He kept up a correspondence with Cotton Mather, and with his father, Increase Mather, through the medium of which he stimulated and encouraged them in their proceedings against supposed witches in Boston and elsewhere.  The divines of that day seem to have persuaded themselves into the belief that the doctrines of demonology were essential to the gospel, and that the rejection of them was equivalent to infidelity.  A writer in one of our modern journals, in speaking of the prosecutions for witchcraft, happily and justly observes, “It was truly hazardous to oppose those judicial murders.  If any one ventured to do so, the Catholics burned him as a heretic, and the Protestants had a vehement longing to hang him for an atheist.”  The writings of Dr. More, of Baxter, Glanvil, Perkins, and others, had been circulating for a long time in New England before the trials began at Salem.  It was such a review of the history of opinion as we have now made, which led Dr. Bentley to declare that “the agency of invisible beings, if not a part of every religion, is not contrary to any one.  It may be found in all ages, and in the most remote countries.  It is then no just subject for our admiration, that a belief so alarming to our fears, so natural to our prejudices, and so easily abused by superstition, should obtain among our fathers, when it had not been rejected in the ages of philosophy, letters, and even revelation.”

The works on demonology, the legal proceedings in prosecutions, and the phraseology of the people, gave more or less definite form to certain prominent points which may be summarily noticed.  Several terms and expressions were employed to characterize persons supposed to be conversant with supernatural and magic art; such as diviner, enchanter, charmer, conjurer, necromancer, fortune-teller, soothsayer, augur, and sorcerer.  These words are sometimes used as more or less synonymous, although, strictly speaking, they have meanings quite distinct.  But none of them convey the idea attached to the name of witch.  It was sometimes especially used to signify a female, while wizard was exclusively applied to a male.  The distinction was not, however, often attempted to be made; the former title being prevailingly applied to either sex.  A witch was regarded as a person who had made an actual, deliberate, formal compact with Satan, by which it was agreed that she should become his faithful subject, and do all in her power to aid him in his rebellion against God and his warfare against the gospel and church of Christ; and, in consideration of such allegiance and service, Satan, on his part, agreed to exercise his supernatural powers in her favor, and communicate to her those powers, in a greater or less degree, as she proved herself an efficient and devoted supporter of his cause.  Thus, a witch was considered as a person who had transferred allegiance and worship from God to the Devil.