On the So-called Antinomy of the Variable

But for some founders of the new logic, the dissociation that Quine mentions simply forced new problems to surface. Bertrand Russell, for example, in his early account of the subject, explicitly rejects the existence of variable objects yet courts the following quandary: “x is, in some sense, the object denoted by any term; yet this can hardly be strictly maintained, for different variables may occur in a proposition, yet the object denoted by any term, one would suppose, is unique.” Russell’s views at the time compel him to postulate a unique object — the variable — denoted by what “The variable” in The Ways of Paradox, revised and enlarged edition (Cambridge, MA: Harvard UP, 1976), p. 272. The Principles of Mathematics, 2nd edition (London: Allen & Unwin, 1937), §93.