FallaciesFormal
Affirming the Consequent
Also called Converse error · Fallacy of the converse
Reasoning that because a result occurred, the thing that would have caused it must have happened.
Definition
Affirming the consequent reasons from “if P, then Q” and “Q is true” to the conclusion that P is true, which doesn’t follow.
It’s a formal fallacy: the error is in the structure of the argument, so it fails no matter what the topic is. The mistake is treating an “if” as if it worked in both directions. Lots of things besides P could make Q true.
Form
- If P, then Q.
- Q.
- Therefore P.
Compare the valid form, modus ponens: if P then Q; P; therefore Q. Affirming the consequent runs it backwards.
How to spot it
“If X were true, we’d see Y. We see Y, so X is true.”
One explanation is offered for an observation, and other explanations aren’t considered.
A symptom is treated as proof of a particular cause.
A prediction coming true is treated as proving the theory behind it.
Swapping in an obviously silly example of the same form makes the argument look absurd.
Examples
01The rain and the wet street
If it rained, the street is wet. The street is wet. Therefore it rained.
What went wrong
A street cleaner, a burst pipe, or a lawn sprinkler would also leave the street wet. The “if” only tells you rain is enough to wet the street, not that it’s the only cause.
02“If he were guilty, he’d hire a lawyer”
A commentator argues that a public figure must be guilty, since guilty people hire defense lawyers and this person hired one.
What went wrong
Innocent people hire lawyers too, often for good reasons. Hiring a lawyer is consistent with guilt, but it’s also consistent with innocence, so it can’t distinguish between them.
03The donor and the vote
A critic argues that a politician is corrupt: corrupt politicians take money from an industry and vote its way, and this politician took industry money and voted its way.
What went wrong
The politician may hold those views for other reasons, and the industry may donate because of the votes, not the other way around. The pattern fits corruption, but it fits other explanations too. Both parties’ supporters make this argument about the other side.
Why it persuades
People naturally reason from effects back to causes, and that habit is usually useful. The trouble is stopping at the first cause that comes to mind. In psychologist Peter Wason’s famous 1966 “selection task,” most people checked for evidence that fit a rule and missed the evidence that could break it. The pull toward confirming evidence is the same one that makes this fallacy feel right.
How to counter it
1Name another cause
The quickest counter is a second explanation that would produce the same result.
That would explain it, but so would this. How do we tell which one it is?
2Use a silly parallel
Show the structure with an example where the conclusion is obviously wrong.
That’s like saying: if it rained the street is wet, the street is wet, so it rained. What about the sprinkler?
3Ask what would rule it out
Ask what evidence would distinguish the proposed cause from the alternatives.
What would we expect to see if you’re right that we wouldn’t see if you’re wrong?
When it's not a fallacy
Reasoning from evidence back to the best explanation is how doctors diagnose, detectives investigate, and scientists test theories. It’s called abduction, or inference to the best explanation, and it’s legitimate as long as it’s treated as probable rather than certain, and the alternatives are actually weighed.
A prediction coming true is real evidence for a theory, especially a surprising prediction that rival theories didn’t make. The fallacy is treating it as proof, or skipping the rivals entirely.
Sources & further reading
- P. C. Wason, “Reasoning,” in New Horizons in Psychology, ed. B. M. Foss (Penguin, 1966), 135–151.
- Bradley Dowden, “Fallacies”, Internet Encyclopedia of Philosophy.
- Hans Hansen, “Fallacies”, Stanford Encyclopedia of Philosophy.
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