Can You Solve This Jewish Riddle?

This is an old Jewish joke/parable that you can find all around but in case you have not read/heard it, here is a parable of men going down a chimney. Can you solve it? 

A young man knocks on the door of the Rabbi. The man says, “I would like to study the Talmud.”

“Do you know Aramaic and Hebrew and have you studied the Torah?” the rabbi asks.

“No, Rabbi. But don’t worry. I graduated summa cum laude in philosophy, and just finished my doctoral dissertation on Socratic logic. I believe that I am ready to study the Talmud.”

The rabbi says, “If you wish I am willing to examine you in logic, and if you pass that test I will teach you Talmud.”

The young man agrees.

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The Rabbi holds up two fingers. “Two men come down a chimney. One comes out with a clean face, the other comes out with a dirty face. Which one washes his face?”

The one with the dirty face washes his face,“ he answers wearily.

“Wrong. The one with the clean face washes his face. Examine the logic. The one with the dirty face looks at the one with the clean face and thinks his face is clean. The one with the clean face looks at the one with the dirty face and thinks his face is dirty. So the one with the clean face washes his face.”

 “I cannot believe I did not think of that!” the young man says. “Give me another test.”

The rabbi again holds up two fingers. “Two men come down a chimney. One comes out with a clean face, the other comes out with a dirty face. Which one washes his face?”

 "The one with the clean face washes his face, you just said.”

 “Wrong. Each one washes his face. Examine the logic. The one with the dirty face looks at the one with the clean face and thinks his face is clean. The one with the clean face looks at the one with the dirty face and thinks his face is dirty. So the one with the clean face washes his face. When the one with the dirty face sees the one with the clean face wash his face, he also washes his face. Therefor they each wash their face.”

“I didn’t think of that, but now I understand. Test me again.” says the young man.

The rabbi holds up two fingers. “Two men come down a chimney. One comes out with a clean face, the other comes out with a dirty face. Which one washes his face?”

 “Each one washes his face."  

“Wrong. Neither one washes his face. Examine the simple logic. The one with the dirty face looks at the one with the clean face and thinks his face is clean. The one with the clean face looks at the one with the dirty face and thinks his face is dirty. But when the one with the clean face sees the one with the dirty face doesn’t wash his face, he also doesn’t wash his face. So neither one washes his face.”

The young man presses on. “I am qualified to study Talmud. Please give me one more test.”

The rabbi groans as he lifts two fingers. “Two men come down a chimney. One comes out with a clean face, the other comes out with a dirty face. Which one washes his face?”

 “Neither one washes his face.”

 “Wrong. Do you now see why Socratic logic is an insufficient basis for studying Talmud? Tell me, how is it possible for two men to come down the same chimney, and for one to come out with a clean face and the other with a dirty face? Don’t you see? The whole question is  foolishness! If you spend your whole life trying to answer foolish questions, all your answers will be foolish, too.”