'reductio ad absurdum' definitions:

Definition of 'reductio ad absurdum'

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 [syn: reductio ad absurdum, reductio]

Definition of 'reductio ad absurdum'

From: GCIDE

Demonstration \Dem`on*stra"tion\, n. [L. demonstratio: cf. F. d['e]monstration.]
1. The act of demonstrating; an exhibition; proof; especially, proof beyond the possibility of doubt; indubitable evidence, to the senses or reason. [1913 Webster]
Those intervening ideas which serve to show the agreement of any two others are called "proofs;" and where agreement or disagreement is by this means plainly and clearly perceived, it is called demonstration. --Locke. [1913 Webster]
2. An expression, as of the feelings, by outward signs; a manifestation; a show. See also sense 7 for a more specific related meaning. [1913 Webster +PJC]
Did your letters pierce the queen to any demonstration of grief? --Shak. [1913 Webster]
Loyal demonstrations toward the prince. --Prescott. [1913 Webster]
3. (Anat.) The exhibition and explanation of a dissection or other anatomical preparation. [1913 Webster]
4. (Mil.) a decisive exhibition of force, or a movement indicating an attack. [1913 Webster]
5. (Logic) The act of proving by the syllogistic process, or the proof itself. [1913 Webster]
6. (Math.) A course of reasoning showing that a certain result is a necessary consequence of assumed premises; -- these premises being definitions, axioms, and previously established propositions. [1913 Webster]
7. a public gathering of people to express some sentiment or feelings by explicit means, such as picketing, parading, carrying signs or shouting, usually in favor of or opposed to some action of government or of a business. [PJC]
8. the act of showing how a certain device, machine or product operates, or how a procedure is performed; -- usually done for the purpose of inducing prospective customers to buy a product; as, a demonstration of the simple operation of a microwave oven. [PJC]
Direct demonstration, or Positive demonstration, (Logic & Math.), one in which the correct conclusion is the immediate sequence of reasoning from axiomatic or established premises; -- opposed to
Indirect demonstration, or Negative demonstration (called also reductio ad absurdum), in which the correct conclusion is an inference from the demonstration that any other hypothesis must be incorrect. [1913 Webster]