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

:<math>P \rightarrow Q</math> (P implies Q)

:<math>\therefore \neg P \rightarrow \neg Q</math> (therefore, not-P implies not-Q)

However, men could still be machines that do not follow a definite set of rules. Thus, this argument (as Turing intends) is invalid.

Another example is:

:If I am President of the United States, then I can veto Congress.

:I am not President.

:Therefore, I cannot veto Congress.

This is a case of the fallacy denying the antecedent as written because it matches the formal symbolic schema at beginning. The form is taken without regard to the content of the language.

See also

  • Affirming the consequent
  • Modus ponens
  • Modus tollens
  • Necessity and sufficiency
  • Plausible reasoning

References

  • FallacyFiles.org: Denying the Antecedent
  • safalra.com: Denying The Antecedent