Consequent
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For other uses, see Consequence.
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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}
, then Q{displaystyle Q}
.
Q{displaystyle Q} is the consequent of this hypothetical proposition.
- If X{displaystyle X}
is a mammal, then X{displaystyle X} is an animal.
Here, "X{displaystyle 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
^ Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004
^ See Conditional sentence.
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