An appeal to fear, also called “argumentum in terrorem”, is an argumentative fallacy in which the speaker or writer aims at gaining support for an idea based on fear of the alternative being the case. In this example, one is encouraged to keep one´s pet on a leash to keep it safe from danger, the alternative being that, if the pet is not on a leash, it may encounter unforeseen circumstances that could put its life or wellbeing in peril.
