The overriding aim of this paper is draw out and examine the tension that arises from two deeply engrained assumptions about aesthetic experience. First, the alleged pervasiveness or ubiquity of the aesthetic. Second, the perceptual nature of aesthetic experience and judgement. How, if at all, can we square the idea that aesthetics is a matter of perception with the claim that aesthetic qualities can be ascribed to things as diverse as artworks, nature, moral character and mathematical principles? My principal task will be to establish the extent to which, if indeed any, there can be such a thing as non-sensible aesthetic value and which argument(s) might provide the strongest support for this claim.
     We begin by looking at non-perceptual art. Here, I will draw on some of my earlier work on conceptual art, and explore what it might mean to say that non-perceptual art can be experienced aesthetically. Underlying my argument is a re-examination of three closely related issues: first, the notion of aesthetic testimony; second, the possible extension of aesthetic concepts in non-artistic contexts; third, the possibility of an intelligible kind of beauty. We then move beyond the context of art and investigate the way in which aesthetic qualities can play an epistemic role in the scientific domain. Reflecting on the way in which mathematicians tend to appeal to aesthetic qualities as markers or indicators of truth in science might provide us with the material necessary to develop a more satisfactory account of non-sensible aesthetic value.