Editing Consequent (section)

{{short description|Hypothetical proposition component}}
{{Other uses|Consequence (disambiguation)}}

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 [[material conditional|implication]], if ''P'' implies ''Q'', then ''P'' is called the [[Antecedent (logic)|antecedent]] and ''Q'' is called the '''consequent'''.<ref>Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004</ref> In some contexts, the consequent is called the '''''apodosis'''''.<ref>See [[Conditional sentence]].</ref>

Examples:

* If <math>P</math>, then <math>Q</math>.

<math>Q</math> is the consequent of this hypothetical proposition.

* If <math>X</math> is a mammal, then <math>X</math> is an animal.

Here, "<math>X</math> 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".