  Methodological naturalism has three principal and related senses in the philosophy of mathematics. The first is that the only authoritative standards in the philosophy of mathematics are those of natural science (physics, biology, etc.). The second is that the only authoritative standards in the philosophy of mathematics are those of mathematics itself. The third, an amalgam of the first two, is that the authoritative standards are those of natural science and mathematics.  We refer to these three naturalisms as scientific, mathematical, and mathematical-cum-scientific. Note that throughout this entry ‘science’ and cognate terms encompass only the natural sciences.