  The third of the three naturalisms of interest, mathematical naturalism, is philosophically but not mathematically revolutionary. Mathematically, it is as conservative as can be: no standards other than mathematical ones are relevant to the assessment of mathematical claims. Thus no accepted mathematics is overturned from without. Yet mathematical naturalism is a revolutionary stance in the philosophy of mathematics.  To see this, suppose that platonism is part of standard, accepted mathematical practice. In that case, mathematical naturalism entails that there is no further question of its truth. Loosely put, simply because mathematicians (qua mathematicians) are platonists, platonism is the correct philosophy of mathematics. This is clearly out of step with philosophical practice: philosophers look to mathematicians' views (qua mathematicians) as defeasible data for the philosophy of mathematics, not its conclusion. Thus we see that the simple characterisation of mathematical naturalism as conservative is not quite right: though mathematically conservative, it is philosophically revolutionary.