# Reductio ad absurdum

**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.