My favorite internet pundit has written a piece on ambiguity in photography. As usual, he's got the highest word:idea ratio on the internet, but as happens from time to time, he's on to something.
Ambiguity is a good thing to keep in mind. The idea is, and this is clearly his idea as well, to leave space for the viewer's imagination. As with all Art, it's as much about creating space for the viewer's conception of the piece as it is about the ideas embedded in the piece.
Ming's problem is that he started here, and then got lost in "How to use DoF to obscure the details of objects" which is to completely miss the point. Sure, making the literal objects in the frame unclear can be useful, but it's not the only way to create space for the imagination. A good portrait might be sharp, fully lit, leaving absolutely nothing in the frame anything less than fully visible. There are no mysteries as to what you're looking at. And yet, yet, the expression of the sitter, what is she thinking?
See also the Mona Lisa.
Whether you choose to obscure what one might choose to describe as The Facts of the Frame is usually almost irrelevant. Who cares if the building in the background is a skyscraper or just a pylon? Absent other reasons to think it's important, the viewer will assume it's irrelevant, not mysterious. Blurring out irrelevant details does not create space for the imagination, generally.
Mystery and ambiguity are potent tools, yep. But it's the mystery and ambiguity in the picture that matters, not the objects within (or left out of) the picture.
As always, worry about the endpoint rather then the point 2 feet down the path.