Etymology
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reasonable (adj.)

c. 1300, resonable, "having sound judgment, endowed with the faculty of reason," from Old French raisonable, from Latin rationabilis, from ratio "reckoning, understanding, motive, cause," from ratus, past participle of reri "to reckon, think" (from PIE root *re- "to reason, count").

Also originally "rational, sane," senses now obsolete. The sense shifted somewhat in Middle English via "due to or resulting from good judgment," then "not exceeding the bounds of common sense."

The meaning "moderate in price" is recorded from 1660s; earlier it meant "moderate in amount" (14c.). Related: Reasonably, which is from late 14c. as "according to reason," c. 1500 as "fairly tolerably;" reasonableness

The adjective reasonable ... denotes a character in which reason, (taking that word in its largest acceptation,) possesses a decided ascendant over the temper and passions: and implies no particular propensity to a display of the discursive power, if indeed it does not exclude the idea of such a propensity. [Dugald Stewart, "Elements of the Philosophy of the Human Mind," 1856]

What the majority of people consider to be 'reasonable' is that about which there is agreement, if not among all, at least among a substantial number of people; 'reasonable' for most people, has nothing to do with reason, but with consensus. [Erich Fromm, "The Heart of Man," 1968]

In law, "befitting a person of reason or sound sense;" reasonable doubt (1670s) is doubt for which a pertinent reason can be assigned and which prevents conviction in the minds of jurors of the truth of the charge.

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Definitions of reasonable

reasonable (adj.)
showing reason or sound judgment;
Synonyms: sensible
reasonable (adj.)
not excessive or extreme;
reasonable prices
Synonyms: fair / fairish
reasonable (adj.)
marked by sound judgment;
Synonyms: sane
From wordnet.princeton.edu