After some experience meditating, it's easy to come to the conclusion that "I am not my thoughts." The more closely one observes one's experience, the more one sees that one is indeed not any of his perceptions, but is merely witness to them. Thoughts come, thoughts go, perceptions come, perceptions go, and "I" stand alone as observer of them all.
But it's easy to get stuck at this realization, and feel there's no more left to discover. Can we go deeper?
Imagine looking at a dog. Now notice that you are not looking at a dog, but more precisely at the image of a dog. For example, in a dream you could have exactly the same visual experience, but there's no dog there.
More generally, one does not experience things, but perceptions of things.
Now, what does it mean for something to be a perception? Would it still deserve that title if it were not being perceived? Was that image of a dog just waiting somewhere for you to perceive it, or was it an "image" only while it was being perceived? Investigate this question very closely in your experience, and resolve that a perception that is not being perceived isn't a perception at all -- it's just the thought of that perception.
Perhaps you can feel the steel jaws of logic getting their grip.
Every "perception" already contains "the perceiving" of it. It is a self-contained unit, and has no need for some "perceiver" to come along and perform some more perceiving. There's no job left for such a perceiver to do.
At best, one could say that there's a subjective aspect to experience, which we sometimes conceptualize as a separate "witness." But like all other conceptualization, it doesn't quite touch the deep truth of things, it seems.