Denial of the antecedent

Denial of the antecedent is a formal fallacy: from “if A then B” it does not follow that “if not A then not B”. The consequence can occur for other reasons.

Example

“If there is fraud, there are irregularities.
There is no fraud, therefore there are no irregularities.”
(There may be irregularities without fraud.)

Applied example (political)

“If there is corruption, there are protests.
There is no corruption, therefore there are no protests.”
(Protests can have other causes.)

Applied example (mystical)

“If someone is cursed, they have nightmares.
They have no nightmares, therefore they are not cursed.”
(The consequence can be absent for other reasons.)

Why it is fallacious

• It confuses sufficient with necessary conditions.
• It ignores alternative causes of B.
• It reduces complex explanations to a single path.

How to spot it

• Form: “If A then B. Not A, therefore not B”.
• A consequence is denied by denying one cause.
• Alternative explanations are ignored.

How to respond

• Offer other possible causes of B.
• Ask for evidence ruling out alternatives.
• Remember that denying A does not eliminate B.