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fallacy

Denying the antecedent

Also called: Inverse error

Denying the antecedent reasons from "if P then Q" and "not P" to "not Q". It is a formal fallacy: Q may still be true for other reasons.

How it works

A sufficient condition is mistaken for a necessary one. Removing one route to Q does not remove all the others.

Examples

"If you study medicine, you'll understand anatomy. You didn't study medicine, so you don't understand anatomy."

There are other ways to learn anatomy.

"If it rains, the match is cancelled. It isn't raining, so the match will go ahead."

The match could still be cancelled for other reasons.

How to spot it

"If P then Q" followed by "not P, therefore not Q".
One condition treated as the only one.
Words like "only if" are implied but not stated.

How to respond

Ask whether P is the only way Q can happen.
Give a counterexample of the same form.
Clarify whether the speaker means "if" or "only if".

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