Etymology
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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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intuit (v.)
1776, "to tutor," from Latin intuit-, past participle stem of intueri "look at, consider," from in- "at, on" (from PIE root *en "in") + tueri "to look at, watch over" (see tutor (n.)). Meaning "to perceive directly without reasoning, know by immediate perception" is from 1840 (De Quincey), in this sense perhaps a back-formation from intuition. Related: Intuited; intuiting.
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counterintuitive (adj.)

also counter-intuitive, "contrary to intuition, opposed to what would be expected," 1955, from counter- + intuitive.

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noumenon (n.)

"that which can be the object only of a purely intellectual intuition" (opposed to a phenomenon), 1796, a term introduced by Kant, from Greek noumenon "that which is perceived," neuter passive present participle of noein "to apprehend, perceive by the mind" (from noos "mind," which is of uncertain origin). With passive suffix -menos.

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science (n.)
Origin and meaning of science

mid-14c., "what is known, knowledge (of something) acquired by study; information;" also "assurance of knowledge, certitude, certainty," from Old French science "knowledge, learning, application; corpus of human knowledge" (12c.), from Latin scientia "knowledge, a knowing; expertness," from sciens (genitive scientis) "intelligent, skilled," present participle of scire "to know," probably originally "to separate one thing from another, to distinguish," related to scindere "to cut, divide" (from PIE root *skei- "to cut, split;" source also of Greek skhizein "to split, rend, cleave," Gothic skaidan, Old English sceadan "to divide, separate").

From late 14c. in English as "book-learning," also "a particular branch of knowledge or of learning;" also "skillfulness, cleverness; craftiness." From c. 1400 as "experiential knowledge;" also "a skill, handicraft; a trade." From late 14c. as "collective human knowledge" (especially that gained by systematic observation, experiment, and reasoning). Modern (restricted) sense of "body of regular or methodical observations or propositions concerning a particular subject or speculation" is attested from 1725; in 17c.-18c. this concept commonly was called philosophy. Sense of "non-arts studies" is attested from 1670s. 

Science, since people must do it, is a socially embedded activity. It progresses by hunch, vision, and intuition. Much of its change through time does not record a closer approach to absolute truth, but the alteration of cultural contexts that influence it so strongly. Facts are not pure and unsullied bits of information; culture also influences what we see and how we see it. Theories, moreover, are not inexorable inductions from facts. The most creative theories are often imaginative visions imposed upon facts; the source of imagination is also strongly cultural. [Stephen Jay Gould, introduction to "The Mismeasure of Man," 1981]
In science you must not talk before you know. In art you must not talk before you do. In literature you must not talk before you think. [John Ruskin, "The Eagle's Nest," 1872]

The distinction is commonly understood as between theoretical truth (Greek epistemē) and methods for effecting practical results (tekhnē), but science sometimes is used for practical applications and art for applications of skill. To blind (someone) with science "confuse by the use of big words or complex explanations" is attested from 1937, originally noted as a phrase from Australia and New Zealand.

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