A TENSION IN QUINE'S THEORY OF EXISTENCE
We begin with a prima facie distinction between general and singular existence. General existence is what is expressed by claims of the form, ‘Fs exist,’ or ‘There are Fs,’ where ‘F’ is a logically general term, whereas singular existence is what is expressed by claims of the form, ‘a exists,’ where ‘a’ is logically singular term. In his famous dictum, “Existence is what existential quantification expresses,”[iv] Quine is referring to general existence. This is clear from the sentence immediately following it: “There are things of kind F if and only if (Ex)(Fx).” Putting the two quoted sentences together, we may infer that (general) existence is a kind’s being instantiated. Quine plausibly maintains that existence in this general sense cannot be explicated in simpler terms. But he also says something far from obvious: singular existence can be explicated in terms of general existence. “We found an explication of singular existence, ‘a exists,’ as ‘(Ex)(x = a)’; but explication in turn of the existential quantifier itself, ‘there is,’ ‘there are,’ explication of general existence, is a forlorn cause.”[v]
There are several things to note about this last passage: (i) Quine endorses the general existence/singular existence distinction in so many words; (ii) Quine appears to conflate singular existence with singular existential sentences by his use of the appositive construction, “singular existence, ‘a exists,’...”; (iii) Quine takes general existence to be logically primitive, with singular existence definable in terms of it. Point (iii) makes it clear that Quine is an instantiation theorist and thus stands in the tradition of Gottlob Frege and Bertrand Russell.
An instantiation theorist is one who holds that existence in its basic or primitive sense is just the being-instantiated of a concept, property, propositional function, or cognate item. In a slogan: existence is instantiation. Thus existence is not a property of individuals but a property of concepts, properties, etc. But there are two ways one can be an instantiation theorist depending on what one decides to do with singular existence. Do we construe it as a special case of general existence or do we dispense with it? If existence is instantiation, the pressure is on to simply dispense with, or eliminate, singular existence. By definition, individuals cannot be instantiated, so if existence is the being-instantiated of a concept or property, then existence cannot be attributed to individuals. On the other hand, it seems as clear as anything that we do sometimes meaningfully attribute existence to individuals when we say things like ‘I exist.’ Think of the Cartesian cogito, the conclusion of which is sum, ‘I am,’ ‘I exist.’ Furthermore, a general existential such as ‘Faithful husbands exist’ cannot be true unless it is at least possible that some such singular existential as ‘NN exists’ is true, even if, in actual fact, no one can name a faithful husband. How then could we simply dispense with singular existence and singular existentials (as opposed to providing an analysis of them that does justice to the datum that existence is sometimes attributed to individuals)?
Thus there is a certain tension at the heart of the instantiation theory of existence. As an instantiation theory, it exhibits a nisus towards the elimination of singular existence, the existence of individuals, and its replacement with the instantiation of concepts/properties. As a theory of existence, however, it must somehow accommodate the meaningfulness of first-level attributions of existence. It is a datum that existence is fundamentally the existence of individuals, a datum innocent until proven guilty. That this is and must be our ‘datanic’ starting point is obvious from the fact that if we had no notion of existence as of individuals, we would have no idea of what we were trying to eliminate or replace by construing existence as exclusively a property of concepts or properties. Part of what I will be urging is that this tension is symptomatic of an underlying incoherence in the instantiation theory.
The path of accommodation is taken by the identitarian according to whom there is singular existence, but singular existence reduces to general existence inasmuch as the existence of a specific individual a is identified with the being-instantiated of some property of that individual, the haecceity-property a-ness perhaps. The path of replacement is taken by the eliminativist according to whom there simply is no such thing as singular existence on the ground that existence cannot be a property of individuals in any sense if it is a property of concepts or properties. The difference, in other words, is that the meaningfulness of the schema ‘a exists if and only if ___’ is presupposed by the identitarian but explicitly rejected by the eliminativist. (The identitarian/eliminativist terminology is modeled on the controversy in the philosophy of mind between the identitarian, who holds that there are mental states, but they are identical to brain states, with the eliminativist, who denies that there are any mental states and who rejoices in the prospect of an eventual replacement of mental concepts with neurophysiological ones.[vi])
It is clear that both Frege and Russell were instantiation theorists who were eliminativists about singular existence. Their aim was not to explicate the existence of individuals, but to demonstrate that there is no such thing. Frege, we will recall, held that it is meaningless to concatenate the predicate ‘...exist(s)’ with a logically singular term. Thus such sentences as ‘Socrates exists,’ ‘I exist,’ and ‘God exists’ are positively meaningless, hence neither true nor false.[vii] To borrow an illustration from Russell, they are as meaningless as ‘Socrates is numerous.’[viii] Humans are unfortunately quite numerous, and Socrates is human; but it would be the fallacy of division to infer that Socrates is numerous. What is true of the class of humans (that it has members), and true of the property of being human (that it is instantiated), is not also true of each human. Similarly, although humans exist, and Socrates is human, Russell held that it was something like the fallacy of division to infer that Socrates exists. This is a simple consequence of the ‘Fressellian’ doctrine that existence is a property of concepts/propositional functions. As such, existence cannot be a property of individuals on pain of a sort of category mistake. If, as Russell says, existence is a propositional function’s being “sometimes true,” then, since no individual is “sometimes true,” no individual exists. If Russell is right, this puts paid to “An almost unbelievable amount of false philosophy...” which “...has arisen through not realizing what ‘existence’ means.”[ix]
But our topic is Quine. Is he an identitarian or an eliminativist instantiation theorist? To answer this question, I examine Quine’s explication of ‘a exists’ in terms of ‘(Ex)(x = a).’[x] My strategy is, first, to argue that Quine’s explication cannot reasonably support an identitarian interpretation, and second, to argue that it is also not susceptible of an eliminativist interpretation. Given that it must admit one or the other interpretation, I conclude that Quine’s theory of existence, according to which, in van Inwagen’s words, “The single sense of being or existence is adequately captured by the existential quantifier of formal logic,”[xi] is of dubious coherence. I further suggest that it is Quine’s waffling between the two interpretations that gives his theory of existence its plausibility.
THE IDENTITARIAN CONSTRUAL OF QUINE’S EXPLICATION
Note for starters that the very attempt to explicate ‘a exists’ strongly suggests that Quine is an identitarian. For if ‘a exists’ were in the same logical boat with ‘a is numerous,’ as the eliminativist ‘Fressellian’ doctrine implies, then it would not call for explication, but for outright elimination. One cannot explicate nonsense. But it turns out that the very natural identitarian reading of Quine’s explication leads to difficulties. One problem is that it issues in vicious circularity. Another is that it fails to solve the problem of negative existentials.
I begin the case for circularity by noting that a formula like ‘(Ex)(x = a)’ is to be evaluated relative to a universe of discourse containing only existing objects and no Meinongian objects. That this is Quine’s intention is clear from his animadversions against ‘Wyman’ (who more or less stands in for Meinong) in “On What There Is,” and from Quine’s constant references to the particular quantifier as an existential quantifier. Given this, it is surely a trivial truth that a exists if and only if there is an x identical to a. For if there is an x identical to a, this cannot be the case unless a exists. After all, it is a and nothing else that is the value of the bound variable in ‘(Ex)(x = a).’ Thus Quine’s explication on the identitarian construal gives us no new insight into what the existence of an individual consists in. He does not deliver what he promises, an explication of singular existence in terms of general existence. We can put this by saying that the explication is circular: the existence of a is explicated in terms of a’s identity with something that exists. But since this thing that exists is a, this boils down to an explication of the existence of a in terms of the existence of a. No explication of the singular existence of a in terms of general existence has been provided. At most, Quine’s explication provides an analysis of the singular existential sentence ‘a exists.’
There is this difference, however. In the singular sentence ‘a exists’ the burden of objective reference is borne by the singular term ‘a.’ But in the existentially general formula ‘(Ex)(x = a)’ the burden is supposed to be shifted to the bound variable which refers without naming. It is Quine’s well-known doctrine that bound variables, represented in English by ‘something,’ ‘nothing,’ and ‘everything,’ “refer to entities generally with a kind of studied ambiguity peculiar to themselves.”[xii] Thus in ‘Something is (identical to) a,’ which is just an ordinary language transcription of ‘(Ex)(x = a),’ it is ‘something’ that does the referring and not ‘a.’ Now the idea that objective reference is routed through quantified variables as opposed to names is not exactly clear; but to pursue this line of critique would take us too far afield. But even if this idea be granted, it not easy to see why ‘a’ in ‘(Ex)(x = a)’ should play no referential role.
One could argue that ‘a,’ though no longer in the limelight, is still shouldering the referential burden. For the x in question is identical to a. ‘a’ must come into the explicans to insure that it is a that gets referred to and not something else. The explicans thus only appears to be a general statement; in reality it is as singular as the explicandum. Whether we say that a exists or say instead that a is such that something is identical to it, the content of our assertion is about a and so is singular. Likewise in the case of ‘a does not exist’ explicated as ‘~(Ex)(x = a).’ Whether we say that a does not exist or say instead that a is such that nothing is identical to it, the content of our assertion is about a and so is singular.
The second problem with the identitarian construal of Quine’s explication of ‘a exists’ concerns negative existentials. Negative singular existentials like ‘Pegasus does not exist’ pose well-known problems. If the meaning of a name is its referent, then presumably Pegasus must exist if ‘Pegasus’ is to be meaningful, in which case ‘Pegasus does not exist’ would appear to be self-contradictory. But rendering ‘Pegasus does not exist’ as ‘~(Ex)(x = Pegasus)’ leads to no improvement whatsoever. For what the quantified formula says is that Pegasus is diverse from each thing that exists. But surely any puzzle to which ‘Pegasus does not exist’ gives rise will also be engendered by ‘Pegasus is diverse from each thing that exists.’ For if Pegasus is diverse from each thing that exists, must not Pegasus exist in order to be thus diverse?
Summing up the identitarian reading of Quine’s explication, we can say that it leads to circularity and offers no solution to the problem of negative singular existentials.
THE ELIMINATIVIST CONSTRUAL AND CONTEXTUAL DEFINITIONS
A defender of Quine might say that the identitarian reading is wrongly foisted upon Quine, and gets the details wrong: the logical form of ‘(Ex)(x = a)’ is general, not singular despite the occurrence of ‘a’ in it, and parsing ‘a does not exist’ as ‘~(Ex)(x = a)’ does afford a solution to the problem of negative singular existentials. What is more, there is no circularity. But to appreciate this, Quine’s defender continues, one must realize that Quine’s explication of ‘a exists’ in terms of ‘(Ex)(x = a)’ is a contextual definition in which ‘a exists’ taken as a whole is replaced by a sentence in which neither ‘a’ (as an independent semantic unit) nor ‘exists’ occurs. Since neither of these terms occurs in the explicans ‘(Ex)(x = a),’ there is no circularity; nevertheless, the entire meaning of the explicandum is captured.
This eliminativist construal of Quine’s explication works only on two conditions. The first is that ‘a’ be replaceable by ‘= a’ and this in turn by a general term. The second is that the context ‘(Ex)(...x...)’ be construable as a second-level predicate. Suppose we take these points seriatim.
A. If ‘(Ex)(x = a)’ is to be a truly general statement, despite the presence in it of singular term ‘a,’ then it must be parsed in such a way that ‘a’ no longer occurs in it as an independent semantic unit. Otherwise, the explicans could be read as ‘a is identical to something’ which is obviously singular, as argued above. The way to do this is, first, by thinking of ‘a’ as indissolubly linked to ‘=,’ and thus not capable of standing on its own, and second, by replacing ‘= a’ with a general term, a predicate constant, call it ‘A,’ which is true solely of the individual a. Quine makes this move.[xiii] It is a recurrent theme of his that names are eliminable through contextual definition. In Word and Object he makes the point by saying that “purely referential occurrences of singular terms other than variables can be got down to the type ‘= a’.”[xiv] This shows that “‘= a’ taken as a whole is in effect a predicate or general term....”[xv] The upshot is that the explicans of ‘a exists’ becomes ‘(Ex)(Ax)’ which is indisputably general. ‘Socrates exists’ would then be explicated as ‘There is an x such that x socratizes’ or ‘Something socratizes.’ ‘Pegasus does not exist’ would be rendered as ‘Nothing pegasizes.’ Clearly, ‘Nothing pegasizes’ is not paradoxical in the way of ‘Pegasus does not exist.’ So on the eliminativist approach, unlike the identitarian, we do have a solution to the problem of negative singular existentials.
The replacement of empty names like ‘Pegasus’ with general or predicable terms seems unproblematic. But it is difficult to see how a denoting name like ‘Socrates’ could be replaced by a general or predicable term. To be able to understand ‘Something socratizes,’ one must be able to understand the predicate ‘socratizes.’ But this predicate cannot be understood as elliptical for something like ‘is the wisest Greek philosopher’ in the way ‘pegasizes’ can be understood as elliptical for ‘is the winged horse of Greek mythology.’ The reason is that Socrates is a genuine individual, one whose identity cannot be captured by a definite description. Socrates is Socrates in every possible world in which he exists including those worlds in which he is not the wisest Greek philosopher. Pegasus, however, is not a genuine individual, but the mere possibility of an individual: Pegasus has no identity apart from that provided by ‘the winged horse of Greek mythology.’
Therefore, to understand ‘socratizes’ one must understand it as an abbreviation of ‘is identical with Socrates.’ What the eliminativist construal demands, however, is that ‘socratizes’ be understood as an indivisible semantic unit, and thus not as built up out of an understanding of ‘Socrates’ and ‘is identical with’ taken separately. This demand cannot be satisfied. The problem in a nutshell is that there is no description, concept, property, or function that captures the haecceity or thisness of Socrates. The thisness of an actual individual is nonqualitative and thus irresolvable into any qualitative property or conjunction of qualitative properties.
Thus the only way to make sense of ‘socratizes’ is by seeing it as short for ‘is identical to Socrates.’ But ‘is identical to Socrates’ is intelligible only as a compound of ‘identity’ and ‘Socrates,’ which of course implies that the proper name ‘Socrates’ has not been eliminated. Hence the singular ‘(Ex)(x = Socrates)’ cannot be eliminated in favor of the general ‘(Ex)(x socratizes).’
B. Suppose I am wrong about this and that ‘(Ex)(x = a)’ unproblematically gives way to ‘(Ex)(Ax),’ which is indisputably general. Still, a second step is needed for the viability of the eliminativist construal. It is not enough to eliminate ‘a,’ we must also so interpret ‘(Ex)(...x...)’ that it does not imply that existence is attributable to individuals. Otherwise, there would be no elimination of singular existence, and the circularity objection bruited above would kick in. The way to do this is to construe the latter expression as second-level predicate, one that cannot be meaningfully attached to a name for an individual. Thus one could read it in the Russellian way as the predicate ‘is sometimes true’ which, when attached to the first-level predicate ‘x is A’ results in the sentence “‘x is A’ is sometimes true.” But this is precisely what Quine does not do. He interprets ‘(Ex)(...x...)’ objectually (as opposed to substitutionally) to mean: there is (exists) an x such that....’ He does not interpret ‘(Ex)(...x...)’ to mean: there is a singular term t such that substituting ‘t’ for ‘x’ yields a true sentence. So what ‘(Ex)(Ax)’ says on Quine’s preferred objectual interpretation is that there exists an x such that x is A. Since the value of the bound variable in this case is a, what the quantified expression says, in effect, is that a exists. The existence of a is the fact that makes it true that (Ex)(x = a). Thus, by taking the quantifiers objectually, Quine is committed to the view that there is first-level existence, that existence belongs to individuals. But this returns us to the identitarian construal. Quine is by no means unambiguously eliminativist with respect to singular existence. At the very most he eliminates singular existentials. It is only by confusing singular existence with singular existentials that one could think he has eliminated the former. Recall that we found evidence of such confusion in the passage quoted above.
To sum up this curious state of affairs: examination of the identitarian construal drives us to the eliminativist, but the untenability of the latter returns us to the former. Evidence is mounting that Quine waffles between them.
QUINE’S MAJOR DICTA INCONSISTENT
The problem, then, is that Quine’s explication of ‘a exists’ can support neither an exclusively identitarian nor an exclusively eliminativist construal. Not an identitarian reading, because this leads to vicious circularity and impotence in the face of the problem of negative singular existentials. Not an eliminativist reading, because the latter cannot handle the haecceity problem and is inconsistent with an objectual interpretation of the quantifiers.
Another way of appreciating the problem is by exploring the tension between Quine’s two most famous ontological dicta, “Existence is what existential quantification expresses,” and “To be is to be the value of a [bound] variable.” These pull in opposite directions. The first, taken straight, implies that existence is a property of properties (or cognate items, Fregean Begriffe, Russellian propositional functions, etc.) but never a property of individuals. It implies that existence is the property of being instantiated, a property no individual can have. The second, taken straight, implies that individuals are or exist, and thus that existence is a property of individuals. These are doctrines that do not mix; or else their mixture evolves inconsistency. How so?
We know from “On What There Is” that for Quine, to be = to exist. Against Wyman and other whipping boys Quine denies any distinction here. There are no modes or kinds of being. Whatever exists exists in the same way. Now a — a itself and not the name ‘a’ — is the value of the bound variable in ‘(Ex)(Ax).’ Values of a variable are not to be confused with their substituends. It therefore follows from the second dictum (“To be is to be the value of a variable”) that a exists. It follows, in other words, that existence is legitimately attributable to a. The argument can put as follows.
a. If x is the value of a bound variable, then x is or exists.
b. a is the value of the bound variable in ‘(Ex)(Ax).’
Therefore
c. a is or exists given that ‘(Ex)(Ax)’ is true.
‘Exists’ must therefore be an admissible first-level predicate. This in turn implies that Quine’s explication of ‘a exists’ in terms of ‘(Ex)(x = a)’ must be given an identitarian interpretation. It must be read as presupposing that there is singular existence and that affirmative singular existentials are meaningful as they stand. By ‘meaningful as they stand,’ I mean that they do not need analysis to lay bare their true logical form: their logical form coincides with their grammatical form. Grammatically, ‘a exists’ appears to attribute existence to a. If, as has just been shown, affirmative singular existentials are meaningful as they stand, then this appearance coincides with reality.
But this conflicts with the first dictum, “Existence is what existential quantification expresses,” which is most naturally taken in an eliminativist way to mean that ‘exist(s)’ is a second-level and never a first-level predicate. It is most naturally taken to mean that existence is just general existence, or instantiation, and that there is no singular existence. We saw above that the eliminativist construal is needed to handle the problem of negative singular existentials. This tension between the two dicta is equivalent to a waffling between an identitarian and an eliminativist reading of Quine’s explication of ‘a exists.’ Quine’s objectual understanding of the quantifiers implies that individuals exist; his commitment to the idea that existence is expressed by the existential quantifier, however, implies that individuals cannot exist.
It is important to note that Quine has, and can have consistently with his objectualism, no principled objection to first-level uses of ‘exists’ as do Frege and Russell. He nowhere says or implies that it is meaningless to attach ‘exists’ to a logically proper name. Indeed, he implies the opposite. In “On What There Is” we read: “we commit ourselves to an ontology containing Pegasus when we say Pegasus is. But we do not commit ourselves to an ontology containing Pegasus...when we say that Pegasus...is not.”[xvi] Note the asymmetry: ‘a exists,’ whether true or false, is ontologically committing, but ‘a does not exist,’ whether true or false, is not ontologically committing. A name by itself is not ontologically committing for the simple reason that some of the terms that count grammatically as names, like ‘Pegasus,’ are empty. But a name concatenated with ‘exists’ is ontologically committing. Now if an utterance of ‘a exists’ commits us to an ontology containing a, then, if ‘a exists’ is true, it follows that a exists, and we are surely entitled to express this by saying, ‘a exists.’ Quine can therefore have no objection to ‘exists’ as a legitimate first-level predicate.
Note also that, a few lines before giving his explication, Quine tells us that “ ‘a’ is used to name an object [in a theory] if and only if the statement ‘a exists’ is true for the theory. He goes on: “This is less satisfactory only [my emphasis] insofar as the meaning of ‘exists’ may have seemed less settled than quantifiers and identity.”[xvii] Clearly, the quantified formula merely regiments ‘a exists’ which is meaningful as it stands. The point is that, at most, Quine shows how one can for certain purposes dispense with singular existentials, but not that one must dispense with them. Affirmative singular existentials need not be dispensed with; they can be allowed to stand. ‘Pegasus exists,’ even though it is false, causes no trouble. Nor does ‘Socrates exists.’ (I am following Quine in using ‘exists’ tenselessly.) Quine nowhere argues that if ‘exists’ were an admissible first-level predicate, then true affirmative singular existentials would be tautologically true. It is only negative singular existentials that must be dispensed with. The same goes for names. At the very most, Quine shows how to eliminate them if they cause trouble; it is apparently not his view that all names must be eliminated.
CONCLUSION: ‘EXISTENTIAL QUANTIFIER’ A MISNOMER
Let us return to van Inwagen’s assurance that it “ought to be uncontroversial” that “The single sense of existence or being is adequately captured by the existential quantifier of formal logic.”[xviii] This strikes me as the exact opposite of uncontroversial. What single sense is expressed by ‘(Ex)(x = a)’ and ‘(Ex)(Fx)’? Do they both say that a certain property is instantiated, a-ness in the one case, F-ness in the other? This eliminativist approach could be maintained only if there are such properties as a-ness. But haecceity properties are as objectionable as Meinongian individuals.[xix] For there is no individuality apart from existence: existence is a necessary condition of being an individual. This is why there are no nonexistent individuals. But there are also no uninstantiated haecceity properties for the same reason. Until an individual exists it has no thisness. A haecceity property is an individual mis-represented as a property just as a nonexistent individual is a complex property mis-represented as an individual. It is as difficult to understand how Socrateity can exist at times and possible worlds at which Socrates does not exist as it is to understand how Pegasus can be an individual and actually have properties without existing.
Therefore, the single sense expressed by ‘(Ex)(x = a)’ and ‘(Ex)(Fx)’ cannot be that both predicate being-instantiated of a property. Are we to say, with the identitarian, that the single sense is that both say that there is an object that satisfies a condition, that of being identical to a, in the one case, that of being an F in the other? But we saw that this approach is unworkable as well, issuing as it does in circularity and failure to solve the problem of negative existentials.
What we should conclude is that there is no single sense of existence or being that is expressed by ‘a exists’ and ‘An F exists.’ The first expresses genuine existence. The second expresses something different, instantiation. The existential quantifier of formal logic captures instantiation; it has nothing to do with existence. Clarity will be served if we speak of it as the particular, not the existential, quantifier. The reason for refusing to call it existential is not that there are nonexistent objects over which we can quantify; the reason is that existence cannot be identified with instantiation, and it is only instantiation that the ‘existential’ i.e., particular quantifier expresses.
Van Inwagen, however, refuses to admit that ‘existential quantifier’ is an obfuscatory and pernicious[xx] misnomer. His argument may be set forth as follows:
a. The existential quantifier expresses the sense of ‘there is’ in ordinary English.
b. ‘There is at least one F’ is equivalent to ‘At least one F exists.’
Therefore
c. The existential quantifier expresses the sense of the ordinary ‘exists’ as well.
Therefore
d. The name ‘the existential quantifier’ is not a misnomer.[xxi]
Although the premises of this argument are both true, the argument falls victim to a fatal equivocation: whereas ‘exists’ in (b) expresses general existence, ‘exists’ in (c) covers both general and singular existence. The plain fact of the matter is that our ordinary uses of ‘exist(s)’ can express either general or singular existence depending on context. The particular quantifier captures the sense of the ‘there is/are’ locution in ordinary English (except perhaps for locative uses[xxii]), and so adequately expresses general existence; what it cannot express is singular existence, the sense of ‘exists’ in a sentence like ‘Quine exists.’ Of course, one can write ‘(Ex)(x = Quine),’ but this is just a notational trick that papers over deep philosophical confusion for the reasons given above. Logical trickery is fine for logical purposes, but not for ontological ones.
The fundamental problem, however, is not Quine’s theory, but the instantiation theory itself. It is untenable whether taken as an identitarian, or as an eliminativist, theory. The problem is the very notion that existence in its basic or logically primitive sense is the being-instantiated of a concept, property, propositional function, etc. I would urge that general existence is no more existence than negative growth is growth: ‘general,’ like ‘negative,’ here functions as an alienans adjective: it ‘alienates’ or shifts the sense of ‘existence.’ If so, it is unwarranted to suppose that there are two kinds of existence, general and singular, on the strength of the fact that there are two uses or senses of ‘exist(s),’ a general and a singular use or sense. To think otherwise would be like assuming that since ‘leather’ occurs in ‘real leather’ and ‘artificial leather,’ that therefore there are two kinds of leather, real and artificial. Obviously enough, ‘artificial’ in ‘artificial leather’ shifts or ‘alienates’ the sense of ‘leather.’ Existence — real, pound-the-table existence — is just singular existence, the existence that belongs to individuals, and belongs to them, I would argue, without being a property of them.[xxiii] Thus the fact that existence is not a first-level property gives no aid and comfort to the view that it is a second-level property. General existence, if we must use this term, is another animal entirely, instantiation. Pace Quine, it is instantiation that existential quantification expresses. Of course, there is a conceptual link between instantiation and existence: necessarily, if first-level property P is instantiated, then P is instantiated by an individual that exists. Quine was surely right to show Meinong and his sidekick Wyman the door. That being said, (singular) existence is not instantiation, nor can it be analyzed in terms of instantiation. I here trespass upon ground thoroughly covered in a recent book.[xxiv] The present article, therefore, may be viewed as an introduction thereto. Here my task was not to take on the instantiation theory as such, but to argue against it in its Quinean manifestation.
NOTES
[i]. Willard van Orman Quine, “On What There Is,” in From a Logical Point of View (New York: Harper and Row, 1963), p. 1.
[ii]. Peter van Inwagen, “Meta-ontology,” Erkenntnis 48, 1998, pp. 233-250. Van Inwagen’s terminology is understandable but overblown. The question about what it is to be ought to be called the ontological question since it deals with the being of what is. The question as to what there is could then be called the ontic question.
[iii]. Ibid., p. 237.
[iv]. W. V. Quine, “Existence and Quantification,” Ontological Relativity and Other Essays (New York: Columbia University Press, 1969), p. 97.
[v]. Ibid.
[vi]. For more on the difference between identitarianism and eliminativism, see William F. Vallicella, “Brentano on Existence,” History of Philosophy Quarterly vol. 18, no. 3 (July 2001), pp. 311-314.
[vii]. Peter Geach and Max Black, Translations from the Philosophical Writings of Gottlob Frege (Oxford: Basil Blackwell, 1960), p. 50. Cf. Gottlob Frege, The Foundations of Arithmetic, trans. J. L. Austin (Evanston: Northwestern University Press, 1968), p. 65.
[viii]. Bertrand Russell, “The Philosophy of Logical Atomism,” (1918) in Logic and Knowledge, ed. Robert C. Marsh (New York: Capricorn Books, 1971), p. 233.
[ix]. Ibid., p. 234.
[x]. W. V. Quine, “Existence and Quantification,” op. cit., p. 94.
[xi]. Peter van Inwagen, op. cit., p. 237.
[xii]. W. V. Quine, “On What There Is,” op. cit., p. 6.
[xiii]. W. V. Quine, Philosophy of Logic, 2nd ed. (Cambridge: Harvard University Press, 1986), p. 25.
[xiv]. W. V. Quine, Word and Object, 8th ed. (Cambridge: M.I.T. Press, 1973), p. 178.
[xv]. Ibid.
[xvi]. “On What There Is,” op. cit., p. 8.
[xvii]. Ontological Relativity, op. cit., p. 94.
[xviii]. Van Inwagen, op. cit., p. 237.
[xix]. For arguments against haecceity properties and Meinongian individuals, see William F. Vallicella, A Paradigm Theory of Existence: Onto-Theology Vindicated, Philosophical Studies Series 89 (Dordrecht: Kluwer Academic Publishers, 2002), pp. 99-104, and pp. 38-42.
[xx]. Why pernicious? Well, it is pernicious if you believe as I do that that a metaphysics of existence is both possible and necessary and that all deflationary approaches to existence are untenable. See my book cited in the previous note. Quine, like Frege and Russell before him, trivializes the question about existence (i.e., the ‘meta-ontological’ question about what it is for a thing to exist, as opposed to the ‘ontological’ question about what exists) by making the question about existence a merely logico-linguistic matter. What our three luminaries do, in effect, is to reduce the rich ontological topic of existence to the lean logical topic of someness. What all three do – albeit with some waffling on the part of Quine – is to replace the fascinating topic denoted by the first-level predicate ‘...exists’ with the boring topic denoted by the second-level predicate, ‘Something is a ....’ To employ a Heideggerian term in an un-Heideggerian way, all three fall victim to Seinsvergessenheit.
[xxi]. Van Inwagen, op. cit., p. 241.
[xxii]. As when, searching for my Meerschaum pipe, I exclaim, finding it, ‘There is my favorite pipe!’ I am not thereby saying that my favorite pipe exists; I am saying that it is located in my visual field.
[xxiii]. I argue this in A Paradigm Theory of Existence: Onto-Theology Vindicated, op. cit.
[xxiv]. Ibid.
Relevant to present concerns is Peter van Inwagen's "McGinn on Existence" which is online 
I am having a hell of a time getting my elite commenters to focus on existence, to 'see' it. No surprise: they are analytic types well-versed in logic, and existence is "odious to the logician" as George Santayana once remarked. (Scepticism and Animal Faith, p. 48) It is so odious, in fact, that they need to mask it under the misnamed 'existential' quantifier. So I need to resort to extreme methods. I will quote from Jean-Paul Sartre's