early 14c., opinioun, "a judgment formed or a conclusion reached, especially one based on evidence that does not produce knowledge or certainty," from Old French opinion "opinion, view, judgements founded upon probabilities" (12c.), from Latin opinionem (nominative opinio) "opinion, conjecture, fancy, belief, what one thinks; appreciation, esteem," from stem of opinari "think, judge, suppose, opine," from PIE *op- (2) "to choose" (see option).
Where there is much desire to learn, there of necessity will be much arguing, much writing, many opinions; for opinion in good men is but knowledge in the making. [Milton, "Areopagitica"]
The word always has tended toward "a judgment or view regarded as influenced more by sentiment or feeling than reason." The meaning "formal statement by a judge or other professional" is from late 15c. The specific sense of "the estimate one forms of the character or qualities of persons or things" is by c. 1500. Public opinion, "the prevailing view in a given community on any matter of general interest or concern," is by 1735.
Middle English, perhaps reflecting the era's concern for obtaining knowledge through learned disputation, had opinional "characterized by likelihood rather than certainty" and opinial "based on probable but not certain evidence" (both mid-15c.).
mid-14c., "condition or relation of being other or different," also "any special mode of non-identity," from Old French difference"difference, distinction; argument, dispute" (12c.) and directly from Latin differentia "diversity, difference," from differentem (nominative differens), present participle of differre "to set apart," from assimilated form of dis- "apart, away from" (see dis-) + ferre "to bear, carry," from PIE root *bher- (1) "to carry." Sense of "controversy, dispute, a quarrel" is from late 14c.
early 14c., dissencioun, "disagreement in opinion," especially strong disagreement which produces heated debate, from Old French dissension (12c.) and directly from Latin dissensionem (nominative dissensio) "disagreement, difference of opinion, discord, strife," noun of action from past participle stem of dissentire "disagree," from dis- "differently" (see dis-) + sentire "to feel, think" (see sense (n.)).
"with the leave of, by the permission of," 1863, from Latin pace, ablative of pax "peace," as in pace tua "with all deference to you;" from PIE root *pag- "to fasten." "Used chiefly as a courteous or ironical apology for a contradiction or difference of opinion" [OED]. It is sometimes misused as though it means "according to" instead of the opposite.
colloquial shortening of difference, attested by 1878 in phrase what's the diff? "what's the difference?"
"slight or delicate degree of difference in expression, feeling, opinion, etc.," 1781, from French nuance "slight difference, shade of color" (17c.), from nuer "to shade," from nue "cloud," from Gallo-Roman *nuba, from Latin nubes "a cloud, mist, vapor," from PIE *sneudh- "fog" (source also of Avestan snaoda "clouds," Latin obnubere "to veil," Welsh nudd "fog," Greek nython, in Hesychius "dark, dusky").
According to Klein, the French secondary sense is a reference to "the different colors of the clouds." In reference to color or tone, "a slight variation in shade," by 1852; of music, by 1841 as a French term in English.
1640s, "making or exhibiting a difference," from Medieval Latin differentialis, from Latin differentia "diversity, difference" (see difference). Related: Differentially. As a noun in mathematics, "an infinitesimal difference between two values of variable quantity," from 1704. Differential calculus is attested from 1702.
1816, transitive, "make different; be what distinguishes between," from Medieval Latin differentiatus, past participle of differentiare, from Latin differentia "diversity, difference" (see difference).
Originally a mathematical term, "obtain the differential coefficient of;" intransitive sense of "acquire a distinct and separate character" is by 1874. Non-technical transitive sense of "discriminate between by observing or describing the difference between" is from 1876; earlier, difference had been used as a verb in this sense. Related: Differentiated; differentiating.