denial of the antecedent

logic

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June 25, 2026

Quick Summary

Denial of the antecedent is a formal logical fallacy. It occurs in conditional reasoning when one incorrectly infers the negation of the consequent from the negation of the antecedent.

The structure of this fallacy is:
If P, then Q.
Not P.
Therefore, not Q.

For example, "If it rains, the game is canceled. It has not rained. Therefore, the game is not canceled." This reasoning is flawed because the game could be canceled for other reasons besides rain. This fallacy is contrasted with affirming the consequent.12

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applied logic
Formal fallacies
Among the best known are denying the antecedent (“If A, then B; not-A; therefore, not-B”) and affirming the consequent (“If A, then B; B; therefore, A”). The invalid nature of these fallacies is illustrated in the following examples:
Read More
Among the best known are denying the antecedent (“If A, then B; not-A; therefore, not-B”) and affirming the consequent (“If A, then B; B; therefore, A”). The invalid nature of these fallacies is illustrated in the following examples:
Read More