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Visualization, Explanation and Reasoning Styles in Mathematics
Contains groundbreaking contributions to the philosophical analysis of mathematical practice. Several philosophers of mathematics have recently called for an approach to philosophy of mathematics that pays more attention to mathematical practice. Questions concerning concept-formation, understanding, heuristics, changes in style of reasoning, the role of analogies and diagrams etc.
The Philosophy of Mathematics Education
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.
The Arché Papers on the Mathematics of Abstraction
Collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines. the present volume is unique in presenting a thorough going examination of the mathematical aspects of the neo-logicist project (and the particular philosophical issues arising from these technical concerns). Attention is focused on extending the Neo-Fregean treatment to all of mathematics, with the reconstruction of real analysis from various cut - or cauchy-sequence-related abstraction principles and the reconstruction of set theory from various restricted versions of Basic Law V as case studies. As a result, the volume provides a test of the scope and limits of the neo-logicist project, detailing what has been accomplished and outlining the desiderata still outstanding.
Rationality and Reality : Conversations with Alan Musgrave
Musgrave’s writings have covered a wide range of topics in epistemology, metaphysics, philosophy of science, philosophy of mathematics, history of science, theories of truth, and economic theory. In this volume a group of internationally-renowned authors discuss themes that are relevant in one way or another to Musgrave’s work. This is not intended as a standard celebratory festschrift but rather as a new examination of topics of current interest in philosophy. The contributory essays are followed by responses from Alan Musgrave himself.
Philosophical Dimensions in Mathematics Education
Philosophical Dimensions in Mathematics Education brings together diverse recent developments exploring philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives from which existing boundaries in mathematics education can be extended. The ten chapters in Philosophical Dimensions in Mathematics Education offer a balance between philosophy of and philosophy in mathematics education. Attention is paid to the implementation of a philosophy of mathematics within the mathematics curriculum to become a philosophy in mathematics education. In doing so, many chapters provide ideas for actual practice and some practical examples directly usable in teacher training and in mathematics classrooms.
Perspectives on mathematical practices : Bringing together philosophy of mathematics, sociology of mathematics, and mathematics Education
Brings together the widest variety of authors from these different domains and, secondly, to show that this diversity does not exclude a sufficient number of common elements to be present. In the eyes of the editors, this book will be considered a success if it can convince its readers of the following: that it is warranted to dream of a realistic and full-fledged theory of mathematical practices, in the plural. If such a theory is possible, it would mean that a number of presently existing fierce oppositions between philosophers, sociologists, educators, and other parties involved, are in fact illusory.
Paul Lorenzen -- Mathematician and Logician
Examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics.
Interactions : Mathematics, Physics and Philosophy, 1860-1930
This is an outstanding collection of original essays. All of them concern the history and philosophy of mathematics and physics in the years from 1870 to 1930. More specifically, they are intellectual histories of the interactions between the three disciplines, philosophy, mathematics and physics, they too often overlook the wealth of philosophical perplexities that can arise in detailed examples and case studies, both contemporary and historical. This volume refocuses our attention by addressing a number of topics connected to applied mathematics, any one of which is worthy of every philosopher’s attention.
18 Unconventional Essays on the Nature of Mathematics
This essays edited by Reuben Hersh contains frank facts and opinions from leading mathematicians, philosophers, sociologists, cognitive scientists, and even an anthropologist. Each essay provides a challenging and thought-provoking look at recent advances in the philosophy of mathematics, demonstrating the possibilities of thinking fresh, sticking close to actual practice, and fearlessly letting go of standard shibboleths.
