Pluralism and "bad" mathematical theories
challenging our prejudices
pp. 277-307
Abstrakt
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.
Seiten: 277-307
DOI: 10.1007/978-94-007-4438-7_15
Referenz:
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.