Etymology
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pagan (n.)

c. 1400, perhaps mid-14c., "person of non-Christian or non-Jewish faith," from Late Latin paganus "pagan," in classical Latin "villager, rustic; civilian, non-combatant" noun use of adjective meaning "of the country, of a village," from pagus "country people; province, rural district," originally "district limited by markers," thus related to pangere "to fix, fasten," from PIE root *pag- "to fasten." As an adjective from early 15c.

The religious sense often was said in 19c. [e.g. Trench] to derive from conservative rural adherence to the old gods after the Christianization of Roman towns and cities; but the Latin word in this sense predates that period in Church history, and it is more likely derived from the use of paganus in Roman military jargon for "civilian, incompetent soldier," which Christians (Tertullian, c. 202; Augustine) picked up with the military imagery of the early Church (such as milites "soldier of Christ," etc.).

The English word was used later in a narrower sense of "one not a Christian, Jew, or Muslim." As "person of heathenish character or habits," by 1841. Applied to modern pantheists and nature-worshippers from 1908.

Pagan and heathen are primarily the same in meaning; but pagan is sometimes distinctively applied to those nations that, although worshiping false gods, are more cultivated, as the Greeks and Romans, and heathen to uncivilized idolaters, as the tribes of Africa. A Mohammedan is not counted a pagan much less a heathen. [Century Dictionary, 1897]

The English surname Paine, Payne, etc., appears by old records to be from Latin paganus, but whether in the sense "villager," "rustic," or "heathen" is disputed. It also was a common Christian name in 13c., "and was, no doubt, given without any thought of its meaning" ["Dictionary of English Surnames"].

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paganism (n.)

"religious beliefs and practices of pagans," early 15c., paganisme, from Church Latin paganismus, from paganus (see pagan). Alternative paganity is from 1540s; pagandom is from 1739.

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peasant (n.)

"rural person of inferior rank or condition," usually engaged in agricultural labor, early 15c., paisaunt, from Anglo-French paisant (early 14c.), Old French paisant, paisent "local inhabitant" (12c., Modern French paysan), earlier paisenc, from pais "country, region" (Modern French pays, from Latin pagus; see pagan) + Frankish suffix -enc "-ing."

Pais is from Late Latin pagensis "(inhabitant) of the district," from Latin pagus "country or rural district" (see pagan). As a style of garment in fashion (such as peasant blouse) from 1953. In German history, the Peasants' War was the rebellion of 1524-25.

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paynim (n.)

early 13c., painime, paynyme, "heathen lands collectively," from Old French paienime, paienisme "heathen, pagan; Saracen lands or culture or faith," from Late Latin paganismus "heathendom" (Augustine), from paganus "heathen" (see pagan). The original sense is obsolete; the mistaken meaning "a heathen person" (c. 1300, also in Old French) is via phrases such as paynim lands. As an adjective, "non-Christian, pagan," c. 1300, from Old French.

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page (n.2)

"youth, lad; boy of the lower orders; personal servant," c. 1300 (early 13c. as a surname), originally also "youth preparing to be a knight" (beneath the rank of a squire), from Old French page "a youth, page, servant" (13c.), possibly via Italian paggio (Barnhart), from Medieval Latin pagius "servant," perhaps ultimately from Greek paidion "boy, lad," diminutive of pais (genitive paidos) "child."

But OED considers this unlikely and, with Century Dictionary, points instead to Littré's suggestion of a source in Latin pagus "countryside," in sense of "boy from the rural regions" (see pagan). Meaning "youth employed as a personal attendant to a person of rank" is first recorded mid-15c.; this was transferred from late 18c. to boys who did personal errands in hotels, clubs, etc., also in U.S. legislatures.

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*pag- 
also *pak-, Proto-Indo-European root meaning "to fasten."

It forms all or part of: Areopagus; appease; appeasement; compact (adj.) "concentrated;" compact (n.1) "agreement;" fang; impact; impale; impinge; newfangled; pace (prep.) "with the leave of;" pacific; pacify; pact; pagan; page (n.1) "sheet of paper;" pageant; pale (n.) "limit, boundary, restriction;" palette; palisade; patio; pawl; pax; pay; peace; peasant; pectin; peel (n.2) "shovel-shaped instrument;" pole (n.1) "stake;" propagate; propagation; travail; travel.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit pasa- "cord, rope," pajra- "solid, firm;" Avestan pas- "to fetter;" Greek pegnynai "to fix, make firm, fast or solid," pagos "pinnacle, cliff, rocky hill;" Latin pangere "to fix, to fasten," pagina "column," pagus "district;" Slavonic paž "wooden partition;" Old English fegan "to join," fon "to catch seize."
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heathen 

Old English hæðen "not Christian or Jewish," also as a noun, "heathen man, one of a race or nation which does not acknowledge the God of the Bible" (especially of the Danes), merged with Old Norse heiðinn (adj.) "heathen, pagan," from Proto-Germanic *haithana- (source also of Old Saxon hedhin, Old Frisian hethen, Dutch heiden, Old High German heidan, German Heiden), which is of uncertain origin.

Perhaps literally "dweller on the heath, one inhabiting uncultivated land;" see heath + -en (2). Historically assumed to be ultimately from Gothic haiþno "gentile, heathen woman," used by Ulfilas in the first translation of the Bible into a Germanic language (as in Mark vii.26, for "Greek"); like other basic words for exclusively Christian ideas (such as church) it likely would have come first into Gothic and then spread to other Germanic languages. If so it could be a noun use of an unrelated Gothic adjective (compare Gothic haiþi "dwelling on the heath," but a religious sense is not recorded for this).

Whether native or Gothic, it might have been chosen on model of Latin paganus, with its root sense of "rural" (see pagan), but that word appears relatively late in the religious sense. Or the Germanic word might have been chosen for its resemblance to Greek ethne (see gentile), or it may be a literal borrowing of that Greek word, perhaps via Armenian hethanos [Sophus Bugge]. Boutkan (2005) presents another theory:

It is most probable that the Gmc. word *haiþana- referred to a person living on the heath, i.e. on common land, i.e. a person of one's own community. It would then be a neutral word used by heathen people in order to refer to each other rather than a Christian, negative word denoting non-Christians.
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miscreant (n.)

late 14c., "a heathen, a Saracen, a pagan, an unbeliever, a non-Christian," from miscreant (adj.) or from Old French mescreant, which also had a noun sense of "infidel, pagan, heretic." Sense of "villain, vile wretch, scoundrel" is first recorded 1590 in Spenser.

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Candlemas (n.)
Church festival, late Old English candelmæsse (from candle + mass (n.2)), feast of the purification of the Virgin Mary (Feb. 2), celebrated with many candles, corresponding to Celtic pagan Imbolc.
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idol (n.)

mid-13c., "image of a deity as an object of (pagan) worship," from Old French idole "idol, graven image, pagan god" (11c.), from Latin idolum "image (mental or physical), form," especially "apparition, ghost," but used in Church Latin for "false god, image of a pagan deity as an object of worship." This is from Greek eidolon "mental image, apparition, phantom," also "material image, statue," in Ecclesiastical Greek," a pagan idol," from eidos "form, shape; likeness, resemblance" (see -oid).

A Greek word for "image," used in Jewish and early Christian writers for "image of a false god," hence also "false god." The Germanic languages tended to form a word for it from the reverse direction, from "god" to "false god," hence "image of a false god" (compare Old English afgod, Danish afgud, Swedish avgud, Old High German abgot, compounds with af-/ab- "away, away from" (source of off) + god).

The older Greek senses sometimes have been used in English. Figurative sense of "something idolized" is first recorded 1560s (in Middle English the figurative sense was "someone who is false or untrustworthy"). Meaning "a person so adored, human object of adoring devotion" is from 1590s.

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