word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
1580s, "suitable connection or dependence, consistency" (in narrative or argument), also more literally "act or state of sticking or cleaving of one thing to another," from French cohérence (16c.), from Latin cohaerentia, abstract noun from cohaerentem(nominative cohaerens), present participle of cohaerere "to stick together, be coherent," from assimilated form of com "together" (see co-) + haerere "to adhere, stick" (see hesitation). Related: Coherency.
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<a href="https://www.etymonline.com/word/incoherence">Etymology of incoherence by etymonline</a>
Harper, D. (n.d.). Etymology of incoherence. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/incoherence