Barber Paradox Possible Solution

They say that there is a "paradox of the sole barber." In a town of just one barber who only shaves those who don't shave themselves, does the barber shave himself?

People who say it's an inescapable paradox say it’s so because the barber can't exist; he defies logic.  After all, if the barber doesn’t shave himself, he would then shave himself; but if he shaves himself, he doesn’t shave himself.  They argue this goes on infinitely and thus negates the barber’s possible existence.

I believe this is fallacious logic and the barber can exist.   The fallacious assumption is that “True” and “False” are a binary in all hypotheticals. In this one, it is not the case and something being True and False at the same time isn't a paradox. The barber shaves himself and doesn't, which cancels out.  That still leaves us with a barber with motive and a quantum state of 50/50. 

The problem assumes a barber who either wants to shave or not to begin with. The further operating instructions mathematically cancel out, so you just encounter whatever we started with which is a quantum state of 50/50. 50 percent of the time he shaves himself when you check, and 50 percent of the time he doesn’t. No paradox, just a misunderstanding of math and statistical probability.

Literally walk up to the barber and ask, "are you going to shave today?" He'll say yes or no and that's your answer. The math doesn't create an impossibility; it simply cancels out the instructions.