That statistics is so often a guide to policy is testimony to the unusual prevalence of statistical issues in policy discussions. It is easy to think of policy questions to which (say) chemistry is relevant, and also easy to think of issues to which chemistry has nothing to contribute. I find it hard to think of policy questions, at least in domestic policy, that have no statistical component. The reason is of course that reasoning about data, variation, and chance is a flexible and broadly applicable mode of thinking. That is just what we most often mean by a liberal art.Moore then goes on to discuss the nature of the liberal arts, which he divides into "philosophical" and "oratorical" traditions (one seeks the truth come what may, the other seeks to instill virtues that are valuable for citizenship); and he suggests that the liberal arts should be thought of as a sort of add-on to our evolutionary heritage. We can instinctively make out the features of a darkened room, say, but we need training to determine if the data in a scatterplot is strongly or weakly correlated.
I thought this was an interesting thesis, in that it's a kind of modern update of the medieval quadrivium: arithmetic, geometry, music, and astronomy. Paired with the trivium (grammar, rhetoric, and logic), it helped prepare students for the more difficult studies of philosophy and theology. (A style of education that, in turn, seems to derive from Socrates' curriculum for the guardians in the Republic.) We live in a post-metaphysical age, of course, so studying mathematical subjects is no longer about training the mind for understanding God, the Good, or Being. But having at least some background in quantitative methods is essential for understanding the modern world: To be able to answer questions about crime, health care, global warming, etc., means, in part, pulling oneself out of the realm of the anecdotal and personal, and knowing how to manipulate data responsibly. Perhaps a modern version of Plato's Academy would have inscribed on its gate, not "ἀγεωμέτρητος μηδεὶς εἰσίτω" (Let no one ignorant of geometry enter), but "ἀστατίστικος μηδεὶς εἰσίτω" (Let no one ignorant of statistics enter).