Antecedent (logic)  

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An antecedent is the first half of a hypothetical proposition.

Examples:

• If P, then Q.

This is a nonlogical formulation of a hypothetical proposition. In this case, the antecedent is P, and the consequent is Q. In an implication, if <math>\phi</math> implies <math>\psi</math> then <math>\phi</math> is called the antecedent and <math>\psi</math> is called the consequent.

• If X is a man, then X is mortal.

"X is a man" is the antecedent for this proposition.

• If men have walked on the moon, then I am the king of France.

Here, "men have walked on the moon" is the antecedent.

See also

• Denying the antecedent (fallacy)
• Necessity and sufficiency