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.”
—Willard Van Orman Quine (b. 1908)
“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)
“Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic.”
—Sir Peter Frederick Strawson (b. 1919)
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)