The Philosophy of Mathematics Education

The Philosophy of Mathematics Education
Author: Paul Ernest,Ole Skovsmose,Jean Paul van Bendegem,Maria Bicudo,Roger Miarka,Ladislav Kvasz,Regina Moeller
Publsiher: Springer
Total Pages: 26
Release: 2016-08-04
ISBN 10: 9783319405681
ISBN 13: 3319405683
Language: EN, FR, DE, ES & NL

The Philosophy of Mathematics Education Book Review:

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 research in the philosophy of mathematics education in Brazil. This illustrates one orientation towards research inquiry in the philosophy of mathematics education. It is part of a broader practice of ‘philosophical archaeology’: the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education. An extensive bibliography is also included.

Thinking about Mathematics

Thinking about Mathematics
Author: Stewart Shapiro
Publsiher: OUP Oxford
Total Pages: 328
Release: 2000-07-13
ISBN 10: 0192893068
ISBN 13: 9780192893062
Language: EN, FR, DE, ES & NL

Thinking about Mathematics Book Review:

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.

Philosophies of Mathematics

Philosophies of Mathematics
Author: Alexander L. George,Daniel Velleman
Publsiher: Wiley-Blackwell
Total Pages: 244
Release: 2001-12-03
ISBN 10: 9780631195443
ISBN 13: 0631195440
Language: EN, FR, DE, ES & NL

Philosophies of Mathematics Book Review:

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.

Philosophy of Mathematics

Philosophy of Mathematics
Author: Øystein Linnebo
Publsiher: Princeton University Press
Total Pages: 216
Release: 2017-05-30
ISBN 10: 0691161402
ISBN 13: 9780691161402
Language: EN, FR, DE, ES & NL

Philosophy of Mathematics Book Review:

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 trying to answer that question: the philosophy of mathematics. Written by Øystein Linnebo, one of the world's leading scholars on the subject, the book introduces all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. It also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms. The groundbreaking work of German mathematician and philosopher Gottlob Frege, one of the founders of analytic philosophy, figures prominently throughout the book. Other important thinkers whose work is introduced and discussed include Immanuel Kant, John Stuart Mill, David Hilbert, Kurt Gödel, W. V. Quine, Paul Benacerraf, and Hartry H. Field. Sophisticated but clear and approachable, this is an essential introduction for all students and teachers of philosophy, as well as mathematicians and others who want to understand the foundations of mathematics.

Philosophy of Mathematics

Philosophy of Mathematics
Author: Ahmet Cevik
Publsiher: CRC Press
Total Pages: 352
Release: 2021-11-09
ISBN 10: 1000468801
ISBN 13: 9781000468809
Language: EN, FR, DE, ES & NL

Philosophy of Mathematics Book Review:

The philosophy of mathematics is an exciting subject. Philosophy of Mathematics: Classic and Contemporary Studies explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians to think about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge. With this new approach, the author rekindles an interest in philosophical subjects surrounding the foundations of mathematics. He offers the mathematical motivations behind the topics under debate. He introduces various philosophical positions ranging from the classic views to more contemporary ones, including subjects which are more engaged with mathematical logic. Most books on philosophy of mathematics have little to no focus on the effects of philosophical views on mathematical practice, and no concern on giving crucial mathematical results and their philosophical relevance, consequences, reasons, etc. This book fills this gap. The book can be used as a textbook for a one-semester or even one-year course on philosophy of mathematics. "Other textbooks on the philosophy of mathematics are aimed at philosophers. This book is aimed at mathematicians. Since the author is a mathematician, it is a valuable addition to the literature." - Mark Balaguer, California State University, Los Angeles "There are not many such texts available for mathematics students. I applaud efforts to foster the dialogue between mathematics and philosophy." - Michele Friend, George Washington University and CNRS, Lille, France

Lectures on the Philosophy of Mathematics

Lectures on the Philosophy of Mathematics
Author: Joel David Hamkins
Publsiher: MIT Press
Total Pages: 352
Release: 2021-02-02
ISBN 10: 0262362651
ISBN 13: 9780262362658
Language: EN, FR, DE, ES & NL

Lectures on the Philosophy of Mathematics Book Review:

An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Philosophy of Mathematics

Philosophy of Mathematics
Author: Paul Benacerraf,Hilary Putnam
Publsiher: Cambridge University Press
Total Pages: 135
Release: 1984-01-27
ISBN 10: 1107268133
ISBN 13: 9781107268135
Language: EN, FR, DE, ES & NL

Philosophy of Mathematics Book Review:

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

An Introduction to the Philosophy of Mathematics

An Introduction to the Philosophy of Mathematics
Author: Mark Colyvan
Publsiher: Cambridge University Press
Total Pages: 188
Release: 2012-06-14
ISBN 10: 0521826020
ISBN 13: 9780521826020
Language: EN, FR, DE, ES & NL

An Introduction to the Philosophy of Mathematics Book Review:

This introduction to the philosophy of mathematics focuses on contemporary debates in an important and central area of philosophy. The reader is taken on a fascinating and entertaining journey through some intriguing mathematical and philosophical territory, including such topics as the realism/anti-realism debate in mathematics, mathematical explanation, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics and the applications of mathematics. Each chapter has a number of discussion questions and recommended further reading from both the contemporary literature and older sources. Very little mathematical background is assumed and all of the mathematics encountered is clearly introduced and explained using a wide variety of examples. The book is suitable for an undergraduate course in philosophy of mathematics and, more widely, for anyone interested in philosophy and mathematics.

Wittgenstein s Philosophy of Mathematics

Wittgenstein s Philosophy of Mathematics
Author: Pasquale Frascolla
Publsiher: Routledge
Total Pages: 200
Release: 2006-12-05
ISBN 10: 113497437X
ISBN 13: 9781134974375
Language: EN, FR, DE, ES & NL

Wittgenstein s Philosophy of Mathematics Book Review:

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'.

Philosophy of Mathematics and Natural Science

Philosophy of Mathematics and Natural Science
Author: Hermann Weyl
Publsiher: Princeton University Press
Total Pages: 311
Release: 2009-05-17
ISBN 10: 9780691141206
ISBN 13: 0691141207
Language: EN, FR, DE, ES & NL

Philosophy of Mathematics and Natural Science Book Review:

History of mathematics.

The Philosophy of Mathematical Practice

The Philosophy of Mathematical Practice
Author: Paolo Mancosu
Publsiher: Oxford University Press on Demand
Total Pages: 447
Release: 2008-06-19
ISBN 10: 0199296456
ISBN 13: 9780199296453
Language: EN, FR, DE, ES & NL

The Philosophy of Mathematical Practice Book Review:

There is an urgent need in philosophy of mathematics for new approaches which pay closer attention to mathematical practice. This book will blaze the trail: it offers philosophical analyses of important characteristics of contemporary mathematics and of many aspects of mathematical activity which escape purely formal logical treatment.

An Introduction to the Philosophy of Mathematics

An Introduction to the Philosophy of Mathematics
Author: Mark Colyvan
Publsiher: Cambridge University Press
Total Pages: 200
Release: 2012-06-14
ISBN 10: 9780521533416
ISBN 13: 0521533414
Language: EN, FR, DE, ES & NL

An Introduction to the Philosophy of Mathematics Book Review:

This introduction to the philosophy of mathematics focuses on contemporary debates in an important and central area of philosophy. The reader is taken on a fascinating and entertaining journey through some intriguing mathematical and philosophical territory, including such topics as the realism/anti-realism debate in mathematics, mathematical explanation, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics and the applications of mathematics. Each chapter has a number of discussion questions and recommended further reading from both the contemporary literature and older sources. Very little mathematical background is assumed and all of the mathematics encountered is clearly introduced and explained using a wide variety of examples. The book is suitable for an undergraduate course in philosophy of mathematics and, more widely, for anyone interested in philosophy and mathematics.

Research in History and Philosophy of Mathematics

Research in History and Philosophy of Mathematics
Author: Maria Zack,Elaine Landry
Publsiher: Birkhäuser
Total Pages: 192
Release: 2015-11-10
ISBN 10: 3319222589
ISBN 13: 9783319222585
Language: EN, FR, DE, ES & NL

Research in History and Philosophy of Mathematics Book Review:

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 •Physical tools used by mathematicians in the seventeenth century •The first historical appearance of the game-theoretical concept of mixed-strategy equilibrium •George Washington’s mathematical cyphering books •The development of the Venn diagram •The role of Euler and other mathematicians in the development of algebraic analysis •Arthur Cayley and Alfred Kempe’s influence on Charles Peirce's diagrammatic logic •The influence publishers had on the development of mathematical pedagogy in the nineteenth century •A description of the 1924 International Mathematical Congress held in Toronto, told in the form of a “narrated slide show” Written by leading scholars in the field, these papers will be accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.

Philosophy of Mathematics

Philosophy of Mathematics
Author: James Robert Brown
Publsiher: Routledge
Total Pages: 250
Release: 2010-03-17
ISBN 10: 1135902380
ISBN 13: 9781135902384
Language: EN, FR, DE, ES & NL

Philosophy of Mathematics Book Review:

In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value? This clear and engaging book takes a unique approach, encompassing non-standard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional topics such as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis.

Philosophy of Mathematics and Economics

Philosophy of Mathematics and Economics
Author: Thomas A. Boylan,Paschal F. O'Gorman
Publsiher: Routledge
Total Pages: 242
Release: 2018-04-09
ISBN 10: 1351124579
ISBN 13: 9781351124577
Language: EN, FR, DE, ES & NL

Philosophy of Mathematics and Economics Book Review:

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 to simply enhancing our understanding of how economics became an applied mathematical science. The authors also critically evaluate developments in the philosophy of mathematics to expose the inadequacy of aspects of mainstream mathematical economics, as well as exploiting the same philosophy to suggest alternative ways of rigorously formulating economic theory for our digital age. This book represents an innovative attempt to more fully understand the complexity of the interaction between developments in the philosophy of mathematics and the process of formalisation in economics. Assuming no expert knowledge in the philosophy of mathematics, this work is relevant to historians of economic thought and professional philosophers of economics. In addition, it will be of great interest to those who wish to deepen their appreciation of the economic contours of contemporary society. It is also hoped that mathematical economists will find this work informative and engaging.

Philosophy of Mathematics

Philosophy of Mathematics
Author: James Robert Brown
Publsiher: Routledge
Total Pages: 232
Release: 2005-08-09
ISBN 10: 1134806434
ISBN 13: 9781134806430
Language: EN, FR, DE, ES & NL

Philosophy of Mathematics Book Review:

Philosophy of Mathematics is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.

Berkeley s Philosophy of Mathematics

Berkeley s Philosophy of Mathematics
Author: Douglas M. Jesseph
Publsiher: University of Chicago Press
Total Pages: 329
Release: 2010-12-15
ISBN 10: 0226398951
ISBN 13: 9780226398952
Language: EN, FR, DE, ES & NL

Berkeley s Philosophy of Mathematics Book Review:

In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work. Jesseph challenges the prevailing view that Berkeley's mathematical writings are peripheral to his philosophy and argues that mathematics is in fact central to his thought, developing out of his critique of abstraction. Jesseph's argument situates Berkeley's ideas within the larger historical and intellectual context of the Scientific Revolution. Jesseph begins with Berkeley's radical opposition to the received view of mathematics in the philosophy of the late seventeenth and early eighteenth centuries, when mathematics was considered a "science of abstractions." Since this view seriously conflicted with Berkeley's critique of abstract ideas, Jesseph contends that he was forced to come up with a nonabstract philosophy of mathematics. Jesseph examines Berkeley's unique treatments of geometry and arithmetic and his famous critique of the calculus in The Analyst. By putting Berkeley's mathematical writings in the perspective of his larger philosophical project and examining their impact on eighteenth-century British mathematics, Jesseph makes a major contribution to philosophy and to the history and philosophy of science.

Research in History and Philosophy of Mathematics

Research in History and Philosophy of Mathematics
Author: Maria Zack,Dirk Schlimm
Publsiher: Springer Nature
Total Pages: 172
Release: 2020-01-02
ISBN 10: 3030312984
ISBN 13: 9783030312985
Language: EN, FR, DE, ES & NL

Research in History and Philosophy of Mathematics Book Review:

This volume contains ten papers that have been collected by the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics from the seventeenth century to the modern era. The volume begins with an exposition of the life and work of Professor Bolesław Sobociński. It then moves on to cover a collection of topics about twentieth-century philosophy of mathematics, including Fred Sommers’s creation of Traditional Formal Logic and Alexander Grothendieck’s work as a starting point for discussing analogies between commutative algebra and algebraic geometry. Continuing the focus on the philosophy of mathematics, the next selections discuss the mathematization of biology and address the study of numerical cognition. The volume then moves to discussing various aspects of mathematics education, including Charles Davies’s early book on the teaching of mathematics and the use of Gaussian Lemniscates in the classroom. A collection of papers on the history of mathematics in the nineteenth century closes out the volume, presenting a discussion of Gauss’s “Allgemeine Theorie des Erdmagnetismus” and a comparison of the geometric works of Desargues and La Hire. Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.

Introduction to the Philosophy of Mathematics

Introduction to the Philosophy of Mathematics
Author: Hugh Lehman
Publsiher: Unknown
Total Pages: 177
Release: 1979
ISBN 10: 1928374650XXX
ISBN 13: STANFORD:36105031438125
Language: EN, FR, DE, ES & NL

Introduction to the Philosophy of Mathematics Book Review:

Frege

Frege
Author: Michael Dummett,Professor of Philosophy Michael Dummett
Publsiher: Harvard University Press
Total Pages: 331
Release: 1991
ISBN 10: 9780674319356
ISBN 13: 0674319354
Language: EN, FR, DE, ES & NL

Frege Book Review:

No one has figured more prominently in the study of the German philosopher Gottlob Frege than Michael Dummett. His magisterial Frege: Philosophy of Language is a sustained, systematic analysis of Frege's thought, omitting only the issues in philosophy of mathematics. In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume of Basic Laws of Arithmetic, establishing what parts of the philosopher's views can be salvaged and employed in new theorizing, and what must be abandoned, either as incorrectly argued or as untenable in the light of technical developments. Gottlob Frege (1848-1925) was a logician, mathematician, and philosopher whose work had enormous impact on Bertrand Russell and later on the young Ludwig Wittgenstein, making Frege one of the central influences on twentieth-century Anglo-American philosophy; he is considered the founder of analytic philosophy. His philosophy of mathematics contains deep insights and remains a useful and necessary point of departure for anyone seriously studying or working in the field.