A New Interpretation of the Indispensability Argument
by Seahwa Kim
I. The Understanding of the
The Quine-Putnam indispensability argument
runs as follows:
(i) We have reason to believe in Fs if Fs
are indispensable to our best available
(ii) Mathematical entities are indispensable
to our best available science.
(iii) Therefore, we have reason to believe
in mathematical entities.
According to the standard understanding, in
order to refute the argument the nominalist
has to show that mathematical entities are
dispensable by providing an at least as good
theory of the same phenomena that is not
ontologically committed to mathematical
entities. Most philosophers who write in this
area, including John Burgess, Mark Colyvan,
Hartry Field, Penelope Maddy, and Gideon
Rosen, accept the standard understanding.
Many nominalists who accept the standard
understanding propose nominalistic paraphrases
or alternatives, claiming that these are
either equally good or better than our current
scientific theories. Platonists deny that they
are either equally good or better.