# Reductio ad absurdum

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− | '''Reductio ad absurdum''' is a type of [[logic]]al [[argument]] where one assumes a claim for the sake of argument, arrives at an absurd result, and then concludes that the original assumption must have been wrong, since it led to this absurd result. | + | '''Reductio ad absurdum''' is a type of [[logic]]al [[argument]] where one assumes a claim for the sake of argument, arrives at an "absurd" result (often a [[contradiction]]), and then concludes that the original assumption must have been wrong, since it led to this absurd result. |

Note that this is a [[Validity vs. soundness|logically valid]] technique. It is a form of ''modus tolens'', an inference rule which takes this form: | Note that this is a [[Validity vs. soundness|logically valid]] technique. It is a form of ''modus tolens'', an inference rule which takes this form: | ||

+ | * If '''P''' then '''Q'''. | ||

+ | * '''Q''' is false. | ||

+ | * Therefore '''P''' is false. | ||

− | : | + | More formally, a ''reductio ad absurdum'' argument typically takes the form: |

− | + | * Assume '''P'''. | |

− | + | * This implies '''Q'''. | |

+ | * It also implies '''R'''. | ||

+ | * But '''Q''' and '''R''' are contradictory ('''Q''' [[iff]] not '''R'''). | ||

+ | * Therefore '''P''' is false. | ||

See [[Can God create a rock so heavy that he can't lift it?]] for an example in the context of [[counter-apologetics]] (the claim being assumed is that God is all-powerful). | See [[Can God create a rock so heavy that he can't lift it?]] for an example in the context of [[counter-apologetics]] (the claim being assumed is that God is all-powerful). |

## Revision as of 15:32, 7 June 2007

For more information, see the Wikipedia article:

**Reductio ad absurdum** is a type of logical argument where one assumes a claim for the sake of argument, arrives at an "absurd" result (often a contradiction), and then concludes that the original assumption must have been wrong, since it led to this absurd result.

Note that this is a logically valid technique. It is a form of *modus tolens*, an inference rule which takes this form:

- If
**P**then**Q**. -
**Q**is false. - Therefore
**P**is false.

More formally, a *reductio ad absurdum* argument typically takes the form:

- Assume
**P**. - This implies
**Q**. - It also implies
**R**. - But
**Q**and**R**are contradictory (**Q**iff not**R**). - Therefore
**P**is false.

See Can God create a rock so heavy that he can't lift it? for an example in the context of counter-apologetics (the claim being assumed is that God is all-powerful).