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The dispute is over land. Putnum seems to have this quarrel with a number of people. He claims that a portion of several people's property belongs to him, and that it was willed to him.
One of these land disputes is between Putnam and Proctor. Proctor has a section of woods that Putnum believes belongs to him. Putnum accuses Proctor of stealing his lumber, but Giles Cory insists that Putnum's grandfather willed land that was not his to leave and that he tried to will away Cory's land as well, but knew he couldn't get away with it.
Putnum has disputes over land and boundaries with all of his neighbors. It is his land-lust, according to Cory, that prompts him to instruct his daughter to cry witch against his neighbor, Mr. Jacobs, knowing that the Jacobs land will be forfeit and put up for auction as a result.