by Prof. Jody Azzouni
(Oxford University Press)

Deflating Existential Consequence: A Case for Nominalism

If we must take mathematical statements to be true, must we also believe in the existence of abstracter--eternal invisible mathematical objects accessible only by the power of pure thought? Jody Azzouni says no, and he claims that the way to escape such commitments is to accept (as an essential part of scientific doctrine) true statements which are "about" objects that don't exist in any sense at all. If we must take mathematical statements to be true, must we also believe in the existence of abstracter--eternal invisible mathematical objects accessible only by the power of pure thought? Jody Azzouni says no, and he claims that the way to escape such commitments is to accept (as an essential part of scientific doctrine) true statements which are "about" objects that don't exist in any sense at all. This is the first time that Quine's criterion of ontological commitment is fundamentally question called into question. Without this criterion, the modal realism of David Lewis collapses. For analytic tradition in philosophy this is a major revisioning of valid argumentation in metaphysics. Perhaps (sad to say, for the question of intellectual freedom within the profession) that it may have been necessary for Quine and Lewis to die before nominal view could get a hearing.

Azzouni illustrates what the metaphysical landscape looks like once we avoid a militant Realism which forces our commitment to any-thing that our theories quantify. Escaping metaphysical straitjackets (such as the corre spondence theory of truth), while retaining the insight that some truths are about objects that do exist, Azzouni says that we can sort scientif­ically given objects into two categories: ones that exist, and to which we forge instrumental access in order to learn their properties, and ones that do not, that is, which are "made up" in exactly the same sense that fictional objects are. He offers as a case study a small portion of Newtonian physics, and one result of his clas sification of its ontological commitments is that it does not commit us to absolute space and time.

Azzouni begins by exaiming the notion of truth. His view on truth is a fairly deflationary one: The role of the truth predicate is to enable us to assent to sentences we cannot explicitly exhibit. He uses this role of the truth predicate plus other subsidiary considerations about scientific theories to show that applied mathematical doctrine and empiri cal laws must be taken by us to be true. For expository purposes, the discussion is divided into two parts. In chapter 1, Azzouni lays out the details about blind truth ascription and the truth predicate that, in a broad way, indicate why we are apt to be committed to the truth of what is indispens ably contained in our body of beliefs. In chapter 2, he fine-tunes the issue and evaluates strategies for being agnostic or fictionalist about applied mathematical doctrine or empirical law despite its indispensability.

Next Azzouni turns to questions of ontological commitment. Quine's criterion for what a discourse is committed to is evaluated and found want ing. There are, that is, alternatives that neither Quine nor anyone else has successfully ruled out. A substantial portion of chapter 3 is dedicated to careful evaluation of Quine's triviality thesis: the claims that "there is" is used in the vernacular to indicate ontological commitment, and that this use is regimented by the first-order existential quantifier. The conclusion is that we cannot say what is the best criterion for what a discourse commits us to until we first establish a criterion for what exists.

Azzouni argues that although no philosophical argument is available to definitively fix a criterion for what exists, still, it can be shown that our linguistic and epistemic community takes something to exist if and only if it is ontologically independent. Azzouni attempts to spell out in some detail what "ontologically independent" might mean.

Next he discusses how speakers in the vernacular indicate ontological commitment. The conclusion argued for is that there are no lin guistic devices, no idioms (not "there is," not "exists") that unequivocally indicate ontological commitment in the vernacular. Nevertheless, speak ers are competent at recognizing when ontological claims are being made (provided, of course, that certain people-e. g., philosophers-avoid being too tricky about it).

In part II, Azzouni turns to the question of how the considerations of part I can be used to evaluate the ontological commitments of scientific theories. To this end, Azzouni sorts the posits (quantifier commitments) of theories into three kinds: thick, thin, and ultrathin, and distinguishes these on the basis of the various epistemic requirements they impose on knowers.

Azzouni argues that we take only thick and thin posits to be ontologically independent (and thus to exist). He also discusses ontological closure conditions, methods in science that characterize limits on what there is. He uses the presence of such conditions to argue for a version of the Eleatic Principle, the claim that, in some sense, everything there is has causal powers.

Azzouni describes ways in which mathematics is applied and gives a number of examples, the most significant being variants on the application of Newtonian cohesive-body mathematics, a mathemati cal system that codifies a (small) portion of Newtonian mechanics. Concluding he turns to the evaluation of the ontological status of various posits in cohesive-body mathematics: Azzouni claims that, for example, despite the presence of spatial and temporal posits in cohesive-body mathematics, such posits are ultrathin, and he also asserts that cohesive-body mathematics is not committed to forces, either.

Excerpt:

Philosophy-at least that tradition of it I choose to work within-has at best an uneasy relationship with ontology. Carnap, notoriously, denied that genuine ontological questions (and purported optional answers to these questions) are meaningful, and this viewpoint is one that continues to be a live possibility (or at least a serious temptation) for contemporary philosophers. On the other hand, Quine's criterion for what a discourse is committed to is widely (and uncritically) adopted despite an official disagreement over what it amounts to, and whether a coherent version of it is even available.' Careful attempts to evaluate the criterion itself are spo radic and rare; conscious and unconscious reliance on it for one or an-other ontological project in philosophy of language, philosophy of logic, philosophy of mathematics, philosophy of science, philosophy of mind, metaphysics proper, ethics, and so on is the norm.

Of course I too understand the appeal of "getting on with it," the somber recognition that life is short, that getting to the bottom of things should not mean staying down there for the rest of our professional ca reers. It's easy to think, "let this, at least, be a fundamental building block in our philosophical arsenal; let this (at least) be something our commu nity of philosophers can hold in common and can use as a common as sumption, as a philosophical paradigm, if you will; let this (at least) unify us as a profession as we pursue our various ambitious metaphysical (or metaphysically deflating) philosophical projects."

As the last paragraph intimates, the book you're reading stays pretty near the bottom of things. Part I of this book evaluates arguments for Quine's criterion and shows them wanting. I consider various alternative criteria and eventually find a way to argue for one. The argument is de tailed-tortured, even-but (I hope) ultimately convincing. I argue that Quine's attempt to substitute a logically prior criterion for what a dis course commits us to, in place of a more traditional metaphysical criterion for what exists, is a sleight of hand. Instead, I find that folk ontology takes the ontological independence of something (in a sense to be specified) as criterial for whether it exists. Accepting this requires us to overturn Quine's decision to take the objectual existential quantifier in a regimented discourse as carrying ontological commitment, and forces us to adopt a spe cial predicate designated to carry ontological commitment instead: an ex istence predicate.

The famous Quine-Putnam indispensability thesis takes the indis pensability of mathematical doctrine to scientific practice to imply (1) the truth of that doctrine, and thus to imply, via Quine's criterion for what a discourse is committed to, (2) the existence of mathematical abstracta. My arguments against Quine's criterion drive a wedge between
(1) and (2): the truth of mathematical doctrine (all by itself) doesn't imply the existence of the abstracta that this doctrine is about.

Traditionally, one of the best arguments for Platonism has been the truth of mathematics-either applied or unapplied. And, unsurprisingly, the standard nominalist response to mathematical truth has been either to try to show that mathematical truths aren't (or needn't be) what they appear to be (they're metaphorical, say, or they actually have very differ ent logical forms in which obnoxious existential commitments to abstracta are missing), or to try to show that they are, if taken literally, not indis pensable to empirical science (despite appearances to the contrary), and thus statements we needn't take to be true.

By contrast, my nominalism steals the best from both sides in this debate: I take true mathematical statements as literally true; I forgo at-tempts to show that such literally true mathematical statements are not indispensable to empirical science, and yet, nonetheless, I can describe mathematical terms as referring to nothing at all. Without Quine's criterion to corrupt them, existential statements are innocent of ontology. (I'll temporarily call this "the separation of existential truth from ontology" or, for short, "the separation thesis.") The separation thesis results in a rather atypical nominalism, but I hope the book will show that, despite this, it's very appealing.

The main advantage of the separation thesis, overall, is that it simpli fies so many metaphysical tangles. I won't illustrate this generally-there are too many topics to cover-but I do discuss (1) mathematical abstracta as they arise in the application of mathematics to science, and (2) fictional or nonexistent objects. I indicate-but hardly in a complete way-the value of the separation thesis to issues regarding properties. It proves equally illuminating to the metaphysics of space and time (I discuss this some what-but there is lots more to say, e. g., purported problems with presentism). The separation thesis provides so many simplifications in meta-physics simply because it eliminates the need to postulate something as existing just because certain truths prove indispensable; many metaphysi cal entanglements arise because this is taken for granted. Coupling the separation thesis with other ways of determining what exists at long last frees ontology from its linguistic straitjacket. (E. g., the linguistic form that fundamental science takes-which predicates appear in its laws-need not determine our most fundamental metaphysical commitments.)

Some philosophers have been exploring what might be called the program of naturalized ontology, the idea that in science ontological practices are already in place that dictate scientific commitments, and that to engage in "naturalized ontology" is simply to adopt those practices. I've some sympathy with this move, and broadly speaking, it's my escape route from ontological nihilism to the safety of a particular criterion for what exists. But there are at least two crucial ways I break with this approach. First, I doubt that one finds in science autonomous practices exemplifying a crite rion for what exists (or a criterion for what scientific discourse commits us to): Science (I claim, and I hope) is not as revolutionary as that. The criterion for what exists operating in science is drawn from epistemic and ontological practices at work in the human community at large-it's a criterion we've adopted in common. (I say a little more about this shortly.) Second, I continue to hold that the "ontological nihilism" of my 1998 is right there are no philosophically conclusive ways to argue for our criterion for what exists. That is, we can imagine alternative com munities with the same science we have but with different beliefs about what exists because (and solely because) they have a different criterion for what exists; they're otherwise unaffected by their choice. In particular, there is nothing we can point to, either practically speaking or in terms of some implicit incoherence in their practices or theories, that shows they've got the wrong criterion for what exists (see chapter 4 for a discus sion of this).

Notice what's required when it's claimed that there is nothing to adjudicate between our criterion for what exists and the different one of the imagined alternative community: I'm not asking for an a priori resolu tion of the disagreement (I don't believe in the existence of things like that). I'm asking for some way of being able to show (empirically) that either we or the members of the alternative community are worse off be-cause of our (or their) choice of criterion for what exists-that, for exam ple, our (or their) scientific or epistemic practices fall short in some way. Only then can we say that there is a genuine issue to be judged rationally.

Unlike the Quinean criterion, which commits us to everything the objectual existential quantifier in (regimented) scientific doctrine ranges over, my criterion is more discriminating. Each scientific case must be individu ally investigated in fair detail to see what it commits us to and what it doesn't. This is because when mathematical discourse is applied empiri cally, the terms in it (which indicate abstracta) can play two very different roles: sometimes they proxy for items that exist, and sometimes they don't.

As an illustration of this complex and interesting phenomenon, part II of this book examines a (small) portion of Newtonian physics. The point of this application is threefold: first, to see in a real but relatively straightforward case how my approach sorts out what exists from what doesn't; second, to see how ontological evaluation can yield principled results even in a context that far outstrips the commonsense arena that our ontological promptings were first honed in; and third, to see how powerful methodological prejudices about explanation can conspire with routine generalizing practices in mathematics to produce (when that mathe matics is applied) strong (and yet unjustified) ontological intuitions. I single out the substantivalist/relationist debate about space and space-time as an excellent illustration of this last phenomenon. I'll show how the appli cation of geometries to motion that yields simple and unified laws leads to intuitions about the existence of absolute space.

In a way, the hope for principled results, raised as my second aim earlier, brings us back to Carnap's original motivation for deflating ontology. What look like bizarre positions-at least from the commonsense point of view-are the primary offering in the history of metaphysics, as even a cursory glance at that history indicates. Monisms of various sorts, denials that humans (or any other macro-object) exist, claims that numbers exist, that only numbers exist, that fictional entities exist, that possible worlds exist, that only atoms exist, that only strings exist, that time doesn't exist-all such positions are available to the thrill-seeking ontologist. (Science fiction isn't half so imaginative or-according to common sense-off-the wall as what can be found in the writings of obsessive ontologists.) Worse, and this is how I read Carnap's motivation for deflating ontology, there seems no principled way to decide among these (competing) positions.

Carnap (1950) famously distinguishes internal questions from external questions. On the latter, he writes: "This question [of the reality of the thing world itself] is raised neither by the man in the street nor by scientists, but only by philosophers. Realists give an affirmative answer, subjective idealists a negative one, and the controversy goes on for centu ries without ever being solved".

Carnap's claim that the ordinary person (or scientist) does not raise ontological questions is explicitly denied by Kant (1783), who wrote:

That the human mind would someday entirely give up metaphysical investi gations is just as little to be expected, as that we would someday gladly stop all breathing so as never to take in impure air. There will therefore be meta-physics in the world at every time, and what is more, in every human being, and especially the reflective ones; metaphysics that each, in the absence of a public standard of measure, will carve out for themselves in their own manner.

Kant's own attempt to short-circuit uncritical ontologizing is hardly straightforward or easy-going. But I think he was right, both about what you might call the human instinct for ontology and about the importance of care and subtlety in sorting out how that instinct-and ontology it­self-should be treated.

I didn't say so earlier, but even the Quinean take on ontology, de-spite its apparent rescue of that subject from the Carnapian limbo of non-sense,' is as deflationary and in a sense as dismissive as the Carnapian position it opposes, at least under a fairly straightforward interpretation: Ontologizing is a philosophical practice, and like all philosophical prac tices, it's continuous with science. Indeed, modulo regimentation, what science tells us there is, is what there is.

But what does science tell us there is? The recent outpouring of onto-logical posturings by professional physicists turned lay-ontologists (for examples of Quine's favorite sort of scientist) indicates nothing particularly straightforward or definitive about ontological readings of science-at least as far as the professional practitioners of those sciences are con cerned. Is the Schrodinger equation real? Weinberg thinks so.' Does time exist? Barbour (1999) thinks not.' Examples can be multiplied easily. It's hard to believe that this can be sorted out neatly by regimenting scientific discourse to see what the quantifiers of the regimented discourse range over.

Why not?" In part because some genuine ontological concerns elude the narrower issue of what the objectual existential quantifiers in a dis course range over. This is even true of Quine's own ontological prompt ings, his physicalism, for example, which is an ontological position he takes but that cannot-as he admits-be represented by what objectual existential quantifiers range over in the best regimentation of the scientific discourse he accepts. To do that successfully, all nonphysicalistic vocabu lary would have to be eliminated. And Quine admits that this can't be done."

Concerns with ontology, on the part of ordinary people, on the part of physicists trying to interpret the ontology of the wild new scientific theories they find themselves committed to the truth of, and even on the part of a grudging Quine trapped within a nonaustere web of beliefs, take the form they've always taken: queries about which things we should take to exist and which not; and this is regardless of what our discourse seems to commit us to.

And let's admit it: For better or worse, the ordinary person's concern with what there is and his or her concern with how we're to read off what there is from what we take to be true are real concerns just like Kant said they were, and ones to be treated with respect. However, as with the more sophisticated ontologizing that philosophers and physicists engage in, the implicit methodology that's actually doing all the work to support both sophisticated and folk ontological positions should not be left at the level of unconscious intellectual reflex or to occasional ritualized nods to philosophical ancestors, such as those to the late Quine. Rather, this methodology should be brought explicitly out into the open, where we can all participate in the evaluation of it.

One point about my footnotes. These are used by many philosophers solely for the purpose of citation. I don't use them that way-the reader intent on seeing the force of the position I offer should read the footnotes along with the main text. This is why I use footnotes rather than end-notes. The same is true, of course, of my previous books. But I've been told that I should point this out.