Grab the Horns of a Dilemma with Both Hands

by Dr. Kim Johnson at The Lukeion Project

Suppose you are a young hobbit, and you are trying to decide whether to go with your friends to Minas Tirith for the defense of Gondor or to go alone to Mount Doom to destroy the One Ring. Both choices seem bad: if you go straight to Mount Doom you will certainly be alone and may be captured before you are able to accomplish your goal. If you go to Minas Tirith, you are guilty of abandoning your quest, and the ring might be captured even within the stronghold of the White City. Either way, the ring will be captured, and you will probably die.

Or suppose that you are a king, deciding whether to follow your friends beyond the edge of the world.If you go, you are abandoning your kingdom and disobeying Aslan. If you don’t go, you will never see what lies in the utter east. 

These examples from fiction (The Two Towers and The Voyage of the Dawn Treader) are types of a logical argument called a “dilemma.” You have two courses of action, both of which lead to some undesirable outcome, and you must take one of these courses of action! Therefore, one of the undesirable outcomes is bound to occur. Written symbolically, the argument is as follows: 

 

The first premise of the argument is called the conjunctive part because it consists of two implications combined with a conjunction. This means that we are assuming both the implications are true. This is where we list the terrible things that might happen if you pursue one of your possible courses of action.  Think of an auntie warning you, “but if you don’t wear your jacket, you’ll get cold!”

The second premise is called the disjunctive part which combines the two possible actions you can take.  This premise implies that you must take one of the two courses of action involved. Sometimes the fact that one will happen is obvious: Either you go alone or you don’t go alone, either you travel on or you don’t travel on.  Sometimes the fact that one must happen is not obvious: either you wear a coat or shirtsleeves (but you might wear a sweater). 

The conclusion is what must follow from the two premises. Sometimes the conclusion is just one statement: whether you go to Gondor or Mordor, you’re going to die!  But often the conclusion states that one of the two terrible consequences from the first premise will happen.

The problem with facing a dilemma is that it is a valid form of argument. If you agree with the premises, the outcome is bound to follow. Since the argument is valid, disagreeing with the conclusion would seem to be illogical. But if you are if you are at the boundary of Mordor, or even if you are just in an argument with your parents, how do you get around a dilemma while still retaining your claim to be logical?

There are three generally recognized ways to defeat a dilemma: Going between the horns, grasping the horns, or rebutting the horns.

The first way to counter a dilemma is to go between the horns. In Frodo’s case, there is a third option that doesn’t involve going with everyone to Minas Tirith or going into Mordor alone. Looking at the logical structure of the argument, this boils down to saying that the disjunctive statement (pVr) does not include all the options.  He could go to Mordor alone, or he could also go to Minas Tirith, or take a third option: he and Sam could go to Mordor together. The premise “You can go to Mordor alone or you can go to Minas Tirith” turns out to be false. Since the premise is false, the conclusion does not follow from the argument.

The second way to counter a dilemma is to seize the horns. Aside from being a great mental image, this method disputes the validity of one of the implications in the premises. Although Caspian fears at the end of The Voyage of the Dawn Treader that he will never see the utter east if he doesn’t go now, those of us who have read further know that his fear is unfounded. The implication “If I  don’t go now, I will never see Aslan’s country” is untrue, and that means the conclusion, “I will either disobey Aslan or never see Aslan’s country” doesn’t follow from the argument.  

The final way to counter a dilemma is to rebut the horns. Rhetorically, this is seen as the strongest rebuttal, since it does not dispute any of the facts but offers a new perspective based on the same argument. Frodo’s dilemma can be rephrased as follows: if he brings his friends to Mordor he will be in a better position to defeat Sauron. If he leaves them he will not put them in more danger so either he will keep them safe away from Mordor or he will keep them safe by defeating evil. Instead of debating the premises of your opponents argument, you give them a new though also difficult, argument to defeat. It does not deny the conclusion of the argument, but it does make clear that there is not only one viewpoint of the argument. I personally find this the least satisfying way to rebut a dilemma, since the terrible consequences do not go away and we just have to take into account some happier consequences instead.

Dilemmas are often used in literature to move the story forward or to create tension and uncertainty. It could be that dilemmas are used so frequently in stories because we face them in real life. Do I go out with friends and miss turning in my Latin homework, or do I turn in my Latin homework and not go out with friends? Now that I think about it, this is not really a dilemma… But at least now you know the precise places to attack the dilemma. You can attack the disjunction in the premises to go between the horns: You only considered two things that could happen, but there may be another option which you haven’t considered yet. You could attack the implication in the premises by grasping the horns: One of the horrible consequences does not have to happen. Or you could rebut the horns by asserting there is another perspective which hasn’t been considered yet. In any case, the dilemmas we face can be overcome with clear thinking.