reductio
Definition
Noun: 1. A logical argument or method of proof: Specifically, a reductio ad absurdum (reduction to the absurd). It is a form of argument that disproves a proposition by showing that its logical consequences lead to an absurd or contradictory conclusion. Conversely, it can prove a proposition by demonstrating that assuming its opposite leads to a contradiction.
Usage
- The philosopher employed a clever reductio to dismantle his opponent's theory, revealing its illogical implications.
- In mathematics, a proof by reductio ad absurdum is a common and powerful technique.
Advanced Usage
- The term is almost exclusively used in its full Latin form, "reductio ad absurdum", or the abbreviated form "reductio". It is a technical term primarily used in logic, philosophy, mathematics, and formal debate.
- The argument proceeds by temporarily accepting a premise as true and then deducing from it a conclusion that is logically untenable, false, or self-contradictory. This then forces the rejection of the original premise.
Variants and Related Words
- Reductio ad absurdum: The full and formal name of the logical technique.
- Proof by contradiction: A closely related, often synonymous term used particularly in mathematics.
Synonyms
- Disproof by absurdity
- Indirect proof (in specific contexts)
- Proof by contradiction
Related Idioms/Phrases
- Reductio ad absurdum: This is the standard phrase. An example of its use: "His entire policy was defeated by a simple ; if everyone acted that way, society would collapse."
Noun
-
(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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