arbitrary

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Etymology tree

Latin arbiter

Proto-Indo-European *-yósder.

Proto-Italic *-āzios

Latin -ārius

Latin arbitrāriusder.

Middle English arbitrarie

English arbitrary

From Middle English arbitrarie, Latin arbitrārius (“arbitrary, uncertain”), from arbiter (“witness, on-looker, listener, judge, overseer”).

usually Based on individual discretion or judgment; not based on any objective distinction, perhaps even made at random. Benjamin Franklin's designation of "positive" and "negative" to different charges was arbitrary.
Determined by impulse rather than reason; often connoting heavy-handedness. 1937/1938, Albert Einstein, letter to Max Born The Russian trials were Stalin's purges, with which he attempted to consolidate his power. Like most people in the West, I believed these show trials to be the arbitrary acts of a cruel dictator.
Any, out of all that are possible. The equation is true for an arbitrary value of x.
Determined by independent arbiter.
Not representative or symbolic; not iconic.

Anything arbitrary, such as an arithmetical value or a fee. And in this long chain of consistence, a chain stretching from the long dead to the far unborn, the notion of the arbitrary could only survive as the notion of a pre-established arbitrary.