The Philosophy of Mathematical Practice

Erscheinungsjahr 2011
ISBN: 978-0-19-964010-2
Verlag: OUP Oxford

Buch, Englisch, 460 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 693 g

Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, and developments at the intersection of history and philosophy of mathematics. But anyone familiar with contemporary philosophy of mathematics will be aware of the need for new approaches that pay closer attention to mathematical practice. This book is the first attempt to give a coherent and unified presentation of this new wave of work in philosophy of mathematics. The new approach is innovative at least in two ways. First, it holds that there are important novel characteristics of contemporary mathematics that are just as worthy of philosophical attention as the distinction between constructive and non-constructive mathematics at the time of the foundational debates. Secondly, it holds that many topics which escape purely formal logical treatment--such as visualization, explanation, and understanding--can nonetheless be subjected to philosophical analysis.

The Philosophy of Mathematical Practice comprises an introduction by the editor and eight chapters written by some of the leading scholars in the field. Each chapter consists of a short introduction to the general topic of the chapter followed by a longer research article in the area. The eight topics selected represent a broad spectrum of contemporary philosophical reflection on different aspects of mathematical practice: diagrammatic reasoning and representational systems; visualization; mathematical explanation; purity of methods; mathematical concepts; the philosophical relevance of category theory; philosophical aspects of computer science in mathematics; the philosophical impact of recent developments in mathematical physics.

Zielgruppe

Advanced students and scholars of philosophy of mathematics. Also mathematicians, historians of mathematics, and cognitive psychologists.

Autoren/Hrsg.

Mancosu, Paolo

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik

Inhaltsverzeichnis

Paolo Mancosu: Introduction
1: Marcus Giaquinto: Visualization
2: Kenneth Manders: Diagrammatic Reasoning and Representational Systems
3: Paolo Mancosu and Johannes Hafner: Explanation
4: Mic Detlefsen and Michael Hallett: Purity of Methods
5: James Tappenden: Mathematical concepts
6: Colin McLarty: Philosophical Relevance of Category Theory
7: Jeremy Avigad: Philosophical Relevance of Computers in Mathematics
8: Alasdair Urquhart: Philosophical Relevance of the interaction between mathematical physics and pure mathematics

Über Autor(innen)

Mancosu, Paolo
Paolo Mancosu is Professor of Philosophy at University of California, Berkeley. His main interests are in logic, history and philosophy of mathematics, and history and philosophy of logic. He is the author of Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century (OUP 1996) and editor of From Brouwer to Hilbert: The debate on the foundations of mathematics in the 1920s (OUP 1988). He has recently co-edited the volume Visualization, Explanation and Reasoning Styles in Mathematics (Springer 2005). He is currently working on mathematical explanation and on Tarskian themes (truth, logical consequence, logical constants, nominalism) in philosophy of logic.