Denying the antecedent

Common card · No. 295906

Denying the antecedent (also known as denial of the antecedent, inverse error, or fallacy of the inverse) is a formal fallacy of inferring the inverse from an original statement. Phrased another way, denying the antecedent occurs in the context of an indicative conditional statement and assumes that the negation of the antecedent implies the negation of the consequent. It is a type of mixed hypothetical syllogism that takes on the following form: If P, then Q. Not P. Therefore, not Q. which may also be phrased as P → Q {\displaystyle P\rightarrow Q} (P implies Q) ∴ ¬ P → ¬ Q {\displaystyle \therefore \neg P\rightarrow \neg Q} (therefore, not-P implies 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...

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