The Applicability Of Mathematics As A Philosophical Problem
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| Author | : Mark Steiner |
| Publisher | : Harvard University Press |
| Total Pages | : 224 |
| Release | : 2009-07-01 |
| Genre | : Mathematics |
| ISBN | : 0674043987 |
This book analyzes the different ways mathematics is applicable in the physical sciences, and presents a startling thesis--the success of mathematical physics appears to assign the human mind a special place in the cosmos. Mark Steiner distinguishes among the semantic problems that arise from the use of mathematics in logical deduction; the metaphysical problems that arise from the alleged gap between mathematical objects and the physical world; the descriptive problems that arise from the use of mathematics to describe nature; and the epistemological problems that arise from the use of mathematics to discover those very descriptions. The epistemological problems lead to the thesis about the mind. It is frequently claimed that the universe is indifferent to human goals and values, and therefore, Locke and Peirce, for example, doubted science's ability to discover the laws governing the humanly unobservable. Steiner argues that, on the contrary, these laws were discovered, using manmade mathematical analogies, resulting in an anthropocentric picture of the universe as "user friendly" to human cognition--a challenge to the entrenched dogma of naturalism.
| Author | : Oriana Walker |
| Publisher | : |
| Total Pages | : 106 |
| Release | : 2001 |
| Genre | : |
| ISBN | : |
| Author | : Reʼuven Agushevits |
| Publisher | : KTAV Publishing House, Inc. |
| Total Pages | : 248 |
| Release | : 2006 |
| Genre | : Philosophy |
| ISBN | : 9780881259100 |
"Rabbi Reuven Agushewitz, a Lithuanian Talmudic genius, emigrated to the United States in 1929. He supported himself by giving Talmud lessons to young boys." "The present volume is a translation of his last book, Emune un Apikorses, published in 1948. It is a sustained attack on the philosophy of materialism, in all its historical versions, from the Greek to modern times - including the Marxist version, to which Agushewitz had been attracted as a youth. Though a highly original work of philosophy (perhaps the only original work of philosophy ever written in Yiddish), it contains valuable discussions of some of the greatest Western philosophers, including the great Greek atomists; Zeno; Aristotle; Descartes; Spinoza; Kant; Bergson; Russell; and many others. This translation will rescue this outstanding philosopher and Yiddish writer from the obscurity which has enveloped him for over half a century." --Book Jacket.
| Author | : Thomas Bedürftig |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 474 |
| Release | : 2018-10-26 |
| Genre | : Mathematics |
| ISBN | : 3110470772 |
The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection
| Author | : Otávio Bueno |
| Publisher | : Oxford University Press |
| Total Pages | : 276 |
| Release | : 2018 |
| Genre | : Mathematics |
| ISBN | : 0198815042 |
How is that when scientists need some piece of mathematics through which to frame their theory, it is there to hand? Bueno and French offer a new approach to the puzzle of the applicability of mathematics, through a detailed examination of a series of case studies from the history of twentieth-century physics.
| Author | : S. Bangu |
| Publisher | : Palgrave Macmillan |
| Total Pages | : 252 |
| Release | : 2012-09-24 |
| Genre | : Science |
| ISBN | : 9780230285200 |
This examination of a series of philosophical issues arising from the applicability of mathematics to science consists of scientifically-informed philosophical analysis and argument. One distinctive feature of this project is that it proposes to look at issues in philosophy of mathematics within the larger context of philosophy of science.
| Author | : Bruno Baron von Freytag Löringhoff |
| Publisher | : |
| Total Pages | : 104 |
| Release | : 1951 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Gabriele Lolli |
| Publisher | : Springer |
| Total Pages | : 346 |
| Release | : 2014-11-28 |
| Genre | : Philosophy |
| ISBN | : 3319104349 |
This book brings together young researchers from a variety of fields within mathematics, philosophy and logic. It discusses questions that arise in their work, as well as themes and reactions that appear to be similar in different contexts. The book shows that a fairly intensive activity in the philosophy of mathematics is underway, due on the one hand to the disillusionment with respect to traditional answers, on the other to exciting new features of present day mathematics. The book explains how the problem of applicability once again plays a central role in the development of mathematics. It examines how new languages different from the logical ones (mostly figural), are recognized as valid and experimented with and how unifying concepts (structure, category, set) are in competition for those who look at this form of unification. It further shows that traditional philosophies, such as constructivism, while still lively, are no longer only philosophies, but guidelines for research. Finally, the book demonstrates that the search for and validation of new axioms is analyzed with a blend of mathematical historical, philosophical, psychological considerations.
| Author | : Bonnie Gold |
| Publisher | : MAA |
| Total Pages | : 392 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9780883855676 |
Sixteen original essays exploring recent developments in the philosophy of mathematics, written in a way mathematicians will understand.
| Author | : James Robert Brown |
| Publisher | : Routledge |
| Total Pages | : 181 |
| Release | : 2005-08-09 |
| Genre | : Philosophy |
| ISBN | : 1134806442 |
Philosophy of Mathematics is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.
