Here is an example of a metaphysical dispute in contemporary analytic philosophy: there are presentists, who say that only the present exists and the past and the future do not, and there are eternalists, who say that the past, present and future all exist. Questions can arise about whether this dispute is substantive. Could it not be the case, one might wonder, that the presentist and the eternalist are simply using the term ‘existence’ in difference ways? If the presentist means to say that only the present exists in the way in which present things exist, whereas the eternalist means to say that past, present and future things all exist in some strictly broader sense of existence, then they might actually agree.
Let us call the idea that all metaphysical disputes about existence are of this sort and can therefore be resolved simply by pointing out that the term existence is used in many ways, deflationism. The problem with deflationism is that the philosophers engaged in these disputes do not take themselves to be in agreement, not even after the deflationist proposal has been made clear to them. A presentist might agree that past and future events exist in some attenuated sense of ‘existence’, but not in the real, full-blooded sense; whereas the eternalist wants to claim that past and future events are just as real as present ones.
This is where neo-Quineanism comes in. It is the claim that, and I’m now citing from Meghan Sullivan’s 2012 The minimal A-theory, “[t]here is a single, fundamental sense of ‘exists’ of interest to metaphysics, and it is denoted by the existential quantifier.” Crucially, this claim is not supposed to be an insight we arrive at at the end of our metaphysical studies, when, after many hard-won breakthroughs, we finally come to see that there is a single fundamental sense of ‘exists’ and that it can be denoted by the existential quantifier. On the contrary. The neo-Quinean claim is supposed to furnish the framework within which metaphysical studies are so much as possible. It is only if there is a single sense of ‘exists’ that is of interest to metaphysics, that a debate such as that between the presentist and the eternalist can be substantial; for then what is at issue between them can be understood as whether or not past and future events exist in that sense of the word. And only if this sense is denoted by the existential quantifier, can the different positions be given the logically perspicuous formulations that make them amenable to serious philosophical treatment. Thus, given neo-Quineanism, we can define presentism as the claim that ∀x:Present(x), or, equivalently, as ~∃x:~Present(x). Quoting Sullivan again, who is talking about theories of change but making a more generally applicable point: “According to neo-Quineans, the debate about change is substantive if we can translate different theories of change into logic-ese and show that they must quantify over different domains. That’s what it is to have a debate about ontology, at least on the anti-deflationist picture I’m assuming.” Here neo-Quineanism is presented very clearly as the necessary framework for ontological disputes, the only alternative being the deflationist attitude that makes substantive metaphysical questions impossible. This is not peculiar to Sullivan’s treatment; it is a wide-spread attitude in analytic metaphysics.
Of course it is one thing to say that there is a single fundamental sense of existence that is of interest to the metaphysician, but something else to say what that sense is. Suppose that someone were to object as follows: “We can come up with many different notions of existence. One covers only present objects; another covers present, past and future, but only actual objects; a third covers both actual and possible objects; a fourth covers even impossible objects. In order to decide which of these notions we need to use in metaphysics, we first have to decide all the metaphysical questions! If the presentist is right, then existence should cover only present objects. If the eternalist is right, it should cover also past and future objects. So how can you possibly claim that we know what a claim like ‘∀x:Present(x)’ even means before you have found out which objects the ∀ is supposed to range over?”
The neo-Quinean answer to this objection is based on the notion of a restricted quantifier. For example, I may correctly say that ‘there is no beer’ if my quantifier is understood to range over only objects in my fridge. This is an example of a restriction. In the same way, I can introduce other quantifiers that are restricted versions of some more general quantifier, for instance, a quantifier that ranges over only objects in a particular country, or over only living beings, or over only objects that exist right now, and so on. Now the neo-Quinean makes their move: the quantifier that we are interested in in metaphysics is the most unrestricted quantifier. It is the one that ranges over everything. By saying that, we explain which quantifier we mean without having to first answer any of the metaphysical disputes. Presentists claim that past and future events do not exist, even in the most unrestricted sense of existence. Eternalists disagree. Thus, we have secured a framework in which ontological disputes can arise and be — hopefully — adjudicated.
It’s time to put my cards on the table: I believe that this method for doing metaphysics is utterly misguided. I don’t want to argue here that neo-Quineanism is false (although I do believe it is false). But I do want to argue that rather than enabling serious metaphysical dispute, it make it impossible to get the most fundamental of those disputes in sight.
I want to start with a worked out example, which will be Kant’s transcendental idealism. If neo-Quineanism is the framework within which ontological disputes have to be formulated, then the very least we can demand of it is that the main ontological theses of philosophers such as Kant can be formulated in it. According to Kant, what exists are spatio-temporal objects that are causally linked to the spatio-temporal objects we perceive. But, and this is absolutely crucial to his entire metaphysical system, there is no such thing as the totality of all objects. This totality is the world, but the world for Kant is something that has to be understood as the teleological goal of inquiry. Every object points beyond itself to its causes and effects. For every event, there is both a prior and a posterior event. Kant emphatically denies that the resulting infinity can be thought as a completed or actual infinity. Rather, it is a potential infinity, essentially incomplete.
The problem with formulating transcendental idealism within the framework of neo-Quineanism should be obvious: transcendental idealism rejects the idea of an unrestricted quantifier that denotes existence as such. There is no domain of all that exists; to believe that there is, is precisely to take a transcendental realist attitude towards the world. It is to fail to understand that any set of objects must fall short of reality.
(As an aside, we may note that Kantian universal claims cannot be formulated using universal quantifiers. ‘All events are caused’ should not be read as ∀x:(Event(x)→Caused(x)), because there is no appropriate interpretation of the quantifier. Instead, it should be read as the open formula Event(x)→Caused(x), which can be applied without limitation. It is also interesting to note that while Kant is often accused of playing fast and loose with the distinction between universality and necessity, this distinction just doesn’t exist in his system in the same way it does for the neo-Quinean. The universally quantified formula ∀x:(Event(x)→Caused(x)) could be true contingently. But when we assert the unlimited applicability of the open formula Event(x)→Caused(x), we are seeing universality and necessity as two sides of the same coin.)
There is something very disconcerting about a supposedly neutral framework for ontological dispute that turns out to presuppose the falsity of transcendental idealism by presupposing that what exists can the thought as a totality. This is surely to prejudge one of the most interesting metaphysical questions concerning existence. And it is likely that the answer to such a question will reverberate through other ontological disputes; e.g., it might well turn out to be the case that eternalism in the philosophy of time is closely linked to the idea that what exists can be thought as a totality, whereas a defensible presentism might turn out to be linked to the idea that any collection of objects is always necessarily incomplete and points beyond itself. Thus, the supposedly neutral framework of neo-Quineanism might generate a space for discussion in which certain points of view can no longer be correctly formulated and hence not effectively defended, or even understood.
Stepping back from transcendental idealism and the problems involved in the introduction of quantifiers, let us look at the neo-Quinean claim that we can start doing philosophy by indicating that we will use ‘existence’ in ‘the most unrestricted sense’, and that this will give us a ‘single, fundamental’ sense of existence. What are the presuppositions of such a methodological move? At first sight, the move seems to involve a rather strange faith in the power of a very inarticulate verbal expression to precisely indicate something. Why would the words ‘existence in the most unrestricted sense’ have a clear meaning if we haven’t first clarified which things are supposed to fall under it, at least in general? Again, at first sight it seems to raise questions such as ‘do you mean so unrestricted that even mere possibilia fall under it, or do you mean something a little less unrestricted than that’?
The neo-Quinean answer seems to involve two presuppositions, which I will call realism and restrictivism. Realism is the idea that we don’t have to gave a precise sense to existence, because the world does so for us. It is the idea that in order to indicate what we mean by the most unrestricted sense of existence, we can simply make a wide gesture and say — well, you know, I mean everything. I call this ‘realism’ because it assumes that we can think the world apart from our ways of approaching that world. For instance, this same approach in the philosophy of mathematics would involve claiming that without having the least insight into how mathematics is done; without having, for instance, decided on adopting a finitist or an intuitionist or a formalist approach; and without having decided, for another instance, on which large cardinal axioms to accept; that without any of that, it already make sense to talk about the realm of mathematical objects as something that is determinate prior to any decisions, or insights, or anything else that smacks of the human. Of course this is already to take up a quite specific position in the philosophy of mathematics, and this is no less true for the analogous realism in general metaphysics.
I call restrictivism the idea that our concept of existence is best understood along the following lines: there is the core concept of existence as such, and all other concepts of existence are to be understood as restrictions of that core concept. So, we can say that there are no dinosaurs, but the existence concept in this sentence is to be understood (if the eternalist is right) as a restriction of the original, primordial existence concept to the domain of present entities.
Now of course this is not the only way to understand the relations between different existence concepts. We could also believe that the core concept of existence is that which pertains only to actual, present, material, observable objects. The core concept can be applied in a loosened and attenuated sense to, say, social groups, or to the mereological sum of my nose and my computer, or to the unobservables entities postulated by science, or (if presentists are right) to past and future events, and so on. These uses of the term would be looser not only in the sense that they are broader, but also in the sense that we lose our grip of the concept as it becomes broader. We become less certain, as we move away from actual, present, material objects, of whether we should still apply the term existence, and what we are committing ourselves to if we do. Ontology then becomes an attempt to work through these uncertainties, to map out and clarify this conceptual space and connect it to other parts of philosophy.
Realism and restrictivism are related and mutually supporting, so it’s no accident that neo-Quineanism is based on both; and, who knows, perhaps a coherent and defensible philosophy can be built on them. (Though I doubt it.) But what’s important for our present purposes is that they are already substantial commitments about existence. And this means that it is methodologically disastrous to present them as elements of a neutral framework within which ontological dispute becomes possible.
It is, I will now claim without arguments, a disaster that generates other disasters. For once we accept the neo-Quinean idea that we don’t need to think through the nature of existence and its role in our cognitive economy, but only need to decide whether certain things do or do not exist, then we are faced with the seemingly impossible-to-answer question: how? How do we find out whether past events are among the things that exist? There is nothing empirical about this dispute. And so the philosophers that work in this tradition, having no real answer to this question, tend to fall back on criteria like ‘simplicity’ and ‘parsimony’ and ‘elegance of the logical system’, and finally, one suspects, on nothing more than an unargued for preference for desert landscapes. Which is indeed very neo-Quinean, but perhaps not very philosophical.