Denying the antecedentDenying the antecedent
is a type of logical fallacy
Suppose in an argument one were to deny the "if" part of a conditional (the antecedent) first, and conclude with the denial of "then" part (the consequent).
- If P, then Q.
- P is false.
- Therefore, Q is false.
This argument form
has the name denying the antecedent,
because in arguing this way one does indeed deny the antecedent in the second premise. This is a non-sequitur
. If we argue this way, we make a mistake. One can see this with an example:
- If there is fire here, then there is oxygen here. (Since oxygen is required for fire.)
- There is no fire here.
- Therefore, there is no oxygen here.
This form of argument may be convincing because of confusion between the meanings of if
and if and only if
. Denying the antecedent is valid
if the first premise asserts "if and only if" rather than "if".
See also: modus ponens, modus tollens, affirming the consequent.