3.316 What values a propositional variable may accept is fixed.

The fixing of the values is the variable.

There seems to be an interesting combination here of agreement (arbitrariness) and absolutism (non-arbitrariness). A variable may be replaced by any range of values, determined by whoever introduces the variable. But once a variable is defined, the definition fixes the range completely. X can mean anything, but if I say “X² = 4” then its meaning is settled (as either 2 or -2). “X” on its own has no meaning, and so is not a variable. In a proposition such as “X² = 4” it is a variable and has a meaning. And its meaning, its possible values, is set.

Cf. 5.501. Black (p. 128) says the procedure referred to is that described in 3.317, not 3.315.