mathematical thought and its objects

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Mathematical Thought And Its Objects

Author : Charles Parsons
ISBN : 1139467271
Genre : Science
File Size : 38. 26 MB
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Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite.

Greek Mathematical Thought And The Origin Of Algebra

Author : Jacob Klein
ISBN : 9780486319810
Genre : Mathematics
File Size : 45. 86 MB
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Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th–16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science — in which the symbolic "form" of a mathematical statement is completely inseparable from its "content" of physical meaning. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.

Mathematics And Logic

Author : Mark Kac
ISBN : 9780486670850
Genre : Philosophy
File Size : 61. 72 MB
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Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."

Mathematical Thought

Author : E.W. Beth
ISBN : 9789401722070
Genre : Science
File Size : 84. 96 MB
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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.

Mathematics And Mind

Author : Alexander George
ISBN : 9780195079296
Genre : History
File Size : 20. 79 MB
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The essays in this volume investigate the conceptual foundations of mathematics illuminating the powers of the mind. Contributors include Alexander George, Michael Dummett, George Boolos, W.W. Tait, Wilfried Sieg, Daniel Isaacson, Charles Parsons, and Michael Hallett.

What Is Mathematics Really

Author : Reuben Hersh
ISBN : 0195130871
Genre : Medical
File Size : 83. 3 MB
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Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

The Objects Of Thought

Author : Tim Crane
ISBN : 9780191505201
Genre : Philosophy
File Size : 77. 75 MB
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The Objects of Thought addresses the ancient question of how it is possible to think about what does not exist. Tim Crane argues that the representation of the non-existent is a pervasive feature of our thought about the world, and that we will not adequately understand thought's representational power ('intentionality') unless we have understood the representation of the non-existent. Intentionality is conceived by Crane in terms of the direction of the mind upon an object of thought, or an intentional object. Intentional objects are what we think about. Some intentional objects exist and some do not. Non-existence poses a problem because there seem to be truths about non-existent intentional objects, but truths are answerable to reality, and reality contains only what exists. The proposed solution is to accept that there are some genuine truths about non-existent intentional objects, but to hold that they must be reductively explained in terms of truths about what does exist. The Objects of Thought offers both an original account of the nature of intentionality and a solution to the problem of thought about the non-existent.

Platonism And Anti Platonism In Mathematics

Author : Mark Balaguer
ISBN : 0195143981
Genre : Mathematics
File Size : 48. 52 MB
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In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He establishes that both platonism and anti-platonism are defensible views and introduces a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, proceeding to defend anti-platonism (in particular, mathematical fictionalism) against various attacks--most notably the Quine-Putnam indispensability attack.

Mathematics In Western Culture

Author : Morris Kline
ISBN : 0195345452
Genre : Mathematics
File Size : 42. 48 MB
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This book gives a remarkably fine account of the influences mathematics has exerted on the development of philosophy, the physical sciences, religion, and the arts in Western life.

Philosophy Of Mathematics

Author : Stewart Shapiro
ISBN : 0198025459
Genre : Philosophy
File Size : 72. 35 MB
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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.

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