Etymology
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insight (n.)
c. 1200, innsihht, "sight with the 'eyes' of the mind, mental vision, understanding from within," from in (prep.) + sight (n.). But the meaning often seems to be felt as "sight into" (something else), and so the sense shifted to "penetrating understanding into character or hidden nature" (1580s). Similar formation in Dutch inzigt, German einsicht, Danish indsigt.
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insightful (adj.)
"with penetrating understanding into character or hidden nature," 1881, from insight + -ful. Some earlier words in the same sense were insighted (c. 1600), inseeing "having insight" (1590s). Related: Insightfully; insightfulness.
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discernment (n.)

1580s, "keenness of intellectual perception, insight, acuteness of judgment;" see discern + -ment. From 1680s as "act of perceiving by the intellect."

Penetration, or insight, goes to the heart of a subject, reads the inmost character, etc. Discrimination marks the differences in what it finds. Discernment combines both these ideas. [Century Dictionary]
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in-depth (adj.)

"profoundly, with careful attention and deep insight," 1967, from the adjective phrase (attested by 1959); see in (adv.) + depth.

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foresight (n.)
also fore-sight, early 14c., "insight obtained beforehand;" also "prudence," from fore- + sight (n.). Perhaps modeled on Latin providentia. Compare German Vorsicht "attention, caution, cautiousness."
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acumen (n.)

"quickness of perception, keen insight," 1530s, from Latin acumen "a point, sting," hence, figuratively, "mental sharpness, shrewdness," from acuere "to sharpen," literal and figurative (of intellect, emotion, etc.), related to acus "a needle" (from PIE root *ak- "be sharp, rise (out) to a point, pierce"). Related: Acuminous.

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clairvoyant (adj.)

"having psychic gifts, characterized by powers of clairvoyance," 1837, earlier "having insight" (1670s), from special use of French clairvoyant "clear-sighted, discerning, judicious" (13c.), from clair (see clear (adj.)) + voyant "seeing," present participle of voir, from Latin videre "to see" (from PIE root *weid- "to see"). Related: Clairvoyantly.

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intuition (n.)
mid-15c., intuicioun, "insight, direct or immediate cognition, spiritual perception," originally theological, from Late Latin intuitionem (nominative intuitio) "a looking at, consideration," noun of action from past participle stem of Latin intueri "look at, consider," from in- "at, on" (from PIE root *en "in") + tueri "to look at, watch over" (see tutor (n.)).
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divine (v.)

"to conjure, to guess," originally "to make out by supernatural insight," mid-14c., divinen, from Old French deviner, from Vulgar Latin *devinare, a dissimilation of *divinare, from Latin divinus "of a god," from divus "of or belonging to a god, inspired, prophetic," related to deus "god, deity" (from PIE root *dyeu- "to shine," in derivatives "sky, heaven, god"). Latin divinus also meant, as a noun, "soothsayer." Related: Divined; divining. Divining rod (or wand) attested from 1650s.

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penetration (n.)

early 15c., penetracioun, "a puncture, a penetrating wound," from Latin penetrationem (nominative penetratio) "a penetrating or piercing," noun of action from past-participle stem of penetrare "to put or get into, enter into" (see penetrate). From c. 1600 as "insight, discernment, shrewdness;"  the sexual sense is attested from 1610s; meaning "act of penetrating or piercing" is from 1620s; in optics, by 1799.

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