Etymology
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Words related to utopia

topos (n.)
"literary theme," 1948, from Greek topos, literally "place, region, space," also "subject of a speech," a word of uncertain origin. "The broad semantic range renders etymologizing difficult" [Beekes].
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*aiw- 

also *ayu-, Proto-Indo-European root meaning "vital force, life; long life, eternity."

It forms all or part of: age; aught (n.1) "something; anything;" aye (adv.) "always, ever;" Ayurvedic; coetaneous; coeval; each; eon; eternal; eternity; ever; every; ewigkeit; hygiene; longevity; medieval; nay; never; no; primeval; sempiternal; tarnation; utopia

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit ayu- "life;" Avestan aiiu "age, life(time);" Greek aiōn "age, vital force; a period of existence, a lifetime, a generation; a long space of time," in plural, "eternity;" Latin aevum "space of time, eternity;" Gothic aiws "age, eternity," Old Norse ævi "lifetime," German ewig "everlasting," Old English a "ever, always."  

eu- 
word-forming element, in modern use meaning "good, well," from Greek eus "good," eu "well" (adv.), also "luckily, happily" (opposed to kakos), as a noun, "the right, the good cause," from PIE *(e)su- "good" (source also of Sanskrit su- "good," Avestan hu- "good"), originally a suffixed form of root *es- "to be." In compounds the Greek word had more a sense of "greatness, abundance, prosperity," and was opposed to dys-.
dystopia (n.)

"imaginary bad place," 1952, from dys- "bad, abnormal" + ending abstracted from utopia. Earlier in medical use, "displacement of an organ" (by 1844), with second element from Greek topos "place" (see topos). Dystopian was used in the non-medical sense in 1868 by J.S. Mill:

I may be permitted, as one who, in common with many of my betters, have been subjected to the charge of being Utopian, to congratulate the Government on having joined that goodly company. It is, perhaps, too complimentary to call them Utopians, they ought rather to be called dys-topians, cacotopians. What is commonly called Utopian is something too good to be practicable; but what they appear favour is too bad to be practicable. [speech, March 12, 1868]
utopian (adj.)

1550s, with reference to More's fictional country; 1610s as "extravagantly ideal, impossibly visionary," from utopia + -an. As a noun meaning "visionary idealist" it is recorded by 1832 (also in this sense was utopiast, 1845). Utopian socialism is from 1849, originally pejorative, in reference to the Paris uprising of 1848; also a dismissive term in communist jargon, in reference to the ideas of Fourier, St. Simon, and Owen, "the pre-scientific and infantile stage" of modern, practical socialism.