Consequent




For other uses, see Consequence.





A consequent is the second half of a hypothetical proposition. In the standard form of such a proposition, it is the part that follows "then". In an implication, if P implies Q, then P is called the antecedent and Q is called the consequent.[1] In some contexts, the consequent is called the apodosis.[2]


Examples:


  • If P{displaystyle P}P, then Q{displaystyle Q}Q.

Q{displaystyle Q}Q is the consequent of this hypothetical proposition.


  • If X{displaystyle X}X is a mammal, then X{displaystyle X}X is an animal.

Here, "X{displaystyle X}X is an animal" is the consequent.


  • If computers can think, then they are alive.

"They are alive" is the consequent.


The consequent in a hypothetical proposition is not necessarily a consequence of the antecedent.


  • If monkeys are purple, then fish speak Klingon.

"Fish speak Klingon" is the consequent here, but intuitively is not a consequence of (nor does it have anything to do with) the claim made in the antecedent that "monkeys are purple".



See also



  • Antecedent (logic)

  • Necessity and sufficiency



References





  1. ^ Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004


  2. ^ See Conditional sentence.









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