Alfonso C. Concepts and the Mangle of Practice Constructing Quaternions Andrew Pickering. Mathematics as Objective Knowledge and as Human Practice The Locus of Mathematical Reality:. An Anthropological Footnote Leslie A. Inner Vision, Outer Truth Skip to main content.
Search form Search. Login Join Give Shops. Halmos - Lester R. Ford Awards Merten M. Reuben Hersh, editor. Publication Date:. Number of Pages:. Philosophy of Mathematics. Log in to post comments. The important point made by Gowers is that questions which philosophers consider important are too far removed from the actual business of doing mathematics.
In chapter 11, Jody Azzouni argues how and why mathematics is a social practice. The basic questions in philosophy have pretty much stayed the same starting with the Greeks. Answers posed by one generation of philosophers end up being revised or rejected by the next generation.
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There are no definitive answers per se. On the other hand, mathematics seems to be the envy of philosophy because mathematicians are able to give definitive answers to the problems that occur within mathematics. This has influenced philosophy to adopt mathematical standards of rigor for the study of philosophical problems. Rota writes: It has not occurred to our mathematizing philosophers that philosophy might be endowed with its own kind of rigor, a rigor that philosophers should dispassionately describe and codify, as mathematicians did Book Reviews with their own kind of rigor a long time ago.
Bewitched as they are by the success of mathematics, they remain enslaved by the prejudice that the only possible rigor is that of mathematics and that philosophy has no choice but to imitate it. Logic which used to traditionally be a part of philosophy has mutated into mathematical logic and consequently become subsumed as one of the many areas of mathematics.
Does philosophy want to meet the same fate?
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This is another provocative piece of writing which the reader will find both entertaining and stimulating. Alfonso C. Chapter 17 is written by the eminent anthropologist Leslie White. Towards the end of his compelling essay, White writes: Thus we see, there is no mystery about mathematical reality. Mathematics is a kind of primate behaviour as languages, musical systems and penal codes are. Mathematical concepts are man- ZDM Vol. Hersh reflects on mathematical ideas that struck him as particularly beautiful, and the strange fit between mathematics and physics.
His explanation of the sometimes miraculous fit between available mathematics and the problems that physicists are grappling with lead the reader to wonder whether this fit is natural or actually imposed simply because of historical precedence. I predict that this book will become a classic for the coming generations of mathematics philosophers as well as for mathematics educators interested in changing dominant conceptions of what is mathematics, finally!
References Ayoub, R. Musings of the masters: An anthology of mathematical reflections. Mathematical Association of America, Spectrum Series. Mathematicians as Enquirers. The mathematical experience. Brighton: Harvester. Dawson, A. The implications of the work of Popper, Polya and Lakatos for a model of mathematics instruction.
Unpublished doctoral dissertation, University of Alberta.
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