Full Idea
A variable is not any term simply, but any term as entering into a propositional function.
Gist of Idea
Variables don't stand alone, but exist as parts of propositional functions
Source
Bertrand Russell (The Principles of Mathematics [1903], §093)
Book Reference
Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.94
A Reaction
So we should think of variables entirely by their role, rather than as having a semantics of their own (pace Kit Fine? - though see Russell §106, p.107).