Full Idea
A customary argument against quantification based on substitution of names for variables refers to the theorem of set theory that irrational numbers cannot all be assigned integers. Although the integers can all be named, the irrationals therefore can't.
Gist of Idea
You can't base quantification on substituting names for variables, if the irrationals cannot all be named
Source
Willard Quine (Philosophy of Logic [1970], Ch.6)
Book Reference
Quine,Willard: 'Philosophy of Logic' [Prentice-Hall 1970], p.92
A Reaction
[He names Ruth Marcus as a source of substitutional quantification] This sounds like more than a mere 'argument' against substitutional quantification, but an actual disproof. Or maybe you just can't quantify once you run out of names.