Reductio ad absurdum (Latin: "reduction to absurdity"), also known as argumentum ad absurdum (Latin: argument to absurdity), is a common form of argument which seeks to demonstrate that a statement is true by showing that a false, untenable, or absurd result follows from its denial,[1] or in turn to demonstrate that a statement is false by showing that a false, untenable, or absurd result follows from its acceptance. First appearing in classical Greek philosophy (the Latin term derives from the Greek "εις άτοπον επαγωγή" or eis atopon epagoge, "reduction to the impossible", for example in Aristotle's Prior Analytics),[1] this technique has been used throughout history in both formal mathematical and philosophical reasoning, as well as informal debate.
The "absurd" conclusion of a reductio ad absurdum argument can take a range of forms:
Rocks have weight, otherwise we would see them floating in the air.
Society must have laws, otherwise there would be chaos.
There is no smallest positive rational number, because if there were, it could be divided by two to get a smaller one.
The first example above argues that the denial of the assertion would have a ridiculous result, against the evidence of our senses. The second argues that the denial would have an untenable result: unacceptable, unworkable or unpleasant for society. The third is a mathematical proof by contradiction, arguing that the denial of the assertion would result in a contradiction (there is a smallest rational number and yet there is a rational number smaller than it).
If everyone used this Religiously this debate would be 2/3 pages and a conclusion.
