Download or read book Relation Philosophy of Mathematics Science and Mind written by Helier J. Robinson and published by Lulu.com. This book was released on 2007-09 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Relation Philosophy of Mathematics Science and Mind electronic Resource Perennial Philosophy for Mathematicians and Scientists written by Helier J. Robinson and published by Fergus, Ont. : Sharebooks Pub.. This book was released on 2006 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Philosophy of Mathematics and Natural Science written by Hermann Weyl and published by Princeton University Press. This book was released on 2021-09-14 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: When mathematician Hermann Weyl decided to write a book on philosophy, he faced what he referred to as "conflicts of conscience"--the objective nature of science, he felt, did not mesh easily with the incredulous, uncertain nature of philosophy. Yet the two disciplines were already intertwined. In Philosophy of Mathematics and Natural Science, Weyl examines how advances in philosophy were led by scientific discoveries--the more humankind understood about the physical world, the more curious we became. The book is divided into two parts, one on mathematics and the other on the physical sciences. Drawing on work by Descartes, Galileo, Hume, Kant, Leibniz, and Newton, Weyl provides readers with a guide to understanding science through the lens of philosophy. This is a book that no one but Weyl could have written--and, indeed, no one has written anything quite like it since.
Download or read book Philosophy of Mathematics written by and published by Elsevier. This book was released on 2009-07-08 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics-Clearly written expositions of fundamental ideas and concepts-Definitive discussions by leading researchers in the field-Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included
Download or read book Mathematical Thought written by E.W. Beth and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: In contributing a foreword to this book I am complying with a wish my husband expressed a few days before his death. He had completed the manuscript of this work, which may be considered a companion volume to his book Formal Methods. The task of seeing it through the press was undertaken by Mr. J. J. A. Mooij, acting director of the Institute for Research in Foundations and the Philosophy of Science (Instituut voor Grondslagenonderzoek en Filoso:fie der Exacte Wetenschappen) of the University of Amsterdam, with the help of Mrs. E. M. Barth, lecturer at the Institute. I wish to thank Mr. Mooij and Mrs. Barth most cordially for the care with which they have acquitted themselves of this delicate task and for the speed with which they have brought it to completion. I also wish to express my gratitude to Miss L. E. Minning, M. A. , for the helpful advice she has so kindly given to Mr. Mooij and Mrs. Barth during the proof reading. C. P. C. BETH-PASTOOR VII PREFACE A few years ago Mr. Horace S.
Download or read book New Directions in the Philosophy of Mathematics written by Thomas Tymoczko and published by Princeton University Press. This book was released on 1998-02 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form. This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.
Download or read book Why Is There Philosophy of Mathematics At All written by Ian Hacking and published by Cambridge University Press. This book was released on 2014-01-30 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.
Download or read book Philosophy of Mathematics written by Gerhard Preyer and published by Walter de Gruyter. This book was released on 2013-05-02 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: One main interest of philosophy is to become clear about the assumptions, premisses and inconsistencies of our thoughts and theories. And even for a formal language like mathematics it is controversial if consistency is acheivable or necessary like the articles in the firt part of the publication show. Also the role of formal derivations, the role of the concept of apriority, and the intuitions of mathematical principles and properties need to be discussed. The second part is a contribution on nominalistic and platonistic views in mathematics, like the "indispensability argument" of W. v. O. Quine H. Putnam and the "makes no difference argument" of A. Baker. Not only in retrospect, the third part shows the problems of Mill, Frege's and the unity of mathematics and Descartes's contradictional conception of mathematical essences. Together, these articles give us a hint into the relationship between mathematics and world, that is, one of the central problems in philosophy of mathematics and philosophy of science.
Download or read book Mysticism and Logic written by Bertrand Russell and published by Perennial Press. This book was released on 2018-03-04 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metaphysics, or the attempt to conceive the world as a whole by means of thought, has been developed, from the first, by the union and conflict of two very different human impulses, the one urging men towards mysticism, the other urging them towards science. Some men have achieved greatness through one of these impulses alone, others through the other alone: in Hume, for example, the scientific impulse reigns quite unchecked, while in Blake a strong hostility to science co-exists with profound mystic insight. But the greatest men who have been philosophers have felt the need both of science and of mysticism: the attempt to harmonise the two was what made their life, and what always must, for all its arduous uncertainty, make philosophy, to some minds, a greater thing than either science or religion...
Download or read book The Language of Nature written by Geoffrey Gorham and published by U of Minnesota Press. This book was released on 2016-06-15 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galileo’s dictum that the book of nature “is written in the language of mathematics” is emblematic of the accepted view that the scientific revolution hinged on the conceptual and methodological integration of mathematics and natural philosophy. Although the mathematization of nature is a distinctive and crucial feature of the emergence of modern science in the seventeenth century, this volume shows that it was a far more complex, contested, and context-dependent phenomenon than the received historiography has indicated, and that philosophical controversies about the implications of mathematization cannot be understood in isolation from broader social developments related to the status and practice of mathematics in various commercial, political, and academic institutions. Contributors: Roger Ariew, U of South Florida; Richard T. W. Arthur, McMaster U; Lesley B. Cormack, U of Alberta; Daniel Garber, Princeton U; Ursula Goldenbaum, Emory U; Dana Jalobeanu, U of Bucharest; Douglas Jesseph, U of South Florida; Carla Rita Palmerino, Radboud U, Nijmegen and Open U of the Netherlands; Eileen Reeves, Princeton U; Christopher Smeenk, Western U; Justin E. H. Smith, U of Paris 7; Kurt Smith, Bloomsburg U of Pennsylvania.
Download or read book Philosophy of Mathematics written by Stewart Shapiro and published by Oxford University Press. This book was released on 1997-08-07 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians.
Download or read book Problems in the Philosophy of Mathematics written by Imre Lakatos and published by Elsevier. This book was released on 1967 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Philosophy written by Cassius Jackson Keyser and published by . This book was released on 2001-06-01 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Philosophy -- A Study of Fate and FreedomMathematics is not what many people think it is - it is not a system of mere formulas and theorems. Mathematics is the science of "exact thought or rigorous thinking," and one of its distinctive characteristics is "precision, sharpness, completeness of definitions." This quality alone is sufficient to explain why people generally do not like mathematics and why even some scientists bluntly refuse to have anything to do with problems wherein mathematical reasoning is involved. In the meantime, mathematical philosophy has very little, if anything, to do with mere calculations or with numbers as such or with formulas; it is a philosophy wherein precise, sharp and rigorous thinking is essential. Those who deliberately refuse to think "rigorously"--that is mathematically--in connections where such thinking is possible, commit the sin of preferring the worse to the better; they deliberately violate the supreme law of intellectual rectitude. For years Keyser meditated upon the nature of mathematics, upon its significance in thought, and upon its bearings on human life. In the following course of lectures he endeavored to present, in the language of educated men and women, some of the maturer fruits of that study.Though the course is designed primarily for students whose major interest is in philosophy, Keyser ventured to hope that a much wider circle of readers and scholars might enjoy the lectures. To all the professional mathematicians, the teachers of mathematics, natural science students, literary critics, sociologists and the rapidly increasing class of engineers who desire to come into touch with the universal spirit of the science that Plato called divine.In 1922, when Mathematical Philosophy was originally published, Dr. Cassius J. Keyser was Adrain Professor Mathematics at Columbia University, New York.
Download or read book Philosophical Papers Volume 1 Mathematics Matter and Method written by Hilary Putnam and published by Cambridge University Press. This book was released on 1979-04-30 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the philosophy of mathematics and of science and the nature of philosophical and scientific enquiry.
Download or read book Mind and Nature written by Hermann Weyl and published by Princeton University Press. This book was released on 2009-03-31 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hermann Weyl (1885-1955) was one of the twentieth century's most important mathematicians, as well as a seminal figure in the development of quantum physics and general relativity. He was also an eloquent writer with a lifelong interest in the philosophical implications of the startling new scientific developments with which he was so involved. Mind and Nature is a collection of Weyl's most important general writings on philosophy, mathematics, and physics, including pieces that have never before been published in any language or translated into English, or that have long been out of print. Complete with Peter Pesic's introduction, notes, and bibliography, these writings reveal an unjustly neglected dimension of a complex and fascinating thinker. In addition, the book includes more than twenty photographs of Weyl and his family and colleagues, many of which are previously unpublished. Included here are Weyl's exposition of his important synthesis of electromagnetism and gravitation, which Einstein at first hailed as "a first-class stroke of genius"; two little-known letters by Weyl and Einstein from 1922 that give their contrasting views on the philosophical implications of modern physics; and an essay on time that contains Weyl's argument that the past is never completed and the present is not a point. Also included are two book-length series of lectures, The Open World (1932) and Mind and Nature (1934), each a masterly exposition of Weyl's views on a range of topics from modern physics and mathematics. Finally, four retrospective essays from Weyl's last decade give his final thoughts on the interrelations among mathematics, philosophy, and physics, intertwined with reflections on the course of his rich life.
Download or read book Objects Structures and Logics written by Gianluigi Oliveri and published by Springer Nature. This book was released on 2022-03-08 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited collection casts light on central issues within contemporary philosophy of mathematics such as the realism/anti-realism dispute; the relationship between logic and metaphysics; and the question of whether mathematics is a science of objects or structures. The discussions offered in the papers involve an in-depth investigation of, among other things, the notions of mathematical truth, proof, and grounding; and, often, a special emphasis is placed on considerations relating to mathematical practice. A distinguishing feature of the book is the multicultural nature of the community that has produced it. Philosophers, logicians, and mathematicians have all contributed high-quality articles which will prove valuable to researchers and students alike.
Download or read book Elements and Relations written by Martin Zwick and published by Springer Nature. This book was released on 2023-08-04 with total page 711 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the core proposition that systems theory is an attempt to construct an “exact and scientific metaphysics,” a system of general ideas central to science that can be expressed mathematically. Collectively, these ideas would constitute a nonreductionist “theory of everything” unlike what is being sought in physics. Inherently transdisciplinary, systems theory offers ideas and methods that are relevant to all of the sciences and also to professional fields such as systems engineering, public policy, business, and social work. To demonstrate the generality and importance of the systems project, the book structures its content in three parts: Essay, Notes, and Commentary. The Essay section is a short distillation of systems ideas that illuminate the problems that many types of systems face. Commentary explains systems thinking, its value, and its relation to mainstream scientific knowledge. It shows how systems ideas revise our understanding of science and how they impact our views on religion, politics, and history. Finally, Notes contains all the mathematics in the book, as well as scientific, philosophical, and poetic content that is accessible to readers without a strong mathematical background. Elements and Relations is intended for researchers and students in the systems (complexity) field as well as related fields of social science modeling, systems biology and ecology, and cognitive science. It can be used as a textbook in systems courses at the undergraduate or graduate level and for STEM education. As much of the book does not require a background in mathematics, it is also suitable for general readers in the natural and social sciences as well as in the humanities, especially philosophy.
