Antecedent (logic)

Short description: First half of an hypothetic statement (in logic)

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

* If X is a man, then X is mortal.

"X is a man" is the antecedent for this proposition while "X 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 y=x+1.

* If x=1 then y=2,.

"x=1" is the antecedent and "y=2" is the consequent of this hypothetical proposition.

## See also

* Consequent
* 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

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