Every experience proves the existence of the non-experiencable experiencer, just as every picture proves the existence of a camera, which does not appear in the picture. Here is the logic:
A. To arrive at the meaning of this statement we have to analyze the features common to both the body-mind and the world (the picture). (1) Both are objects of experience, (2) both are matter, (3) both have properties and attributes, (4) both are subject to continuous transformation and (5) both are only available in the waking state.
B. Both the body and mind are insentient, but appear to be sentient.
C. Therefore the body and mind must borrow sentiency from the self (the camera) whose “features” negate the features of the body-mind-sense complex. What are these featureless features? (1) It is not experienciable as an object, (2) it is consciousness, not a material substance, (3) it is free of properties and attributes (nirguna), (4) it doesn’t change, because it is unborn and non-dual, (5) it doesn’t come and go; it is present in all states of mind (waking, dream and deep sleep).
D. You think you are conscious as a person, but you are actually conscious as the self. The person is never conscious.
Why is this logic necessary? The self is only available for a person through inference. But inference is a valid means of direct knowledge because it removes ignorance.