The Philosophy of Mathematics Education

• Author : Paul Ernest,Ole Skovsmose,Jean Paul van Bendegem,Maria Bicudo,Roger Miarka,Ladislav Kvasz,Regina Moeller
• Publisher : Springer
• Release : 04 August 2016

This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of

• Author : Stewart Shapiro
• Publisher : OUP Oxford
• Release : 13 July 2000

Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.

• Author : Pasquale Frascolla
• Publisher : Routledge
• Release : 05 December 2006

Wittgenstein's role was vital in establishing mathematics as one of this century's principal areas of philosophic inquiry. In this book, the three phases of Wittgenstein's reflections on mathematics are viewed as a progressive whole, rather than as separate entities. Frascolla builds up a systematic construction of Wittgenstein's representation of the role of arithmetic in the theory of logical operations. He also presents a new interpretation of Wittgenstein's rule-following considerations - the `community view of internal relations'.

• Author : Maria Zack,Elaine Landry
• Publisher : Birkhäuser
• Release : 10 November 2015

This volume contains thirteen papers that were presented at the 2014 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques, held on the campus of Brock University in St. Catharines, Ontario, Canada. It contains rigorously reviewed modern scholarship on general topics in the history and philosophy of mathematics, as well as on the meeting’s special topic, Early Scientific Computation. These papers cover subjects such as •

• Author : Hugh Lehman
• Publisher : Unknown
• Release : 25 September 1979

• Author : Ian Hacking
• Publisher : Cambridge University Press
• Release : 30 January 2014

Hacking explores how mathematics became possible for the human race, and how it ensured our status as the dominant species.

• Author : Russell Marcus,Mark McEvoy
• Publisher : Bloomsbury Publishing
• Release : 11 February 2016

As the first comprehensive collection of historical readings in the philosophy of mathematics, this much-needed introduction reveals the rich history of the subject. Focusing on the philosophy of mathematics before the 20th-century, An Historical Introduction to the Philosophy of Mathematics: A Readerbrings together an impressive collection of primary sources from ancient, medieval and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from Plato, Aristotle,

• Author : John Stillwell
• Publisher : Cambridge University Press
• Release : 06 June 2019

This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to

• Author : Hermann Weyl
• Publisher : Princeton University Press
• Release : 17 May 2009

History of mathematics.

• Author : Øystein Linnebo
• Publisher : Princeton University Press
• Release : 30 May 2017

A sophisticated, original introduction to the philosophy of mathematics from one of its leading contemporary scholars Mathematics is one of humanity's most successful yet puzzling endeavors. It is a model of precision and objectivity, but appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic yet accessible introduction to the field that is

• Author : Anonim
• Publisher : Elsevier
• Release : 08 July 2009

One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have

• Author : Brouwer
• Publisher : Elsevier
• Release : 14 October 2011

Problems in the Philosophy of Mathematics

• Author : Thomas A. Boylan,Paschal F. O'Gorman
• Publisher : Routledge
• Release : 09 April 2018

With the failure of economics to predict the recent economic crisis, the image of economics as a rigorous mathematical science has been subjected to increasing interrogation. One explanation for this failure is that the subject took a wrong turn in its historical trajectory, becoming too mathematical. Using the philosophy of mathematics, this unique book re-examines this trajectory. Philosophy of Mathematics and Economics re-analyses the divergent rationales for mathematical economics by some of its principal architects. Yet, it is not limited

• Author : Alexander L. George,Daniel Velleman
• Publisher : Wiley-Blackwell
• Release : 03 December 2001

This book provides an accessible, critical introduction to the three main approaches that dominated work in the philosophy of mathematics during the twentieth century: logicism, intuitionism and formalism.

• Author : Stewart Shapiro
• Publisher : Oxford University Press
• Release : 10 February 2005

Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics