  Quine took from his discussions with Leśniewski the idea that the quantifiers were somehow substitutional. There is an element of truth in this. A universally quantified formula \(\forall X\ldots \ulcorner\)—\(X\)—\(\urcorner\) licenses the inference to any formula —\(C\)— obtained by substituting any well-formed expression \(C\) of the appropriate category in place of the bound variable \(X\), and likewise for all the other variables occurring bound by the same quantifier. Dually, from —\(C\)— one may infer \(\exists X\ldots \ulcorner\)—\(X\)—\(\urcorner\) for suitable categories of bound variable. These are the usual quantifier rules, liberalized to apply to any categories of variable in batches of one or more. So for example if there is a theorem universally quantifying nominal variables, such as ‘\(\forall a\ulcorner\)any \(a\) is an \(a\urcorner\)’, we can validly infer ‘any \(\Lambda\) is a \(\Lambda\)’ even though the name is empty. Quine assumed that the lack of ontological commitment must entail that the quantifiers range over expressions rather than things. This would not have been acceptable to Leśniewski, because it would constitute use/mention confusion, and because while it is true for the nominalist that there are only finitely many expressions, it is not known to be true, and may in fact be false, that there are only finitely many things.