Consequent  

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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 <math>\phi</math> implies <math>\psi</math> then <math>\phi</math> is called the antecedent and <math>\psi</math> is called the consequent.

Examples:

• If P, then Q.

Q is the consequent of this hypothetical proposition.

• If X is a mammal, then X is an animal.

Here, "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