In 'Against Vague Existence', Ted Sider argues that our quantifiers cannot be vague, because it is impossible to characterize semantic vagueness in our quantifiers in the usual way; that is, in terms of multiple admissible precisifications. Sider considers as a test case whether it could be indeterminate, due to vagueness in the existential quantifier, whether the following was true:
(E): Ex (x is composed of the F and the G).
Sider claims that the ‘familiar model’ for spelling out how such indeterminacy comes about would apply to this case as follows:
(P1): ‘E’ has at least two precisifications, call them E1 and E2. There is an object, x, that is in E1’s domain but not in E2’s domain, and which is composed of the F and the G. Thus, (E) is neither definitely true nor definitely false.
But, as Sider points out, ‘the defender of vague existence thinks that it is not definitely true that there is something composed of the F and the G ... She will therefore not make this speech’ (p. 139).
Sider proceeds to offer three options to the defender of vague existence: rejecting the need to non-vaguely describe the precisifications, using vague quantifiers to non-vaguely describe them, and finding non-quantificational non-vague language to describe them. None of these is my preferred way of resisting Sider’s argument. Nor do I wish to resist (here) his two presuppositions: that the indeterminacy of (E) would have to be semantic (as opposed to ontic), and that this means we need to explain it in terms of multiple admissible precisifications of the existential quantifier.
Instead, I propose we investigate how much can be achieved through paying careful attention to scope in describing the relevant precisifications. Instead of (P1) above, perhaps we can appeal to:
(P2): ‘E’ has at least two precisifications. On the first precisification, there is an object, x, which is composed of the F and the G. But on the second precisification, there is no such object. Thus, (E) is neither definitely true no definitely false.
Note that, now, the existential quantifiers appearing in the account of why (E) is neither definitely true nor definitely false occur within the scope of the operators ‘on the first precisification’ and ‘on the second precisification’. Hence there is no need for any metalanguage commitment to an object which is composed of the F and the G.
(P2) seems to do what Sider requires: it talks about two precifications for ‘E’, and explains what it is about these two precisifications which results in the indeterminacy of (E). So what’s wrong with (P2)?