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 $\phi$ implies $\psi$ then Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wiki.x.io/v1/":): {\displaystyle \phi} is called the antecedent and $\psi$ 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