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 P{displaystyle P}P, then Q{displaystyle Q}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 }phi implies ψ{displaystyle psi }psi then ϕ{displaystyle phi }phi is called the antecedent and ψ{displaystyle psi }psi is called the consequent.[2]


  • If X{displaystyle X}X is a man, then X{displaystyle X}X is mortal.

"X{displaystyle X}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





  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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