines how Husserl's philosophical views responded to these changes, and offers a pluralistic and open-ended picture of Husserl's phenomenology of mathematics. Her study shows Husserl's phenomenology to be a method capable of both shedding light on and internally criticizing scientific practices and concepts.
Book Synopsis Phenomenology and Mathematics by : Michael Roubach
Download or read book Phenomenology and Mathematics written by Michael Roubach and published by Cambridge University Press. This book was released on 2023-11-30 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Element explores the relationship between phenomenology and mathematics. Its focus is the mathematical thought of Edmund Husserl, founder of phenomenology, but other phenomenologists and phenomenologically-oriented mathematicians, including Weyl, Becker, Gödel, and Rota, are also discussed. After outlining the basic notions of Husserl's phenomenology, the author traces Husserl's journey from his early mathematical studies. Phenomenology's core concepts, such as intention and intuition, each contributed to the emergence of a phenomenological approach to mathematics. This Element examines the phenomenological conceptions of natural number, the continuum, geometry, formal systems, and the applicability of mathematics. It also situates the phenomenological approach in relation to other schools in the philosophy of mathematics-logicism, formalism, intuitionism, Platonism, the French epistemological school, and the philosophy of mathematical practice.
Book Synopsis Mathematical Intuition by : R.L. Tieszen
Download or read book Mathematical Intuition written by R.L. Tieszen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as if it were the Third Eye, something only mathematical "mystics", like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser! there will be a kind of Kantian argument underlying the entire book.
Book Synopsis Sedimentation and Thickening by : E.M. Tory
Download or read book Sedimentation and Thickening written by E.M. Tory and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present a rigorous phenomenological and mathematical formulation of sedimentation processes and to show how this theory can be applied to the design and control of continuous thickeners. The book is directed to stu dents and researchers in applied mathematics and engineering sciences, especially in metallurgical, chemical, mechanical and civil engineering, and to practicing en gineers in the process industries. Such a vast and diverse audience should read this book differently. For this reason we have organized the chapters in such a way that the book can be read in two ways. Engineers and engineering students will find a rigorous formulation of the mathematical model of sedimentation and the exact and approximate solutions for the most important problems encountered in the laboratory and in industry in Chapters 1 to 3, 7 and 8, and 10 to 12, which form a self-contained subject. They can skip Chapters 4 to 6 and 9, which are most important to applied mathematicians, without losing the main features of sedimentation processes. On the other hand, applied mathematicians will find special interest in Chapters 4 to 6 and 9 which show some known but many recent results in the field of conservation laws of quasilinear hyperbolic and degenerate parabolic equations of great interest today. These two approaches to the theory keep their own styles: the mathematical approach with theorems and proofs, and the phenomenological approach with its deductive technique.
Book Synopsis Constitution and Production of Mathematics in the Cyberspace by : Maria Aparecida Viggiani Bicudo
Download or read book Constitution and Production of Mathematics in the Cyberspace written by Maria Aparecida Viggiani Bicudo and published by Springer Nature. This book was released on 2020-04-29 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together various studies that assume phenomenology to analyze how mathematics education is affected by the experience of being in the cyberspace. The authors of the chapters included in this contributed volume work with the theoretical framework developed by authors such as Edmund Husserl, Martin Heidegger and Maurice Merleau-Ponty to investigate how mathematics is produced and comprehended in a new way of being in the world, with digital technologies. The aim of this book is not to explain the tools used and how one works with them in the cyberspace, aiming at better teaching and learning mathematics. Its purpose is to present philosophical investigations that contribute to the understanding of the complexity of the world in which we are being researchers and mathematics teachers. By doing so, Constitution and Production of Mathematics in the Cyberspace – A Phenomenological Approach will help researchers and mathematics teachers understand their role in a world in which the experience of teaching and learning mathematics is being radically changed by new technologies and new ways of being in this world.
Download or read book Shapes of Forms written by L. Albertazzi and published by Springer Science & Business Media. This book was released on 1999 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Development of research connected with artificial intelligence and the cognitive sciences obliges us to confront further components of the traditional problem of form. Contributors analyze the concept of form from the perspective of fields such as ontology, language, and mathematics, and look at form in its different aspects according to a more modern theory of knowledge. Subjects include experimental phenomenology, a theory of figural form, form metaphysics, and forms in algebras. Of interest to systematic philosophers, philosophers of language, psychologists, and linguists. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis The Mathematical Experience, Study Edition by : Philip Davis
Download or read book The Mathematical Experience, Study Edition written by Philip Davis and published by Springer Science & Business Media. This book was released on 2011-10-27 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of the 1983 National Book Award! "...a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." - The New Yorker (1983 National Book Award edition) Mathematics has been a human activity for thousands of years. Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations. The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Many people from around the world have told the authors that they have done precisely that with the first edition and they have encouraged publication of this revised edition complete with exercises for helping students to demonstrate their understanding. This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about. It will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications. The text is ideal for 1) a GE course for Liberal Arts students 2) a Capstone course for perspective teachers 3) a writing course for mathematics teachers. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto ([email protected]) upon request.
Book Synopsis The Origin of the Logic of Symbolic Mathematics by : Burt C. Hopkins
Download or read book The Origin of the Logic of Symbolic Mathematics written by Burt C. Hopkins and published by Indiana University Press. This book was released on 2011-09-07 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts—especially mathematical concepts and the process of mathematical abstraction that generates them—have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.
Book Synopsis The Mathematical Imagination by : Matthew Handelman
Download or read book The Mathematical Imagination written by Matthew Handelman and published by Fordham Univ Press. This book was released on 2019-03-05 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an archeology of the undeveloped potential of mathematics for critical theory. As Max Horkheimer and Theodor W. Adorno first conceived of the critical project in the 1930s, critical theory steadfastly opposed the mathematization of thought. Mathematics flattened thought into a dangerous positivism that led reason to the barbarism of World War II. The Mathematical Imagination challenges this narrative, showing how for other German-Jewish thinkers, such as Gershom Scholem, Franz Rosenzweig, and Siegfried Kracauer, mathematics offered metaphors to negotiate the crises of modernity during the Weimar Republic. Influential theories of poetry, messianism, and cultural critique, Handelman shows, borrowed from the philosophy of mathematics, infinitesimal calculus, and geometry in order to refashion cultural and aesthetic discourse. Drawn to the austerity and muteness of mathematics, these friends and forerunners of the Frankfurt School found in mathematical approaches to negativity strategies to capture the marginalized experiences and perspectives of Jews in Germany. Their vocabulary, in which theory could be both mathematical and critical, is missing from the intellectual history of critical theory, whether in the work of second generation critical theorists such as Jürgen Habermas or in contemporary critiques of technology. The Mathematical Imagination shows how Scholem, Rosenzweig, and Kracauer’s engagement with mathematics uncovers a more capacious vision of the critical project, one with tools that can help us intervene in our digital and increasingly mathematical present.
Download or read book After Gödel written by Richard L. Tieszen and published by Oxford University Press. This book was released on 2011-05-05 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Tieszen analyzes, develops, and defends the writings of Kurt Gödel (1906-1978) on the philosophy and foundations of mathematics and logic. Gödel's relation to the work of Plato, Leibniz, Husserl, and Kant is examined, and a new type of platonic rationalism that requires rational intuition, called 'constituted platonism', is proposed.
Book Synopsis Phenomenological Approaches to Physics by : Harald A. Wiltsche
Download or read book Phenomenological Approaches to Physics written by Harald A. Wiltsche and published by Springer Nature. This book was released on 2020-06-23 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers fresh perspective on the role of phenomenology in the philosophy of physics which opens new avenues for discussion among physicists, "standard" philosophers of physics and philosophers with phenomenological leanings. Much has been written on the interrelations between philosophy and physics in the late 19th and early 20th century, and on the emergence of philosophy of science as an autonomous philosophical sub-discipline. This book is about the under-explored role of phenomenology in the development and the philosophical interpretation of 20th century physics. Part 1 examines questions about the origins and value of phenomenological approaches to physics. Does the work of classical phenomenologists such as Husserl, Merleau-Ponty or Heidegger contain elements of systematic value to both the practice and our philosophical understanding of physics? How did classical phenomenology influence “standard” philosophy of science in the Anglo-American and other traditions? Part 2 probes questions on the role of phenomenology in the philosophies of physics and science: - Can phenomenology help to solve “Wigner’s puzzle”, the problem of the "unreasonable effectiveness" of mathematics in describing, explaining and predicting empirical phenomena? - Does phenomenology allow better understanding of the principle of gauge invariance at the core of the standard model of contemporary particle physics? - Does the phenomenological notion of “Lifeworld” stand in opposition to the “scientific metaphysics” movement, or is there potential for dialogue? Part 3 examines the measurement problem. Is the solution outlined by Fritz London and Edmond Bauer merely a re-statement of von Neumann’s view, or should it be regarded as a distinctively phenomenological take on the measurement problem? Is phenomenology a serious contender in continuing discussions of foundational questions of quantum mechanics? Can other interpretational frameworks such as quantum Bayesianism benefit from implementing phenomenological notions such as constitution or horizonal intentionality?
Book Synopsis Phenomenology and Logic by : Robert S. Tragesser
Download or read book Phenomenology and Logic written by Robert S. Tragesser and published by . This book was released on 1977 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Phenomenology and the Formal Sciences by : Thomas M. Seebohm
Download or read book Phenomenology and the Formal Sciences written by Thomas M. Seebohm and published by Springer. This book was released on 1991-11-30 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thomas A. Fay Heidegger and the Formalization of Thought 1 Dagfinn F011esdal The Justification of Logic and Mathematics in Husserl's Phenomenology 25 Guillermo E. Rosado Haddock On Husserl's Distinction between State of Affairs (Sachverhalt) and Situation of Affairs (Sachlage) . . . . 35 David Woodruff Smith On Situations and States of Affairs 49 Charles W. Harvey, Jaakko Hintikka Modalization and Modalities . . . . . . . . . . . . . . . . . . . 59 Gilbert T. Null Remarks on Modalization and Modalities 79 J. N. Mohanty Husserl's Formalism 93 Carl J. Posy Mathematics as a Transcendental Science 107 vi Gian-carlo Rota Mathematics and the Task of Phenomenology 133 John Scalon "Tertium Non Datur: " Husserl's Conception of a Definite Multiplicity . . . . . 139 Thomas M. Seebohm Psychologism Revisited 149 Gerald J. Massey Some Reflections on Psychologism 183 Robert S. Tragesser How Mathematical Foundation all but come about: A Report on Studies Toward a Phenomenological Critique of Godel's Views on Mathematical Intuition. . 195 Kenneth L. Manders On Geometric Intentionality 215 Dallas Willard Sentences which are True in Virtue of their Color . . . 225 John J. Drummond Willard and Husserl on Logical Form 243 Index of Names 257 Index of Subjects 259 PREFACE The phenomenology of logic and ideal objects is the topic of Husserl's Logical Investigations. This book determined the early development of the so called phenomenological movement. It is still the main source for many phenomenologists, even if they disagree with Husserl's transcendental turn and developed other phenomenological positions or positions beyond phenomenology he early sense.
Book Synopsis Indiscrete Thoughts by : Gian-Carlo Rota
Download or read book Indiscrete Thoughts written by Gian-Carlo Rota and published by Springer Science & Business Media. This book was released on 2009-11-03 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Indiscrete Thoughts gives a glimpse into a world that has seldom been described - that of science and technology as seen through the eyes of a mathematician. The era covered by this book, 1950 to 1990, was surely one of the golden ages of science and of the American university. Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period. Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. This beautifully written book is destined to become an instant classic and the subject of debate for decades to come.
