reductio ad absurdum

Unadapted borrowing from Latin reductiō ad absurdum.

reductio ad absurdum (usually uncountable, plural reductio ad absurdums)

1. (mathematics, logic) The method of disproving a statement by assuming the statement is true and, with that assumption, arriving at a blatant contradiction.

   Synonyms: apagoge, proof by contradiction

   • 1894, Flora Helm, “Concerns a Talk in Which Anarchy and Love Are Blended”, in Between Two Forces: A Record of a Theory and a Passion, Boston, Mass.: Arena Publishing Company. […], pages 149–150:

     “You, gentlemen, as representatives of that institution which recognizes only truths that are deduced from reductio ad absurdums will probably have no difficulty in perceiving the truth of this absurdity and hence be ready to excuse the outcome of it—my absence.”

   • 1998, Mark H. Bickhard, “Constructivisms and Relativisms: A Shopper’s Guide”, in Michael R[obert] Matthews, editor, Constructivism in Science Education: A Philosophical Examination, Dordrecht, Boston, Mass., London: Kluwer Academic Publishers, →ISBN, page 106:

     Constructing representations out of atoms that are already themselves representations cannot address the origins of the atoms per se. Careful pursuit of such approaches has yielded bizarre reductio ad absurdums such as the implication that virtually all concepts that human beings are capable of having are already in the genes.

   • 2009, Michael S. Moore, “Normative Problems in Applying the Harm-within-the-Risk Test to Crimes/Torts of Negligence”, in Causation and Responsibility: An Essay in Law, Morals, and Metaphysics, Oxford University Press, published 2010, →ISBN, section III (The First Blind Alley: The Attempt to Replace Proximate Causation with Culpability as a Prerequisite for Legal Liability), page 208:

     One way to argue against a position is to demonstrate that it proves too much. Proponents of an HWR analysis of negligence may insist that the conceptual and normative arguments that have been directed against their project ultimately generate reductio ad absurdums suggesting that I have proved too much.

• reductio ad Hitlerum

Possibly a loose calque of Ancient Greek ἡ εἰς τὸ ἀδύνατον ἀπόδειξις (hē eis tò adúnaton apódeixis, “demonstration towards the impossible”).

reductiō ad absurdum f sg (genitive reductiōnis ad absurdum); third declension

1. reductio ad absurdum; reduction to the absurd

Third-declension noun with an indeclinable portion, singular only.