psychosociopathic
He looked but some subconscious part of his vast mind must have prevented him from seeing. He could have seen if he wanted to, but he just didn't want to believe the truth. It was like that with Redbeard and Mary. Some part of him knew, but he didn't want to listen. It was all very irrational and didn't make sense, which was the very aspect that annoyed Sherlock beyond belief. He didn't like not knowing.
So when Doctor John Watson showed him the x-ray of a rather large tumor in his brain, he simply nodded, somehow expecting this very moment to happen exactly when it did. Knowing that he didn't know was nerve wracking, but actually knowing wasn't as reassuring as he thought it would be.
.o.O.o.
A bit of context: Taking place after Mary dies, ignoring The Final Problem and the fact that there is a there is a third Holmes. As if Moriarty were actually still alive. Miss me?