I've been reading Demonology by James I [1] as an excercise in trying to understand the thought process behind those who genuinely believed in witches and sought to 'punish' them.
James I reasoning seems fairly logical if you accept certain axioms (truth of the 'scripture' for example). However witchcraft trials at the time seem to have relied heavily on confessions extracted by torture.
It seems obvious to me that if you torture someone long enough, they will confess to anything. However according to Wikipedia James I himself often personally oversaw torture of the accused and I do get the impression he genuinely believed in witches.
Why then, didn't he or others at the time think "Maybe these people are confessing because of the torture rather than being actual witches"?
[1] http://www.gutenberg.org/files/25929/25929-h/25929-h.html
I'd recommend reading "Cunning-Folk and Familiar Spirits" by Emma Wilby. In it, she makes a convincing case that there was a survival of pre-Christian fairy faith into early modern Britain, and that in many of the witchcraft cases she examines, the people charged were practicing what they believed to be magic with the assistance of what they believed to be a fairy familiar. Obviously most people will make false confessions under torture, but not all confessions were extracted under torture. Many people freely confessed to dealings with fairies or spirits because execution was actually fairly rare, with many defendants simply set free after they agreed to repent of their ways and live a pious life.
So if there were people out there genuinely practicing magic, it becomes easier to believe that a confession extracted under torture is real.