Etymology
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fairness (n.)

Old English fægernes "beauty;" see fair (adj.) + -ness. Meaning "even-handedness, impartiality" is from mid-15c. Meaning "lightness of complexion" is from 1590s.

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impartiality (n.)

"fairness, freedom from bias," 1610s; see impartial + -ity.

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soothfast (adj.)

"truthful," Old English soðfæst "true, trustworthy, honest, just, righteous;" see sooth (n.) + fast (adj). Related: Old English soðfæstnes "truthfulness, fairness, fidelity;" soðfæstlic "true, sincere;" soðfæstlice "truly, honestly."

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equanimity (n.)

c. 1600, "fairness, impartiality," from French équanimité, from Latin aequanimitatem (nominative aequanimitas) "evenness of mind, calmness; good-will, kindness," from aequanimis "mild, kind," literally "even-minded," from aequus "even, level" (see equal (adj.)) + animus "mind, spirit" (see animus). Meaning "evenness of temper" in English is from 1610s.

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pulchritude (n.)

"beauty, fairness," c. 1400, pulcritude, from Latin pulchritudo "beauty; excellence, attractiveness," from pulcher "beautiful," a word of unknown origin. De Vaan writes that Latin the -ch- spelling is by Greek influence and posits a stem *polkro- or *pelkro-, but that's as far as he confidently takes it.

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lily (n.)

Old English lilie, from Latin lilia, plural of lilium "a lily," cognate with Greek leirion, both perhaps borrowed from a corrupted pronunciation of an eastern Mediterranean word (de Vaan compares Coptic hreri, hleli "lily"). Used in Old Testament to translate Hebrew shoshanna and in New Testament to translate Greek krinon. As an adjective, 1530s, "white, pure, lovely;" later "pale, colorless" (1580s).

Figurative of whiteness, fairness, purity. The Latin word has become the general word in languages across Europe: German lilie, Dutch lelie, Swedish lilja, French lis, Spanish lirio, Italian giglio, Polish lilija, Russian liliya. The French word is contracted from Latin lilius, a rare surviving nominative form in French. In Old French lilie (12c.) also existed. Related: Lilied; lilaceous.

The lily of the valley translates Latin lilium convallium (Vulgate), a literal rendition of the Hebrew term in Song of Solomon ii:1; in modern times the name was applied to a particular plant (Convallaria majalis) apparently first by 16c. German herbalists. Lily pad is from 1834, American English. For gild the lily see gilded.

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conscience (n.)
Origin and meaning of conscience

c. 1200, "faculty of knowing what is right," originally especially to Christian ethics, later "awareness that the acts for which one feels responsible do or do not conform to one's ideal of right," later (late 14c.) more generally, "sense of fairness or justice, moral sense."

This is from Old French conscience "conscience, innermost thoughts, desires, intentions; feelings" (12c.) and directly from Latin conscientia "a joint knowledge of something, a knowing of a thing together with another person; consciousness, knowledge;" particularly, "knowledge within oneself, sense of right and wrong, a moral sense," abstract noun from conscientem (nominative consciens), present participle of conscire "be (mutually) aware; be conscious of wrong," in Late Latin "to know well," from assimilated form of com "with," or "thoroughly" (see con-) + 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").

The Latin word is probably a loan-translation of Greek syneidesis, literally "with-knowledge." The sense development is perhaps via "to know along with others" (what is right or wrong) to "to know right or wrong within oneself, know in one's own mind" (conscire sibi). Sometimes it was nativized in Old English/early Middle English as inwit. Russian also uses a loan-translation, so-vest, "conscience," literally "with-knowledge."

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equity (n.)

early 14c., equite, "quality of being equal or fair, impartiality;" late 14c., "that which is equally right or just to all concerned," from Old French equite (13c.), from Latin aequitatem (nominative aequitas) "the uniform relation of one thing to others, equality, conformity, symmetry;" also "just or equitable conduct toward others," from aequus "even, just, equal" (see equal (adj.)).

In law, "fairness in the adjustment of conflicting interests; the settlement of controversies by the dictates of good conscience" (natural equity), late 14c., from Roman naturalis aequitas, the general principles of justice which corrected or supplemented the legal codes ("governed by benevolence, while justitia yields to another only what is strictly due," Lewis & Short).

Hence, in England and U.S., also "justice based on such principles, the system of jurisprudence as to what is fair and what is not," and "a court or jurisdiction in which these doctrines are applied" (1590s).

The Latin word also meant "a quiet, tranquil state of mind; moderation, evenness of temper."

The L. æquitas was somewhat influenced in meaning by being adopted as the ordinary rendering of Gr. ἐπιεικεια ...,which meant reasonableness and moderation in the exercise of one's rights, and the disposition to avoid insisting on them too rigorously. [OED]

From 1620s as "an equitable right, that to which one is justly entitled," especially a right recognized by courts of equity that is not provided for in the common or statute law (such as certain property rights of wives). Equities, "the ordinary shares of a limited company," carrying certain rights to assets and profits, is attested by 1904.

By 1980s it had taken on extended senses in sociology, e.g.: "allocating benefits in various policy fields in such a way as to provide groups, persons, and places with at least a minimum level of benefits so as to satisfy basic needs" [Stuart S. Nagel, "Equity as a Policy Goal," 1983].

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