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Denying The Antecedent

Denying the antecedent, sometimes also called inverse error, is a formal fallacy, committed by reasoning in the form:

If P, then Q.
Not P.
Therefore, not Q.

Source: A. R. Lacey, Dictionary of Philosophy (Third Revised Edition) (1996).

Thus, it is the mistake of treating a Sufficient Condition? (i.e. "if") as a Necessary Condition? (e.g. "if and only if").


If you washed the dishes, then they are clean.
You did not wash the dishes.
Therefore, the dishes are not clean.

Explanation: The dishes could have been washed by someone else or could be clean for some other reason. The premise does NOT state that ONLY IF you wash the dishes will they be clean.

See Also

Affirming The Consequent?
Sufficient Condition?
Necessary Condition?

Page last modified on July 16, 2012, at 05:34 PM