The most respected scholars in this era published books detailing the evidence for the existence of witches and how to exterminate them.
These books include, but are not limited to
The Malleus Maleficarum (Hammer against Witches)
Demonology, by King James I of England
The Discovery of Witches (1647)
The Wonders of the Invisible World (by Dr. Cotton Mather)
And most importantly, the Bible included references to witches, which sealed the question according to the Puritans.
In seventeenth century New England, intellectuals believed in witchcraft as much as scientists today believe in cancer. Their existence was not debated.
DECISION: Assume that you live in Puritan New England. You only have the scientific knowledge of the world that is available at the time. You probably accept the Bible as authoritative. You also respect the great scholars such as Cotton Mather. Do you think you would you believe in witches? Do you think you would be worried about them?
Click here to discover the Puritans' view