In two posthumously published essays, ‘History of Astronomy’ and ‘Of the Nature of that Imitation which takes place in what are called The Imitative Arts’, Adam Smith suggests provocatively that philosophy is an ‘art of imagination’ and that we take the same ‘very high intellectual pleasure’ in appreciating systematic scientific theories and in listening to musical ‘systems’, i.e., complex works of non-programmatic instrumental music. In this paper, I reconstruct the view of imagination, as the cognitive faculty primarily responsible for perception and appreciation of such ‘systems’, that undergirds these claims, and argue that it is to be understood as aiming at ideal ends – in the first instance, at beauty or an order among variety (systematicity). Smith thus offers a distinctive view of aesthetic imagination, as neither freely playing nor imitative (two common views of imagination both in his time and ours) but rather as aiming at, and progressively realizing non-rational norms of order (again, at least in the first instance, an ideal of beauty).