18 Unconventional Essays on the Nature of Mathematics

2006
ISBN: 978-0-387-25717-4
Verlag: Springer

Buch, Englisch, 326 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1090 g

This book collects some of the most interesting recent writings tackling the problem of giving an account of the nature, purpose, and justification of mathematics as actually done by real live mathematicians. What is the nature of the objects being studied? What determines the directions and styles in which mathematics progresses (or, perhaps, degenerates)? What certifies its claim to certainty, or to a priori status, to independence of experience? Why is mathematics the same for all times and places, or is it really the same, or in what senses is it the same and in what senses different?

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Hersh, Reuben

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik

Inhaltsverzeichnis

A Socratic Dialogue on Mathematics.- “Introduction” to Filosofia e matematica.- On Proof and Progress in Mathematics.- The Informal Logic of Mathematical Proof.- Philosophical Problems of Mathematics in the Light of Evolutionary Epistemology.- Towards a Semiotics of Mathematics.- Computers and the Sociology of Mathematical Proof.- From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management.- Do Real Numbers Really Move? Language, Thought, and Gesture: The Embodied Cognitive Foundations of Mathematics.- Does Mathematics Need a Philosophy?.- How and Why Mathematics Is Unique as a Social Practice.- The Pernicious Influence of Mathematics upon Philosophy.- The Pernicious Influence of Mathematics on Science.- What Is Philosophy of Mathematics Looking for?.- Concepts and the Mangle of Practice Constructing Quaternions.- Mathematics as Objective Knowledge and as Human Practice.- The Locus of Mathematical Reality: An Anthropological Footnote.- Inner Vision, Outer Truth.

Über Autor(innen)

REUBEN HERSH is professor emeritus at the University of New Mexico, Albuquerque. He is the recipient (with Martin Davis) of the Chauvenet Prize and (with Edgar Lorch) the Ford Prize. Hersh is the author (with Philip J. Davis) of The Mathematical Experience and Descartes' Dream, which won the National Book Award in l983, and What is Mathematics, Really?