Reduction To Absurdity: Reductio Ad Absurdum in Polemics, Logic and Mathematics
Reductio ad absurdum, reducing to an absurdity, is a method of proof in logic and mathematics, whereby assuming that a proposition is true leads to absurdity; a proposition is assumed to be true and this is used to deduce a proposition known to be false, therefore the original proposition must have been false. It is also an argumentation style in polemics, whereby a position is demonstrated to be false, or "absurd", by assuming it and reasoning to reach something known to be believed to be false or to violate common sense; e.g., as used by Plato to argue against other philosophical positions.
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Famous quotes containing the words reduction, reductio, absurdum, logic and/or mathematics:
“The reduction of nuclear arsenals and the removal of the threat of worldwide nuclear destruction is a measure, in my judgment, of the power and strength of a great nation.”
—Jimmy Carter (James Earl Carter, Jr.)
“Some have said that the thesis [of indeterminacy] is a consequence of my behaviorism. Some have said that it is a reductio ad absurdum of my behaviorism. I disagree with this second point, but I agree with the first. I hold further that the behaviorism approach is mandatory. In psychology one may or may not be a behaviorist, but in linguistics one has no choice.”
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“Some have said that the thesis [of indeterminacy] is a consequence of my behaviorism. Some have said that it is a reductio ad absurdum of my behaviorism. I disagree with this second point, but I agree with the first. I hold further that the behaviorism approach is mandatory. In psychology one may or may not be a behaviorist, but in linguistics one has no choice.”
—Willard Van Orman Quine (b. 1908)
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“... though mathematics may teach a man how to build a bridge, it is what the Scotch Universities call the humanities, that teach him to be civil and sweet-tempered.”
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