Etymology
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polytheism (n.)

"belief in more gods than one," 1610s, from French polythéisme (16c.), formed from Greek polytheia "polytheism," polytheos "of or belonging to many gods," from polys "many" (from PIE root *pele- (1) "to fill") + theos "god" (from PIE root *dhes-, forming words for religious concepts).

The various modes of worship, which prevailed in the Roman world, were all considered by the people, as equally true; by the philosopher, as equally false; and by the magistrate, as equally useful. And thus toleration produced not only mutual indulgence, but even religious concord. [Gibbon]
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polytheist (n.)

"one who believes in or maintains the doctrine of the plurality of gods," 1610s; see polytheism + -ist. Related: Polytheistic (1706); polytheistical (1670s).

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theism (n.)

1670s, "belief in a deity or deities," (as opposed to atheism); by 1711 as "belief in one god" (as opposed to polytheism); by 1714 as "belief in the existence of God as creator and ruler of the universe" (as opposed to deism), the usual modern sense; see theist + -ism.

Theism assumes a living relation of God to his creatures, but does not define it. It differs from deism in that the latter is negative and involves a denial of revelation, while the former is affirmative, and underlies Christianity. One may be a theist and not be a Christian, but he cannot be a Christian and not be a theist. [Century Dictionary]
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*dhes- 
*dhēs-, Proto-Indo-European root forming words for religious concepts. Possibly an extension of PIE root *dhe- "to set, put."

It forms all or part of: apotheosis; atheism; atheous; Dorothy; enthusiasm; fair (n.) "a stated market in a town or city;" fanatic; ferial; feast; fedora; -fest; festal; festival; festive; festoon; Festus; fete; fiesta; henotheism; monotheism; pantheism; pantheon; polytheism; profane; profanity; Thea; -theism; theist; theo-; theocracy; theodicy; Theodore; Theodosia; theogony; theology; theophany; Theophilus; theosophy; theurgy; tiffany; Timothy.

It is the hypothetical source of/evidence for its existence is provided by: Greek theos "god;" Latin feriae "holidays," festus "festive," fanum "temple."
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*pele- (1)
*pelə-, Proto-Indo-European root meaning "to fill," with derivatives referring to abundance and multitude.

It forms all or part of: accomplish; complete; compliment; comply; depletion; expletive; fele; fill; folk; full (adj.); gefilte fish; hoi polloi; implement; manipulation; nonplus; plebe; plebeian; plebiscite; pleiotropy; Pleistocene; plenary; plenitude; plenty; plenum; plenipotentiary; pleo-; pleonasm; plethora; Pliocene; pluperfect; plural; pluri-; plus; Pollux; poly-; polyamorous; polyandrous; polyclinic; polydactyl; polydipsia; Polydorus; polyethylene; polyglot; polygon; polygraph; polygyny; polyhedron; polyhistor; polymath; polymer; polymorphous; Polynesia; polyp; Polyphemus; polyphony; polysemy; polysyllabic; polytheism; replenish; replete; supply; surplus; volkslied.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit purvi "much," prayah "mostly;" Avestan perena-, Old Persian paru "much;" Greek polys "much, many," plethos "people, multitude, great number," ploutos "wealth;" Latin plus "more," plenus "full;" Lithuanian pilus "full, abundant;" Old Church Slavonic plunu; Gothic filu "much," Old Norse fjöl-, Old English fela, feola "much, many;" Old English folgian; Old Irish lan, Welsh llawn "full;" Old Irish il, Welsh elu "much."
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Hinduism (n.)
blanket term for "polytheism of India," 1786, from Hindu + -ism.
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henotheism (n.)
"devotion to a single god without asserting that he or she is the only god," 1860, from Greek henos (neuter of heis "one;" from PIE root *sem- (1) "one; as one, together with") + -theism. Coined by (Friedrich) Max Müller (1823-1900), professor of comparative philology at Oxford. Supposedly a characteristic of the oldest Hindu religion; or a system between monotheism and polytheism. Related: Henotheist; henotheistic.
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kathenotheism (n.)
"a form of polytheism characteristic of the Vedic religion, in which one god at a time is considered supreme," 1865, coined in German by Max Müller from Greek kath' hena "one by one" (from kata- "according to" + en- "one") + -theism. Müller also coined the nearly synonymous henotheism (1860, from Greek henos "one") for "faith in a single god" as distinguished from exclusive belief in only one god, in writings on early Hebrew religion. He also has adevism (from Sanskrit deva "god") for "disbelief in the old gods and legends").
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