Fallacy 2 of 3

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Denying the Antecedent

F002 • Formal - Propositional Logic

Also known as: Inverse Error, Fallacy of the Inverse

Difficulty 1/10Low LoadCommon

Definition

Inferring the falsehood of the consequent from the falsehood of the antecedent in a conditional statement.

Why Invalid

The consequent can be true even when the antecedent is false. The conditional only tells us what happens when P is true.

Examples

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Scope of Applicability

  1. Identify conditional statement (if P then Q)
  2. Check if antecedent (P) is denied
  3. Check if conclusion denies consequent (Q)
  4. Verify no additional information makes inference valid

Common Mistakes

  • Confusing with valid modus tollens (If P then Q; not Q; therefore not P)
  • Treating biconditionals as simple conditionals

Related Concepts

Affirming the ConsequentCommutation of Conditionals

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F001 Affirming the ConsequentF003 Commutation of Conditionals
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