 The two approaches discussed in Sections 3 and 4—a priori rationalism and naturalized empiricism—are both in some sense extreme. Simplicity principles are taken either to have no empirical grounding, or to have solely empirical grounding. Perhaps as a result, both these approaches yield vague answers to certain key questions about simplicity. In particular, neither seems equipped to answer how exactly simplicity ought to be balanced against empirical adequacy. Simple but wildly inaccurate theories are not hard to come up with. Nor are accurate theories which are highly complex. But how much accuracy should be sacrificed for a gain in simplicity? The black-and-white boundaries of the rationalism/empiricism divide may not provide appropriate tools for analyzing this question. In response, philosophers have recently turned to the mathematical framework of probability theory and statistics, hoping in the process to combine sensitivity to actual practice with the ‘trans-empirical’ strength of mathematics.