In logic, the premise
If P, then Q
is logically equivalent to its contrapositive
If not Q, then not P.
The contrapositive, however, is not what is involved in denying the antecedent.
• Premise: When it rains, the ground gets wet. If P, then Q. • Premise: It isn't raining. Not P. • Conclusion: Therefore, the ground is not wet. Therefore, not Q.
Do you see why the type of fallacy is called denying the antecedent?
A “lemon” is referred to as a new car that repeatedly fails to meet standards of quality and performance. “Lemon law” is the common name for the laws that help consumers if a new car fails and the manufacturer does not honor the warranty.
Here is the original statement.
The buyer of a new vehicle brought claims against a manufacturer under Ohio's Lemon Law and for breaches of a warranty act. The trial court ruled in favor of the defendant on both claims. The court of appeals analyzed the trial court's logic. The trial court first addressed the plaintiff's Lemon Law claim and determined that it was invalid. Next, the trial court concluded that since the Lemon Law claim was not valid, the warranty act claim was not valid. The court of appeals rejected the trial court's reasoning, based on the fallacy of denying the antecedent.
Summarized from "Conventional Logic: Using the Logical Fallacy of Denying the Antecedent as a Litigation Tool," Stephen Rice
Here is a possible rewriting as a syllogism.
• Premise: If the Lemon Law claim is valid, then the automobile warranty is valid. • Premise: The Lemon Law claim is not valid. • Conclusion: Therefore, the automobile warranty is not valid.
In this form, you can see that the syllogism is a fallacy and that it is of the form denying the antecedent.
These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.