• Source: Antecedent (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.
Examples:

If



P


{\displaystyle P}

, then



Q


{\displaystyle Q}

.
This is a nonlogical formulation of a hypothetical proposition. In this case, the antecedent is P, and the consequent is Q. In the implication "



ϕ


{\displaystyle \phi }

implies



ψ


{\displaystyle \psi }

",



ϕ


{\displaystyle \phi }

is called the antecedent and



ψ


{\displaystyle \psi }

is called the consequent. Antecedent and consequent are connected via logical connective to form a proposition.

If



X


{\displaystyle X}

is a man, then



X


{\displaystyle X}

is mortal.
"



X


{\displaystyle X}

is a man" is the antecedent for this proposition while "



X


{\displaystyle 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


{\displaystyle y=x+1}

.

If



x
=
1


{\displaystyle x=1}

then



y
=
2


{\displaystyle y=2}

,.
"



x
=
1


{\displaystyle x=1}

" is the antecedent and "



y
=
2


{\displaystyle y=2}

" is the consequent of this hypothetical proposition.




See also


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




References

Kata Kunci Pencarian:

• Antecedent (logic)
• Relevance logic
• Denying the antecedent
• Antecedent
• Index of logic articles
• History of logic
• Modus ponens
• Antecedent (grammar)
• Consequent
• List of logic symbols