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Mathematics as a Science of Patterns - Michael D. Resnik

Mathematics as a Science of Patterns

Hardcover

Published: 1st September 1997
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Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defence of realism about the metaphysics of mathematics--the view that mathematics is about things that really exist. Resnik's distinctive philosophy of mathematics is here presented in an accessible and systematic form: it will be of value not only to specialists in this area, but to philosophers, mathematicians, and logicians interested in the relationship between these three disciplines, or in truth, realism, and epistemology.

`In terms of topic this is a big book, presenting a complete philosophy of mathematics, surveying the recent work in the field, and dealing with myriad problems while attempting to sketch solutions to each of them ... he has presented an admirably clear discussion of the main issues and arguments that define the philosophy of mathematics. His excellent exposition of the issues and his exploration of new solutions constitute an important advance in the discussion.' David J. Stump, History and Philosophy of Logic `This is a fine book on the central philosophical questions about mathematics, unsurpassed among the recent crop of impressive books on the subject that I have read ... there is a wealth of novel arguments and considerations, which illuminate the field and advance the subject, irrespective of the ultimate standing of the overall thesis ... what Resnik gives us is a forceful case for mathematical realism within an uncompromising Quinean framework ... There are unconveyed depths to this book, and anyone concerned with central questions of epistemology and metaphysics can profit from it; for philsophers of mathematics it is essential reading.' M Giaquinto, Mind, Vol 108, 432, October 1999 `In terms of topic this is a big book, presenting a complete philosophy of mathematics, surveying the recent work in the field, and dealing with myriad problems while attempting to sketch solutions to each of them ... he has presented an admirably clear discussion of the main issues and arguments that define the philosophy of mathematics. His excellent exposition of the issues and his exploration of new solutions constitute an important advance in the discussion.' David J. Stump, History and Philosophy of Logic `In this interesting an important book, Michael Resnik brings together various ideas on the philosophy of mathematics that he has been developing over the last three decades. I highly recommend the work to everyone ... Resnik's book is an extremely rich and interesting one. Moreover, the book is loaded with very bold claims, backed up by interesting arguments and explanations.' Mark Balaguer, Philosophia Mathematica `It is no criticism to say that a philosophical book leaves questions unanswered -- they all do. What matters is that an author should answer the questions he set out to address, and raise new ones of sufficient interest to sustain further debate. In this, Resnik has succeeded admirably.' International Studies in the Philosophy of Science `With great clarity and thoroughness, Michael D. Resnik, in Mathematics as a Science of Patterns, and Stewart Shapiro, in Philosophy of Mathematics, both articulate versions of an attractive programme for those who take ontology as primary.' Philip Kitcher, Times Literary Supplement `perfect for classroom use: it is extremely clear, and Resnik ensures that even the novice is with him at every stage ... It articulates an ambitious and forceful position, only parts of which most of us have seen before. I recommend it without reservation to everyone interested in these topics.' Jody Azzouni, Jrnl of Symbolic Logic, June 99

PART ONE: PROBLEMS AND POSITIONS 1:: Introduction 2:: What Is Mathematical Realism? 3:: The Case for Mathematical Realism 4:: Recent Attempts at Blunting the Indispensability Thesis 5:: Doubts about Realism PART TWO 6:: The Elusive Distinction between Mathematics and Natural Science 7:: Holism: Evidence in Science and Mathematics 8:: The Local Conception of Mathematical Evidence: Proof, Computation, and Logic 9:: Positing Mathematical Objects PART THREE: MATHEMATICS AS A SCIENCE OF PATTERNS 10:: Mathematical Objects as Positions in Patterns 11:: Patterns and Mathematical Knowledge 12:: What is Structuralism? and Other Questions Bibliography Index

ISBN: 9780198236085
ISBN-10: 0198236085
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 298
Published: 1st September 1997
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 22.4 x 14.4  x 3.1
Weight (kg): 0.52