A Nominalist's Dilemma and its Solution
Authors
Otávio Bueno and Edward N. Zalta
Reference
Philosophia Mathematica, 13 (2005): 297-307.
Abstract
Abstract: Current versions of nominalism in the
philosophy of mathematics have the benefit of avoiding commitment to
the existence of mathematical objects. But this comes with a cost:
to avoid commitment to mathematical entities, nominalists cannot
take mathematical theories literally, and so, they seem unable to
accommodate mathematical practice. In a recent work, Jody Azzouni
(2004) has challenged this conclusion, by formulating a nominalist
view that doesn't have this cost. In this paper, we argue that, as
it stands, Azzouni's proposal doesn't yet succeed. It faces a
dilemma to the effect that either the view isn't nominalist or it
fails to take mathematics literally. So, in the end, it still
doesn't do justice to mathematical practice. After presenting the
dilemma, we suggest a solution for Azzouni's version of
nominalism.
[Note: The final version has not yet been sent to the publisher. This
version may change in minor ways.]
[Preprint available online in PDF]