Consequent

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. In some contexts, the consequent is called the apodosis.

Examples:

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

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

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

Here, "${\displaystyle X}$ 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

Look up consequent in Wiktionary, the free dictionary.

• Antecedent (logic)
• Conjecture
• 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.