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 the implication " implies ", 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 while " is mortal" is the consequent of the 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 and "I am the king of France" is the consequent.
Let .
- If then ,.
"" is the antecedent and "" is the consequent of this hypothetical proposition.