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{{Other uses|Consequence (disambiguation){{!}}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 [[material conditional|implication]], if <math>\phi</math> implies <math>\psi</math> then <math>\phi</math> is called the [[Antecedent (logic)|antecedent]] and <math>\psi</math> is called the '''consequent'''.<ref>Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004</ref>
 
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]]
 
==References==
{{reflist}}
 
[[Category:Conditionals]]
 
{{Logic-stub}}

Revision as of 16:10, 4 October 2013

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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 ϕ implies ψ then ϕ is called the antecedent and ψ is called the consequent.[1]

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

References

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Template:Logic-stub

  1. ↑ Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004
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