Knowledge of mathematical objects
pp. 155-182
in: Irvine (ed), Physicalism in mathematics, Berlin, Springer, 1990Abstract
Is there a real world of abstract mathematical objects? At first sight it might seem tempting to deny this. However, this denial carries a sting in its tail. If you deny the existence of abstract mathematical objects, then you are committed to rejecting all claims that commit you to such objects, which means rejecting most of accepted mathematics as standardly understood.