Challenges to the value of art are not new. Since the time of Plato, lovers of art have had to justify its importance. We encounter one line of defence in Kierkegaard’s writings. Like other 19th century thinkers, he embraced a ‘cognitivist’ picture of the arts. He located art’s value in its ability to teach or educate—to provide cognitive benefits. There was pushback against this view in Kierkegaard’s day. Many German Idealists were willing to concede that art had the ability to teach important truths. But, they objected, it could not do so as well as philosophy or the sciences. For the lessons communicated through works of art are never as clear-cut or well-supported by reasons. In this paper, I explain how Kierkegaard turns this objection on its head. First, he argues that art does not teach ‘directly,’ as philosophy and the sciences typically do. It does not instruct by explicitly telling us truths and offering supporting evidence. Instead, art educates indirectly by helping us make our own discoveries. Second, Kierkegaard argues that the fact that art does not teach us straightforwardly is not a defect, as the Idealists maintained. On the contrary, it is precisely because art teaches us indirectly that it teaches us better than philosophy and science manage to do. The centrepiece of Kierkegaard’s ‘indirect cognitivism’ is the idea that cognitive value tends not to reside in the work of art itself. Works of art seldom contain or convey much knowledge. Nevertheless, they provide us with tools we can use to acquire knowledge for ourselves. In particular, they offer us lenses through which to see ourselves better or view ourselves afresh. To use Kierkegaard’s expression, works of art matter because they can serve as mirrors in which to see who we really are.