Consequent

2024-12-31T09:28:07Z

2A02:3035:660:D159:2408:E57B:EB7C:49C8: Fixed typo

{{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".

==See also==
{{wikt}}
* [[Antecedent (logic)]]
* [[Conjecture]]
* [[Necessity and sufficiency]]

==References==
{{reflist}}

[[Category:Conditionals]]
[[Category:Logical_consequence]]

{{Logic-stub}}

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Consequent