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jimrandomh comments on Harry Potter and the Methods of Rationality discussion thread, February 2015, chapter 108 - Less Wrong Discussion
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Harry and Quirrell are about to enter the room containing the Mirror of Erised (desire), which shows the viewer's deepest desire. It contains the philosopher's stone, and (Ch. 104)
So, what is Harry's deepest desire? There are several candidates, but I think a strong contender is a Quirrell who isn't evil. Transfiguration can only create things that already exist. It is plausible that being seen in the mirror, modified as it is by the magic of the Stone, counts as existence for this purpose. So, Harry's win condition is: transfigure Quirrell into redeemed Quirrell. Due to the destructive interaction of their magics, this would require disabling Quirrell and then getting someone else to do the transfiguration.
That's his (currently strongest) instrumental desire. What is his terminal desire? Something about humanity conquering death and reaching towards stars perhaps...
Question is, which desire does the mirror show?
Perhaps neither. Canon Harry originally saw himself surrounded by a family, a desire which was both obviously unfulfillable and outside Harry's known range of explicit wishes (we know he wishes his parents were still alive, but the mirror showed a more extended family of whom Harry had never thought as far as we know).
For more direct relevance, Ron saw himself being popular and successful (terminal desire) but at the end of the book Harry saw himself finding the Stone (instrumental desire).