Antecedent (logic)
Multi tool use
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{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 an implication, if ϕ{displaystyle phi }
implies ψ{displaystyle psi }
then ϕ{displaystyle phi } is called the antecedent and ψ{displaystyle psi } is called the consequent.[2]
- 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.
- 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 y=x+1. If x=1 then y=2
See also
Affirming the consequent (fallacy)
Denying the antecedent (fallacy)
- Necessity and sufficiency
References
^ See Conditional sentence.
^ Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004
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