### Reductio Ad Absurdum

Reduction to the Absurd

Proof By Contradiction

Reductio ad absurdum is sometimes used fallaciously, using a poorly constructed chain of reasoning from the target proposition. It is itself a perfectly good technique, being an application of the hypothetical syllogistic form

If A, then B.... where B includes a chain of one or more items. Any argument may be explored to find resulting contradictions which, the reasoning being valid, show one or more of the premises to be false.

Not B.

Therefore, not A.

A → B

Not B

∴ Not A

The fallacious uses of reductio ad absurdum come about by using weak or fallacious reasoning as proposition B.

Philosophy Pages

A method of proving that a proposition must be false [or true] by assuming the truth [or falsity] of the proposition and then showing that this assumption, taken together with other premises whose truth is already established, would lead to a contradiction (or, at least, to an obvious falsehood). This method is sometimes calledindirect proof.