"Answers Given" joke

Jon and Adam are in a mental institution. This place has an annual contest, where they pick two of the best patients and give them two questions. If they get them correct, they are deemed cured and are free to go.
Jon is called into the doctor's office first and asked if he understands that he would be free if he answers the questions correctly. The doctor says, "Jon, what would happen if I poked out one of your eyes?"
Jon answers, "I'd be half blind, doc."
"That's correct. What if I poked out both of your eyes?"
"I'd be completely blind." The doctor got up, shook his hand and told him he was free.
On Jon's way out, while the doctor is filling out the paperwork, Jon mentions the exam to Adam. He tells him what questions are going to be asked, and also the answers. Adam is called in. The doctor goes through the formalities and asks, "What would happen if I cut off one of your ears?"
Adam, remembering what Jon said was the correct answer, says, "I'd be half blind."
The doctor is a little puzzled, but he carries on. "What if I cut off both of your ears?"
"I'd be completely blind." Adam answers.
"Adam, can you explain how you'd be blind?"
"My hat would fall over my eyes."