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.^[1]

Examples:

• If [math]\displaystyle{ P }[/math], then [math]\displaystyle{ Q }[/math].

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 [math]\displaystyle{ \phi }[/math] implies [math]\displaystyle{ \psi }[/math] then [math]\displaystyle{ \phi }[/math] is called the antecedent and [math]\displaystyle{ \psi }[/math] is called the consequent.^[2] Antecedent and consequent are connected via logical connective to form a proposition.

• If [math]\displaystyle{ X }[/math] is a man, then [math]\displaystyle{ X }[/math] is mortal.

"[math]\displaystyle{ X }[/math] is a man" is the antecedent for this proposition while "[math]\displaystyle{ X }[/math] 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 [math]\displaystyle{ y=x+1 }[/math].

• If [math]\displaystyle{ x=1 }[/math] then [math]\displaystyle{ y=2 }[/math],.

"[math]\displaystyle{ x=1 }[/math]" is the antecedent and "[math]\displaystyle{ y=2 }[/math]" is the consequent of this hypothetical proposition.

See also

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

References

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