Ontology & Ontological Relativity

“To Be Is to Be the Value of a Variable”

W. V. O. Quine by Licentia Poetica

Criterion of Ontological Commitment

Quine’s most enduring contribution to the theory of ontology was made in his 1948 essay On What There Is, later reprinted in From a Logical Point of View, where he proposed that the existential commitments of a theory are not read off from its predicates, its names, or its ordinary vocabulary but exclusively from the values its bound variables must be capable of taking in order for the theory’s affirmations to come out true. On this view a theory is committed to those and only those entities that must lie within the range of its quantifiers for its sentences to be true, so that saying some dogs are white commits a speaker only to there being things that are both dogs and white, and not to any further entity such as doghood or whiteness considered as an abstract universal, since the bound variable something ranges over concrete dogs rather than over properties. Quine summarized this standard in the celebrated formula to be is to be the value of a variable, though he was careful to note, particularly in later restatements of the point, that this formula does not itself settle which entities we ought to countenance, since it functions only as a test of what a given theory or discourse is already committed to rather than as an independent criterion for deciding what really exists, and adjudicating between rival ontologies remains a further and separate question to be settled on grounds of simplicity, economy, and explanatory power. This criterion had the effect, in the judgment of philosophers such as Hilary Putnam, of making ontology a respectable and tractable subject for analytic philosophy after decades in which existence claims had been regarded as either trivially obvious or hopelessly metaphysical, since Quine offered a precise logical technique, regimentation into the canonical notation of first-order quantification theory, for exposing exactly what a theory does and does not presuppose to exist.

Ontological Relativity and the Inscrutability of Reference

Quine’s criterion of ontological commitment tells us what a theory quantifies over only once its sentences have been regimented into a canonical logical form and interpreted against some domain of objects, and in his 1968 lecture Ontological Relativity, collected in the volume of the same title, Quine pressed the further question of what fixes that interpretation in the first place, arguing that any theory can be reinterpreted through a systematic proxy function that reassigns every object the theory apparently quantifies over to some other object entirely, in such a way that every sentence of the theory retains exactly the same truth value under the reinterpretation. Because this substitution can be carried out globally and without any change of truth value, Quine concluded that the question of what a theory is really about cannot be answered from within the theory itself, but only relative to some background theory whose own ontology we are not simultaneously placing in question, an idea he illustrated with Otto Neurath’s image of sailors who must rebuild their ship plank by plank while it remains afloat, unable ever to dry-dock the entire vessel and inspect it from outside. This relativity of ontology to a background frame of reference is continuous with the inscrutability of reference Quine had already established in Word and Object through the gavagai example, since both theses show that reference is never fixed by the totality of available evidence alone but always presupposes some antecedently accepted scheme of objects and identities that is doing unacknowledged work, and Quine insisted that this consequence, disquieting as it may seem, is simply the sober upshot of taking naturalism and empiricism seriously rather than an invitation to say that anything goes.

Preference for Desert Landscapes

Quine famously described his own ontological temperament, in a phrase from On What There Is that has since become one of the most quoted lines in twentieth-century philosophy, as a taste for desert landscapes, expressing a methodological preference for the sparsest ontology capable of doing the theoretical work required rather than for a profuse or gerrymandered universe crowded with entities introduced merely to accommodate every grammatically well-formed noun phrase. This preference reflects Quine’s conviction that ontological economy is a genuine theoretical virtue on a par with simplicity in the natural sciences, so that when two theories are otherwise equally adequate to the evidence, the theory committed to fewer or more familiar kinds of entities is to be preferred, and it also explains his lifelong hostility to what he regarded as needlessly inflated ontologies populated by merely possible objects, unactualized entities, or intensional entities such as attributes and propositions distinct from the extensions with which they are coextensive. The desert landscape metaphor should not be mistaken for a rigid nominalist dogma, however, since Quine’s own mature ontology, as his later concessions on abstract objects show, was considerably less austere than the phrase might suggest, and the preference functioned for him more as a default methodological pressure toward parsimony than as an absolute constraint on what could ultimately be admitted.

Critique of Abstract Objects and Modality in the Early Views

In the period surrounding On What There Is and continuing through much of the 1940s, Quine, often in explicit collaboration with Nelson Goodman, pursued a nominalist program that sought to avoid commitment to abstract entities such as classes, properties, attributes, and propositions wherever a physicalist or extensionalist paraphrase could be constructed instead, on the grounds that abstract objects lack the spatiotemporal location and causal efficacy that Quine took to be marks of a properly disciplined ontology. Alongside this suspicion of abstracta, Quine mounted an equally sustained attack on modal notions such as necessity and possibility, most influentially in his paper Reference and Modality and in related discussions, arguing that quantifying into modal contexts generates insoluble problems of referential opacity, since substituting codesignative terms within the scope of a modal operator can change a sentence’s truth value, which Quine took to show that modal logic rests on an untenable notion of essential properties known independently of any particular way of describing an object. Both lines of criticism, the nominalist suspicion of abstract objects and the rejection of quantified modal logic, expressed the same underlying commitment to extensionality and to a naturalistic ontology answerable to the methods of empirical science rather than to intuitions about meaning or necessity that Quine regarded as ultimately ungrounded.

Later Concessions on Abstract Objects

Despite this early nominalist ambition, Quine came to accept, particularly from the 1950s onward, that a thoroughgoing nominalism could not accommodate the mathematics indispensable to empirical science, since modern physics and its surrounding mathematical apparatus require quantification over sets and numbers that cannot plausibly be paraphrased away without loss, and Quine’s own systems of logic, notably in Mathematical Logic and later in Set Theory and Its Logic, were built on an ontology that unapologetically included classes. This shift produced what came to be called the Quine-Putnam indispensability argument, developed further by Hilary Putnam, according to which we are rationally committed to the existence of mathematical objects because our best scientific theories quantify over them and we have no principled way of accepting the scientific theory while rejecting the mathematical ontology it presupposes, so that Quine’s mature position accepted an ontology of sets and abstract mathematical objects as part of the price of naturalism rather than as a violation of it. This concession illustrates that Quine’s actual ontological practice was considerably more moderate than the slogan of a desert landscape suggests, since for Quine the test was never abstractness as such but rather whether a purported entity earns its keep within our best overall theory of the world, a test that abstract mathematical objects, on his mature view, ultimately satisfy while other candidates such as unactualized possibilia or Meinongian nonexistent objects do not.

Relation to Nominalism and Physicalism

Quine’s ontology is best understood as occupying an unstable middle position between strict nominalism and an unrestricted Platonism, since he retained from his early nominalist period a physicalist insistence that concrete physical objects, individuated by their spatiotemporal boundaries, constitute the paradigm case of what there is, while nonetheless admitting an ontology of sets as mathematically indispensable, a combination sometimes described as a reluctant or minimal Platonism grafted onto an otherwise resolutely physicalist worldview. This hybrid stance generated considerable debate among Quine’s contemporaries and successors, with philosophers sympathetic to nominalism, including Nelson Goodman and later Hartry Field, seeking to show that the mathematics needed for physical science could after all be reconstructed or dispensed with in nominalistically acceptable terms, while others accepted Quine’s indispensability reasoning as decisive grounds for a moderate mathematical realism, and the resulting dispute over whether Quine’s own criterion of ontological commitment ultimately forces a choice between physicalism and Platonism, or instead permits the qualified coexistence of both, remains a live topic in the philosophy of mathematics.

Contemporary Relevance: Meta-Ontology and Quantifier Variance

Quine’s framework, though developed in the middle of the twentieth century, continues to structure much of contemporary meta-ontology, the branch of metaphysics concerned not with what exists but with what it means to ask and answer existence questions in the first place, and his insistence that quantification in a single univocal first-order sense is the sole legitimate vehicle for ontological commitment has become the principal target as much as the principal resource for later meta-ontologists. Philosophers such as Eli Hirsch have challenged this univocality directly through the thesis of quantifier variance, arguing that there can be multiple equally legitimate meanings for the existential quantifier, so that apparent disputes about what exists may sometimes be merely verbal disagreements generated by speakers using different but equally admissible quantifier meanings rather than substantive disagreements about the world, a position that inherits much of its motivating force from Quine’s own thesis of ontological relativity even as it departs from his commitment to a single canonical logic. Other contemporary metaphysicians, including Theodore Sider, have instead sought to rehabilitate a more robustly realist meta-ontology by arguing that reality has a privileged joint-carving structure that can adjudicate among rival ontological frameworks in a way Quine’s purely pragmatic and holistic criteria cannot, and the resulting three-way conversation among broadly Quinean deflationism, Hirsch-style quantifier variance, and Sider-style metaphysical realism continues to define the central debates of contemporary meta-ontology, attesting to the continuing centrality of Quine’s original questions even where his specific answers are contested.

Further Readings

• Quine, W. V. (1948). “On What There Is.” Reprinted in From a Logical Point of View (1953). Harvard University Press.
• Quine, W. V. (1969). Ontological Relativity and Other Essays. Columbia University Press.
• Quine, W. V. (1981). Theories and Things. Harvard University Press.
• Gibson, Roger F., ed. (2004). The Cambridge Companion to Quine. Cambridge University Press.
• Blatti, Stephan, and Sandra Lapointe, eds. (2016). Ontology After Carnap. Oxford University Press.
• Putnam, Hilary (1971). Philosophy of Logic. Harper & Row.
• Hirsch, Eli (2011). Quantifier Variance and Realism: Essays in Metaontology. Oxford University Press.
• Sider, Theodore (2011). Writing the Book of the World. Oxford University Press.