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.
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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 (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:
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* If '''P''' then '''Q'''.
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* '''Q''' is false.
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* Therefore '''P''' is false.
  
: If '''P''' then '''Q'''.
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More formally, a ''reductio ad absurdum'' argument typically takes the form:
: '''Q''' is false.
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* Assume '''P'''.
: Therefore '''P''' is false.
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* This implies '''Q'''.
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* It also implies '''R'''.
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* But '''Q''' and '''R''' are contradictory ('''Q''' [[iff]] not '''R''').
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* 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

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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).

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