Strategies for Navigating Through Dilemmas in Logic

Every now and then, an argument corners you. Someone presents a choice – option A or option B – and both feel like traps. You’re told to pick one, and no matter which you choose, the result isn’t good. This is the structure of a logical dilemma, and it has been used in debate, rhetoric, and philosophy for centuries precisely because it feels airtight. But is it really? Logicians have long identified three specific strategies for navigating these traps: escaping between the horns, taking the dilemma by the horns, and rebuttal by counterdilemma. Each one targets a different weakness in the dilemma’s structure. Understanding them doesn’t just make you a sharper thinker – it changes how you engage with arguments altogether.

What is a dilemma in logic? 🔗

In everyday speech, a “dilemma” simply means a tough choice. In formal logic, it has a more precise meaning. A logical dilemma is an argument built from two or more conditional (if-then) premises and a disjunctive premise (either-or), designed to force an opponent into accepting an undesirable conclusion no matter which option they choose. As Wikipedia’s entry on the dilemma explains, the possibilities are called the “horns” of the dilemma – and the structure is designed to impale you on one of them.

A classic example: “Either you tell the truth or you stay silent. If you tell the truth, you will offend someone. If you stay silent, you will be seen as dishonest. Therefore, either you will offend someone or be seen as dishonest.” Both outcomes are bad. That’s the point. The dilemma works by narrowing your options down to two equally uncomfortable paths.

It’s important to note that a dilemma, while formally valid in structure, is not always logically sound. Its premises may be false, incomplete, or misleading. This is precisely where the three strategies for avoiding a dilemma become useful – they don’t attack the form of the argument, but rather its premises.

Strategy 1: Escaping between the horns 🔗

The first and most commonly used strategy is to show that the dilemma presents a false dichotomy – that the “either A or B” premise is not actually exhaustive. In other words, there is a third option the argument has overlooked, and choosing that option avoids the undesirable conclusion entirely.

As Effectiviology’s guide to false dilemmas explains, this method works by refuting the premise of collective exhaustivity – demonstrating that the options presented are not the only ones available. The dilemma is strongest when its two alternatives are genuine contradictories (like “p” and “not-p”), because then there truly is no middle ground. But when the alternatives are merely contraries – both can be false – a third path often exists.

A practical example 🔗

Consider a politically charged dilemma: “Either we cut education funding or we cut healthcare funding to balance the budget.” This appears to leave no room for alternatives. But a respondent could escape between the horns by pointing out that there are other areas of the budget – defense spending, administrative costs, subsidies – that haven’t been considered. By introducing this third option, the disjunctive premise collapses, and the dilemma is neutralised.

Another example: “You are either with us or against us.” This is a textbook false dichotomy. Someone could escape between the horns by noting that it is entirely possible to support some aspects of a group’s goals while opposing others – a position of nuance that neither horn accommodates, as noted in Irving Copi’s Introduction to Logic.

This strategy is most effective when the dilemma’s disjunction is clearly not exhaustive. It requires the respondent to identify what the argument has left out, rather than accepting the framing as complete.

Strategy 2: Taking the dilemma by the horns 🔗

Sometimes, escaping between the horns isn’t possible – the two alternatives genuinely are the only options. In that case, a second strategy becomes available: grasping the dilemma by the horns. This means accepting one of the alternatives but denying that it leads to the bad consequence the dilemma claims.

In other words, you challenge one of the conditional (if-then) premises. You say: yes, I accept that we’re in situation A – but I reject the claim that A necessarily leads to outcome X. As Amateur Logician’s overview of dilemmas puts it, this approach targets the conditional premise itself rather than the disjunctive one. A conditional proposition is false whenever its antecedent is true but its consequent is false – and demonstrating this breaks the chain of reasoning.

A practical example 🔗

Take the classic argument against protective tariffs: “If the tariff produces scarcity, it will be injurious to the economy; and if it produces abundance, it will lower prices and hurt local producers. It must produce either scarcity or abundance. Therefore it will be injurious either way.” A defender of tariffs could grasp the dilemma by the horns and challenge the first conditional – arguing that even if scarcity occurs, it would stimulate domestic production, create employment, and ultimately prove beneficial rather than harmful. The if-then link has been broken, not the either-or structure.

This strategy demands a direct confrontation with one of the argument’s key premises. It requires showing that the stated consequence does not necessarily follow from the stated condition – which often involves providing a counterexample or a more nuanced analysis of the causal relationship being claimed.

Strategy 3: Rebuttal by counterdilemma 🔗

The third strategy is perhaps the most dramatic: rather than dismantling the dilemma’s premises, you construct an opposing dilemma that uses the same materials to reach the opposite conclusion. This is called rebutting the dilemma by counterdilemma.

As Copi’s Introduction to Logic notes, this method is the most entertaining and ingenious of the three – but it is also the least logically decisive. The counterdilemma does not show that the original argument is unsound; it simply presents an equally compelling case for the opposite conclusion. At best, both dilemmas illuminate partial truths about the same situation, suggesting that reality is more complex than either argument alone can capture.

The classic example: Protagoras and Euathlus 🔗

No discussion of the counterdilemma would be complete without the celebrated ancient Greek case of Protagoras and Euathlus. Protagoras, a famous sophist, agreed to teach Euathlus the art of rhetoric on the condition that Euathlus would pay his fee after winning his first court case. After completing his training, Euathlus chose not to practice law – and never won a case. Tired of waiting, Protagoras sued his pupil and framed his argument as a dilemma:

“If Euathlus loses this case, he must pay me by court order. If he wins this case, he must pay me by the terms of our contract – since winning would mean he has now won his first case. He must either lose or win. Therefore, he must pay me.”

Euathlus, having learned well from his teacher, responded with a counterdilemma built from the very same facts: “If I win this case, I need not pay Protagoras by court order. If I lose this case, I need not pay him by the contract – because losing means I have not yet won my first case. I must either win or lose. Therefore, I need not pay Protagoras.”

The two dilemmas are structurally symmetric. Each appears sound. Each reaches the opposite conclusion. The jurors, reportedly baffled, postponed the case indefinitely. This paradox – known as the Paradox of the Court – has fascinated logicians for millennia, and it illustrates both the rhetorical power and the logical limitations of the counterdilemma strategy.

Another classic example: the Athenian mother 🔗

A simpler and equally famous counterdilemma appears in another ancient anecdote. An Athenian mother tries to persuade her son not to enter politics: “If you say what is just, men will hate you; if you say what is unjust, the gods will hate you. You must say one or the other. Therefore you will be hated.” Her son responded: “If I say what is just, the gods will love me; if I say what is unjust, men will love me. I must say one or the other. Therefore I will be loved.” As Effectiviology notes, this counterdilemma draws on the same facts to yield a directly opposite conclusion – showing how both arguments simply illuminate different aspects of the same situation rather than genuinely refuting each other.

The logical limits of these strategies 🔗

It’s worth being clear about what these three strategies actually accomplish – and what they don’t. None of them challenge the formal validity of the dilemmatic argument. A dilemma can be perfectly valid in its logical structure and still be defeated using these methods, because the attack is always on the premises, not the form.

Escaping between the horns and taking the dilemma by the horns both aim to show that the argument is unsound – that one of its premises is false. If successful, these strategies genuinely refute the dilemma. The counterdilemma, by contrast, does not refute anything. It only raises rhetorical doubt by showing that an opposite conclusion is equally defensible with the same facts. As logicians have noted, this can be a powerful debating tool, but it should not be mistaken for a logical proof.

There is also a deeper point here. As some philosophers of logic have argued, all three strategies are ultimately “escapist” in the strict logical sense – they are ways of resisting the dilemma’s conclusion without always resolving the underlying problem. A dilemma constructed from genuine contradictories and true conditional premises may be inescapable. This is why the ability to identify a dilemma’s weaknesses – whether in its disjunction or its conditionals – is such a valued critical thinking skill.

Why these strategies matter beyond the classroom 🔗

Dilemmas appear everywhere – in political rhetoric, ethical debates, legal arguments, and everyday decision-making. The framing “you’re either with us or against us” is a dilemma. So is “either we raise taxes or we cut services.” So is the trolley problem in moral philosophy. Recognising when an argument takes dilemmatic form, and knowing how to probe its premises, is not merely an academic exercise.

The false dilemma fallacy is one of the most frequently used rhetorical devices, precisely because it simplifies complex issues into binary choices that pressure listeners into agreement. Being equipped with the vocabulary and reasoning skills to identify and challenge these structures gives thinkers a significant advantage – not to win arguments for their own sake, but to ensure that the options being considered are genuinely complete and the consequences being claimed are genuinely accurate.

Each of the three strategies – escaping between the horns, taking it by the horns, and rebuttal – is essentially a discipline in examining premises with care. They ask: Are these really the only choices? Does this condition really lead to that consequence? Does an opposing interpretation of the same facts hold equal weight? These are the questions that good reasoning demands.

What do you think? When you encounter an “either-or” argument in everyday life – in a political speech, a workplace debate, or a moral dilemma – do you think it’s usually possible to find a third option between the horns, or are some dilemmas genuinely inescapable? And if a counterdilemma can be built from the same facts to reach the opposite conclusion, what does that tell us about the nature of the original argument?

References

1. https://en.wikipedia.org/wiki/Dilemma
2. https://effectiviology.com/false-dilemma/
3. https://groups.google.com/g/talk.philosophy.misc/c/ciHvt6e8mno
4. https://amateurlogician.com/dilemmas/
5. https://en.wikipedia.org/wiki/Paradox_of_the_Court
6. https://www.memoriapress.com/articles/protagoras-dilemma/
7. https://philosophicain.wordpress.com/dilemma-and-fallacies/