When I read a philosopher (particularly someone like Schopenhauer or Kiergegaard) how would I be able to tell if I was engaged philosophically rather than aesthetically?
On one widely-accepted picture, philosophical engagement is marked by a particular sensitivity to the truth or falsity of claims made, and to the structure and strength of arguments presented, whereas aesthetic engagment is marked by a particular sensitivity to the ways in which the claims are presented -- their degree of elegance, harmony, simplicity, emotional purity, etc. This distinction can be difficult to make in the case of philosophical authors for whom the specific ways in which the ideas are presented seems tighly linked to the content of the claims being made. Schopenhauer and Kirkegaard are two such authors: other examples may include Plato, Nietzsche, Wittgenstein and Iris Murdoch. That said, it still seems possible to distinguish roughly between an author's engaging one's attention by presenting something beautiful, and an author's engaging one's attention by presenting something true or well-reasoned.