Mathematical Knowledge Objects And Applications
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Mathematical Knowledge, Objects and Applications
This book provides a survey of a number of the major issues in the philosophy of mathematics, such as ontological questions regarding the nature of mathematical objects, epistemic questions about the acquisition of mathematical knowledge, and the intriguing riddle of the applicability of mathematics to the physical world. Some of these issues go back to the nascent years of mathematics itself, others are just beginning to draw the attention of scholars. In addressing these questions, some of the papers in this volume wrestle with them directly, while others use the writings of philosophers such as Hume and Wittgenstein to approach their problems by way of interpretation and critique. The contributors include prominent philosophers of science and mathematics as well as promising younger scholars. The volume seeks to share the concerns of philosophers of mathematics with a wider audience and will be of interest to historians, mathematicians and philosophers alike.
Mathematical Cultures
This collection presents significant contributions from an international network project on mathematical cultures, including essays from leading scholars in the history and philosophy of mathematics and mathematics education. Mathematics has universal standards of validity. Nevertheless, there are local styles in mathematical research and teaching, and great variation in the place of mathematics in the larger cultures that mathematical practitioners belong to. The reflections on mathematical cultures collected in this book are of interest to mathematicians, philosophers, historians, sociologists, cognitive scientists and mathematics educators.
Mathematisation and Demathematisation
In this volume scholars from diverse strands of research have contributed their perspectives on a process of mathematisation, which renders social, economical or political relationships increasingly formal. At the same time, mathematical skills lose their importance as they become replaced by diverse technological tools; a process of demathematisation takes place. The computerization of financial transactions, calculation of taxes and fees, comparison of prices as well as orientation by means of GPS, visualisation of complex data and electronic voting systems—all these mathematical technologies increasingly penetrate the lifestyle of consumers. What are the perils and promises of this development? Who is in charge, who is affected, who is excluded? A common concern of all the authors of this volume is an attempt to draw attention to issues related to the formatting power of mathematics and to its role as implicit knowledge, which results in a process of demathematisation. This process, having once received considerable attention, is now threatened to be eclipsed by the proliferation of a discussion of school mathematics, which shows a tendency of cutting off its own philosophical and political roots. Taken together, the contributions reveal a rather complex picture: They draw attention to the importance of clarifying epistemological, societal and ideological issues as a prerequisite for a discussion of curriculum.