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Author: J. Franklin
Publisher: Springer
Published: 2014-04-09
Total Pages: 308
ISBN-13: 1137400730
DOWNLOAD EBOOK →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
Published: 2005-08-09
Total Pages: 181
ISBN-13: 1134806434
DOWNLOAD EBOOK →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: James Franklin
Publisher: JHU Press
Published: 2015-08-01
Total Pages: 767
ISBN-13: 1421418819
DOWNLOAD EBOOK →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: Geoffrey Hellman
Publisher: Cambridge University Press
Published: 2018-11-29
Total Pages: 167
ISBN-13: 110863074X
DOWNLOAD EBOOK →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: M. F. Burnyeat
Publisher: Cambridge University Press
Published: 2012-06-14
Total Pages: 393
ISBN-13: 0521750725
DOWNLOAD EBOOK →The first of two volumes collecting the published work of one of the greatest living ancient philosophers, M.F. Burnyeat.
Author: Michael D. Resnik
Publisher: Oxford University Press
Published: 1997
Total Pages: 300
ISBN-13: 9780198236085
DOWNLOAD EBOOK →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: Stewart Shapiro
Publisher: Oxford University Press
Published: 1997-08-07
Total Pages: 290
ISBN-13: 0190282525
DOWNLOAD EBOOK →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: Penelope Rush
Publisher: Cambridge University Press
Published: 2014-10-16
Total Pages: 279
ISBN-13: 1107039649
DOWNLOAD EBOOK →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
Published: 2013-04-17
Total Pages: 456
ISBN-13: 9401595585
DOWNLOAD EBOOK →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.
Author: David Corfield
Publisher: Cambridge University Press
Published: 2003-04-24
Total Pages: 300
ISBN-13: 1139436392
DOWNLOAD EBOOK →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.
