Etymology
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belief (n.)

late 12c., bileave, "confidence reposed in a person or thing; faith in a religion," replacing Old English geleafa "belief, faith," from West Germanic *ga-laubon "to hold dear, esteem, trust" (source also of Old Saxon gilobo, Middle Dutch gelove, Old High German giloubo, German Glaube), from *galaub- "dear, esteemed," from intensive prefix *ga- + PIE root *leubh- "to care, desire, love." The prefix was altered on analogy of the verb believe. The distinction of the final consonant from that of believe developed 15c.

The be-, which is not a natural prefix of nouns, was prefixed on the analogy of the vb. (where it is naturally an intensive) .... [OED]

Meaning "conviction of the truth of a proposition or alleged fact without knowledge" is by 1530s; it is also "sometimes used to include the absolute conviction or certainty which accompanies knowledge" [Century Dictionary]. From c. 1200 as "a creed, essential doctrines of a religion or church, things held to be true as a matter of religious doctrine;" the general sense of "That which is believed" is by 1714. Related: Beliefs.

Belief meant "trust in God," while faith meant "loyalty to a person based on promise or duty" (a sense preserved in keep one's faith, in good (or bad) faith, and in common usage of faithful, faithless, which contain no notion of divinity). But faith, as cognate of Latin fides, took on the religious sense beginning in 14c. translations, and belief had by 16c. become limited to "mental acceptance of something as true," from the religious use in the sense of "things held to be true as a matter of religious doctrine."

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system (n.)
1610s, "the whole creation, the universe," from Late Latin systema "an arrangement, system," from Greek systema "organized whole, a whole compounded of parts," from stem of synistanai "to place together, organize, form in order," from syn- "together" (see syn-) + root of histanai "cause to stand," from PIE root *sta- "to stand, make or be firm."

Meaning "set of correlated principles, facts, ideas, etc." first recorded 1630s. Meaning "animal body as an organized whole, sum of the vital processes in an organism" is recorded from 1680s; hence figurative phrase to get (something) out of one's system (1900). Computer sense of "group of related programs" is recorded from 1963. All systems go (1962) is from U.S. space program. The system "prevailing social order" is from 1806.
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Dewey Decimal system (n.)

library classification system that organizes information into 10 broad areas subdivided numerically into progressively smaller topics, by 1885, named for Melvil Dewey (1851-1931) who proposed it 1876 while acting librarian of Amherst College. He also crusaded for simplified spelling and the metric system.

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credence (n.)

"belief, trust in facts derived from other than personal knowledge; that which gives a claim to belief," mid-14c., from Medieval Latin credentia "belief," from Latin credentum (nominative credens), past participle of credere "believe, trust" (see credo).

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misbelief (n.)

"heresy, erroneous or unorthodox religious belief," early 13c., from mis- (1) "bad, wrong" + belief. Related: Misbelieve; misbelieving; misbeliever.

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monotheism (n.)

"doctrine or belief that there is but one god," 1650s, from mono- "single, alone" + -theism "belief (of a specified kind) in God, a god, or gods."

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mercantile (adj.)

"of or pertaining to merchants, trade, or commerce," 1640s, from French mercantile (17c.), from Italian mercantile, from Medieval Latin mercantile, from Latin mercantem (nominative mercans) "a merchant," also "trading," present participle of mercari "to trade," from merx "wares, merchandise" (see market (n.)). Mercantile system first appears in Adam Smith (1776).

Mercantile system, in polit. econ., the belief generally held till the end of the last century, that all wealth consists in gold and silver, and that therefore the exportation of goods and importation of gold should be encouraged by the state, while the importation of goods and the exportation of gold should be forbidden, or at least restricted as much as possible. [Century Dictionary, 1895]
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unbelief (n.)
mid-12c., "absence or lack of religious belief; disbelief of the truth of the Gospel," from un- (1) "not" or un- (2) "opposite of" + belief. Old English had ungeleafa in this sense.
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bitheism (n.)
"belief in two gods" (typically a good and an evil one), 1857, from bi- "two" + -theism.
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incredible (adj.)
early 15c., "unbelievable, surpassing belief as to what is possible," from Latin incredibilis "not to be believed, extraordinary," from in- "not" (see in- (1)) + credibilis "worthy of belief" (see credible). Used c. 1400 in a now-extinct sense of "unbelieving, incredulous." Related: Incredibly; incredibility.
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