J Robert G Williams

Carrie Jenkins recently posted on Ted Sider‘s paper “Against Vague Existence“.

Suppose you think it’s vague whether some collection of cat-atoms compose some further thing (perhaps because you’re a organicist about composition, and it’s vague whether kitty is still living). It’s then natural to think that there’ll be corresponding vagueness in the range of (unrestricted) first order quantifier: it might be vague whether it ranges over one billion and fifty five thing or one billion and fifty six things, for example: with the putative one billion and fifty-sixth entity being kitty, if she still exists. Sider thinks there are insuperable problems for this view; Carrie thinks the problems can be avoided. Below the fold, I present a couple of problems for (what I take to be) Carrie’s way of addressing the Sider-challenge.

Sider’s interested in “precisificational” theories of vagueness, such as supervaluationism and (he urges) epistemicism. The vagueness of an expression E consists in there being multiple ways in which the term could be made precise, between which, perhaps, the semantic facts don’t select (supervaluationism), or between which we can’t discriminate the uniquely correct one (epistemicism). (On my account, ontic vagueness turns out to be precisificational too). The trouble is alleged to be that vague existence claims can’t fit this model. One underlying idea is that multiple precifications of an unrestricted existential quantifier would have to include different domains: perhaps precisification E1 has domain D1, whereas precisification E2 has domain D2, which is larger since includes everything in D1, plus one extra thing: kitty.

But wait! If it is indeterminate whether kitty exists, how can we maintain that the story I just gave is true? When I say “D2 contains one extra thing: kitty”, it seems it should be at best indeterminate whether that is true: for it can only be true if kitty exists. Likewise, it will be indeterminate whether or not the name “kitty” suffers reference-failure.

Ok, so that’s what I think of as the core of Sider’s argument. Carrie’s response is very interesting. I’m not totally sure whether what I’m going to say is really what Carrie intends, so following the standard philosophical practice, I’ll attribute what follows to Carrie*. Whereas you’d standardly formulate a semantics by using relativized semantic relations, e.g. “N refers to x relative to world w, time t, precification p”, Carrie* proposes that we replace the relativization with an operator. So the clause for the expression N might look like: “At world w, At time t, At precisification p, N referes to x”. In particular, we’ll say:

“At precisfication 1, “E” ranges over the domain D1;
At precisification 2, “E” ranges over the domain D1+{kitty}.”

In the metalanguage, “At p” works just as it does in the object language, binding any quantifiers within its scope. So, when within the scope of the “At precisification 2” operator, the metalinguistic name “kitty” will have reference, and, again within the scope of that operator, the unrestricted existential quantifier will have kitty within its range.

This seems funky so far as it goes. It’s a bit like a form of modalism that takes “At w” as the primitive modal operator. I’ve got some worries though.

Here’s the first. A burden on Carrie*’s approach (as I’m understanding it) will be to explain under what circumstances a sentence is true. usually, this is just done by quantification into the parameter position of the parameterized “truth”, i.e.

“S” is true simpliciter iff for all precisifications p, “S” is true relative to p.

What’s the translation of this into the operator account? Maybe something like:

“S” is true simpliciter iff for all precisifications p, At p “S” is true.

For this to make sense, “p” has to be a genuine metalinguistic variable. And this undermines some of the attractions of Carrie*’s account: i.e. it looks like we’ll now the burden of explaining what “precisifications” are (the sort of thing that Sider is pushing for in his comments on Carrie’s post). More attractive is the “modalist” position where “At p” is a primitive idiom. Perhaps then, the following could be offered:

“S” is true simpliciter iff for all precisification-operators O, [O: “S” is true].

My second concern is the following: I’m not sure how the proposal would deal with quantification into a “precisification” context. E.g. how do we evaluate the following metalanguage sentence?

“on precisification 2, there is an x such that x is in the range of “E”, and on precisification 1, x is not within the range of “E””

The trouble is that, for this to be true, it looks like kitty has to be assigned as the value of “x”. But the third occurence is within the scope of “on precisification 2”. On the most natural formulation, for “on precisification 2, x is F” to be true on the assignment of an object to x, x will have to be within the scope of the unrestricted existential quantifier at precisification 1. But Kitty isn’t! There might be a technical fix here, but I can’t see it at the moment. Here’s the modal analogue: let a be the actual world, and b be a merely possible world where I don’t exist. What should the modalist say about the following?

“At a, there is an object x (identical to Robbie) and At b, nothing is identical to x”

Again, for this to be true, we require an open sentence “At b, nothing is identical to x” to be true relative to an assignment where some object not existing at b is the value of “x”. And I’m just not sure that we can make sense of this without allowing ourselves the resources to define a “precisification neutral” quantifier within the metalanguage in reference to which Sider’s original complaint could be reintroduced.