To make any contribution worth caring about, a philosopher's study of Shakespeare should do three things. First and most centrally, it should really do philosophy, and not just allude to familiar philosophical ideas and positions. It should pursue tough questions and come up with something interesting and subtle--rather than just connecting Shakespeare to this or that idea from Philosophy 101. A philosopher reading Shakespeare should wonder, and ponder, in a genuinely philosophical way. Second, it should illuminate the world of the plays, attending closely enough to language and to texture that the interpretation changes the way we see the work, rather than just uses the work as grist for some argumentative mill. And finally, such a study should offer some account of why philosophical thinking needs to turn to Shakespeare's plays, or to works like them. Why must the philosopher care about these plays? Do they supply to thought something that a straightforward piece of philosophical prose cannot supply, and if so, what?
I don't understand a word of it, but I've never let that stop me before. There's plenty of folks in the audience who are far more well-read than I.