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        In Favor of the Classical Quine on Ontology
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        In Favor of the Classical Quine on Ontology
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I make a Quinean case that Quine’s ontological relativity marked a wrong turn in his philosophy, that his fundamental commitments point toward the classical view of ontology that was worked out in most detail in his Word and Object (1960). This removes the impetus toward (a version of) structuralism in his later philosophy.

By the “classical Quine,” I mean the philosophical position which reached its culmination in Word and Object of 1960. By the “later Quine,” I mean the philosophical position which first flowered with “Ontological Relativity” of 1968 and grew to arguably more precise expression in Quine’s books and papers of the 1990s. (This distinction is something of an idealization but, on the whole, I do think that the earlier flesh-and-blood Quine and the later held the views as I’m characterizing them). An important difference is over ontology, and I shall argue that there are good reasons for preferring the classical Quine’s view of ontology over the later Quine’s. The later Quine maintained that since reference is inscrutable, the ontology of the entirety of “our theory” is relative to its interpretation, and consequently the scientific importance of ontology is decidedly secondary to that of the total structure of predicates of the theory—its “ideology.” I shall argue that the inscrutability of reference does not establish the relativity of ontology: the relativity cannot be nearly so rampant as is often supposed, and more generally the classical Quine was right in not treating the semantics of reference as peculiarly relevant to ontology in the way assumed by many of his later writings, which is necessary for the inference to relativity. A further implication is that the apparent support received for Quine’s version of structuralism from that quarter is nullified.

I shall not question the essential Quinean commitments germane to this discussion, commitments to which both the classical Quine and the later Quine subscribed: to extensionalism; to the maxim that to be is to be the value of a variable; 1 to existence’s being expressed by the existential quantifier; to there not being any properties, relations, universals or attributes (beyond the sets of objects denoted by such terms as “the set of chickens”); 2 to there not being any merely possible objects or possible worlds; to classical mathematics—or rather to a standard set theory or to a nonstandard alternative such Quine’s own “New Foundations” theory; to Quine’s naturalism—that scientific practice sets the norms for philosophy and that there is no choice but to “speak within” our science as we have it, rather than from some transcendent or prior philosophical position; and lastly, to a certain notion of reference to be explained presently.

1. Relativity tamed

Quine opened “On What There Is” ([1948] 1961) by declaring that the basic question of ontology is just the question: “What is there?” That was in 1948, and there is little reason to believe that he changed his mind on the point. Early and late, the fundamental question of ontology is for him the question of which entities do we accept (as “existing,” we may redundantly add). His immediate answer in 1948 was straightforward: Everything. But what is covered by the label “everything”? Somewhat less straightforwardly: Boil down the entirety of “our theory”—the latest version of established science—into a maximally streamlined set of sentences of the first-order predicate calculus with identity; by “everything” is meant all objects composing the quantificational domain or universe of the resulting theoretical formulation. Quine calls the procedure “regimentation,” and the result is not a “transcendent” conception of existence but an “immanent” one: ontology is simply a part of natural science, is, in principle, no less fallible than it is, and can change as theories change. As we will see in more detail later, the classical Quine differs from the later Quine over the relation—and its explanation—between the total set of the statements of science and the quantificational domain: is the latter in some sense variable even where the truth values of the statements are held constant (the later Quine), or not (the classical Quine)?

Here is the point about reference. Quine’s practice as a logician and philosopher of language confirms his general agreement with Tarski in his understanding of reference (a relation which includes that between predicates or general terms and the objects which fall under them; Quine often called the relation “denotation”). 3 A consistent theory of truth for a given language L is adequate if it entails all T sentences—sentences in the metalanguage of the form “s is true iff p,” where p is a metalinguistic translation of the L sentence named by the singular term s (if the metalanguage includes L, then s may name the very sentence put for p). A scheme of reference for a given language entirely subserves a theory of truth for the language: given the standard clauses for “true,” quantifiers and sentence connectives, it is adequate so long as it delivers the T sentences. More narrowly, and more to the point, it is adequate if each sentence of a theory expressed in the language with a given truth value retains that truth value according to that scheme, given the clauses for quantifiers and sentence connectives. Many people nowadays who work on the theory of reference think that there is more to reference than that, but as I said I will not question Quine on either this commitment or the others listed above.

This is the basis for holding that reference is “inscrutable,” as Quine put it in 1968 in “Ontological Relativity,” or that reference is “indeterminate” as he put it in the 1990s (a slightly changed version of the former appeared as an essay in the familiar book of that title in 1969). More complicated and more piecemeal arguments for this occur in chapter 2 of Word and Object in the context of radical translation involving the notorious undetached rabbit parts and temporal stages of rabbits, but shortly afterward he espoused a simple argument by “proxy functions,” one that works globally. 4 A proxy function is an explicitly given one-to-one function that takes any object of the domain of the theory as argument and, at least for a substantial portion of the domain, delivers a different object as value. 5 Examples include “the singleton of x” (“the unit set of x”), and “the spatiotemporal complement of x” (“the cosmic complement of x”), where an object’s spatiotemporal complement is the object itself for nonspatiotemporal objects. (The spatiotemporal complement of the Parthenon, for example, is a certain universe-sized, 4-D physical object with a Parthenon-shaped hole in it.) Then, for each simple, quantifier-free n-place open sentence of the existing theory, specify a new n-place open sentence that is true of just those n-tuples that are the proxy n-tuples of those of which the original open sentence was true. Standard clauses ensure that the truth values of truth-functionally simple sentences fix those of truth-functionally complex sentences; likewise the truth values of sentences involving quantifiers are fixed, since for any assignment of values to free variables, the corresponding open sentences will retain their truth values through the proxy change. 6 Thus an arbitrary sentence of the proxy-theory is true just in case the corresponding sentence of the original theory is true, but is about the proxies. For illustration, assume the theory has constant singular terms and that “Fb” is any true sentence comprising a one-place predicate and such a term; then “the proxy of b is the proxy of an F” is also true: the latter sentence is true since the proxy-extension of F includes the proxy of b. 7 So far as the truth of our theory of the world goes, then, it does not matter if we accept the customary objects as referents of our terms or we construe them as about the proxies of those objects. (Nor need it disturb the theory’s “empirical content,” but I will leave this aside. 8 )

The later Quine concludes further that ontology—the ontology of “our theory,” of all science—is relative. It is relative to the choice of translation into a “background language,” as he first put it in “Ontological Relativity” (1968, 48–50, 54–55), which we can abridge as its being relative to a particular scheme of reference. Ontological statements are still truth-apt—are not simply nonfactual—but ontology is not fundamental to our theory of the world since we can, due to the availability of proxy functions, freely change the ontology our theory without changing the truth value of any sentence of the theory. It is “defused” or “indifferent,” as Quine put it in the second edition of Pursuit of Truth (secs. 12–13); it has suffered a “humiliating demotion,” as he put it in “Ontology and Ideology Revisited” ([1983] 2008, 317).

I believe that this further conclusion is far from being a mere corollary of the inscrutability of reference (despite Quine’s having said that the argument from the one to the other is “trivial”; 1992, 50). There are three varieties of the application of proxy functions to consider.

  1. A. Permutations. This is the case where the quantificational domain is simply mapped onto itself, as in “the spatiotemporal complement of x.” But if the question of ontology is as above, if it is the basic and maximally general scientific question, “What is there?” then the customary answer is precisely the same as any proxy answer by permutation. Our ontology consists of everything, whatever the quantifier ranges over. For ontology to be relative in the way just described, that would have to change with (at least some) interpretations by permutation. And by definition, it does not. If a proxy transformation for a regimented theory does not change theory’s domain of quantification, then the theory’s ontology is not relative to that transformation. All that is shown by the argument via permutations is that swapping round systematically the references of particular terms for their proxies is immaterial to the truth values of sentences. If an object was in the domain of discourse to start with—whether it’s a dog or the proxy of a dog, for example—then the object will remain in the domain after the permutation, and if there were no such object to start with, no such object will appear in the domain after the permutation. Ontology wholesale is not shown to be relative to a scheme of reference.The ontology of particular regions of discourse, such as the ontology of tennis commentary, will shift to the proxies, but that is not relevant to the broadest-spectrum question “What is there?” The indifference of the interpretation of terms for lesser regions of discourse does not imply a like conclusion concerning the content of the total domain for the theory as a whole. As part of a proxy transformation, the vocabulary of tennis could be conceived as being about not tennis balls and tennis racquets but spatiotemporal complements of tennis balls and tennis racquets, yet the spatiotemporal complements of tennis balls and tennis racquets are already in the general universe of discourse. (If, at a certain public park, the tennis balls were equinumerous to the croquet balls, and the tennis balls had been covertly swapped with the croquet balls, an equipment monitor might reasonably complain of mischief, but not of theft.) Likewise for any permutation one can name. There may not be any customary, noncomplex terms for the proxies, but that does not affect the point.

  2. B. Disjoint domains. This is the case where the new quantificational domain (the range of the proxy function) lies outside the old quantificational domain (the domain of the proxy function) either partially or wholly. The impediment here to the inference to ontological relativity is not the lack of ontological repercussions, but Quine’s ban on quantifying over merely possible objects, on mere make-believe as opposed to serious science. 9 A well-founded proxy function, like any function, cannot pertain to merely imaginary or hypothetical things as values (or as arguments for that matter), as indicated in the second paragraph and as is well-attested by Quine’s writings. 10 They pertain only to actual things. For the naturalistic ontologist, one cannot rise above scientific findings to opine based upon mere possibilia; ontological relativity is meant as a serious thesis, not a sideshow. A proxy function must be a one-to-one mapping of the quantificational domain into or onto itself, and candidates for proxies figure in the domain irrespective of whether they are considered arguments or values of a proxy function.The foregoing is a simple—some might say wooden—point, sure to be resisted by the defender of the argument for ontological relativity from proxy functions. If ontology is relative, the defender might say, then what counts as actual as opposed to possible, or serious science as opposed to make-believe science, will also be relative. But not only does Quine never make that argument, the argument commits the simple fallacy of affirming the consequent. Ontology’s being relative is what is in question; it’s what we’re looking for a reason to accept. I refer the defender to Quine on possibilia (e.g., Quine [[1948] 1961, 2–3]), and observe that Quine never actually gives an example of a general proxy function with a nonactual range of values. 11

  3. C. Proper subsets. This is the case where the proxy function maps its domain into itself, where the range is a proper subset of its domain. Unlike type B, this type of proxy interpretation is not illegitimate, and unlike type A, the ontological consequences one envisages are material. Taking the singleton of x as our proxy function, for example, there is no obvious Quinean bar, as there was in the previous case, to a reinterpretation of science in which x is interpreted in every case as {x}. This particular example suggests that reality, so to speak, can be chased up the set-theoretic hierarchy by repeated applications of the singleton function (from x to {x} to {{x}} and so on); the situation is much as it is for the receptionist in Hilbert’s hotel except that rather than welcoming guests in to a full hotel, she throws guests out without creating empty rooms. My full objection to the inference to relativity by this route is more complex and will not emerge until the next section. But we can observe at this point that this much so-called relativity has none of the sense of giddiness of type B: the example, at least, shows that our familiar ontology is still visible as in type A, if now slightly obfuscated by iterations of the singleton function. As we’ll see more substantively in the next section, type C is better regarded as a form of ontological reduction rather than as a type of ontological relativity (where “reduction” is replacing the total domain with a proper subset of it, not necessarily anything about relations between different levels of theory).

2. Ontology, semantics, and working within science

My preliminary conclusion is that the existence and implementation of proxy functions have significant bearing on the most comprehensive question of ontology only in the third kind of case, the case of proper subsets. In sub section 2.a (Interpretation and the Use of Language), I shall sketch the reason for not accepting the third case as demonstrating ontological relativity—a reason that I believe undermines the idea of ontological relativity generally and thus confirms the arguments just advanced against disjoint domains and permutations. In 2.b (Regimentation and the Place of Reference), I will draw some further support from what I take to be Quine’s classical estimate of the role and status of semantics in ontology, in particular that of the concept of reference in ontology; I will articulate the view with guidance from Quine’s pre-1964 remarks on ontology—the classical Quine—and will assess the implications for ontological relativity. In 2.c (Summary and Addenda) I will expand slightly upon the reason of 2.a for not accepting the third case, before turning explicitly to Quine’s later writings in section 3.

2.a Interpretation and the Use of Language

My view is that the relatively straightforward path of the classical Quine—the author of Word and Object of 1960—was decidedly preferable to the route taken first in “Ontological Relativity” of 1968, a route which he pioneered so brilliantly but ultimately led into the weeds. In rough outline, the case follows a simpleminded but standard response to the so-called “paradox” presented by the downward Löwenheim-Skolem theorem. There are models of the axioms of standard set theory (for example ZFC) expressed in first-order logic that are countable, that is, that have a denumerable overall domain; yet the axioms of ZFC imply the existence of uncountable sets. A simple way out is to pay more attention to what language we are using, and in particular to prioritize the content of object-language statements of ZFC over those of model theory when assessing the ontology of ZFC. The techniques of semantics or model theory—despite their manifest uses as in the establishment of the consistency and completeness of first-order logic, the analysis of logical consequence, and the showing of the relative consistencies of theories—do not (in particular not in the case where they are applied to otherwise fully interpreted theories) reveal the true content of the statements that they concern. They are just more mathematics whose peculiarity, in this case, consists in their explicitly having a subject matter expressed not by fully interpreted sentences of ZFC, but by statements in the metatheory concerning sentence forms of ZFC. Just as the existential import of a statement that there is a cat on the mat does not stand in need of a model theoretician’s ordination, so it is with the theorems of ZFC: they are statements whose import can be discovered only by working within ZFC, in particular by being conversant with its existential statements. And, likewise, for the contents of scientific statements in general: “… all ascription of reality must come rather from within one’s theory of the world; it is incoherent otherwise” (Quine 1981a, 21; emphasis added).

This quote is from a later period, discussed in Section 3, but the Quinean naturalism it sums up was very much awakened by 1960, the year Quine wrote Word and Object. The popular fame of Word and Object rests largely on Quine’s laying out his case for the indeterminacy of translation and, though not called by that name, the inscrutability of reference, but ontology is no less important and is treated quite separately in the closing chapter VII, without a hint of the former subjects’ encroaching upon it. In my view, this is consistent and right, and a point emphasised by Peter Hylton will help clarify. According to Hylton’s reading of Quine, my language, as I’m speaking it, is for me bedrock, despite the fact that it is variously translatable into a given target language (including itself), despite the fact that from a certain point of view the meaning of what I’m saying is indeterminate. Speaking as I do—meaning and understanding as I do, in the best sense a naturalist can muster of the notions of meaning and understanding—is simply a matter of my doing as I do, of my exhibiting certain behavioural regularities that accord more or less with those of others, of my having a system of linguistic dispositions that significantly overlap those of my community—not of my interpreting or translating anything (Hylton 1990, 275; 2007, 213–14). Quine’s view is that an exact science employing the concept of meaningfulness, significance, or of understanding, is viable even if one employing the notion of the meaning of an individual statement is not. Such a science is described most painstakingly in Quine’s Word and Object (1960, chap. 3), The Roots of Reference (1974, chaps. I–II), “Mind and Verbal Dispositions” ([1975] 2008), and was foreshadowed in 1953 with “The Problem of Meaning in Linguistics” ([1953] 1961)—but a science that uses the more powerful notions of “the meaning of a statement” and “the reference of a term” as they are often understood among philosophers cannot be justified and collapses into indeterminacy, as argued in the chapter 2 of Word and Object. Questions of interpretation, including proxy considerations, presuppose that the linguistic dispositions in which understanding is embodied and the behavior which constitutes communication are up and running. Yes, as with model theory, those too are legitimate scientific questions, but when pressed, what they show is not that the very idea of understanding or communication is a fraud, but that the collection of dispositions which constitutes competence with a language do not add up to what we may have pretheoretically thought: From the point of view of radical translation, translation is indeterminate and reference inscrutable, conclusions which put the kibosh on the idea that propositions are the real contents of sentences, and that reference in the substantial or extra-disquotational sense has much to do with understanding and communication. But they don’t undermine understanding or communication.

Quine, according to this reading, was on board with Wittgenstein’s comment that there must be a way of being competent with language “which is not an interpretation” (Wittgenstein 1953, sec. 201; though, unlike Quine, the point for Wittgenstein concerned materially inequivalent interpretations). Implicit in this is a simple argument that understanding—linguistic competence—cannot be translation (or interpretation) on pain of vicious regress: If to understand s I had to translate or interpret it as another (possibly homophonic) sentence s*, then for it to be of any use to me, I must understand s*; but if to understand a sentence is to translate it as a further sentence, say s**, then … and so on ad absurdum. Therefore, there must be such a thing as understanding, which is neither translation or interpretation; understanding much of one’s language must be direct. 12 Quine’s paradigm-shaking views on translation do not affect the underlying view of what it is to meaningfully speak a language. This is not to say that there is a privileged view on meaning or reference to which indeterminacy arguments do not apply, namely the first-person view. It is to say merely that “acquiescing in our mother tongue and taking its words at face value” (Quine 1968, 49) is compatible with translational indeterminacy; to so acquiesce is not to translate or interpret one’s words, not even homophonically, but is simply to use one’s language. 13 In the sophisticated sense in which the orthodox semanticist intends the words, questions of the meanings or references of terms normally do not arise within the ordinary use of language any more than questions of mass, flexibility, and kinetic energy must arise for a dancer.

I am not trying to prove the veracity of what I am calling the classical Quine on semantics so much as to sketch the position and to emphasise its merits. And to point out that it jibes with the classical Quine on ontology. At the outset of section 1, I cited Quine’s 1948 straightforward contention that the proper aim of the ontological enterprise is to answer the most general scientific question, “What is there?” and averred that there is no reason to believe that he took it back—even if he would come later substantively to qualify the scientific importance he attached to ontology. This aim was reiterated with some vehemence in “On Carnap’s View of Ontology” ([1951] 1976) when he said that ontological questions are simply the most general questions of existence, that “[t]he question of the ontological commitments of a theory … is the question what, according to that theory, there is” (66), and further that “[o]ntological questions then end up on a par with questions of natural science” (71). And, again, in the penultimate paragraph in Word and Object (1960), when he compared the existential claims of the special sciences: “What distinguishes the ontological philosopher’s concern and all this is only breadth of categories” (275). The statements we dignify with the appellation “ontological” are just the most general statements of existence asserted within science, typically “categorical” to use some older terminology, such as “There are physical objects,” rather than narrower statements of existence such as “There are black swans.” There is nothing categorically special or distinctive about ontological claims.

2.b Regimentation and the Place of Reference

It does not follow that the concept of reference is no more relevant to ontology than it is to mathematics, chemistry, or tennis commentary. Semantics remains uniquely relevant to ontology due to the “boiling down” operation described in the opening paragraph of section 1—a quintessentially Quinean procedure whose ultimate issue is a regimented, first-order version of our maximally inclusive theory of reality that is nevertheless pronounced within science. There are two ways in which semantics figures: in the formulation of the ontological framework and in its application.

The formulation of the framework affects our very conception of reference, of the distinction between referring and non-referring terms, and hence of which aspects of a theoretical formulation carries ontological import and which do not. In work up to and including Word and Object, including “On What There Is,” Quine sought to justify his favored procedure of regimentation—including its being extensional, its denial that general terms refer (aside from figuring in open sentences satisfied by values of variables), and its famous equation of existence with being the value of a variable. The famous equation, to consider the most pertinent item, is not an analysis of the former in terms of the latter; it is a metalinguistic statement that indicates the variety of statement in which ontological commitments are housed. It’s like saying that for a pair of objects to be identical is for them to satisfy the equation “x = y.” More generally, the imposition of a scheme of regimentation, if not exactly of executive character, involves the sort of general rulings that often take place near the centre of Quine’s web, with reverberations for all science.

By contrast, the application of the framework is relatively low-falutin’ if sometimes ontologically pivotal. In advance of regimentation, ordinary language is far from having a sharp or “fenced” ontology (Quine 1981a, 9); but with a certain plan for regimentation in place, the blue-collar ontologist may now set to work: difficult judgements are taken, general concepts explicated, statement forms paraphrased and proposals for reduction weighed. Do we admit sakes? Behalves? Immaterial minds? Sense data? Physical objects? Numbers? Sets or classes? Mereological sums? Quine’s naturalist seeks an all-things-considered ontology minimally sufficient for science—deferential to science, to be sure, but exercising his or her special expertise as a logician well aware of the existential and referential issues in play in ways that the practicing scientist typically is not. We see the procedure implemented in some detail in chapter 7 of Word and Object among other locations (Kemp and Lugg, forthcoming; for a more concise account see Quine’s [1954] 1976). The result is not an alternative interpretation of the ordinary language arrangement, but a substantial sharpening and streamlining, unlike the original in being readily amenable to algorithmic methods, with a sharp ontology where the original was lax and sometimes mute or even contradictory. 14

Not that the significance of regimentation is always ontological. The significance of particular moves within it may rather be only “ideological” or “conceptual,” as when Quine points out that the number of primitive notions needed for set theory is a miniscule three—a Sheffer stroke for the truth functions, the existential (or the universal) quantifier, and the sign of class or set membership (Quine [1937] 1961, 80–88). Set the sign of class membership aside; since the truth functions and quantifiers are for Quine syncategorematic, any dividends paid by the reductions of those notions are not ontological but ideological.

What I mean to deny is that once we have settled upon a regimented version of a maximally inclusive theory, semantics remains pertinent in a special way to ontology, a way that it is not pertinent to chemistry. It is not; we elucidate the ontological implications of a theory formulation simply by voicing the existential generalizations it implies.

In his discussion of “Semantic Ascent” in Word and Object (1960, chap. 7, sec. 56), the classical Quine stresses that finished ontological statements do not intrinsically involve the explicit use of semantic concepts despite the importance for ontological philosophy of semantic ascent. Among other examples, he considers the comparison of Einsteinian relativistic physics with Newtonian nonrelativistic physics, carried out metalinguistically in terms of reference and truth (272). The detour via semantics is only instrumental. The two theories are sufficiently disparate that simply comparing them as they stand is practically unmanageable, and it risks recklessly assuming a theory-neutral understanding of words such as “line” and “mass.” It behoves one to undertake a “shift from talking in certain terms to taking about them” (271); to do so avoids the dangers of faulty generalization and question-begging, as well as affording vital insights of an expanded perspective, perhaps ones which cannot feasibly be had otherwise. But, still, the purpose is conceptual; the theories themselves are not semantic and have the existential implications that they have.

The ontology to which a person subscribes, according to this view, cannot fully be grasped without understanding the person’s language (see McGee 2005, 409–17; Ricketts 2011, esp. 294–97). Trivially, every claim is “relative to language” in that they are made using a language, but it is a mistake to infer from this that ontological claims are significantly relative in some further sense to language—or to culture, form of life, or what have you. For example, nineteenth-century European scientists had an ontology which includes the ether; some remoter cultures are said to have an animistic ontology. In Quine’s way of thinking, those ontological commitments are just mistaken. Contrary to Carnap, ontological disagreements are always as real and as substantive as any other disagreements, never just practical differences of language. The ultimate ontological question is a scientific question like any other—correctly, but potentially misleadingly, characterized as “What is our ontology?” as if it were a matter of style, each person or group their own. Ontology is a scientific matter of the most general existential statements, statements which are accepted though fallible, and no more relative than the gaseousness of Jupiter.

2.c Summary and Addenda

Now that I have outlined the relation of semantics to ontology as I believe the classical Quine envisaged it, I wish to sum up and add marginally to the basic reasons vis-à-vis the classical Quine for not accepting the third case—the proper subsets case—as itself establishing ontological relativity (which, in turn, adds to the arguments against the first two cases).

The ontology of our total theory, in the sense of the later Quine, is relative to its interpretation due to the availability of proxy functions. According to the classical Quine, ontology is not intrinsically a matter of interpretation or semantics, and is certainly not in any way transcendental, but fully immanent. In harmony with naturalism, it is fully part of science, developed within science, intrascientific rather than superscientific. Our epistemic relation to reality is a straightforward first-order relation to reality and there is no superior vantage point on the claims of science than that achieved by stating the regimented, fully interpreted versions of those claims, including ontological claims. To point out that one can make other interpretations of the claims is nothing but a change of subject, making broadly the same sort of error as the person who sees the downward Löwenheim-Skolem theorem as representing an antinomy, or as proving that there aren’t really any uncountable infinities.

True, a reduction by proxy functions lacks the evident defects of the reasoning via the Löwenheim-Skolem theorem: unlike the latter, one explicitly specifies the relevant function giving a recipe for identifying the relevant proxy in every case, and it does not suggest any outright contradiction. But it remains a case of reinterpretation, like the proxy function argument involving the paring down of the domain. Whether or not it avails itself of the tools of semantics, the place of any such ontological reduction is at a prior point where, working with dirty hands, the ontological under-laborer is genuinely amenable to praise or criticism—not after the work has been completed and the finished product delivered, as if we had reached a unexpected coda wherein the curtain is raised again, and the masked interpreter (or perhaps semiotician) leaps in announcing amidst diabolical laughter, “But all this is relative!” 15

I stress that the Löwenheim-Skolem parallel is only illustrative. I’m not saying that the failure of the reasoning from the Löwenheim-Skolem theorem establishes my conclusion about general ontology. The parallel is only that, in either case, one cannot take what one can correctly assert from outside the theory—the place where sentences of the theory are mentioned rather than used and where wholesale reassignment of the references of terms is freely allowed—as bearing without further ado on what one can correctly assert from inside the theory—where sentences of the theory are used rather than mentioned. A second-order, metalinguistic stance in which one reflects on one’s total theory as an object contrasts with an ordinary first-order stance in which one does not regard one’s total theory as an object, but as the great many objects, statements, and verbal dispositions that figure in it. In the Löwenheim-Skolem case, malign symptoms arise over the cardinality of the domain; the diagnosis is that of equivocation between the two stances on the interpretation of “uncountable,” “set,” and so on. In the case of ontological relativity, although there is no material disagreement over the cardinality of the domain, the symptoms are much broader if more diffuse, involving the interpretation of humble terms such as “rabbit” as well as the quantifiers (except in the first case). The diagnosis and, indeed, the remedy I have advanced is to be reminded of Wittgenstein’s point which, as was explained in section 2.a, was embraced by Quine himself at least at certain pertinent moments: that to speak and understand a language, to use a language, cannot be to interpret the language, even if it does put one in a position to “interpret” expressions merely by disquotation.

As in Gödel’s theorems, Tarski’s 1933 results, or as noted in the procedure of regimentation, there is a multitude of facts that are intrinsically metalinguistic. There is nothing dubious with such endeavours even in the case of general ontology; based on one’s results, one may propose that such-and-such ontological reductions should be adopted. But if as I’m urging we adopt a “use-first” conception of language—as with the later Wittgenstein and, at least for a while, Quine—the possibility of an alternative, shrunken ontology would not establish that ontology is relative.

3. The post-classical Quine on ontology

The only way in which ontological relativity could be thought to hold without violating basic Quinean strictures is via proper subsets of the overall domain, and there are good reasons—reasons consonant with the classical Quine—for resisting that too, as just explained. This position is manifestly at odds with the later views of Quine. According to the later Quine, every sentence one accepts is susceptible to reinterpretation “within the reach … of proxy functions” (Quine 1992, 33), and there’s no getting out of it. I’m saying that so far as ontology is concerned, this change in his views was a mistake, the ploy involving proxy functions only a distraction.

I turn now to a critical and admittedly selective reading of Quine’s later postclassical writings—not to refute the later Quine but just to offer a few comments from the classical point of view. I’ve just said that the concept of reference will be central to the ontologist’s work involving analysis, deconstruction, and reconstruction, but needn’t figure specially in the ontologist’s pristine final claims. These—consisting of statements of the form “There are … ”—will be as Quine seems to have envisaged in the remarks of 1948, 1951, and 1960. Things began to change with the 1964 paper “Ontological Reduction and the World of Numbers” and changed decisively with “Ontological Relativity” of 1968, but there was some wavering in later years, most notably with his assertion in his “Things and Their Place in Theories” (1981a) and “Ontology and Ideology Revisited” ([1983] 2008), that “the point about proxy functions is a point only about evidence, a point not of ontology but of the epistemology [i.e., of what is involved in our knowledge] of ontology” ([1983] 2008, 317; cf. 1981a, 21), which might seem more amenable to the classical Quine, the position outlined and advocated here. But he reverted back to ontological relativity full stop in Pursuit of Truth (revised edition 1992) and also the paper “Structure and Nature” published the same year ([1992] 2008). Throughout this period, it is evident that Quine sought to reconcile proxy functions and relativity with something approaching common sense. Perhaps as his friend Burton Dreben is reported to have said, Quine was shifting back and forth from the one foot to the other. 16 Without saying exactly what these feet represent—perhaps abstract semantics or epistemology versus straightforward ontology—when he was on the former foot, I fear his position was too close that of nonnaturalist first philosophy, as if semantics afforded a transcendental vantage point superior to science. “There is no such cosmic exile” (Quine 1960, 275) warned the classical Quine (see Ricketts 2011, 297).

The view I am pushing contrasts starkly with the stirring close of “Ontological Relativity,” where Quine writes:

We know from Tarski’s work how the semantics … of a theory regularly demands an in some way more inclusive theory. This similarity should perhaps not surprise us, since both ontology and satisfaction are matters of reference. In their elusiveness, at any rate—in their emptiness now and again except relative to a broader background—both truth and ontology may in a suddenly rather clear and even tolerant sense be said to belong to transcendental metaphysics.

(1968, 212; 1969a, 68)

Truth and reference make perfect sense “relative to a broader background”—a background of a metalanguage—but not in an absolute sense; what is transcendental in a tolerable sense is the open-above ascent of metalanguages which supply ever-better truth predicates but no best. But, according to the view taken here, ontology is not a matter of reference, but of straightforward existence statements. Ontology is not relative, yet there is no hint of its being transcendental.

In Pursuit of Truth (1990 and 1992, sec. 20), 17 looking back at the years that had passed since “Ontological Relativity” of 1968, he wrote “The phrases ‘inscrutability of reference’ and ‘ontological relativity’ dominated my account of these matters, and kindly readers have sought a technical distinction between them that was never clear in my own mind.” He continued:

… I can now say what ontological relativity is relative to, more succinctly than I did in the lectures, paper, and book of that title. It is relative to a manual of translation. To say that “gavagai” denotes rabbits is to opt for a manual of translation in which “gavagai” is translated as “rabbit,” instead of opting for any of the alternative manuals. (51)

Yes, where translation is involved, the question ineluctably arises of the references of particular terms, and hence of the ontology of the speakers of the source language. But on the way of conceiving the matter I’m pursuing, a finished ontology is just not intrinsically a matter of semantics or translation, is not and cannot be a matter to which proxy functions might be relevant, and is no more relative than any other set of claims. The finished register is only a straightforward nonsemantical answer to the straightforward question which Quine posed in 1948, “What is there?” In the same passage, he goes on:

And does the inscrutability or relativity extend also somehow to the home language? In “Ontological Relativity” I said it did, for the home language can be translated onto itself by permutations that depart materially from the mere identity transformation, as proxy function bear out. But if we choose our manual of translation the identity transformation, thus taking the home language at face value, the relativity is resolved. Reference is then explicated in paradigms analogous to Tarski’s truth paradigm; thus “rabbit” denotes rabbits, whatever they are, and “Boston” designates Boston. (51–52)

Given the earlier part of this passage as well as other remarks in the text, this is not a straight denial of the inference from inscrutability to relativity. Ontology is still relative; yet the relativity is not threatening to ordinary speech, because the expedient is available of the “identity transformation” by which the relativity is “resolved” (it is not eliminated but concealed, as it were). But now the reference to translation begins to look like a mere epicycle (even if Quine achieves the desired balance on the two feet in the end, since ontology can be seen as straightforwardly involving such clauses as “‘rabbit’ denotes rabbits”; see also Quine 1968, 49; 1981a, 19). If we ask point-blank the question of ontology, then there is no reason to begin with for translating, for choosing a manual of translation.

Slightly later, in From Stimulus to Science of 1995, Quine acknowledged that proxy functions needn’t have any bearing on the wholesale question of ontology:

The simplest sort of reinterpretation meeting our conditions is mere permutation, redistributing but preserving the ontology. Cosmic complement is an example, if the universe contains those complements as objects to begin with. Spatiotemporal objects are permuted with their complements, and nonspatiotemporal objects are permuted into themselves. (72)

But he does so while continuing to speak as if there is some way that nonlocal, one-to-one proxy functions could fail to preserve the ontology without violating naturalism or the ban on quantifying over the nonexistent. He then says that in view of the lesson of proxy functions, “Such is ontological relativity, as I have called it, or the indeterminacy of reference” (72–73). It would have been better if he were to have dropped the equation outright, if he were indeed to have dropped entirely the allusion to ontology in discussing proxy functions. A couple of pages later, he adds:

Having appreciated this point [learned from proxy functions], let us adjust our usage to it rather than bask in paradox. The very freedom vouchsafed us by the indeterminacy of reference allows us to adopt ostension as decisive for reference to observable concrete objects. We end up as we began, then, agreeing on the denotations of “rabbit” after all: rabbits for all concerned. We may then merely differ on the deeper nature of rabbits: they are spatiotemporal regions for some, number tables for others, and sui generis for most. Adaptation of our usage must not, however, be allowed to obscure the lesson of proxy functions. Namely, a language-wide one-to-one reassignment of values to our variables has no effect on the truth or falsity of our statements.

(Quine 1995, 75)

It now looks as if he were denying the inscrutability of reference, but that is not what is going on. To “adopt ostension as decisive for reference to observable concrete objects” falls short of elevating ostension to a criterion for reference, which would be to abandon his Tarskian orientation to reference (note also that ostensive definitions can themselves be interpreted in various ways consistently with all evidence). This is clear in the penultimate sentence, that the fix must not be “allowed to obscure the lesson of proxy functions” (combined with the final sentence). His speaking of “[a]daptation of our usage” confirms that the point concerns the practice of language use—to communicate best, we should use “rabbit” rather than “cosmic complement of a rabbit”—not semantics. Once the semantical game is begun, there is no stopping the regress of interpretations, but equally there is no gainsaying one’s choice of the identity interpretation as the easiest in practice. The digression via proxy functions shows that reference is inscrutable but, as I have been at pains to establish, ontology is simply not in play and is unaffected.

4. Closing remarks

I close with remarks about two other features of Quine’s later philosophical picture that might seem to be borne on by the considerations advanced here. The first one is not so borne on but the second one is.

The first is Quine’s occasional warmth towards “Hyper-Pythagoreanism”—a general ontology of pure abstract sets. 18 Although he does sometimes discuss it alongside the inscrutability of reference or proxy functions, the thesis and the case for it are crucially independent of those doctrines, at least on the perspective taken here, for what is proposed is a straightforward ontological reduction involving certain theoretical or conceptual adjustments such as counting sentences such as “Rabbits are sets” as true. It is therefore a theoretical proposal to be adjudicated on its scientific merits. Evidently, then, nothing I have said here tells either for or against Hyper-Pythagoreanism in this latter sense (for Quine-style case positively in favor of the view; see Kemp 2017).

The second is Quine’s calling for a form of structuralism as a central part of his case for downgrading ontology—the idea being that the scientific importance of a theory lies not so much in its ontology but in its sentence-to-sentence links, its predicative or quantificational structure. 19 “Save the surface [the sentences] and you save all,” Quine borrows from the paint manufacturer Sherman Williams’s motto as part of the epigraph for Pursuit of Truth (and “Structure is what matters to a theory, and not the choice of its objects” [1981a, 20; compare Pursuit of Truth 1990 and 1992, 36]). According to this “global structuralism,” reality—the universe, the cosmos—does not receive its most fundamental characterization in terms of what exists, but in terms of how it is, in terms of the (predicative) structure of the theory describing it. Why accept it? On the grounds of naturalism, Quine denies that theories refer only to their structures, as a full-blown structuralist might hold; reference to objects is adjudged to be of minimal scientific importance, but not unreal. 20 But the latter idea depends on the inference from proxy functions to ontological relativity. According to the main conclusion of this piece—that Quine is not in a position positively to infer the relativity of ontology—there is no pressure from that quarter to accept structuralism even in Quine’s denuded form (of course, one may argue for forms of structuralism along other lines).

The Quinean should hold that reference is inscrutable but deny that this bears on the answer to the central question of ontology, “What is there?” The finished claims of ontology are as nonsemantical as those of physics or tennis commentary and are as absolute as anything in Quine’s scheme.


Thanks to Juliet Floyd, Peter Hylton, Stephan Leuenberger, Andrew Lugg, and two referees for this journal.

Gary Kemp is a senior lecturer at the University of Glasgow. He writes on Quine, Davidson, Frege, and Wittgenstein, and also on aesthetics.

1 Sometimes Quine formulated and sang the praises of “predicate functor” logic—a logic without variables (first conceived by Schönfinkel). It drives home the point that variables do nothing but keep track of sameness of reference, the expression of which depends on the locations in predicates being quantified over. But he was quick to point out that “to be is to be the value of a variable” translates easily into “to be is to be denoted by a predicate” in the new setting. See Quine (1995, 35, 101–6).

2 In various places, Quine says that objects can be got up to play (many of) the roles of properties or universals. For example, the sum total of all red objects—past, present, and future—may be thought of as “redness.”

3 Or “satisfaction” as Tarski called it in his simplified version (1955) of his 1933 ideas concerning truth (satisfaction in the 1933 sense was a relation between closed or open sentences and infinite sequences of objects). Reference or denotation in Quine’s work, covers the relation between the general term “dog” and an arbitrary dog, as well as between the singular term “Fido” and Fido. Since singular terms save variables can, according to Quine be eliminated during the procedure of regimentation, any problems pertaining to the latter are also eliminated in Quine’s view.

4 Proxy functions first appeared by name in Quine ([1964] 1976, 217–18), and figured more definitively in 1969a, 55ff.

5 Quine says that because of the role that they play, proxy functions must be explicitly named (Quine 1992, 31; [1964] 1976, 218): merely knowing that there are proxy functions is not sufficient for purposes of actual ontological reduction, or giving alternative reference schemes, because one needs to know which object is the proxy of a given object. They can, however, be merely virtual functions rather than ones that exist as objects in the domain (Quine 1969a, 57). Sometimes Quine speaks of proxy functions that are not one-one (e.g., 1969a, 56) but only, as far I know, for special cases dealing with parts of reality—for example, persons can be identified with their incomes for certain purposes.

6 In later presentations of the idea (e.g., 1995, 75), Quine speaks directly of systematic reinterpretations of free variables. Now the proxy action explicitly occurs at the level of interpretation, and the theories are syntactically identical. For example, where we had “In an interpretation I which features arbitrary assignments i of objects o1 om … to (free) variables “x1 …xm …”, we would write something like “In an interpretation I* which is just like I except that in place of each i it features the proxy-assignment Pr(i) where for each object ok which was assigned by i to a variable xk , it assigns the proxy of ok to xk ….” The reinterpretation of predicates would have, e.g., a clause for “dog” as {x: x is the proxy of a dog} for {x: x is a dog}, etc. (or “dog” denotes o iff o is the proxy of a dog, for “dog” denotes o iff o is a dog).

7 Quine sometimes speaks for expository convenience of a theory which contains singular terms other than variables, but, as is well known, Quine takes it that in the most conceptually austere presentation of knowledge, that is not so.

8 The empirical content of a theory is for Quine given by its observation categoricals, which are standing sentences formed of pairs of observation sentences, as in “If smoke, fire.” Observation sentences are explained in terms of the sensory stimulations that dispose a subject to assent to it. In Quine’s picture observation sentences, and hence observation categoricals, do not require reference for their explanation. Therefore, the empirical content of a theory, no matter how extensive, is independent of the references of its terms. See the essay “Empirical Content” (Quine 1981b).

9 Eklund (2007, 128) seems to foreshadow this part of my argument. He writes, “…in running the argument we will be presupposing that there are objects corresponding to all the different acceptable interpretations. This might seem plainly incoherent. On the one hand, we presuppose that objects corresponding to all the acceptable interpretations exist; on the other hand, we are saying that, for each interpretation, it is indeterminate whether it is the objects that exist on this interpretation that really exist. So, if [so], inscrutability is paradoxical.” But strictly speaking I don’t see that Quine says or implies that for a given interpretation, things exist but it is indeterminate whether they exist. Closer would be to say it is indeterminate which things exist independently of a given interpretation. The problem, as I see it, is rather that of the assumption of possibilia to run the argument where disjoint domains are concerned (see the next note and Quine 1969b for a momentary lapse of this policy).

10 In fact, Quine worries that smaller-scale, reductive applications of proxy functions involve mere “make-believe” ([1964] 1976, 219; 1969a, 57), as if one must pretend that certain objects exist. Some small-scale cases of ontological reduction can be explained as arguments by reductio ad absurdum as in 1969a, 58. Quine never gives an example of a maximal case for the very good reason that there isn’t any. For a full account see section 2.

11 One might point to cases like a function from natural numbers as primitive to Fregean natural numbers (classes), with the function amounting to identity in the case where the input is not a natural number (Quine [1964] 1976, 219). However, such small-scale examples are better understood as cases of conceptual explication or ontological reduction, not as ones which demonstrate ontological relativity; again, see section 2.

12 I do not believe that this contradicts Davidson’s position as instigated in his “Truth and Meaning” (1967). His theories of meaning are not meant as theories which explain actual linguistic competence; they are meant only to describe linguistic competence.

13 Compare Putnam: “…when one is speaking a natural language, one treats a sentence as the same sentence whether it occurs in what a logician might view as the metalanguage or in what a logician might view as the object language. This is what Quine calls taking one’s language at face value, or ‘acquiescing’ in one’s language. To ‘acquiesce’ in one’s language is to translate it homophonically into its own metalanguage” (1985, 69; emphasis added). This appears to be denied in the very passage which Putnam goes on to quote: “The point is not that we ourselves are casting about in vain for a mooring. Staying aboard our own language and not rocking the boat, we are borne smoothly along on it and all is well; ‘rabbit’ rabbit” denotes rabbits, and there is no sense in asking ‘Rabbits in what sense of “rabbit”?’ Reference goes inscrutable if, rocking the boat, we contemplate a permutational mapping of our language on itself, or if we undertake translation” (Quine 1981a, 19–20; emphasis added). In speaking our language, we do not rock the boat. That includes the ordinary use of “refers” and “means”; that much is disquotational in character, “immanent,” or “parochial”; there is there is no thought of dragging in the Tarskian apparatus. To acquiesce in one’s own language is simply to use one’s language, not to translate it, as I have emphasised.

14 A referee points out that nothing I have said rules out the possibility that the same corpus of natural-language behavior might have two equally successful regimentations with different ontologies (as one might suppose in the case of rabbits/rabbit stages); this is different from the scenario of a single regimented theory having different interpretations. As far as I’m aware, Quine never considers exactly this, because Word and Object does not explicitly advance ontological relativity, and when he does come to advance it, he did so via proxy functions (see Quine [1970] 2008, 213–14). But though this possibility does not strictly involve proxy functions, the gist of the arguments in section 1 go through: to be in a position in which either strategy is acceptable, one must already be in a position of quantifying over the objects needed for each theory (and there are rabbits and rabbit stages, so that example is without ontological repercussions). I believe that this is why in Word and Object Quine was right to treat the case as demonstrating referential inscrutability, as what he would later term an “argument from below” ([1970] 2008, 214) for the indeterminacy of translation, not as demonstrating ontological relativity.

15 Eklund mentions two possible reactions to ontological relativity. The first is the “homely view” that accords with Quine’s suggestion that “we can ‘acquiesce’ in our mother tongue; we take the words of our mother tongue ‘at face value’” (2007, 122). I am myself arguing for something like the homely view, but I do not accept an immanent view of reference. As Ricketts (2011) stresses (cf. McGee 2005), an immanent view of reference is adequate for intralinguistic disquotational constructions such as “‘a’ refers to a,” but is not sufficient for interlinguistic uses. The other reaction is the “despair view”, that one must “be silent about the issues of ontology …Take our best theory of the world…. It is indeterminate what is the ontology of this theory. But then one cannot plausibly maintain, concerning a given ontology, that it is the true ontology.” (122) Eklund appears not to find room for the later Quine’s actual view: there is a “true ontology,” but it can be exchanged for another. Eklund asks “What exactly would the despair view entail? That we should avoid making quantified claims?… That we should … adopt some more instrumentalist or fictionalist attitude?” (2007, 123) The consequences of the view would be indeed be alarming, since for Quine all regimented sentences are quantified. But Quine does not subscribe to it. Again, Quine’s view is that ontology is relative, but not out-and-out nonfactual in the way Eklund suggests. He comments further: “Quine appears to suggest that we can simply assume ‘rabbit’ to refer to rabbits—that, after all, is what the talk of what we ‘take at face value’ suggests—and thus, provisionally so to speak, resolve the indeterminacy. But if ‘rabbit’ is for principled reasons inscrutable, then there is nothing I can do or say that resolves the inscrutability—saying ‘let “rabbit” refer to rabbits’ doesn’t help” (124). The envisaged “resolution” of the inscrutability of reference was not to eliminate it, but only to hide it by showing that inscrutability needn’t interrupt the normal use of such terms as “refers.”

16 Informal conversation in the 1980s at Boston University, as reported by Andrew Lugg.

17 The passage originally occurred in Quine’s talk “Three Indeterminacies” of 1988, published in 1990.

18 He advanced it in his “Whither Physical Objects” (1976) and more equivocally in various later writings, including From Stimulus to Science (1995, 70–1).

19 For example, in “Things and Their Place in Theories” (1981a), “Structure and Nature” ([1992] 2008), and Pursuit of Truth (1992, 33–6).

20 This is connected with a point about realism that is often missed. For example, Fogelin says “… observation sentences taken holophrastically cannot be otherwise than indifferent to ontology” (1997, 560), and then seems to flirt with equating ontological relativity with a denial that there are really objects, that “Objects are posits (reifications, fictions); and which posits we make is a function of our theoretical concerns” (557; my emphasis), that all there are really are observation sentences construed holophrastically: “Quine is making a much stronger claim,” avers Fogelin, “… that objects are ‘neutral nodes in [the] logical structure’ of our ‘overall theory of the world’” (557), a thesis that “puts forward a complex claim concerning the operations of our cognitive apparatus.” Even aside from the evidently false claim of identity of objects with neutral nodes, this seems to misfire, as the point of proxy functions is that precisely nothing is changed, and in particular nothing is changed about our cognitive apparatus, by their invocation.


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