  In our terminology, Maddy's heterogeneous naturalism is a trumping thesis. As she puts it, ‘if our philosophical account of mathematics comes into conflict with successful mathematical practice, it is the philosophy that must give’ (1997, 161). Neither philosophy nor science can overturn mathematics' ‘methodological verdicts’ (2007, 361), since they are both extra-mathematical tribunals. However, Maddy takes the philosophy of mathematics as opposed to mathematics proper to be a branch of natural science, as she explains in the following passage: