Arbitrary: Unconditioned, as one pleases, up to one's own decision or volition.
One needs a concept like arbitrary to explain substitution for variables: That any arbitrary number will do in the equation x=x means that whichever number that is chosen and substituted uniformly for "x" in "x=x" will do, in the sense that it results in a true statement, such as 5=5 or 9=9 or whatever.
Note that the notion of an unconditioned choice sounds a bit paradoxical, but when the choice is arbitrary it does mean that whichever one chooses from a set of possibilities will do.
