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What does reductio ad absurdum mean?

Looking for the meaning or definition of the word reductio ad absurdum? Here's what it means.

Noun
  1. (mathematics) The method of proving a statement by assuming the statement is false and, with that assumption, arriving at a blatant contradiction.
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The argument that says no individual has power leads to a reductio ad absurdum.
This is at the same time a difference with the ordinary hypothetical syllogism: insincerity essentially colors the reductio ad absurdum.
For some reason, this strikes me as the reductio ad absurdum of the whole project.
Is not that a reductio ad absurdum for this system of pure and direct democracy?
Also, employing reductio ad absurdum to show the rigor of syllogistical uses, is a recognition that it's exterior and prior to the syllogism.
Opposition to stem-cell research is the reductio ad absurdum of the right-to-life argument.

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