I develop a uniform treatment of free-choice effects with English 'any', 'or', and wh-ever free relatives within different environments in terms of the notion of an arbitrary object (Fine 1983, 1985, Horsten 2019). In the resulting theory, there are two kinds of indefiniteness or variableness in natural language semantics. There is the indefiniteness of a Hamblin-style alternative set (i.e., variable reference to a definite thing), which behaves in a disjunctive manner due to its being the input to a pointwise compositional principle. And there is the indefiniteness of an arbitrary object (i.e., definite reference to a variable thing), which may be regarded as a peg for hanging properties common to a range of things, with resulting law-like universal or conjunctive effects.