C.K. RAJU. Cultural Foundations of Mathematics: The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe in the 16th c. CE [Book Review]
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica 17 (3):378-381 (2009)
This book is part of a major project undertaken by the Centre for Studies in Civilizations , being one of a total of ninety-six planned volumes. The author is a statistician and computer scientist by training, who has concentrated on historical matters for the last ten years or so. The book has very ambitious aims, proposing an alternative philosophy of mathematics and a deviant history of the calculus. Throughout, there is an emphasis on the need to combine history and philosophy of mathematics, especially in order to evaluate properly the history of mathematics in India, in particular the history of the calculus.The pivotal goals of the book are to oppose the Eurocentric account of the history of science in general and mathematics in particular; to avoid the usual philosophical idea of the centrality of proof for mathematical knowledge, in favour of the traditional Indian notion of pramāṇa [validation] encompassing empirical elements and emphasizing calculation; to analyze the thousand-year-long development of infinite series in India, starting in the fifth century; and to show ‘how and why the calculus was imported into Europe’ from about 1500. The result is a picture in which inputs from the Indian subcontinent and epistemology are the driving forces of the history of mathematics, as people in the European subcontinent struggle to adopt new calculation techniques from the East in spite of Western philosophico-religious biases . Thus, a ‘first math war’ involved the algorismus de numero indorum, adopted for practical reasons, which forced Europeans to modify their epistemology of number and quantities. A ‘second math war’ revolved around infinite series and the calculus, since the background of Western epistemology created ‘spurious difficulties’ about infinities and infinitesimals, partially resolved with theories of real numbers. And a ‘third math war’ is …
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Frank Plumpton Ramsey (1960). The Foundations of Mathematics and Other Logical Essays. Paterson, N.J.,Littlefield, Adams.
R. Lee Lyman (2006). Cultural Traits and Cultural Integration. Behavioral and Brain Sciences 29 (4):357-358.
James Franklin (1996). Proof in Mathematics. Quakers Hill Press.
Paul Jorion (1999). What Do Mathematicians Teach Us About the World? An Anthropological Perspective. Philosophical Explorations.
Marian Mrozek & Jacek Urbaniec (1997). Evolution of Mathematical Proof. Foundations of Science 2 (1):77-85.
C. K. Raju (2001). Computers, Mathematics Education, and the Alternative Epistemology of the Calculus in the Yuktibhāṣā. Philosophy East and West 51 (3):325 - 362.
Added to index2010-07-27
Total downloads22 ( #181,553 of 1,934,425 )
Recent downloads (6 months)2 ( #269,405 of 1,934,425 )
How can I increase my downloads?