The difference between the ordinary person and the enlightened is that the ordinary person accepts the dual world as 'real', while the enlightened see into its illusory nature, but at the same time, must still continue to function in a world of clocks, schedules, money, good and evil, etc. It's just that he is awake within the dream-illusion, while the unenlightened are still asleep. The case for 'true reality' (actually, there is nothing to prove), is made not on the basis of rational thought, but rather on the basis of reality itself, rational thought and conventional language merely being the vehicles through which a communication must be made to the unenlightened. In other words, when the enlightened person attempts to communicate what he knows to others, he is using the source that is reality itself to draw upon, but must use conventional language in a paradoxical way so as to awaken the intuitive mind of the listener, as in:
"What did your face look like before your mother was born?"
Sometimes, silence itself is utilized, as when the Buddha simply twirled a flower before the assembly. Everyone was silent. Only Mahakashyapa smiled. Buddha said: "I have the eye treasury of the true teaching, the heart of nirvana, the true form of non-form, and the ineffable gate of dharma. It is a special transmission outside the teaching. I now entrust it to Mahakashyapa."
Appearances are not reality. They are appearances only.
The snake that is actually a rope and thought to be real is an appearance only. It is not real. It never existed to begin with. In my example, there never was a double-world at all. Only the real world ever existed. The veil that was the lenses were never detected to exist. Had they been detected, the illusion they produced may have been discovered.