An Aristotelian Realist Philosophy Of Mathematics

Author : J. Franklin
Publisher : Springer
ISBN 13 : 1137400730
Total Pages : 308 pages
Book Rating : 4.34/5 ( download)

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Download or read book An Aristotelian Realist Philosophy of Mathematics written by J. Franklin and published by Springer. This book was released on 2014-04-09 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.

Author : James Robert Brown
Publisher : Routledge
ISBN 13 : 1134806434
Total Pages : 181 pages
Book Rating : 4.30/5 ( download)

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Download or read book Philosophy of Mathematics written by James Robert Brown and published by Routledge. This book was released on 2005-08-09 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : M. F. Burnyeat
Publisher : Cambridge University Press
ISBN 13 : 0521750725
Total Pages : 393 pages
Book Rating : 4.21/5 ( download)

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Download or read book Explorations in Ancient and Modern Philosophy written by M. F. Burnyeat and published by Cambridge University Press. This book was released on 2012-06-14 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of two volumes collecting the published work of one of the greatest living ancient philosophers, M.F. Burnyeat.

Author : Geoffrey Hellman
Publisher : Cambridge University Press
ISBN 13 : 110863074X
Total Pages : 167 pages
Book Rating : 4.40/5 ( download)

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Download or read book Mathematical Structuralism written by Geoffrey Hellman and published by Cambridge University Press. This book was released on 2018-11-29 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the Element considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical possibilities, and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives.

Author : James Franklin
Publisher : JHU Press
ISBN 13 : 1421418819
Total Pages : 767 pages
Book Rating : 4.10/5 ( download)

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Download or read book The Science of Conjecture written by James Franklin and published by JHU Press. This book was released on 2015-08-01 with total page 767 pages. Available in PDF, EPUB and Kindle. Book excerpt: How did we make reliable predictions before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? In The Science of Conjecture, James Franklin examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates. The Science of Conjecture provides a history of rational methods of dealing with uncertainty and explores the coming to consciousness of the human understanding of risk.

Author : Stewart Shapiro
Publisher : Oxford University Press
ISBN 13 : 0190282525
Total Pages : 290 pages
Book Rating : 4.23/5 ( download)

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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 290 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.

Author : Michael D. Resnik
Publisher : Oxford University Press
ISBN 13 : 9780198236085
Total Pages : 300 pages
Book Rating : 4.85/5 ( download)

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Download or read book Mathematics as a Science of Patterns written by Michael D. Resnik and published by Oxford University Press. This book was released on 1997 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Resnik expresses his commitment to a structuralist philosophy of mathematics and links this to a defence of realism about the metaphysics of mathematics - the view that mathematics is about things that really exist.

Author : David Corfield
Publisher : Cambridge University Press
ISBN 13 : 1139436392
Total Pages : 300 pages
Book Rating : 4.97/5 ( download)

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Download or read book Towards a Philosophy of Real Mathematics written by David Corfield and published by Cambridge University Press. This book was released on 2003-04-24 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done.

Author : Penelope Rush
Publisher : Cambridge University Press
ISBN 13 : 1107039649
Total Pages : 279 pages
Book Rating : 4.43/5 ( download)

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Download or read book The Metaphysics of Logic written by Penelope Rush and published by Cambridge University Press. This book was released on 2014-10-16 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This wide-ranging collection of essays explores the nature of logic and the key issues and debates in the metaphysics of logic.

Author : Emily Grosholz
Publisher : Springer Science & Business Media
ISBN 13 : 9401595585
Total Pages : 456 pages
Book Rating : 4.82/5 ( download)

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Download or read book The Growth of Mathematical Knowledge written by Emily Grosholz and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics has stood as a bridge between the Humanities and the Sciences since the days of classical antiquity. For Plato, mathematics was evidence of Being in the midst of Becoming, garden variety evidence apparent even to small children and the unphilosophical, and therefore of the highest educational significance. In the great central similes of The Republic it is the touchstone ofintelligibility for discourse, and in the Timaeus it provides in an oddly literal sense the framework of nature, insuring the intelligibility ofthe material world. For Descartes, mathematical ideas had a clarity and distinctness akin to the idea of God, as the fifth of the Meditations makes especially clear. Cartesian mathematicals are constructions as well as objects envisioned by the soul; in the Principles, the work ofthe physicist who provides a quantified account ofthe machines of nature hovers between description and constitution. For Kant, mathematics reveals the possibility of universal and necessary knowledge that is neither the logical unpacking ofconcepts nor the record of perceptual experience. In the Critique ofPure Reason, mathematics is one of the transcendental instruments the human mind uses to apprehend nature, and by apprehending to construct it under the universal and necessary lawsofNewtonian mechanics.