early 15c., reduccioun, "a restoring to a former state" (a sense now obsolete), also "a conquest or subjugation" (of a people, etc.), from Old French reducion (13c., Modern French réduction) and directly from Latin reductionem (nominative reductio) "a leading back, restoration," noun of action from past-participle stem of reducere (see reduce). The meaning "diminution, a lessening" is from 1670s; chemical sense of "reversion to a simpler form" is from 1660s.
"plainly illogical," 1550s, from French absurde (16c.), from Latin absurdus "out of tune, discordant;" figuratively "incongruous, foolish, silly, senseless," from ab- "off, away from," here perhaps an intensive prefix, + surdus "dull, deaf, mute," which is possibly from an imitative PIE root meaning "to buzz, whisper" (see susurration). Thus the basic sense is perhaps "out of tune," but de Vaan writes, "Since 'deaf' often has two semantic sides, viz. 'who cannot hear' and 'who is not heard,' ab-surdus can be explained as 'which is unheard of' ..." The modern English sense is the Latin figurative one, perhaps "out of harmony with reason or propriety." Related: Absurdly; absurdness.
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Definitions of reductio ad absurdum from WordNet
reductio ad absurdum (n.)
(reduction to the absurd) a disproof by showing that the consequences of the proposition are absurd; or a proof of a proposition by showing that its negation leads to a contradiction;