Etymology
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incurable (adj.)
mid-14c., from Old French incurable "not curable" (13c.), from Late Latin incurabilis "not curable," from in- "not" (see in- (1)) + curabilis "curable" (see curable). As a noun, "incurable person," from 1650s. Related: Incurably.
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irremediable (adj.)
"beyond remedy," mid-15c., from Late Latin irremediabilis "incurable," from assimilated form of in- "not, opposite of" (see in- (1)) + remediabilis "that may be healed, curable" (see remediable).
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cacoethes (n.)

"itch for doing something," 1560s, from Latinized form of Greek kakoēthēs "ill-habit, wickedness, itch for doing (something)," from kakos "bad" (from PIE root *kakka- "to defecate") + ēthē- "disposition, character" (see ethos). Most famously, in Juvenal's insanabile scribendi cacoethes "incurable passion for writing."

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certifiable (adj.)

1846, "capable of being declared as true," from certify + -able. Meaning "so deranged as to be certifiably insane" is recorded from 1870, from certify in the specific sense "officially declare (someone) to be insane" (1822). The certification was done by local officials, later medical officers, and often included a statement as to whether the person was harmless or dangerous, curable or incurable.

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incorrigible (adj.)
mid-14c., "incurable (of diseases, venom, etc.); extravagant (of expense); implacable (of hearts)," from Old French incorrigible "perfect, beyond rebuke or discipline" (14c.) or directly from Latin incorrigibilis "not to be corrected," from in- "not, opposite of" (see in- (1)) + corrigibilis, from corrigere "to correct," from com-, intensive prefix (see com-), + regere "to lead straight, rule" (from PIE root *reg- "move in a straight line," with derivatives meaning "to direct in a straight line," thus "to lead, rule"). From mid-15c. as "incapable of improvement" (of persons). Related: Incorrigibly. As a noun, from 1746.
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