Antecedent (logic)

An antecedent is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause. It is also known for a person's principles to a possible or hypothetical issue. In some contexts the antecedent is called the protasis.^[1]

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 $\phi$ implies $\psi$ then $\phi$ is called the antecedent and $\psi$ is called the consequent.^[2]

• 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

• Affirming the consequent (fallacy)
• Denying the antecedent (fallacy)
• Necessity and sufficiency

References

1. See Conditional sentence.
2. Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004