Abstract
Sider (Four-dimensionalism 2001; Philos Stud 114:135–146, 2003; Nous 43:557–567, 2009) has developed an influential argument against indeterminacy in existence. In what follows, I argue that the defender of metaphysical forms of indeterminate existence has a unique way of responding to Sider’s argument. The response I’ll offer is interesting not only for its applicability to Sider’s argument, but also for its broader implications; responding to Sider helps to show both how we should think about precisification in the context of metaphysical indeterminacy and how we should understand commitment to metaphysically indeterminate existence. And if I’m right that metaphysical indeterminacy can allow for indeterminate existence in a way that semantic indeterminacy can’t, indeterminate existence might actually give us a reason to accept metaphysical indeterminacy (rather than a reason to reject it, as is commonly assumed).
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Notes
To see why this isn’t required by Sider’s set-up, consider a world in which, ex hypothesi, it’s determinate that only one thing exists, but indeterminate what one thing exists. To precisfy this world, both precisifications of the existential quantifier would be of equal size (they’d each contain one object, since determinately only one thing exists), but their domains would be different—one would contain only a, the other only b, for example. I’ll be using the ‘larger than/smaller than’ model in subsequent discussion for the sake of simplicity. As far as I can tell, it doesn’t introduce any unwarranted noise.
Standard supervaluationism preserves classical logic, though not classical metatheory. ‘Non-standard’ supervaluationism preserves classical metatheory as well. Other notable classical treatments of indeterminacy—Williamson’s (1994) epistemicism and Graff-Fara’s (2000) interest-relative contextualism, for example—are not available to the defender of metaphysical indeterminacy, so precisificational theories are of particular importance if classical logic is to be preserved. See Barnes and Williams (forthcoming) for a precisificational theory of metaphysical indeterminacy which is fully classical (preserving both classical logic and metatheory).
If you thought the openness of the future was a kind of metaphysical indeterminacy, for example, the indeterminacy you commit to wouldn’t require indeterminacy in existence. Future-directed indeterminacy can lead to indeterminate existence: if, for example, the openness of the future involves indeterminacy in what future ontology exists. But while indeterminacy in what future ontology exists would be sufficient for generating metaphysical indeterminacy for future facts, it isn’t necessary—you might think there’s future-directed indeterminacy but be a presentist. See Barnes and Cameron (2009) for discussion.
Or, perhaps more carefully, the semantic value. For ease of explanation, I’ll speak loosely about ‘the reference’ of things like quantifiers, but if this strikes you as objectionable just sub in ‘semantic value’.
That is, all the individuals—whether actual or possible—which satisfy the predicate.
Contrast the view which says that indeterminate predicate have a determinate extension, which is a ‘vague set’.
Though they all respect penumbral connections—for any x they contain, they contain all the things redder than x.
E.g., Classes, or sui generis values of second order variables.
After all, if the language in which we use ‘∃*’ contains the predicate ‘is a unicorn’, then ∃*x(x is a unicorn) will be true. As Turner says: ‘surely we ought not to think that, really, there are unicorns after all.’
This is a classic case of inherited vagueness. ‘In the kitchen’ is vague, but is not used in the sentence (the sentence is just ‘There is a dog’, with ‘there is’ suitably restricted). Rather, we’ve placed a vague restriction on ‘there is’, so ‘there is’ inherits the vagueness from the description we’re using to restrict it.
On a non-deflationary understanding of ontological commitment, that is.
There will, of course, be different ways to characterize what I’m calling ‘pseudo-quantifiers’. But the important point is simply that we often find things in natural language which look quantificational, but which fail to genuinely be quantifiers because they try to quantify over things that don’t exist.
This point needs to be put carefully. It’s not that there is some thing, b, such that that thing exists indeterminately. This de re claim will make Sider’s conclusion unavoidable. Rather, it’s indeterminate whether there is any such thing as b (and so indeterminate whether or not b refers). The claim of indeterminate existence needs to be made de dicto rather than de re.
Why isn’t it just indeterminate whether ∃1 has domain {a} or domain {a,b}? Because for the precisificational model to work ∃1 and ∃2 need to be determinately distinct.
Sub in your favorite story here for how to deal with non-referring terms like ‘b’.
To evaluate ‘from the perspective’ of a precisification is, roughly, to treat that precisification as giving the actual truth conditions of the terms in question. So, for example, from the perspective of the precisification that says the rose is red, the precisification that says it isn’t red has too strict criteria for redness. Precisifications are pseudo-modal, so the idea is analogous to treating a possible world as actualized.
Or, if you prefer: if ∃1 has a domain, that domain is unrestricted. But it’s indeterminate whether it has a domain.
Or perhaps more accurately, functions from reference-fixing descriptions to extensions.
There may well be multiple reference-fixing descriptions that yield the same extension, e. In that case, we either have to say that one description is privileged (because of facts about simplicity or naturalness or whatever) or instead say that precisification at least enables us to pick out a specific set of reference-fixing descriptions.
Is the ‘be bold’ command satisfied at ∃2? After all, ∃2 quantifies only over a, so isn’t it the case that according to ∃2 we do take everything, even the indeterminate stuff (there just isn’t any indeterminate stuff according to ∃2)? No. Remember that to evaluate the truth of ‘determinately’ and ‘indeterminately’ statements, we have to look at what’s going on at all precisifications—the truth conditions for determinacy-involving statements require us to ask whether something is represented at all or merely some precisifications. According to ∃2, a determinately exists—but we can only say this by looking at ∃1, which also represents a as existing (a only determinately exists if each precisification represents it as existing). Likewise, according to ∃2 b indeterminately exists—because ∃1 represents b as existing but ∃2 does not. So ∃2’s quantifier does not meet the ‘be bold’ command simply in virtue of not quantifying over b. (It’s helpful to think about the analogy to modality. Suppose that a necessarily exists and b contingently exists. It’s true according to w that a necessarily exists, but the truth of this is determined by what’s going on at other worlds in addition to w: a has to exist at all worlds to be necessary. And it can likewise be true according to w that b possibly exists, even if b doesn’t exist at w, so long as b exists at some other world w*. Again, we have to look at more than just what’s going on at w to evaluate what modal statements are true according to w. Determinacy works the same way.).
The ‘be bold’ precisification will have to be much more complicated than this—and probably formulated counterfactually—if we want to avoid commitment to de re indeterminate existence (which is a much stronger commitment than de dicto indeterminate existence). The way it’s stated here is just to give you the basic idea.
References
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Barnes, E. Metaphysically indeterminate existence. Philos Stud 166, 495–510 (2013). https://doi.org/10.1007/s11098-012-9979-3
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DOI: https://doi.org/10.1007/s11098-012-9979-3