Platonism And Anti Platonism In Mathematics
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Platonism And Anti Platonism In Mathematics
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Author : Mark Balaguer
language : en
Publisher:
Release Date : 2001
Platonism And Anti Platonism In Mathematics written by Mark Balaguer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible. (Philosophy)
Proof And Other Dilemmas
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Author : Bonnie Gold
language : en
Publisher: MAA
Release Date : 2008
Proof And Other Dilemmas written by Bonnie Gold and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
During the first 75 years of the twentieth century almost all work in the philosophy of mathematics concerned foundational questions. In the last quarter of the century, philosophers of mathematics began to return to basic questions concerning the philosophy of mathematics such as, what is the nature of mathematical knowledge and of mathematical objects, and how is mathematics related to science? Two new schools of philosophy of mathematics, social constructivism and structuralism, were added to the four traditional views (formalism, intuitionalism, logicism, and platonism). The advent of the computer led to proofs and the development of mathematics assisted by computer, and to questions of the role of the computer in mathematics. This book of 16 essays, all written specifically for this volume, is the first to explore this range of new developments in a language accessible to mathematicians. Approximately half the essays were written by mathematicians, and consider questions that philosophers are not yet discussing. The other half, written by philsophers of mathematics, summarize the discussion in that community during the last 35 years. In each case, a connection is made to issues relevant to the teach of mathematics.
What Is Mathematics Really
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Author : Reuben Hersh
language : en
Publisher:
Release Date : 1997
What Is Mathematics Really written by Reuben Hersh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Tries to refine the philosophy of mathematics to reflect what mathematicians really do, and argues that mathematics must be understood in a social context.
Plato S Ghost
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Author : Jeremy Gray
language : en
Publisher: Princeton University Press
Release Date : 2008-09-02
Plato S Ghost written by Jeremy Gray and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-02 with Mathematics categories.
Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method—debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.
An Introduction To The Philosophy Of Mathematics
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Author : Mark Colyvan
language : en
Publisher: Cambridge University Press
Release Date : 2012-06-14
An Introduction To The Philosophy Of Mathematics written by Mark Colyvan 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 2012-06-14 with Mathematics categories.
A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.
The Nature Of Mathematical Knowledge
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Author : Philip Kitcher
language : en
Publisher:
Release Date : 1984
The Nature Of Mathematical Knowledge written by Philip Kitcher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
This book argues against the view that mathematical knowledge is a priori, contending that mathematics is an empirical science and develops historically, just as natural sciences do. Kitcher presents a complete, systematic, and richly detailed account of the nature of mathematical knowledge and its historical development, focusing on such neglected issues as how and why mathematical language changes, why certain questions assume overriding importance, and how standards of proof are modified.
Loving And Hating Mathematics
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Author : Reuben Hersh
language : en
Publisher: Princeton University Press
Release Date : 2010-12-13
Loving And Hating Mathematics written by Reuben Hersh and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-13 with Mathematics categories.
An exploration of the hidden human, emotional, and social dimensions of mathematics Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions—and inspire more love and hatred—than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathematics brings home the intense pleasures and pains of mathematical life. These stories challenge many myths, including the notions that mathematics is a solitary pursuit and a "young man's game," the belief that mathematicians are emotionally different from other people, and even the idea that to be a great mathematician it helps to be a little bit crazy. Reuben Hersh and Vera John-Steiner tell stories of lives in math from their very beginnings through old age, including accounts of teaching and mentoring, friendships and rivalries, love affairs and marriages, and the experiences of women and minorities in a field that has traditionally been unfriendly to both. Included here are also stories of people for whom mathematics has been an immense solace during times of crisis, war, and even imprisonment—as well as of those rare individuals driven to insanity and even murder by an obsession with math. This is a book for anyone who wants to understand why the most rational of human endeavors is at the same time one of the most emotional.
Platonism At The Origins Of Modernity
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Author : Douglas Hedley
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-22
Platonism At The Origins Of Modernity written by Douglas Hedley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-22 with Philosophy categories.
commentary, but by selection and accretion. Those inspired by Plato form as intrinsic a part of Platonism as Plato himself—these are the so-called Neo-P- tonists (a divisive latter-day term which implies discontinuity between Plato and 6 his later followers to the disadvantage of the latter). In the process of its long course of development, Platonism has gathered a long tradition of interpr- ers, whose contributions have been enriched by other philosophical strands—for example Stoicism, which is an important element in the philosophy of Plotinus. To this it must be added that so much of the impact of Platonism is indirect. The Platonism of many thinkers, especially in medieval times, was more often than not implicit, rather than conscious borrowing. It derived not from the Platonic corpus (most of which was unknown at that time), but indirectly through Philo, and theologians like Augustine and Origen. The combined effect of these factors is that the legacy of Platonism is rich, varied and extensive, but eludes the scope of focused enquiry. A further factor complicating assessments of Platonism in the modern era, is polarisation in the historiography itself. Historians of modern philosophy—at least in the anglophone world—readily adopt a model which counterposes ancient and modern. Drawing on a division, which the early modern philosophers themselves invoked, they employ an ‘ancient- 7 modern distinction’ as a principle for organising the history of philosophy.
From Plato To Platonism
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Author : Lloyd P. Gerson
language : en
Publisher: Cornell University Press
Release Date : 2013-11-27
From Plato To Platonism written by Lloyd P. Gerson and has been published by Cornell University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Philosophy categories.
Was Plato a Platonist? While ancient disciples of Plato would have answered this question in the affirmative, modern scholars have generally denied that Plato’s own philosophy was in substantial agreement with that of the Platonists of succeeding centuries. In From Plato to Platonism, Lloyd P. Gerson argues that the ancients were correct in their assessment. He arrives at this conclusion in an especially ingenious manner, challenging fundamental assumptions about how Plato’s teachings have come to be understood. Through deft readings of the philosophical principles found in Plato's dialogues and in the Platonic tradition beginning with Aristotle, he shows that Platonism, broadly conceived, is the polar opposite of naturalism and that the history of philosophy from Plato until the seventeenth century was the history of various efforts to find the most consistent and complete version of "anti-naturalism."Gerson contends that the philosophical position of Plato—Plato’s own Platonism, so to speak—was produced out of a matrix he calls "Ur-Platonism." According to Gerson, Ur-Platonism is the conjunction of five "antis" that in total arrive at anti-naturalism: anti-nominalism, anti-mechanism, anti-materialism, anti-relativism, and anti-skepticism. Plato’s Platonism is an attempt to construct the most consistent and defensible positive system uniting the five "antis." It is also the system that all later Platonists throughout Antiquity attributed to Plato when countering attacks from critics including Peripatetics, Stoics, and Sceptics. In conclusion, Gerson shows that Late Antique philosophers such as Proclus were right in regarding Plotinus as "the great exegete of the Platonic revelation."
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 Mathematics categories.
Hacking explores how mathematics became possible for the human race, and how it ensured our status as the dominant species.