Constructive dilemma
from 300 BCE Stoic; the horns metaphor is Greek
Show that every available option leads to the same place, and the conclusion holds without your ever having to say which option is the real one.
- Active
- from 300 BCE
- Where
- Athens
- Status
- In use
- Tradition
- Forms of inference
What it is
A constructive dilemma takes a disjunction and two conditionals, one for each branch, both leading to the same result. Since one branch or the other must hold, the result follows either way.
Its distinctive value is that it settles a question while leaving another question open. You never have to establish which alternative is true, which is often the harder and sometimes the impossible task.
How it works
Establish that the options are exhaustive. Take each in turn and show where it leads. If they lead to the same place, that place is reached.
Called *destructive* when the branches lead to the same impossibility instead, in which case the disjunction itself comes down. The two forms are the same manoeuvre pointed in opposite directions.
The form of the inference
- Either P or Q
- If P, then R
- If Q, then R
- Therefore R
The argument
Proposition Rates will rise this year whatever the council decides.
- The council must either approve the new depot or reject it; there is no third option before them.
- If they approve it, the build is funded by a special levy, which raises rates.
- If they reject it, the existing depot must be brought up to code within twelve months, and the works are funded from general revenue, which also raises rates.
- Both branches are costed in the same report and neither is disputed.
Therefore Rates will rise this year, and knowing how the vote goes would not change that.
The force of this is that it makes the decision irrelevant to the conclusion. That is also what makes it feel like a trap, and why the natural reply is to look for a third option rather than to argue with either branch.
What it is good for
Situations where the outcome matters and the route to it does not — risk assessment, contingency planning, and any argument where establishing which alternative holds would be expensive or impossible.
Where it fails
Its weak point is always the disjunction, and it is attacked by finding a third horn. In practice most dilemmas presented in public argument are false ones, and the two branches are exhaustive only because the arguer has framed them that way.
The second line of attack is to grasp a horn: accept one branch and deny that it leads where the arguer says. That is often more honest than hunting for a third option, and it is almost always harder work.
Common misconceptions
That a dilemma means a difficult choice. In logic it means an argument of this shape, and the two senses have drifted so far apart that the ordinary usage now obscures the technical one.
Where it came from
Stoic in origin and beloved of ancient rhetoric, where the two branches were called horns because whichever one you took, you were caught on it.
What became of it
A standard rule in propositional logic and a standard move in legal and political argument.
Lasting influence
It is the structure of a great many arguments in ethics and public policy, and of the strongest form of the problem of evil.
Why it still matters
Very high, and correspondingly abused. Most of what is called a false dilemma is this rule with a bad first premise.
Put another way
Two roads to the same town. It does not matter which one the traveller took.
Texts
Sextus Empiricus, Against the Logicians
Reports the Stoic treatment along with the sceptical objections to it, which are mostly objections to the disjunction.
Where to start
Learn to find the third horn. It is the reply that works, and it takes practice to see where one is hiding.
The surprising bit
Its rhetorical power comes from a feature that is logically irrelevant: because it never says which branch is true, the audience cannot escape by disputing the branch they were minded to defend.
In their own words
Whichever horn he takes, he is caught
Who held it
Sextus Empiricus
Connections
- Relies on
- Disjunctive syllogism, Modus ponens
- Parallel to
- Disjunctive syllogism
The verdict
Genuinely valid, genuinely useful, and the single most common vehicle for a false premise in public argument.