When you imagine a Penrose triangle, what are you imagining?

On the one hand, clearly you can imagine that the world is such that you see such a thing. For this world is such a world. But then "such a thing" is just a particular two-dimensional image. So this isn't what we mean when we put forth the Penrose triangle as something imaginable but impossible.

What is meant is that if we see the Penrose triangle as a three-dimensional object--as we are inclined to see it, by seeing the shading as suggesting variations of depth and shadow, and by seeing each of the acute (in the two-dimensional representation) angles as right angles--then we are seeing it as something which is impossible. And that seems to be correct. The three "sides" of the Penrose triangle could not each be perpendicular to the others and form a triangle as the image impresses they do. (Though it should be possible in non-Euclidean space.)

Greg wrote:

(Though it should be possible in non-Euclidean space.)

(As I think about it, though, when we typically imagine it, we are imagining it in Euclidean space.)

Here are some other candidates for impossible yet imaginable things. I can imagine that the Morning Star and the Evening Star were not identical. I can imagine that human beings speak unsystematic gibberish instead of their usual languages, yet go about their lives just as we do. I can imagine that water lack some of the chemical properties it has (say, those due to its polarity, like its cohesiveness--I can imagine, for instance, that water were more like non-polar liquids in not forming or forming less stable droplets).