reductio ad absurdum

For the mathematical form of proof by contradiction, see Proof by contradiction.

Reductio ad absurdum (Latin: "reduction to the absurd") is a form of argument in which a proposition is disproven by following its implications logically to an absurd consequence.^[1]

A common type of reductio ad absurdum is proof by contradiction (also called indirect proof), where a proposition is proved true by proving that it is impossible for it to be false. That is to say, if A being false implies that B must also be false and it is known that B is true, then A cannot be false and therefore A is true.

Where such an argument is premised on a false dichotomy, the ostensible proof is a logical fallacy.

Two simple examples of reductio ad absurdum are:

Proposition: "Raising taxation rates always results in increased tax revenue."
Proposition: "Lowering taxation rates always results in increased tax revenue."

These can both be disproved using reductio ad absurdum as follows:

"If taxes were raised to 100% of income, individuals would not work, and companies would not operate, resulting in zero income, and thus zero tax. That is less than current tax income, thus the proposition is false."
"If taxes were lowered to 0%, no taxes at all would be collected. Zero will always be less revenue than even the lowest non-zero tax rate would produce, thus the proposition is false."

This is also illustrated by the Laffer curve. The ontological argument for the existence of God, as it was originally stated by Anselm of Canterbury, is an example of an attempted reductio ad absurdum.^[2]

See also

• Contraposition
• Slippery slope fallacy
• Reductio ad ridiculum
• Reductio ad Hitlerum

References