Science Without Numbers
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Science Without Numbers
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Author : Hartry Field
language : en
Publisher: Oxford University Press
Release Date : 2016-10-13
Science Without Numbers written by Hartry Field and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-13 with Philosophy categories.
Science Without Numbers caused a stir in philosophy on its original publication in 1980, with its bold nominalist approach to the ontology of mathematics and science. Hartry Field argues that we can explain the utility of mathematics without assuming it true. Part of the argument is that good mathematics has a special feature ("conservativeness") that allows it to be applied to "nominalistic" claims (roughly, those neutral to the existence of mathematical entities) in a way that generates nominalistic consequences more easily without generating any new ones. Field goes on to argue that we can axiomatize physical theories using nominalistic claims only, and that in fact this has advantages over the usual axiomatizations that are independent of nominalism. There has been much debate about the book since it first appeared. It is now reissued in a revised contains a substantial new preface giving the author's current views on the original book and the issues that were raised in the subsequent discussion of it.
Science Without Numbers
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Author : Hartry H. Field
language : en
Publisher: Oxford University Press
Release Date : 2016
Science Without Numbers written by Hartry H. Field and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.
Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.
Science Without Numbers
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Author : Hartry H. Field
language : en
Publisher:
Release Date : 1980
Science Without Numbers written by Hartry H. Field and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
The Description for this book, Science Without Numbers: The Defence of Nominalism, will be forthcoming.
Science Without Numbers
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Author : Hartry Field
language : en
Publisher:
Release Date : 2015-08-11
Science Without Numbers written by Hartry Field and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-11 with Mathematics categories.
According to the doctrine of nominalism, abstract entities--such as numbers, functions, and sets--do not exist. The problem this normally poses for a description of the physical world is as follows: any such description must include a physical theory, physical theories are assumed to require mathematics, and mathematics is replete with references to abstract entities. How, then, can nominalism reasonably be maintained? In answer, Hartry Field shows how abstract entities ultimately are dispensable in describing the physical world and that, indeed, we can "do science without numbers." The author also argues that despite the ultimate dispensability of mathematical entities, mathematics remains useful, and that its usefulness can be explained by the nominalist. The explanation of the utility of mathematics does not presuppose that mathematics is true, but only that it is consistent. The argument that the nominalist can freely use mathematics in certain contexts without assuming it to be true appears early on, and it first seems to license only a quite limited use of mathematics. But when combined with the later argument that abstract entities ultimately are dispensable in physical theories, the conclusion emerges that even the most sophisticated applications of mathematics depend only on the assumption that mathematics is consistent and not on the assumption that it is true. Originally published in 2050. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
The Indispensability Of Mathematics
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Author : Mark Colyvan
language : en
Publisher: Oxford University Press
Release Date : 2001-03-22
The Indispensability Of Mathematics written by Mark Colyvan and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-22 with Philosophy categories.
The Quine-Putnam indispensability argument in the philosophy of mathematics urges us to place mathematical entities on the same ontological footing as other theoretical entities essential to our best scientific theories. Recently, the argument has come under serious scrutiny, with many influential philosophers unconvinced of its cogency. This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.
Math Without Numbers
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Author : Milo Beckman
language : en
Publisher: Penguin
Release Date : 2021-01-05
Math Without Numbers written by Milo Beckman and has been published by Penguin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-05 with Mathematics categories.
An illustrated tour of the structures and patterns we call "math" The only numbers in this book are the page numbers. Math Without Numbers is a vivid, conversational, and wholly original guide to the three main branches of abstract math—topology, analysis, and algebra—which turn out to be surprisingly easy to grasp. This book upends the conventional approach to math, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs, and how these concepts all fit together. What awaits readers is a freewheeling tour of the inimitable joys and unsolved mysteries of this curiously powerful subject. Like the classic math allegory Flatland, first published over a century ago, or Douglas Hofstadter's Godel, Escher, Bach forty years ago, there has never been a math book quite like Math Without Numbers. So many popularizations of math have dwelt on numbers like pi or zero or infinity. This book goes well beyond to questions such as: How many shapes are there? Is anything bigger than infinity? And is math even true? Milo Beckman shows why math is mostly just pattern recognition and how it keeps on surprising us with unexpected, useful connections to the real world. The ambitions of this book take a special kind of author. An inventive, original thinker pursuing his calling with jubilant passion. A prodigy. Milo Beckman completed the graduate-level course sequence in mathematics at age sixteen, when he was a sophomore at Harvard; while writing this book, he was studying the philosophical foundations of physics at Columbia under Brian Greene, among others.
Science Without Numbers
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Author : Hartry H. Field
language : en
Publisher:
Release Date : 2016
Science Without Numbers written by Hartry H. Field and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with SCIENCE categories.
'Science Without Numbers' caused a stir when it was originally published in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for 20 years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.
Philosophy Of Mathematics
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Author : Stewart Shapiro
language : en
Publisher: Oxford University Press
Release Date : 1997-08-07
Philosophy Of Mathematics written by Stewart Shapiro and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-07 with Philosophy categories.
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.
Numbers Without End
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Author : Cornelius Lanczos
language : en
Publisher:
Release Date : 1968
Numbers Without End written by Cornelius Lanczos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Arithmetic categories.
Why Is There Philosophy Of Mathematics At All
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Author : Ian Hacking
language : en
Publisher: Cambridge University Press
Release Date : 2014-01-30
Why Is There Philosophy Of Mathematics At All written by Ian Hacking and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-30 with Science categories.
This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.