Neither. Just good old-fashioned delusional thinking. Unfortunately, though, when it comes to diagnosing, we're not allowed to call anyone delusional if their delusions are consistent with the beliefs of a particular community. So religious fanatics are usually spared a psychiatric diagnosis.
Diagnostic Manual of Mental Disorders, Fourth Edition, Text Revision (DSM-IV-TR) (APA, 2000) defines delusions as false beliefs based on incorrect inference about external reality that persist despite the evidence to the contrary and these beliefs are not ordinarily accepted by other members of the person's culture or subculture.
There's the loophole. I still think a hefty dose of antipsychotics would be worth a try.
