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Author: J. Franklin
Publisher: Springer
Published: 2014-04-09
Total Pages: 316
ISBN-13: 1137400730
DOWNLOAD EBOOKMathematics 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: Psychology Press
Published: 1999
Total Pages: 181
ISBN-13: 0415122759
DOWNLOAD EBOOKPhilosophy of Mathematicsis clear and engaging, and student friendly The book discusses the great philosophers and the importance of mathematics to their thought. Among topics discussed in the book are the mathematical image, platonism, picture-proofs, applied mathematics, Hilbert and Godel, knots and notation definitions, picture-proofs and Wittgenstein, computation, proof and conjecture.
Author: David Corfield
Publisher: Cambridge University Press
Published: 2003-04-24
Total Pages: 300
ISBN-13: 1139436392
DOWNLOAD EBOOKIn 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: James Franklin
Publisher: JHU Press
Published: 2015-08-01
Total Pages: 767
ISBN-13: 1421418819
DOWNLOAD EBOOKHow 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 EBOOKThe 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: Bertrand Russell
Publisher: W. W. Norton & Company
Published: 1996
Total Pages: 580
ISBN-13: 9780393314045
DOWNLOAD EBOOKRussell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical--that what is commonly called mathematics is simply later deductions from logical premises.
Author: Michael D. Resnik
Publisher: Oxford University Press
Published: 1997
Total Pages: 300
ISBN-13: 9780198236085
DOWNLOAD EBOOKResnik 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: Penelope Rush
Publisher: Cambridge University Press
Published: 2014-10-16
Total Pages: 279
ISBN-13: 1107039649
DOWNLOAD EBOOKThis wide-ranging collection of essays explores the nature of logic and the key issues and debates in the metaphysics of logic.
Author: M. F. Burnyeat
Publisher: Cambridge University Press
Published: 2012-06-14
Total Pages: 393
ISBN-13: 0521750725
DOWNLOAD EBOOKThe first of two volumes collecting the published work of one of the greatest living ancient philosophers, M.F. Burnyeat.
Author: Hartry H. Field
Publisher: Wiley-Blackwell
Published: 1991-01-01
Total Pages: 290
ISBN-13: 9780631180876
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