himself vs himself

This is a difficult question; to determine whether William Wilson is, in fact, normal, we consider a few stipulations. Firstly, "normal" is a fairly relative term. What is normal in this story? Very little, at least not through the lens of our speaker. Even the house he went to school in seems warped; though he describes it as a "spirit-soothing" places, he doesn't fail to note the "gigantic and gnarled trees." Therefore, we must apply the same subjective terms to the way our speaker describes himself.
William Wilson certainly doesn't think he is normal; from the start, he describes himself as being a "cause of serious disquietude to his friends," and that it was perhaps that he was "left to the guidance of his own will" that he was such trouble to himself and to others. However, though he is very quick to notice his own introspective faults, he remains (perhaps willfully) in the dark about his other, William Wilson part II. If we return to the primary question, as to whether William Wilson part I is "normal," I would say that, to some extent, he is. What he is essentially doing is focusing on his internal faults, as opposed to his external faults, the latter represented by William Wilson part II. While he finds it easy to criticize himself for being "weak-minded," he cannot conceptualize that he may have external faults as well. Thus, his creation of William Wilson part II; he detests William Wilson part II for being "rebellious," for continuing to pursue his shared interests, hobbies, etc, something that he fears will sully their shared name.
This projection of himself is essentially a projection of his "bad side;" while anxiety about selfhood is presumed to be "normal," anxieties about the ego, about inheritence and about name are viewed in the public eye to be ugly. When Wilson I kills Wilson II, and Wilson II utters those searing words ("how utterly thou hast murdered thyself"), he is not merely stating the obvious; in his quest to rid himself of his "evil" and "hated" outside (ego, appearance, etc), he had shed himself of his inside. So no, I don't think Wilson is insane, or crazy. Just a lil' insecure, that's all.