Reductio ad absurdum

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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).

The problem with this type of argument is that the "absurdity" one reaches really must be a logical contradiction in order for the argument to be logically valid.

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