Denying the antecedent
Denying the antecedent, sometimes also called
inverse error or
fallacy of the inverse, is a formal fallacy of inferring the inverse from the original statement. It is committed by reasoning in the form: If
P, then
Q. Not
P. Therefore, not
Q. Arguments of this form are invalid. Informally, this means that arguments of this form do not give good reason to establish their conclusions, even if their premises are true. The name
denying the antecedent derives from the premise "not
P", which denies the "if" clause of the conditional premise. One way to demonstrate the invalidity of this argument form is with a counterexample with true premises but an obviously false conclusion. For example: If it is raining, then the grass is wet. It is not raining. Therefore, the grass is not wet. The argument is invalid because there are other reasons for which the grass could be wet. Another example: If Queen Elizabeth is an American citizen, then she is a human being. Queen Elizabeth is not an American citizen. Therefore, Queen Elizabeth is not a human being.