Etymology
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deductive (adj.)

1640s, "derivative" (a sense now obsolete); from 1660s in logic, "consisting of deduction; based on inference from accepted principles," from Latin deductivus"derivative," from deduct-, past-participle stem of deducere "to lead down, derive" (in Medieval Latin, "infer logically"), from de "down" (see de-) + ducere "to lead" (from PIE root *deuk- "to lead"). Related: Deductively.

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deduce (v.)

early 15c., deducen, "to show, prove, demonstrate;" late 15c., "to deduct," from Latin deducere "lead down, derive" (in Medieval Latin, "infer logically"), from de "down" (see de-) + ducere "to lead" (from PIE root *deuk- "to lead"). The usual modern sense of "draw a conclusion from something already known" is first recorded 1520s, from Medieval Latin. Related: Deduced; deducing.

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induce (v.)

formerly also enduce, late 14c., "to lead by persuasions or other influences," from Latin inducere "lead into, bring in, introduce, conduct; persuade; suppose, imagine," from in- "into, in, on, upon" (from PIE root *en "in") + ducere "to lead" (from PIE root *deuk- "to lead"). Meaning "to bring about" in any way (in reference to a trance, a fever, etc.) is from early 15c.; sense of "to infer by reasoning" is from 1560s. Electro-magnetic sense first recorded 1777. Related: Induced; inducing.

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ratiocination (n.)

"process of reasoning, mental process of passing from the cognition of premises to the cognition of the conclusion," 1520s, from Latin ratiocinationem (nominative ratiocinatio) "a reasoning, calm reasoning," noun of action from past-participle stem of ratiocinari "to reckon, compute, calculate; to deliberate, meditate; to reason, argue, infer." This is a compound of ratio "reckoning, calculation," also "judgment, reason" (see ratio) + -cinari, which probably is related to conari "to endeavor, to try," from PIE *kona-, from root *ken- "to hasten, set oneself in motion" (see deacon).

Most writers make ratiocination synonymous with reasoning. J.S. Mill and others hold that the word is usually limited to necessary reasoning. [Century Dictionary]
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conclude (v.)

early 14c., "confute or frustrate an opponent in argument, end an argument by winning it," from Latin concludere "to shut up, enclose," from assimilated form of com "together" (see con-) + -cludere, combining form of claudere "to shut" (see close (v.)).

Meanings "reach a mental determination, deduce; infer or determine by reason" are from late 14c., a sense also in Latin. General sense of "bring to an end, finish, terminate," and intransitive sense of "come to an end" are from late 14c. Meaning "settle, arrange, determine finally" is from early 15c. Sometimes in Middle English it was used in the etymological sense, "shut in" (late 14c.). Related: Concluded; concluding.

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deduction (n.)

early 15c., deduccioun, "a bringing, a leading;" mid-15c., "action of deducting; a taking away, a number or amount subtracted," from Old French deduction (Modern French déduction) and directly from Latin deductionem (nominative deductio) "a leading away, an escorting; a diminution," noun of action from past-participle stem of deducere "lead or bring away or down; derive" (in Medieval Latin, "infer logically"), from de "down" (see de-) + ducere "to lead," from PIE root *deuk- "to lead."

Meaning "that which is deducted" is from 1540s. As a term in logic, "derivation as a result from a known principle, an inference, conclusion," 1520s, from Late Latin use of deductio as a loan-translation of Greek apagoge. Related: Deductional.

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inferior (adj.)
early 15c., of land, "low, lower down, lower in position," from Latin inferior "lower, farther down" (also used figuratively), comparative of inferus (adj.) "that is below or beneath," from infra "below" (see infra-). Meaning "lower in degree, rank, grade, or importance" is from 1530s; absolutely, "of low quality or rank," also from 1530s.
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inferiority (n.)

"state of being inferior," 1590s, probably from Medieval Latin *inferioritas; see inferior + -ity. Inferiority complex first attested 1919.

The surrender of life is nothing to sinking down into acknowledgment of inferiority. [John C. Calhoun, Senate debate, Feb. 19, 1847]
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inferno (n.)
1834, "Hell, the infernal regions," from Italian inferno, from Late Latin infernus "Hell," in classical Latin "the lower world" (see infernal). As "a large, raging fire" from 1928.
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inferential (adj.)
1650s, from Medieval Latin inferentia (see inference) + -al (1). Related: Inferentially.
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