Difference between revisions of "Sufficient condition"
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A '''sufficient condition''' is one for which the following is true: | A '''sufficient condition''' is one for which the following is true: | ||
: If A is a sufficient condition of B, then if A is true, B ''must'' be true. | : If A is a sufficient condition of B, then if A is true, B ''must'' be true. | ||
| − | For example, "I heard thunder" is a sufficient condition of "There was lightning nearby," because if I heard thunder, there ''must'' have been lightning nearby to cause it. | + | For example, "I heard [[thunder]]" is a sufficient condition of "There was lightning nearby," because if I heard thunder, there ''must'' have been [[lightning]] nearby to cause it. |
However, "There was lightning nearby" is ''not'' a sufficient cause of "I heard thunder," because there may have been lightning nearby that I did not hear. | However, "There was lightning nearby" is ''not'' a sufficient cause of "I heard thunder," because there may have been lightning nearby that I did not hear. | ||
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| + | Confusing a sufficient condition with a [[necessary and sufficient condition]] is a [[logical fallacy]] known as [[affirming the consequent]]. | ||
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| + | From the affirmation of a sufficient condition, one may infer that the [[necessary condition]] is true. | ||
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| + | [[Category:Logic]] | ||
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| + | ==See also== | ||
| + | [[Modus ponens]] | ||
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| + | [[Modus tollens]] | ||
Latest revision as of 19:52, July 13, 2016
A sufficient condition is one for which the following is true:
- If A is a sufficient condition of B, then if A is true, B must be true.
For example, "I heard thunder" is a sufficient condition of "There was lightning nearby," because if I heard thunder, there must have been lightning nearby to cause it. However, "There was lightning nearby" is not a sufficient cause of "I heard thunder," because there may have been lightning nearby that I did not hear.
Confusing a sufficient condition with a necessary and sufficient condition is a logical fallacy known as affirming the consequent.
From the affirmation of a sufficient condition, one may infer that the necessary condition is true.