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Originally "virtual" comes from Latin virtus, which can be translated like "force", "ability", "fact".

Why nowadays in many languages word derived from "virtual" mean something exactly opposite - something that cannot be touched.

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    Это не относится только к Русскому языку. "Virtual" - он и в Африке "virtual". – Matt Mar 27 '15 at 10:39
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There's a whole class of words, called Antagonyms (Auto-antonyms, Contranyms). By definition, words that are antonyms to themselves.

There's a brief list of such words in English; Wikipedia also has a decent list of those.

As of "virtual", Etymonline article says:

The meaning "being something in essence or effect, though not actually or in fact" is from mid-15c., probably via sense of "capable of producing a certain effect" (early 15c.). Computer sense of "not physically existing but made to appear by software" is attested from 1959.

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    I suggest changing OED to Etymoline (or Online Etymology Dictionary) since most people associate OED with the Oxford English Dictionary. – Alex B. Mar 28 '15 at 16:56
  • "Vitrual" had a meaning of "physically impossible" long before computers were invented. It was very actively used in a context of classical mechanics (see virtual work, virtual displacement and virtual force). It appears in textbooks as old as of 19th century, and most likely was coined even earlier. – user58697 Mar 30 '15 at 19:05
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But it doesn't mean the opposite. A force cannot be touched, nor can an ability or a fact. A thing can; the Latin for "thing" is res, whence real.

Words like "virtual", "practical", or "effective" all mean "for all intents and purposes — but not in essence". They refer to something that, if you like, walks like a duck, swims like a duck, and quacks like a duck, but isn't a duck. Which is why in spite of their denoting a positive property rather than a lack of one, they can still be contrasted with "real", "literal" and "tangible".

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