Mary Leng offers a defense of mathematical fictionalism, according
to which we have no reason to believe that there are any
mathematical objects. Perhaps the most pressing challenge to
mathematical fictionalism is the indispensability argument for the
truth of our mathematical theories (and therefore for the existence
of the mathematical objects posited by those theories). According
to this argument, if we have reason to believe anything, we have
reason to believe that the claims of our best empirical theories
are (at least approximately) true. But since claims whose truth
would require the existence of mathematical objects are
indispensable in formulating our best empirical theories, it
follows that we have good reason to believe in the mathematical
objects posited by those mathematical theories used in empirical
science, and therefore to believe that the mathematical theories
utilized in empirical science are true. Previous responses to the
indispensability argument have focussed on arguing that
mathematical assumptions can be dispensed with in formulating our
empirical theories. Leng, by contrast, offers an account of the
role of mathematics in empirical science according to which the
successful use of mathematics in formulating our empirical theories
need not rely on the truth of the mathematics utilized.
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