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Dilemmas
Colloquially, a “dilemma” is a situation or argument with unsatisfactory or undesirable choices. There’s a fork in the road, and one irreversible choice has to be made, yet both options are not good.
Simple Constructive Dilemma . . .
Either A or B.
But if A then C, and if B then C.
Therefore, C.
Complex Constructive Dilemma. . .
Either A or B.
But if A then C, and if B then D.
Therefore, either C or D.
Simple Destructive Dilemma. . .
If A, then B and C.
But either not B or not C.
Therefore, not A.
Complex Destructive Dilemma. . .
If A then C, and if B then D.
But either not C or not D.
Therefore, either not A or not B.
Construction of Dilemmas
A dilemma will contain two premises:
(1) a disjunctive proposition
(2) a proposition that will be a conditional or contain multiple conditionals
The dilemma’s “formal” structure is not what makes it especially interesting.
What makes it interesting is its “informal” (or “material”) uses in real life, in debates, and in philosophical puzzles. In such dilemmas, it’s essential that it will lead to an undesirable conclusion. And the dilemma must be exhaustive, i.e., it lists all of the alternatives.
Complex Destructive Dilemma Example
(taken from Principles of Logic by George Joyce, p. 211):
“If he were intelligent, he would see the worthlessness of his argument; if he were honest, he would own himself wrong. But either he does not see that his arguments are worthless; or seeing it, he will not own himself in the wrong. Therefore, either he is wanting in intelligence, or he is dishonest.”
The above example is formally “destructive” because one of the consequents (of either of its conditionals) must be false. That is, either he doesn’t see the worthlessness of his argument or he will not own himself wrong. It is formally “complex” because those consequents are different.
In (mathematical) propositional logic, we can represent that example this way:
Premise 1: (I → W) & (H → O)
Premise 2: -W v -O
Conclusion: -I v -H
Note that the “[complex] destructive dilemma” is, definitely, formally valid!
When constructing your own dilemma, generally speaking, it’s first important to consider the conclusion you desire to prove. Next, think of two alternatives, which are ideally mutually exclusive and together exhaustive, that lead to that conclusion. Finally, create the dilemma. One premise is the “either-or” disjunction that forces the opponent into a choice between the two alternatives. The other premise is the “if, … then” conditional that helps to take your opponent to the conclusion.
Responding to Dilemmas!
Since a dilemma is predicated on being exhaustive and on leading to an undesirable conclusion, insofar as it is shown not to be exhaustive or not to lead to an undesirable conclusion, a dilemma can be shown not to work.
Alternatives in a dilemma are called “horns.” The question, then, must be if those horns are exhaustive. If there is another alternative not given and this new alternative does not lead to something undesirable, then we can “escape between the horns.”
Note that this implies that a dilemma is strongest when the alternatives involve contradictories (p versus non-p) such that there is no possibility of another alternative and, therefore, no escaping between the horns.
It also might be the case that at least one “horn” of the dilemma actually doesn’t lead to the bad consequences. (The premise with the conditional[s] might be false.) If this is the case, then we are “taking the argument by the horns.”
Let’s return to the example above: “If he were intelligent, he would see the worthlessness of his argument; if he were honest, he would own himself wrong. But either he does not see that his arguments are worthless; or seeing it, he will not own himself in the wrong. Therefore, either he is wanting in intelligence, or he is dishonest.”
How can the gentleman respond?
He can take the argument by the horns! The first premise, he can claim, is false. He admits he is intelligent but denies that his argument is worthless. In other words, the link between the antecedent and consequent he denies.
Rebutting the dilemma?
Another approach, especially popular due to its rhetorical appeal, is to offer a counter-dilemma that shows the given alternatives lead to a conclusion that is opposed by the person who offered the initial dilemma. This is called “rebutting the dilemma.”
The problem with “rebutting the dilemma,” though, is that it doesn’t show that the original argument was unsound. The counter-dilemma derives a conclusion exactly contradictory to the original. The new premise will contain contraries vis-à-vis the original. To be sure, sometimes rebutting the dilemma will show that both dilemmas only reach “half-truths,” at best. So, it does have its logical uses. The following is a classic example. . .
Athenian mother telling her son not to enter politics: “If your speech is just, men will hate you; and if is unjust, the gods will hate you; but your speech must be one or the other; therefore, you will be hated.”
Son’s counter-dilemma: “If I say what is just, the gods will love me; and if I say what is unjust, men will love me. My speech must be the one or the other; therefore, I shall be loved.”
Another Classic Dilemma: The Litigiosus
Protagoras, a pre-Socratic rhetorician, agrees to instruct the poor student Eulathus. By agreement, Eulathus must pay the remaining half of the bill after he wins his first lawsuit. Some time passes. Eulathus becomes involved in no lawsuits and, therefore, didn’t pay.
So, Protagoras tells Eulathus he will take him to court. He gives a dilemma. On the one hand, Protagoras argues, if the court rules in his favor (i.e., Protagoras’ favor), then Eulathus will have to pay. However, if, on the other hand, the court doesn’t rule in his favor (i.e., Protagoras’ favor), then Eulathus will have to pay based on the terms of the agreement.
Eualthus responds, on the contrary: If the court rules against Eualthus, then by the terms of the agreement he doesn’t have to pay. And, if the court rules in favor of Eualthus, then he doesn’t have to pay.
Solution? Supposedly, the courts didn’t come to a decision. But we can solve it as long as we reject both dilemmas. Answering it must be based either on the agreement or on the court ruling exclusively (unlike the dilemmas offered).
Protagoras can “win” in the following way: He can stick to the terms of the agreement and then lose in court, since Eualthus has yet to win a case. Then Protagoras can bring Eualthus back to court. This time Protagoras will win, since Eualthus has won his first case.
And Another Classic Dilemma: The Euthyphro
The Euthyphro Dilemma has been debated for some time, tracing back to Plato’s Socratic dialogue. God commands us to do what is good. The question to ask, though, is what makes something good. On reflection, it seems to be the case that either morality becomes arbitrarily based on God’s will, which then could change what was once an “evil” to a “good” (or vice versa), or to something independent of God and, thus, His sovereignty.
Both horns lead to what appear are bad consequences – and in fact, they are bad!
Solution?
It is possible to “escape between the horns.”
In other words, there is a third option. This is based on what is called “divine simplicity.” Rather than God “having” goodness, God is goodness itself. Goodness is not independent of God nor is goodness based on God’s arbitrary will. In fact, the traditional view is that goodness and God’s will are not distinct from each other such that what is objectively good cannot be different from what God immutably wills. Prima facie, understanding this can be difficult for our discursive minds, but it is the strongest solution to the dilemma.
Technically, a man’s actions may or may not have the attribute of goodness, and that attribute is a predicate in the role of a contingent participation in goodness, but God’s goodness is in no way separate from His very being nor is His goodness any kind of contingent participation in goodness judged from an “external” standard. Hence Fr. Reginald Garrigou-Lagrange writes, “Only the Savior can say, ‘I am the truth and the life,’ which presupposes that he can say: ‘I am Being Itself. Ego sum qui sum (Exod 3:14)” (The Sense of Mystery, p. 68).
The Trilemma, The Tetralemma, etc.
Above and beyond the dilemma, there is the trilemma, tetralemma, pentalemma, and polylemma. Obviously, there’s no “logical” reason that an argument stick with only two horns! So, we can have the disjunction p or q, or something like p or q or r.
There’s really no limit to the number.
- Trilemma – three horns
- Tetralemma (aka quadrilemma) – four horns
- Pentalemma (aka quintilemma) – five horns
- Polylemma – more than five horns
Perhaps the most famous example is “Lewis’s trilemma.”
C. S. Lewis argued, in his Mere Christianity (Bk. II, Ch. 3), that Jesus must either be a lunatic, a liar, or the Lord.
“A man who was merely a man and said the sort of things Jesus said would not be a great moral teacher. He would either be a lunatic – on level with the man who says he is a poached egg – or else he would be the Devil of Hell. You must make your choice. Either this man was, and is, the Son of God: or else a madman or something worse. You can shut Him up for a fool, you can spit at Him and kill Him as a demon; or you can fall at His feet and call Him Lord and God” (p. 52).
Is this really a trilemma? Strictly speaking, not all of the three options lead to undesirable conclusions. Therefore, in that strict sense, it is not a trilemma. Modern logic, nevertheless, treats inferences like the “destructive dilemma” without considering if the alternatives are bad or not. Under a more loose definition, then, we can treat it as a trilemma.
Does C. S. Lewis exhaust all other possibilities? It is not exhaustive, and so from the strict point of view of logic, it’s not as strong of an argument as may appear. There are other possibilities. Those would have to be listed and then considered.
To be fair, his argument presupposes a hermeneutics. When Lewis is read within that context, the argument is more powerful because it closes off some of the other possible interpretations someone might give it. Given the cultural context that Jesus was in, it seems we can give more definitive and accurate interpretations of his sayings. For example, it’s not plausible to think Jesus was engaging in some kind of “New Age” mysticism where everything said is metaphorical.