1
Not knowing what to do is a different thing
A dilemma in this sense is not uncertainty. Every sentence in the set can be settled, and the set is still unsatisfiable. The conflict is among the principles, not in the agent’s knowledge.
Lesson · Ethics and the Arithmetic of Welfare · Deontology
Moral Dilemmas and Deontic Consistency
A moral dilemma is a situation in which you ought to do each of two things and cannot do both. Written as a set of sentences, two oughts, a principle that oughts combine, a principle that ought implies can, and a fact of inability, it has no model, and all five sentences are needed for the clash. Each way out rejects exactly one.
two oughts, and you cannot do both
agglomeration: oughts combine
ought implies can
five sentences, no model: drop one
A dilemma as an inconsistent set
Core ideas
What this lesson establishes
Arguments and Validity gave the consistency check and the smallest subset that cannot be true together. The dilemma is a case for both.
2
A set can fail in one place or in many
A smallest inconsistent subset is a set that cannot hold but each of whose parts can. If it is the whole set, every sentence is doing work, and any one sentence given up restores a model.
3
Every exit has a price
The set is consistent once a sentence is rejected, but each rejection has a cost, and the genuine dilemma is the case where none is free.
The material
Two promises at six o’clock
A dilemma written out, its smallest inconsistent subset, and four ways out.
You have promised Ana to be at her door at six, and promised Bo to be at his, on the other side of town, at the same hour. Each promise gives you an obligation, and you cannot keep both. Philosophers who call this a moral dilemma mean something stronger than that it is hard: that you ought to do each, you cannot do both, and neither obligation overrides the other.
Definition · Moral dilemma
A moral dilemma is a situation in which an agent ought to do each of two actions, cannot do both, and has no further reason that makes one of the oughts lapse.
The standard argument that dilemmas are impossible uses two principles. Write a for “you ought to keep your promise to Ana”, b for “you ought to keep your promise to Bo”, c for “you ought to keep both” and d for “you can keep both”. The five sentences are below.
1 a you ought to keep the promise to Ana
2 b you ought to keep the promise to Bo
3 (a and b) → c agglomeration: oughts combine
4 c → d ought implies can
5 not d you cannot keep both
The lab finds no assignment of truth values that makes all five true. Sentences 1, 2 and 3 give c; with 4 that gives d; and 5 says not d. The smallest inconsistent subset is all five, so none of them is idle: take any one away and a model exists. This is the sense in which a dilemma is a set that cannot be true together, and it is a fact about the principles and the situation, not about the agent’s ignorance.
The set is also why people disagree about dilemmas, because each of the four ways of restoring consistency is held by someone. Williams keeps both oughts: the remorse you owe whichever promise you break shows, he argues, that the obligation you set aside did not lapse, and what he gives up is agglomeration, since from “you ought to keep each” it does not follow that “you ought to keep both”, and the combined obligation is never formed. A second camp keeps agglomeration and gives up ought-implies-can: you ought to keep both though you cannot, and an obligation can outrun what the situation allows. A third denies one of the first two sentences, holding that when two obligations conflict one of them lapses, so there was never a dilemma; that is the orthodox view, and standard deontic logic is built to deliver it. The fourth says you can keep both after all, by a plan not yet considered, and so denies the situation that made it a dilemma.
Marcus adds a point the lab makes visible. Delete sentence 5 and the remaining four have a model, so the principles were never inconsistent with one another; the clash needed the world to supply not d. On her view that is what a dilemma is, a consistent code meeting an unlucky situation, and it is why she holds there is a further obligation to arrange one’s life so that such situations are rare.
Example · The cost of each exit
Reject agglomeration, and you have two separate obligations and no obligation to meet them jointly, so it is unclear what a person is doing who fails one. Reject ought-implies-can, and an obligation no longer guides action, since it can demand the impossible. Drop one of the oughts, and the guilt you feel at breaking the promise you set aside has nothing to be about. The lab shows the set is consistent in each case; it does not say which price is the lowest.
The lab sees four letters. That c stands for the conjunction of what a and b say is not something it can tell, which is why agglomeration appears as a sentence in the set. Standard deontic logic builds in agglomeration and ought-implies-can, and so makes dilemmas inconsistent by design. That is itself a position, and the set above lets it be stated rather than assumed.
Interactive
Consistency and what must go
Every model, and every minimal inconsistent subset
Method
Writing a dilemma as a set
Five steps. The fourth is a table and the fifth is a choice, and the lab only does the fourth.
1
State the two oughts
Give each action its own sentence saying you ought to do it, with a letter each.
2
Add the principles the argument uses
Write the agglomeration principle and ought-implies-can as conditionals over the letters. If the argument uses a third principle, add it too.
3
Add the fact of inability
Write that you cannot do both. This is a claim about the situation, not a principle.
4
Check the set for a model
The lab reports that no assignment makes all the sentences true, and which sentences are the smallest subset that cannot. If that is all of them, each is needed.
5
Choose the sentence to give up, and name its price
Delete one sentence at a time and see which deletion restores a model. Then say what the deletion costs, because the dilemma is genuine only if each exit does.
What the set shows
Score 0 / 0Choose the answer you can justify.
Ana and Bo, five sentences
Write the situation, find the smallest set that cannot hold, then try each exit.
1 a 2 b 3 (a and b) imply c 4 c implies d 5 not d
all five together: no model
smallest inconsistent set: 1, 2, 3, 4, 5
drop 3: a model exists drop 4: a model exists
drop 1 or 2: a model exists drop 5: a model exists
Each deletion works, which is exactly the problem. A dilemma is real only if every sentence is held for good reason, so that giving any one up has a cost someone will not pay.
Common mistakes
1
Thinking a dilemma is not knowing what to doEvery sentence in the set is settled: you know what each promise requires and you know you cannot keep both. The set still has no model, and that is the dilemma. Uncertainty would be a case in which one of the sentences has not yet been settled, and the lab does not need to know which sentences are true to report that these five cannot be true together.
2
Thinking an inconsistent set shows the situation is impossibleThe set is about principles and a situation. Someone who holds all five holds something inconsistent, and the repair is to give up a sentence, not to deny that you made two promises. Whether a real dilemma remains depends on which sentence you give up.
3
Expecting the lab to pick the exitEach of the four exits is consistent, and consistency is all the lab checks. The price of each is a judgment about what the ought is for, and that judgment is the argument.
Check your understanding
✓
Finish when you can write a dilemma as a set and name the sentence each exit rejects.
Given two conflicting obligations, you should be able to write the five sentences, report that they have no model, name the smallest inconsistent subset, and say for each deletion which principle was rejected and what that costs.
Note: A fuller treatment would use a logic of obligation with its own axioms. Here the principles are written as sentences, so each can be deleted separately, which is the point of the exercise and also its limit.