Metodo

International Studies in Phenomenology and Philosophy

Series | Book | Chapter

191932

Pluralism and "bad" mathematical theories

challenging our prejudices

Michèle Friend

pp. 277-307

Abstract

Here, pluralism is introduced as a new and independent philosophy of mathematics in its own right. One of the marks of independence from more main-stream philosophical positions is that pluralists take seriously "bad" mathematics. Under "bad mathematics' I include: inconsistent theories, trivial theories, not yet completed theories and intensional theories. Bad mathematical theories are ignored by main-steam philosophers of mathematics because they take it as read that the philosopher's task is to give a philosophy of successful mathematics. In contrast, the pluralist contends that bad mathematical theories are as much a part of "mathematics' as are the successful parts. Moreover, they are philosophically important. Who is this pluralist? A pluralist in the philosophy of mathematics is someone who places pluralism as the chief virtue in her philosophy of mathematics. She brings the attitude to bear on: conflicting mathematical theories, including different foundations of mathematics, on different philosophies of mathematics and uses (what are usually dismissed as) "bad mathematical theories' to inform her philosophy.

Publication details

Published in:

Tanaka Koji, Berto Francesco, Mares Edwin D., Paoli Francesco (2013) Paraconsistency: logic and applications. Dordrecht, Springer.

Pages: 277-307

DOI: 10.1007/978-94-007-4438-7_15

Full citation:

Friend Michèle (2013) „Pluralism and "bad" mathematical theories: challenging our prejudices“, In: K. Tanaka, F. Berto, E. D. Mares & F. Paoli (eds.), Paraconsistency, Dordrecht, Springer, 277–307.