reductio ad absurdum
Noun: 1. A method of logical argument or refutation: A technique of proving a statement false by demonstrating that its logical consequences lead to an absurd or contradictory conclusion. It is also used to prove a statement true by showing that assuming its opposite leads to an absurdity or contradiction.
This term is used in formal logic, mathematics, philosophy, and debate to describe a specific form of argument. * It is often employed to disprove a claim by showing its implications are ridiculous or impossible. * It can also be used to prove a claim by demonstrating that its negation results in a logical contradiction.
- Disproof Example: To disprove the claim "More laws always create a safer society," one might use by arguing: "If that were true, then passing a law requiring everyone to stay indoors at all times would maximize safety, which is an absurd and undesirable outcome. Therefore, the original claim is flawed."
- Proof Example: In mathematics, to prove "there is no largest prime number," one assumes the opposite (that a largest prime exists) and then shows this assumption logically leads to a contradiction (one can always construct a larger number), thereby proving the original statement.
- The phrase is frequently shortened to "reductio" in academic and philosophical discourse.
- It is a cornerstone of indirect proof or proof by contradiction, where the validity of a proposition (P) is established by demonstrating that assuming not-P leads to an impossibility.
- Reductio (n.): An abbreviated, informal form of .
- Proof by contradiction (n.): A synonymous logical method.
- Indirect proof (n.): A broader category of proof that includes .
- Disproof by absurdity
- Argument to absurdity
- (reduction to the impossible)
While not idioms, these related logical concepts are often discussed alongside reductio ad absurdum: * Straw man argument: Misrepresenting an opponent's position to make it easier to attack (this is a fallacy, whereas a proper reductio accurately follows the logical consequences of the original claim). * Slippery slope: Arguing that a small first step will inevitably lead to a chain of related, extreme events (often criticized as a fallacy, but can be a valid reductio if the logical connections are sound).
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(reduction to the absurd) a disproof by showing that the consequences of the proposition are absurd; or a proof of a proposition by showing that its negation leads to a contradiction
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