Reductio ad absurdum

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(Modus tolens)
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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, 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:
+
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''.
+
: If '''P''' then '''Q'''.
# ''q'' is false.
+
: '''Q''' is false.
# Therefore ''p'' is false.
+
: 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 11:08, 31 August 2006


Reductio ad absurdum is a type of logical 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.

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.

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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