Denying the Antecedent
From “if P then Q” and not-P, wrongly concluding that not-Q.
- formal
Denying the antecedent is an invalid form: from “if P then Q” and the fact that P is false, it concludes that Q must be false. But the conditional never claimed P was the only route to Q — Q can still be true even when P is not.
Examples
- “If you're a doctor, you've studied biology. You're not a doctor, so you haven't studied biology.” — plenty of non-doctors study biology.
- “If it rains, the match is cancelled. It didn't rain, so the match must be going ahead.” — it could be cancelled for other reasons.
Why it works & how to counter
Persuasive because ruling out the condition feels like ruling out the result. Counter it by remembering the rule only tells you what happens when P is true — it says nothing about when P is false.