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.
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