reductio ad absurdum
(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.
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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.
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2. An expression, as of the feelings, by outward signs; a
manifestation; a show. See also sense 7 for a more
specific related meaning.
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Did your letters pierce the queen to any
demonstration of grief? --Shak.
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Loyal demonstrations toward the prince. --Prescott.
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3. (Anat.) The exhibition and explanation of a dissection or
other anatomical preparation.
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4. (Mil.) a decisive exhibition of force, or a movement
indicating an attack.
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5. (Logic) The act of proving by the syllogistic process, or
the proof itself.
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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.
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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.
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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.
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