Antecedent (logic)

First half of an hypothetic statement (in logic) / From Wikipedia, the free encyclopedia

An antecedent is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause. In some contexts the antecedent is called the protasis.[1]

Examples:

  • If , then .

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 implies then is called the antecedent and is called the consequent.[2] Antecedent and consequent are connected via logical connective to form a proposition.

  • If is a man, then is mortal.

" 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.

Let . If then