Etymology
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ambivalence (n.)

"simultaneous conflicting feelings," 1924 (1912 as ambivalency), from German Ambivalenz, coined 1910 by Swiss psychologist Eugen Bleuler on model of German Equivalenz "equivalence," etc., from Latin ambi- "both, on both sides" (see ambi-) + valentia "strength," abstract noun from present participle of valere "be strong" (from PIE root *wal- "to be strong"). A psychological term that by 1929 had taken on a broader literary and general sense.

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ambivalent (adj.)

"having simultaneous conflicting feelings or contradictory ideas about something," 1916, originally a term in psychology; back-formation from ambivalence. In general use by 1929.

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*wal- 

Proto-Indo-European root meaning "to be strong."

It forms all or part of: ambivalence; Arnold; avail; bivalent; convalesce; countervail; Donald; equivalent; evaluation; Gerald; Harold; invalid (adj.1) "not strong, infirm;" invalid (adj.2) "of no legal force;" Isold; multivalent; polyvalent; prevalent; prevail; Reynold; Ronald; valediction; valence; Valerie; valetudinarian; valiance; valiant; valid; valor; value; Vladimir; Walter; wield.

It is the hypothetical source of/evidence for its existence is provided by: Latin valere "be strong, be well, be worth;" Old Church Slavonic vlasti "to rule over;" Lithuanian valdyti "to have power;" Celtic *walos- "ruler," Old Irish flaith "dominion," Welsh gallu "to be able;" Old English wealdan "to rule," Old High German -walt, -wald "power" (in personal names), Old Norse valdr "ruler."

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bad (adj.)

c. 1300, "inadequate, unsatisfactory, worthless; unfortunate;" late 14c., "wicked, evil, vicious; counterfeit;" from 13c. in surnames (William Badde, Petri Badde, Asketinus Baddecheese, Rads Badinteheved). Rare before 1400, and evil was more common until c. 1700 as the ordinary antithesis of good. It has no apparent relatives in other languages.* Possibly from Old English derogatory term bæddel and its diminutive bædling "effeminate man, hermaphrodite, pederast," which probably are related to bædan "to defile."

The orig. word, AS. bæddel, ME. baddel, on account of its sinister import, is scarcely found in literature, but, like other words of similar sense, it prob. flourished in vulgar speech as an indefinite term of abuse, and at length, divested of its original meaning, emerged in literary use as a mere adj., badde, equiv. to the older evil. [Century Dictionary, 1897]

Comparable words in the other Indo-European languages tend to have grown from descriptions of specific qualities, such as "ugly," "defective," "weak," "faithless," "impudent," "crooked," "filthy" (such as Greek kakos, probably from the word for "excrement;" Russian plochoj, related to Old Church Slavonic plachu "wavering, timid;" Persian gast, Old Persian gasta-, related to gand "stench;" German schlecht, originally "level, straight, smooth," whence "simple, ordinary," then "bad").

Comparative and superlative forms badder, baddest were common 14c.-18c. and used as recently as Defoe (but not by Shakespeare), but yielded to comparative worse and superlative worst (which had belonged to evil and ill).

Meaning "uncomfortable, sorry" is 1839, American English colloquial. To go bad "putrefy" is from 1884. Not bad "fairly good" is by 1771. Ironic use as a word of approval is said to be at least since 1890s orally, originally in African-American vernacular, emerging in print 1928 in a jazz context. It might have emerged from the ambivalence of expressions like bad nigger, used as a term of reproach by whites, but among blacks sometimes representing one who stood up to injustice, but in the U.S. West bad man also had a certain ambivalence:

These are the men who do most of the killing in frontier communities, yet it is a noteworthy fact that the men who are killed generally deserve their fate. [Farmer and Henley, "Slang and Its Analogues"]

*Persian has bad in more or less the same sense as the English word, but this is regarded by linguists as a coincidence. The forms of the words diverge as they are traced back in time (Persian bad comes from Middle Persian vat), and such accidental convergences exist across many languages, given the vast number of words in each and the limited range of sounds humans can make to signify them. Among other coincidental matches with English are Korean mani "many," Chinese pei "pay," Nahuatl (Aztecan) huel "well," Maya hol "hole."

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