1.1 Basic Principles

By default, Meinongianism is roughly understood as the view that there are objects that do not exist, or, in short, that there are nonexistent objects.Footnote ¹ It goes back to the Austrian philosopher Alexius Meinong (1853–1920).Footnote ² Its basic tenet was first formulated in Meinong’s famous paper “Über Gegenstandstheorie” (Reference Meinong and Meinong1904, English translation: “The Theory of Objects”, Reference Meinong and Meinong1960): “Those who like paradoxical modes of expression could very well say: ‘There are objects of which it is true that there are no such objects’” (Meinong, Reference Meinong and Meinong1904/1960: 83Footnote ³).

Meinong, however, is quick to clarify that the “paradoxical mode of expression” is not to be taken at face value. He immediately resolves the apparent paradox as follows: The first occurrence of “there are” in “There are objects of which it is true that there are no such objects” differs in meaning from its second occurrence. The second occurrence (“there are no such objects”) is close to its standard meaning in everyday language, for instance in: “There is a prime number between 3 and 7,” “There is no largest natural number,” “There are black swans,” “There are no unicorns.” “There are no such objects” means, in Meinong’s own terms: “These objects do not have being of any kind.” The whole principle is therefore to be read as follows: “There are objects of which it is true that these objects do not have being of any kind,” or, briefly: “There are beingless objects.”

For the sake of historical accuracy, it should be noted that Meinong distinguishes between two kinds of being, which he calls subsistence (Bestand) and existence (Existenz). Some kinds of objects (notably those which Meinong calls “ideal objects”, for instance numbers, propositions, and properties) only subsist (bestehen); others (the “real objects”, i.e., material and mental objects) both subsist and exist.

For the sake of simplicity, however, I will ignore this distinction and simply treat “being” and “existence” as synonyms (in accordance with most neo-Meinongians). Hence we arrive at the formulation: There are objects that do not exist, or, alternatively: There are nonexistent objects. In what follows, I shall refer to this basic Meinongian principle as “M”.

So it is clear that within Meinongianism it is assumed that there is a semantic difference between “there is” and “exists”. Moreover, “exists” entails “there is”, but not the other way around: “Fs exist” implies “There are Fs”; but “There are Fs” does not imply “Fs exist.” It should also be sufficiently clear what the Meinongian “exists” means: Its meaning is close (if not identical) to the standard natural language meaning of “there is” in most everyday contexts, such as in “There are white whales”; “There are prime numbers bigger than 100”; “There is an interesting exhibition in the MOMA right now.” It is not yet clear, however, just what the Meinongian “there is” is supposed to mean. This is one of the notorious questions of Meinongianism.

There are, in principle, two possible explanations: Some assume that the Meinongian “there is” expresses a different kind of being, distinct from existence. Others claim that it expresses no kind of being at all, that it is – as it were – “ontologically neutral”.Footnote ⁴ This issue is closely related to the question of how the quantifier is to be interpreted in Meinongianism (which will be discussed in Section 3).

Standard examples of nonexistent objects are the golden mountain, the round square, Pegasus (i.e., the flying horse from Greek mythology), Sherlock Holmes, the present king of France. The two most basic principles of Meinongianism can be formulated, in a slightly simplified manner, as follows:

The first of these two principles (CP) is often called the Characterization Principle or Characterization Postulate; the second (IP) is known as the Principle of Independence.Footnote ⁷ Take, for instance, the description “the blue”. According to CP, there is an object corresponding to this description that has being blue as its sole property – namely, the object The Blue.Footnote ⁸ Similarly, there is an object corresponding to the description “the golden mountain”, namely, The Golden Mountain, that is, an object that is golden and a mountain and has no further properties. There is even an object corresponding to every incoherent description; for instance, there is an object that corresponds to the description “the round square”, that is, an object that is both round and a square.

It should be noted that The Blue, The Golden Mountain, The Round Square, and so on, are objects that have the properties mentioned in the respective descriptions – but they are not properties themselves.Footnote ⁹ It should also be clear that these objects are not mental entities. They are objective and independent of (and therefore not constitutive parts of) anybody’s thoughts, imaginations, or other mental acts.

A note on terminology: As we will see, there are various versions of Meinongianism, and some of them are incompatible with others. At least two versions of Meinongianism can be found in Meinong himself (see Section 4), plus a variety of distinct “neo-Meinongian” theories (see Section 5), some of which diverge considerably from both versions of Meinong’s Meinongianism. This diversity threatens to render the very concept of Meinongianism elusive. In order to avoid this consequence, I will restrict the use of the term “Meinongianism” in the following way: I classify all and only those philosophers as “Meinongians” who accept (1) principle M (and a distinction between “there is” and “exists”), (2) some version of CP (not necessarily the one previously formulated), and (3) IP.

At the same time, the term “neo-Meinongianism” is often used in the current literature, but – to my knowledge – it is nowhere explicated in terms of common principles, and its extension is not clearly delimited. It is usually used as a collective term denoting philosophers from 1950 onwards who were somehow interested in, and sympathetic to, Meinongian ideas, and who wanted to show that Meinongianism is consistent (or can be reconstructed so that it is) and has a number of interesting applications.

Not all of the philosophers who are usually subsumed under the heading “neo-Meinongianism” accept the principles M, CP, and IP. However, since the purpose of this Element is to introduce the reader to Meinongianism as it is usually understood in contemporary philosophy, prominent so-called neo-Meinongian theories will also be included even if they are not Meinongian in the sense characterized here. I will use the term “neo-Meinongianism” to include all contemporary philosophers who are Meinongians in the sense explained in this subsection and/or consider themselves to be Meinongians, and/or are usually classified as Meinongians in the current literature.

According to this taxonomy, some neo-Meinongians are not Meinongians (see Section 5); and there is evidence that even Meinong himself ultimately ceased to be a Meinongian (see Section 4). On the other hand, some neo-Meinongians are Meinongians in the explicated sense (or at least have been Meinongians during a certain period); and I will use the term “Meinongian” for them too.Footnote ¹⁰

1.2 Motivations

1.3 A Very Brief History

Meinong’s theory of objects has had a chequered history. In Germanophone philosophy, it basically disappeared after Meinong’s death. This was partly due to the fervent opposition of the Brentano school, but also to the fact that Meinong’s disciple and follower Ernst Mally turned his back on object theory in his later years (although he had made very important contributions to its development).

In Anglophone philosophy, at the beginning of the twentieth century, Meinong’s object theory was received almost exclusively through Bertrand Russell’s comments.Footnote ²⁶ Russell, though originally sympathetic to Meinong’s theory, put forward two (seemingly devastating) objections against it in his seminal paper “On Denoting” (1905). For decades, Russell’s criticism determined the assessment of object theory in analytic philosophy. A pointed formulation of the mainstream view up to the 1970s is the following infamous judgment of Gilbert Ryle: “Let us frankly concede from the start that Gegenstandstheorie itself is dead, buried and not going to be resurrected” (Ryle, Reference Ryle1973: 255).

In 1933, the South African philosopher John N. Findlay submitted a dissertation at the University of Graz (supervised by Ernst Mally), originally published as Meinong’s Theory of Objects and, in the second edition, as Meinong’s Theory of Objects and Values (Findlay, Reference Findlay1963). For a long time, this book was the main source on Meinong’s theory for Anglophone philosophers.

The first sympathetic treatment of object theory after Findlay’s dissertation was Roderick M. Chisholm’s paper “Beyond Being and Nonbeing” (Reference Chisholm and Haller1972). In the following decades, Meinong’s object theory was revived by a number of philosophers and logicians who worked on its consistent logical reconstruction and tried to show that it is a viable option, with a number of fruitful and important applications (see Section 5). Today, Meinongianism is perhaps livelier than ever, defended in a variety of versions and taken seriously by its opponents.

2.1 The Distinction between “There Is” (“∃x”) and “Exists” (“E!”)

To make sense of M (“There are objects that do not exist”), one needs to distinguish between “There are objects that are such-and-such” and “Objects that are such-and-such exist.” However, standard logical notation (with the quantifier “∃x” as the sole symbol for expressing “there is” as well as “exist”) does not provide the means for such a distinction.

There are two possible reactions to this. The Quinean reaction is to declare M – even in its natural language formulation – to be nonsensical. For a Quinean, the formal language of standard logic (which allows us to express existence solely by means of the quantifier) is perfectly adequate. The impossibility of expressing M in this formal language is just a symptom of M’s being nonsensical in the first place. For a Quinean, the distinction between “there are Fs” and “Fs exist” simply does not make sense.

For a Meinongian, however, it is the other way around: A Meinongian considers the distinction between “there is” and “exists” as a basic metaphysical distinction. If this distinction cannot be expressed in a given formal language, this is considered to be a shortfall of the formal language.

Meinongians and Quineans agree, in principle, that a formal language should be as clear and simple as possible. They also agree that a formal language should have maximum expressive power, that is, it should – ideally – allow for the symbolic representation of any meaningful natural language expression. This should be possible in a way that does justice to important distinctions that can be expressed in natural languages. In the case of M, the disagreement concerns the question of whether M is a meaningful sentence in the first place.

Since Meinongians answer this question affirmatively, they consider it a shortfall of standard logical notation that it does not allow for a formal rendering of M. The usual remedy for this shortfall is the addition of an existence predicate to the vocabulary of the symbolic language. Most neo-Meinongian logicians make use of an existence predicate (mostly represented as “E!” or simply “E”) in their formal language.Footnote ²⁷ This is a natural consequence of the doctrine that there are objects that do not exist. At the same time, it is a serious deviation from standard logics. The use of “E!” allows for representing M in logical notation as follows:

Ever since Kant’s famous critique of Anselm’s so-called ontological proof of God’s existence,Footnote ²⁸ however, philosophical mainstream has it that existence is not a logical predicate. The most perspicuous rendering of this view is to be found in Gottlob Frege (Reference Frege, Frege and Rami1891, Reference Frege, Frege and Rami1892a, Reference Frege, Frege and Rami2021a, and Reference Frege and Rami2021b), which is the source of the previously mentioned Quinean postulate that existence is what the quantifier expresses. According to the Kant–Frege doctrine of existence, the introduction of an existence predicate in a formal language is a gross mistake, since it is in deep conflict with the very nature of existence.

In defense of the Meinongian view, one could argue that standard, Quinean logical notation does not only lack the power to express the controversial metaphysical principle M. Perhaps the much more serious failure is that standard logical notation does not allow for a symbolic rendering of singular existence statements – at least not in a straightforward manner.

The problem concerns positive and negative singular existence statements (see Subsection 1.2.2) alike. Consider, for instance, the following exchange: “God exists.” – “No, God does not exist.”Footnote ²⁹ Although it may be difficult to assign a truth value to either statement, both of them seem to be perfectly meaningful – as theists, atheists, and agnostics agree. But rendering them in standard logical notation proves difficult. Given that existence is expressed by the existential quantifier, a beginner in symbolic logic might expect that “God exists” could be rendered as follows: (G*) ∃x (g), where “g” is an individual constant that stands for the (alleged) proper name “God”. However, G* is not a well-formed formula because the quantifier “∃x” must be followed by a predicate expression (“Fx”, “Gx” etc.) in order to yield a complete and well-formed existential quantification. It is not permitted to put an individual constant at the place of the predicate – as in G*.

Quineans do not deny that there are meaningful singular existence statements in natural languages. Thus, on pain of having to admit that their formal language has inadequately poor expressive power, they are pressed to find a way of somehow expressing such statements in their logical notation. A simple solution would be to make use of complex predicates of the form “= a” (read: “is identical with a”), where “a” is a singular term.Footnote ³⁰ Accordingly, “God exists” could be rendered as (G¹) ∃x (x = g). (Read: There is an x, such that x is identical with God.) However, as pointed out above, the negation of “∃x (x = g)” is logically false in classical logic because standard logic involves an existence assumption with respect to singular terms. Therefore, this option is not available to Quineans who want to allow for the possibility that “∃x (x = g)” is false. Alternatively, one might do without the identity sign and simply take an arbitrary predicate constant (say, “G”), which could be taken to stand for the complex natural language predicate “is identical with God”. If one chooses this option, “God exists” can be rendered as (G²) ∃x (Gx).Footnote ³¹ Either way, the (grammatical) singular existence statement “God exists” has been transformed into a general existence statement “There is an x, such that x ….”

There is still another option, which makes use of Bertrand Russell’s theory of definite descriptions, combined with a descriptive theory of proper names.Footnote ³² Consider (to use Russell’s original example): (K) “The present king of France is bald.” Since there is no present king of France, the definite description “the present king of France” is an empty singular term. If (as the reference theory has it) the meaning of a term is its denotation, and if (as the composition principle states) in a meaningful sentence, every component must be meaningful, K turns out to be meaningless (see Subsection 1.2.2) – which may seem counterintuitive.

Russell’s problem was related to this, but not exactly the same: He was worried about a looming “truth value gap”. If there is no present king of France, it seems that one can neither affirm nor deny that he is bald. Hence it seems that K is neither true nor false, which struck Russell as hard to swallow. His solution was to interpret K in the following way: (K^R) There is exactly one x, such that x is a king of France, and x is bald. Thus, Russell analyzed sentence K, which has the grammatical structure of a predication, as a complex existence quantification. Since it is false that there is exactly one x, such that x is a king of France (because there is no king of France), the whole complex is false. The truth value gap is avoided.

Russell’s theory of definite descriptions can also be used to resolve the problem of singular existence statements. Consider: “The present king of France does not exist.” A Russellian analysis of this looks as follows: “It is not the case that there is exactly one present king of France.”Footnote ³³ According to this analysis, the seeming singular existence statement turns out to be a general existence statement, that is, an existential quantification.

Russell’s theory of definite descriptions may work well for definite descriptions, but what about proper names such as “Pegasus”, “Atlantis”, and so on? If a singular existence statement contains a proper name in its subject position (as in “Atlantis does not exist”), Russell’s analysis cannot be applied, at least not directly. In order to make the theory of definite descriptions applicable to such cases, one has to substitute a definite description for the proper name, for example, “the winged horse from Greek mythology” for “Pegasus”. Russell indeed thought that proper names are “truncated descriptions” (Russell, Reference Russell1918–1919: 208) or “abbreviations for descriptions” (Russell, Reference Russell1918–1919: 524), such that a substitution of a definite description for a proper name is always possible and unproblematic. However, this so-called descriptive theory of proper names is controversial – and with good reason.Footnote ³⁴ To mention just one of its well-known problems, consider the sentence: “Pegasus is the winged horse from Greek mythology.” Given that “Pegasus” is short for the definite description “the winged horse from Greek mythology”, this would turn out as the tautological truth “The winged horse from Greek mythology is the winged horse from Greek mythology.” However, the original sentence does not seem to be trivially true.

To sum up: Quineans do have resources to account for the truth of singular existence statements, but one may feel that their proposals are somewhat awkward. Either they have to work with artificial predicate expressions (like “is identical with Pegasus” or “pegasizes”), or they have to rely on a controversial theory of proper names.

Meinongians, on the other hand, have no problem with singular existence statements in the first place. Their symbolic rendering of “God does not exist,” for example, is simply and straightforwardly “¬E!g” (where “g” stands for the singular term “God”). Meinongians do not have to paraphrase grammatical singular existence statements into general existence statements, they do not have to introduce artificial predicate expressions, and they can do justice to the distinction between definite descriptions and proper names. This seems to be a point in favor of Meinongianism, or, more exactly: a point in favor of the distinction between “there is” (the quantifier, “∃x”) and “exists” (the predicate, “E!”).

2.2 Meinongianism and the Principle of Excluded Middle

Consider, for instance, the object The Blue, that is, the object that has the property of being blue as its sole determination (i.e., the object that corresponds to the set that has the property of being blue as its sole element). According to CP, this object does not have any shape, any size, does not consist of any particular material, is not located anywhere in space, and so on. According to CP, it holds, among other things, that neither “The Blue is round” nor “The Blue is not round” is true. This seems to contradict the principle of excluded middle (PEM), which states that, for every proposition p, either p or non-p is true.

This can be generalized in the following way: It is a consequence of CP that most nonexistent objects are, as Meinong pointedly puts it, “incompletely determined” or, in short: “incomplete” objects. This means (in most cases) that, if x is a nonexistent object, then, for some general term $\phi$ , neither “x is $\phi$ ” is true nor “x is not $\phi$ ” is true (Meinong, Reference Meinong1915/1972: §25).Footnote ³⁵ Thus, (most) nonexistent objects seem to violate PEM.

Meinong observes that incomplete determination (in short, incompleteness) is indeed a peculiarity of nonexistent objects: Existent objects (both real and ideal ones) are always completely determined.Footnote ³⁶ That is, for any existent object x (be it real or ideal) and any $\phi$ , it holds, without restriction: Either x is $\phi$ or x is not $\phi$ (Meinong, Reference Meinong1915/1972: §25).

Meinong notes that incomplete objects seem to violate PEM – and he readily accepts this violation. He states that PEM is valid only under the presupposition of complete determination. Incomplete objects simply fall outside its scope (Meinong, Reference Meinong1915/1972: §25).

However, as closer inspection shows, there is no need to restrict the validity of PEM to complete objects only. One may argue that incomplete objects do not violate PEM, if the principle is properly conceived. This claim is based on a distinction between two kinds of negation, namely external and internal negation. External negation is sentence (proposition) negation. This is how negation, in standard logics, is usually conceived: The negator has a complete assertive statement (“Fa”, in the simplest case) within its scope. Internal negation, by contrast, is predicate negation: The internal negator has only the predicate term within its scope. In the example at the beginning of this subsection, the distinction between internal and external negation is the distinction between “It is not the case that the Blue is round” and “The Blue is non-round.” The former expresses (in terms of property exemplification) that The Blue does not exemplify the property of being round. The latter expresses that The Blue does exemplify the negative property of being non-round.Footnote ³⁷

In logical notation, predicate negation can be distinguished from sentence negation either by using distinct symbols for each or by using the same symbol in a distinct grammatical structure. One might use “¬” for sentence negation and “~” for predication negation – or the other way around. For instance, “It is not the case that The Blue is round, and it is not the case that The Blue is non-round” can be represented in the following way: ¬(Rb) ∧ ¬(~Rb). Alternatively, one might render this as follows: ~(bR) ∧ ~(b~R) (see Routley, Reference Routley1980: 89). Often, negative predicates are symbolized as $\overline{F}$ , $\overline{G}$ , $\overline{H}$ …, in contrast to F, G, H … Accordingly, the previously mentioned sentence would be represented as: ¬Rb ∧ ¬ $\overline{R}$ b. It does not matter which of these alternatives is chosen (and which symbols are used). It is important, however, to note that neo-Meinongians like Routley and Jacquette adhere to the following principles:

As long as we are only concerned with existent objects, the distinction between internal and external negation may easily escape our attention. This is because, for existent objects, it is hardly relevant. Take an arbitrary material object, say, my desk: Since it is not the case that my desk is round, it is also the case that my desk is non-round. Analogous considerations seem to hold for any existent object and any predicate. However, as soon as we take nonexistent objects into account, the distinction becomes immensely relevant. Consider again The Blue: While The Blue is indeed neither round nor non-round, it is nevertheless true that it is not the case that The Blue is round. Moreover, it is not the case that The Blue is non-round.

As it is usually conceived, PEM involves external negation. That is, it says that, for all x, and all $\phi$ : Either x is $\phi$ , or it is not the case that x is $\phi$ . As can be seen from the reasoning in the previous paragraph, The Blue does not violate this principle. For it holds indeed, for all $\phi$ , that either The Blue is $\phi$ , or it is not the case that the Blue is $\phi$ . If we insert the predicate expression “blue” for “ $\phi$ ” in “The Blue is $\phi$ ,” we get a true sentence, since it is the case that The Blue is blue. With all other possible insertions (“round”, “rectangular”, “wooden”, “iron” …), we get a false sentence, since The Blue is neither round nor rectangular, neither wooden nor iron, and so on. Analogous reasoning holds for every incompletely determined object x: For any $\phi$ , if being $\phi$ belongs to the determinations of x, it is the case that x is $\phi$ , and if being $\phi$ does not belong to the determinations of x, it is not the case that x is $\phi$ . So far, incomplete objects behave exactly like complete ones. The difference comes to the fore as soon as we consider internal negation: While, for complete objects, usually “It is not the case that x is $\phi$ ” implies “It is the case that x is non- $\phi$ ,” this implication does not hold for incomplete objects.

Now it is clear that Meinongianism need not be in conflict with PEM. If PEM is understood as the principle that, for every p, either p or the external negation of p must be true, no conflict arises. “The Blue is not round” can be read either externally or internally, that is, as “It is not the case that The Blue is round” or as “The Blue is non-round.” The former (the external negation) is true, while the latter (the internal negation) is false. It is true that The Blue is neither round nor non-round; but this is compatible with PEM. PEM only requires that either The Blue is round, or it is not the case that The Blue is round. Since it is indeed not the case that The Blue is round, PEM applies to The Blue without restriction.

2.3 Meinongianism and the Principle of Noncontradiction

Consider, for instance, the object The Round Square. As Russell famously noted, objects of this kind seem to contradict the principle of noncontradiction (PNC). For, according to CP, The Round Square is both round and a square; and, under the plausible assumption that being a square entails being non-round, both “The Round Square is round” and “The Round Square is non-round” are true – which is ruled out by PNC. (Russell, Reference Russell1905a and Reference Russell1905b) Of course, by Russell’s lights, this would be reason enough to reject Meinongianism.

Meinong was unimpressed by this objection: He replied that PNC was designed for the domain of existent and possible objects only, and that it is therefore not surprising that it does not hold for impossible objects as well (Meinong, Reference Meinong1907/1973: §3).

But was Meinong perhaps too quick to admit the violation of PNC in his reply to Russell? There is an alternative rejoinder that, again, relies on the distinction between internal and external negation: Clearly, PNC is to be understood in an external manner. It says that for any proposition p, it cannot be the case that both “p” and “ ¬p” are true. From this, it follows that there is no x such that both “x is round” and “It is not the case that x is round” are true. However, The Round Square does not violate PNC, thus understood. For the statement “The Round Square is round” is true, and its external negation – “It is not the case that The Round Square is round” – is false. In the same vein, the statement “The Round Square is non-round” is true and its external negation is false. “The Round Square is not round” is ambiguous between “The Round Square is non-round” (predicate negation) and “It is not the case that the Round Square is round” (sentence negation). “The Round Square is non-round” does not imply “It is not the case that the Round Square is round.” The impression that The Round Square violates PNC can arise only if one ignores the distinction between the external negation “It is not the case that The Round Square is round” and the internal negation “The Round Square is non-round.”Footnote ³⁸

However, Russell has a second objection up his sleeve: According to CP, there is not only The Round Square but also The Existent Round Square; and, again according to CP, just as The Round Square is round and a square, The Existent Round Square is not only round and a square, but it also exists (Russell, Reference Russell1905a and Reference Russell1905b). This is, of course, a problem for Meinong, because he is not prepared to accept that something that is both round and a square exists.

Meinong himself considers this the more serious challenge for object theory. He observes that this objection does not only apply to impossible objects, like The Round Square, but also to possible ones, like The Golden Mountain. For, according to CP, there is not only The Golden Mountain but also The Existent Golden Mountain, and The Existent Golden Mountain is not just golden and a mountain but also existent (Meinong, Reference Meinong1907/1973: §3). However, according to Meinong’s theory of objects, The Existent Golden Mountain no more exists than does The Golden Mountain. Thus, even if one puts aside impossible objects, object theory seems to be inconsistent.

Meinong counters this objection by claiming that there is a semantic difference between “The Existent Golden Mountain exists” and “The Existent Golden Mountain is existent” and that, while the latter is true, the former is false (Meinong, Reference Meinong1907: §3). Russell dismisses this rejoinder as incomprehensible (Russell, Reference Russell1907). This was the end of the debate between Russell and Meinong.

It was not, however, the end of the debate between Meinongians and Anti-Meinongians. As we shall see in Section 4, Meinong’s distinction between being existent and existing is not the desperate ad hoc maneuver that it may seem to be at first glance. Moreover, neo-Meinongians have developed a variety of strategies to resolve the paradox of The Existent Golden Mountain (see Subsection 5.4).

2.4 Remaining Problems

Even if one accepts the Meinongian solutions outlined in the previous subsections, a number of problems remain. There is still the problem of The Existent Golden Mountain, for which it has yet to be shown that Meinong’s distinction between existing and being existent can provide a viable solution.

Furthermore, there is the paradox of simplicity: According to CP, it is true of the object The Blue that it has being blue as its sole property. However, this seems to entail that The Blue has in fact (at least) two properties, namely being blue and having exactly one property, which seems to contradict the postulate that it has being blue as its sole property.Footnote ³⁹

Moreover, the Meinongian interpretation of existence as a predicate is highly controversial, and it is still unclear what the quantifier “∃x” is supposed to express if it does not express existence. This question will be discussed in the next section.

The problem of The Existent Golden Mountain will be taken up again in Section 4, where a refinement and extension of Meinongianism will be presented, and it will be shown that it has the resources to solve this problem. It will also be shown that the same extension provides a solution to the paradox of simplicity.

3.1 Modes of Being versus Ontological Neutrality

As noted in Section 1, one of the basic tenets of Meinongianism is a distinction between “there is” and “exists”. The relationship between “there is” and “exists” is as follows: If entities that are F (in short, Fs) exist, then there are Fs. However, the reverse does not hold: From “There are Fs” one may not infer “Fs exist.” For instance, from “Black swans exist” one may infer “There are black swans.” However, from “There are black swans” one may not infer “Black swans exist.”Footnote ⁴⁰ In principle, analogous reasoning holds for singular existence sentences, although in this context, the use of “there is” is uncommon and sounds odd.Footnote ⁴¹ However, regardless of the linguistic oddity, from “(A particular thing) a exists,” one may infer “There is a.” But from “There is a,” one may not infer “a exists.” For instance, from “God exists” one may infer “There is God.” But from “There is God,” one may not infer “God exists.”

As noted in Section 2, in Meinongian logics, “there is” is usually expressed by means of the quantifier “∃x”, while “exists” is represented as a predicate letter (commonly “E” or “E!”) in symbolic notation.Footnote ⁴² Accordingly, “Fs exist” (e.g., “Black swans exist”) can be rendered in logical notation as “∃x (Fx ∧ E!x)”. This implies, trivially, “∃xFx” (e.g., “There are black swans”). However, “∃xFx” does not imply “∃x (Fx ∧ E!x)”. “a exists” (e.g., “Pegasus exists”) is rendered as “E!a”. “There is a” (e.g., “There is Pegasus”) may be symbolized as “∃x (x = a)”; and “E!a” implies “∃x (x = a)”, but “∃x (x = a)” does not imply “E!a”.

The logical relationship between “∃x” and “E!” is quite clear. However, the distinction between “∃x” and “E!” raises further questions, notably the following: If the quantifier “∃x” does not express existence, what else does it express? What is expressed by “Black swans exist” that is not expressed by “There are black swans”? Is there really a semantic difference between “There is something that is identical with Pegasus” and “Pegasus exists”? If so, what exactly does it consist in?

Before considering various answers to these questions, it should be noted that the interpretation of “∃x” is discussed not only within Meinongianism or Meinongian logics. Rather, it is a fundamental problem of the philosophy of logic in general. However, it becomes particularly pertinent for those logics that have an existence predicate “E!” in addition to the quantifier “∃x” in their vocabulary.

There are, in principle, two possible explanations for the alleged difference between “∃x” and “E!”. I call them the modes of being view and the ontological neutrality view, respectively. According to the modes of being view, there are various modes of being, with existence being just one of them. In light of this view, one may assume that nonexistent objects have a different kind of being, distinct from existence, but nevertheless a kind of being. Thus conceived, “being” is a generic concept. Furthermore, one may assume that the quantifier “∃x” just expresses this generic concept of being. Accordingly, “∃xFx” expresses that at least one F has some kind of being or other (perhaps existence, but not necessarily so); “∃x (x=a)” expresses that the particular entity a has some kind of being (either existence or something else).

Consequently, according to the modes of being view, the use of the quantifier “∃x” is – to use a familiar phrase – “ontologically committing” (or “ontologically loaded”, as it is sometimes called). That is to say, whenever a person S claims truth for an existential quantification (say, something of the form “∃xFx”), S implicitly assumes entities of a certain sort in her ontological framework (S is ontologically committed to Fs). For instance, assume that S subscribes to the statement “There is a prime number bigger than 100,” and S is apt to render this by means of the quantifier “∃x” in symbolic notation as follows: “∃x (x is a number, and x is prime, and x is bigger than 100).” Obviously, this implies “∃x (x is a number).” According to the modes of being view, S is ontologically committed to numbers. In other words, by accepting “∃x (x is a number)” as true, S implicitly admits numbers in her ontological framework. Thus, S cannot claim, on pain of inconsistency, that there is a prime number bigger than 100 and, in the same breath, deny that there are numbers, that is, deny that numbers have being of some sort (say, because numbers are abstract objects and S believes that there are only concrete objects).

Suppose S is a mathematician and a philosopher. As a mathematician, S believes that there are prime numbers bigger than 100. As a philosopher, however, S is a materialist, and she sees no way to interpret numbers as material entities. Therefore, as a philosopher, S denies that there are numbers. Thus, according to the modes of being view, a materialist philosopher-mathematician easily gets into a conflict between her philosophical views and her mathematical knowledge.

Conflicts of this sort are not only threatening to mathematicians. Linguists, literary theorists, even physicists, may easily run into similar predicaments. Just as mathematicians are likely to accept as true existential quantifications over numbers, literary theorists are likely to accept existential quantifications over fictitious characters. However, a philosophically educated literary theorist should be aware of the various paradoxes of fiction (see Section 1) and thus may come to the view that fictitious objects do not have any kind of being whatsoever. Similarly, physicists are likely to accept as true existential quantifications over “theoretical entities” such as the ideal gas. However, from a philosophical point of view, those physicists may tend to deny that entities of this sort have being. According to the modes of being view of quantification, all of these cases involve inconsistency.

By contrast, according to the ontological neutrality view, the quantifier “∃x” does not express any kind of being whatsoever. Accordingly, the acceptance of an existential quantification is not ontologically committing in any sense. In other words, the quantifier “∃x” is not ontologically loaded in any way. A mathematician-philosopher may well believe that there is a prime number bigger than 100 – in the sense of “∃x (x is a number, and x is prime, and x is bigger than 100)” – and at the same time deny that numbers have some kind of being, without being entangled in any inconsistency. Similarly, a literary theorist may claim that there are fictitious characters that are such-and-such and in the same breath reject any ontological commitment to fictitious entities. The same applies to the physicist and the ideal gas, and so forth.

Often advocates of the ontological neutrality view of the quantifier hold (implicitly or explicitly) that there is an ambiguity in the natural language expression “there is”: In one sense, “there is” is the natural language equivalent to the quantifier, and in that sense, “there is” is ontological neutral (i.e., noncommitting, not ontologically loaded). In another sense, “there is” may well be used to express an ontological commitment. In that sense, it is not ontologically neutral but ontologically loaded. If used in the latter sense, it must not be represented by means of the quantifier “∃x” in symbolic notation.

The claim that the English “there is” (and the corresponding expression in other natural languages) is ambiguous in this way suggests itself because it seems obvious – even to defenders of the neutrality view of the quantifier – that natural language speakers sometimes want to talk in an ontological committing way. Apparently, at least sometimes, they use “there is” (or its cognates in other natural languages) for this task.Footnote ⁴³ This is clearly the case in certain philosophical contexts: When, for instance, Platonists claim that there are universals and nominalists deny this, “there are” is obviously meant in an ontologically committing way – for this is just what the whole debate is about. Platonists want to commit themselves to the assumption that universals belong to the realm of being, while nominalists reject this commitment. The same holds for the debates between moral realists and antirealists, psychophysical dualists and materialists, and so forth.

But ontologically committing talk occurs not only within philosophy, but in all kinds of scientific and everyday contexts. If entomologists and epidemiologists state that, recently, tiger mosquitos have been found in Western Europe, one can hardly doubt that they, in this context, understand “there are” in a robust ontological sense. (Otherwise, it would not make sense to recommend measures against the spread of tiger mosquitos in order to avoid infections with the dengue fever.) Similarly, if one states that there is apple juice in the fridge, and so forth. However, according to ontological neutralism, this kind of (ontologically committing) talk cannot be expressed by means of “∃x”, at least not by means of “∃x” alone.

Advocates of ontological neutralism shy away from using the term “existence quantifier” or “existential quantifier” for “∃x”, because it would suggest an “existential” (i.e., ontological) reading. Therefore, some prefer to call it “e-quantifier”. Others use the term “particularizer”. The latter is meant to suggest that “∃x” should be read as “For some x, … ” or “For at least one x, … ” instead of “There is an x ….” Hence, “∃xFx” is not supposed to be read as “There are Fs” or “There is something that is F,” but rather as “Some x is F” or “At least one x is F.”

It is important to understand that the distinction between the modes of being view and the ontological neutrality view is not a matter of logical syntax or of logical inference rules, but a matter of the philosophical interpretation of the logical constant “∃x”. Modes of being theorists and ontological neutrality theorists may use the same logical vocabulary, the same logical syntax, and the same inference rules. From the point of view of pure symbolic logic, it doesn’t matter whether “∃x” is read as “There is … ”, or even “There exist … ”, or rather as “Some x … ”. It is solely from a philosophical (more exactly: ontological) point of view that this issue becomes relevant. It concerns the relation between natural language expressions and logical symbols, as well as the relation between language in general and systems of beliefs/theories and reality.

3.2 Varieties of the Ontological Neutrality View

In the preceding subsection, it was pointed out that the quantifier may be interpreted as existentially loaded (ontologically committing) or as ontologically neutral, that is, noncommitting. The question of how the quantifier is to be interpreted is particularly salient for Meinongians, since they (typically) use an existence predicate in addition to the quantifier. This raises the question of whether the quantifier is supposed to express another kind of being besides existence (in which case it would be ontologically committing) or no being at all (in which case it would be ontologically neutral). In order to better understand what is at stake here, it is helpful to consider some of the most influential varieties of the ontological neutrality view and see whether they can be put to use for Meinongians. This is the task of the present subsection.

A prominent variety of the ontological neutrality view is the substitutional interpretation of the quantifier. It goes back to Ruth Barcan Marcus and is explained as follows: Consider a propositional function “A” which contains “x” as a free variable. A substitution instance of “A” is a formula that results in the substitution of a value of the free variable x for the variable.Footnote ⁴⁴ The substitutional interpretation of “∃xA” goes: Some substitution instance of A is true; or: there is at least one value of “x” such that “A” is true. The substitutional interpretation of “∀xA” goes: All substitution instances of “A” are true; or: for all values of “x”, “A” is true. (Marcus, Reference Marcus1962: 252f.) According to Marcus, quantification, thus conceived, does not, by itself, involve any ontological commitment. Marcus writes:

The important point to note here is that Marcus’ interpretation of the quantifiers allows for the use of variables other than individual variables (i.e., variables that stand for names). As noted in Section 2 (Subsection 2.2, note 35), in standard logic, only individual variables are permitted, that is, variables in standard logic are to be replaced exclusively with names. It does not matter what kind of entities these names stand for. Standard logic allows for quantification over all kinds of things: not only individuals (in the usual sense) but also properties (conceived as Platonist ideas), classes, propositions, numbers, names, and other linguistic entities. This is so because we can name all these entities. Consider, for instance: “Some properties are rarely exemplified.” In standard notation, this may be rendered as: “∃x (Px ∧ Rx)” (where “P” stands for “is a property” and “R” stands for “is rarely exemplified”). A (probably true) substitution instance of “Rx” would be: “Wisdom is rarely exemplified.” “Wisdom” is a singular term (a name) that stands for a universal. Therefore, the substitution of “wisdom” for “x” is wholly unproblematic, from the point of view of Quinean logic.

Marcus’ point is not that we should interpret quantification substitutionally in order to allow for quantification over other things than individuals. Rather, her point is that we should interpret quantification substitutionally in order to allow for the substitution of linguistic expressions other than names for variables. Consider, for instance: “There is something that Ann and Bob have in common: They both like cold pizza.” In order to render this sentence in standard logical notation, one would have to paraphrase it in terms of properties: “There is a property that both Ann and Bob exemplify … ”; “∃x (Px ∧ Eax ∧ Ebx …)” (read: There is an x, such that x is a property, and Ann exemplifies x and Bob exemplifies x). Here, the variable x is to be replaced with a name for a property, for example, “the property of liking cold pizza”. However, the substitutional interpretation of the quantifier à la Marcus allows for a straightforward rendering: “∃Φ (Φa ∧ Φb)” (read: There is a Φ, such that Ann Φ and Bob Φ).Footnote ⁴⁵ Here, the variable “Φ” is to be replaced not with a name but with the predicate “likes cold pizza”.

As stated in the previous quotation, Marcus’ interpretation of the quantifiers is independent of ontological considerations. Her point is simply that the very notion of quantification does not, by itself, force us to restrict ourselves to the exclusive use of nominal variables. The use of quantifiers requires variables. Variables are placeholders for linguistic expressions. For what kind of linguistic expressions? For any kind we like! Nothing in the concept of a variable prevents us from using variables for predicate expressions, propositions, adverbs, prepositions, or connectives.

Marcus’ lucid observations about the nature of quantification and variables and her conclusion that the use of nonnominal variables should be admitted are surely correct. Moreover, as can be seen in the example of Ann and Bob, who both like cold pizza, the use of nonnominal variables may help to avoid unwanted ontological commitments. In this sense, one may say that quantification – substitutionally interpreted – is ontologically neutral. However, Marcus does not claim that quantifier statements never carry ontological commitments. As she puts it: “If we choose as values of the variables the names of things, the names of classes, or the names of properties, then it is no metaphysical mystery that instantiation and quantification will be about things, properties, and classes” (Marcus, Reference Marcus1962: 253). In other words, it is not the quantifier “∃x” that carries the ontological commitment but the nominal variables, that is, the variables that are placeholders for names. As soon as we connect the quantifier with a nominal variable, the quantification carries ontological commitment. Marcus’ claim is not that quantifications per se are ontologically neutral but rather the much more cautious claim that it depends on the choice of variables whether a quantification carries ontological commitment. Consider, for instance, the following statement: “∃x (x is a fictitious entity).” Given that x is a nominal variable (to be replaced, for instance, with “Pegasus”), someone who accepts this statement as true is ontologically committed to fictitious objects, according to Marcus’ substitutionalism.

Similar considerations can already be found more than ten years earlier in Peter Geach’s critical discussion of Quine:

Geach’s point is very similar in spirit to Marcus’ insight: The (natural language) quantifier “something” does not necessarily involve nominal quantification. Although it may sound a bit odd as an English sentence, one can say: “There is something that Jemima and Ahab both are.” The statement can be continued with “ … namely, a cat/red/hungry etc.” But “a cat”, “red”, “hungry”, and so on, are not names. In this case, the quantifier “something” is not tied to a variable that is a placeholder for a name.

In this sense, Geach as well as Marcus and Prior (see note 45) argue for an ontologically neutral interpretation of quantification, but neither of them denies that ontological commitment is carried by the use of nominal variables. Therefore, this kind of neutrality view – although extremely useful in certain contexts – cannot be applied to the topic discussed in the preceding subsection, where we considered only quantification with nominal variables. After all, Meinongianism is about the existence or nonexistence of objects. When Meinongians talk about nonexistent objects, they make use of nominal variables.

However, there are more radical varieties of the ontological neutrality view that are directly relevant to the topic under discussion. Some philosophers claim that utterances in the “object language” are ontologically neutral tout court. It is only at the level of metalanguage that we get involved in ontological commitments. In this context, an utterance in the object language is meant to be an utterance about nonlinguistic items, whereas an utterance in the metalanguage is an utterance about language (i.e., about linguistic items). Frank Jackson, for instance, puts this as follows:

If one appropriates Jackson’s view on the meaning of “there is” in the object language and uses the quantifier as the logical symbol for “there is”, this entails that the quantifier is ontologically neutral. Therefore, Jackson’s version of the ontological neutrality view proves relevant to the topic under discussion.

Jackson’s view is reminiscent of Rudolf Carnap’s distinction between “internal” and “external” existence statements (Carnap, Reference Carnap1950). Basically, Carnap’s idea is this: Both in everyday talk and in science, our use of general terms always happens within a particular “framework”. If a speaker claims that there is a prime number bigger than 100, she presupposes the framework of numbers. If a speaker asks whether there is a mythical figure that is half-man and half-horse, he presupposes the framework of mythology, and so forth. Questions and statements of this kind are internal statements and questions. According to Carnap, internal statements and questions are, in principle, ontologically innocuous. They are not to be answered by philosophers but by mathematicians, literary theorists, or other specialists – depending on what kind of expertise a particular framework requires. The internal existence statement that there is a prime number bigger than 100 entails, trivially, the more general existence statement that there are numbers. This can also be regarded as an internal statement within the framework of numbers (though a trivial one).

However, Carnap (rightly) observes that ontologists do not think that questions like “Are there numbers?”, “Are there mythical creatures?”, and so on can be trivially answered on the basis of some kind of nonphilosophical expertise. Carnap concludes that, in ontology, these questions must be understood in a different way – namely, in an external way. When an ontologist asks, for instance, whether numbers exist, she does not presuppose the framework of numbers. Instead, it is the very presupposition of this framework that is at stake.

As Carnap sees it, external questions of this kind do not have a cognitive sense. If they are meaningful at all, they have to be understood as mere pragmatic questions, in the sense of: Should we accept the framework of numbers/mythical creatures, and so on? In other words, according to Carnap, external existence statements are to be understood as mere recommendations to make use of a certain framework. Such statements do not have any claim to truth. If they are neither understood in this pragmatic way nor in an internal sense, they are simply meaningless. One could say that Carnap, just like Jackson, considers the “object language” to be ontologically neutral.Footnote ⁴⁶ Thus, Carnap’s view on ontology also suggests an ontologically neutral interpretation of the quantifier.

3.3 Is Außersein a Third Mode of Being?

In the previous subsections of this section, two possible interpretations of the quantifier “∃x” have been presented: the modes of being view and the ontological neutrality view. Which one of these is “the Meinongian” interpretation? The short answer is: There is no single Meinongian interpretation of the quantifier. Meinongianism is compatible with both the modes of being view and the neutrality view. Thus, it does not come as a surprise that there is no uniform position among Meinongians with regard to this issue.

Moreover, there is no uniform position among historians of Meinongianism with regard to the question of whether Meinong himself held the modes of being view or the neutrality view.Footnote ⁴⁷ The truth is that Meinong struggled with this issue for decades, from the earliest presentation of object theory until the end of his life – although (of course) not in terms of the interpretation of “∃x”,Footnote ⁴⁸ but in terms of the interpretation of Außersein. His views changed over time. At the beginning, he tended toward the neutrality view; at the end, he opted for the modes of being view.

In order to get a complete picture of the development of Meinong’s views about this issue, one has to take into account not only his more prominent early writings on the theory of objects, but also some later material, part of which was only published posthumously and is not yet available in an English translation. As mentioned en passant in Subsection 1.1, Meinong indeed distinguishes between various modes of being, namely, existence and subsistence. Objects like The Golden Mountain and The Round Square, however, have neither of these. They are, as Meinong calls it in one place, “beyond being and non-being”. For this particular status, Meinong coined the term Außersein (Meinong, Reference Meinong and Meinong1904/1960: §4). The objects that we are calling, in the present Element, nonexistent are, in Meinong’s terms, außerseiend.Footnote ⁴⁹ The question is: Is Außersein a third mode of being, over and above existence and subsistence? There is textual evidence that Meinong originally considered this option seriously, albeit reluctantly:

However, immediately following this passage, Meinong himself raises doubts about this interpretation:

In order to understand Meinong’s worries, one has to take into account that Außersein is a status that does not only belong to nonexistent (and nonsubsistent) objects, but also to existent and subsistent objects. Thus, every object is außerseiend; there is no such thing as an object that lacks Außersein. There is no negative opposition to Außersein, whereas the established modes of being (existence and subsistence) have this negative opposition.

Of course, these considerations are far from ruling out definitely that Außersein is a third mode of being.Footnote ⁵¹ Meinong himself takes up the question again in his monograph Über Annahmen (On Assumptions) from 1910.Footnote ⁵² There, he fails to give a definite answer, although it becomes clear that he wishes to have an argument for the view that Außersein is not a third kind of being (Meinong, Reference Meinong1910/1968: §12, 78–80). In several later writings, however, Meinong explicitly declares that Außersein is indeed a third kind of being, over and above existence and subsistence.Footnote ⁵³

3.4 Neo-Meinongian and Other Contemporary Interpretations of “∃x”

Despite the almost universal occurrence of an existence predicate in neo-Meinongian logics, Meinongian logicians differ in their use of the quantifier “∃x”. Some interpret it – as one might expect – as “ontologically neutral”, that is, as not expressing existence;Footnote ⁵⁴ others, however, use it as “ontologically loaded”.Footnote ⁵⁵

Kit Fine defends an ontology of what he calls “arbitrary objects”. Arbitrary objects are abstract objects akin to Meinongian incompletely determined nonexistent objects (at least in one important interpretation of Meinongian nonexistent objects):

Fine is aware that many philosophers would deny that there are such things as arbitrary objects. His reply is: It depends on how one interprets “there are”. If one interprets it in an ontological sense, he would agree. However, he himself interprets it in an ontologically neutral way when he claims that “there are arbitrary objects” (Fine, Reference Fine1983: 56f.).

In a similar spirit, Tim Crane argues that the use of the quantifier “∃x” (or its natural-language equivalent “there is”) does not entail any ontological commitment. Therefore, the claim that there are objects that do not exist is ontologically unproblematic and does not entail a distinction between “modes of being” in an ontologically relevant way (Crane, Reference Crane2012: 425f. and Reference Crane2013).Footnote ⁵⁶

In a recent paper, Nathanael Gan argues that Meinongianism in general is an anti-realist view, in that Meinongians “are not ontologically committed to the objects in question” (Gan, Reference Gan2021: 53). The objection that Meinongianism involves “an unacceptably profligate ontology” (Gan, Reference Gan2021: 54) is at least premature, if not wholly beside the point.Footnote ⁵⁷ Obviously, the crucial question is how the “there are” in “there are nonexistent objects” is understood.

A neutrality view of quantification is also defended – for various reasons – in Routley, Reference Routley1980; Lewis, Reference Lewis1990; Priest, Reference Priest2005, and Paoletti, Reference Paoletti2015. Others argue for what one could call a “plurality view” of quantification, that is, that quantification can be used in various ways, both ontologically committing and noncommitting (see Linsky, Reference Linsky1972 and Hofweber, Reference Hofweber, Everett and Hofweber2000).

By contrast, in so-called Free Logics, the quantifier is always interpreted as having “existential import” (see Lambert, Reference Lambert1983: 105; Lambert, Reference Lambert1991: 3). Free Logics are free from existence assumptions, both with respect to general and to singular terms. The latter kind of freedom (freedom of existence assumptions with respect to singular terms) distinguishes them from standard logics of the Quinean brand. In Quinean logic, it is simply assumed that singular terms that are substituted for individual variables are denoting singular terms. That is why, in Quinean logics, the principle of existential generalization (EG) holds unrestrictedly: Fa → ∃xFx. That is, in a formula “Fa”, the “a” must be understood as a nonempty singular term. Free logicians, by contrast, feel that logical principles should hold independently of contingent matters of existence and denotation. Therefore, they reject (EG). As soon as (EG) is rejected, however, there is no need to interpret the quantifier “∃x” in an ontologically neutral way.

Still others, for instance the neo-Meinongian logician Terence Parsons, remain impartial with respect to the interpretation of the quantifier.Footnote ⁵⁸ Parsons even surmises (wrongly, in my view) that the issue might be merely terminological (Parsons, Reference Parsons1980: 10f.).

The neo-Meinongian logician Edward N. Zalta, however, explicitly holds a modes of being view. He takes the quantifier to express being (that is, “logical or metaphysical existence”), in contrast to the existence predicate “E!”, which expresses “physical existence” (Zalta, Reference Zalta1988: 102f.).

A special case is Nino Cocchiarella. He distinguishes between various modes of existence (actual existence, past existence, future existence, merely possible existence) and proposes to introduce for each mode of existence an existential quantifier of its own. Alluding to Quine’s famous slogan, he says “that to be (of a given mode of being) is to be the value of a variable bound by a quantifier (comprehending that mode of being)”. (Cocchiarella, Reference Cocchiarella1969: 42; emphasis in original text)

To sum up: Meinongianism is compatible with both the neutrality view and the modes of being view of the quantifier. Meinongians (including Meinong himself) do not have a uniform stance with regard to this question.Footnote ⁵⁹

3.5 Existential Generalization, Universal Instantiation, and the Predication Principle

Existential Generalization (EG), Universal Instantiation (UI), and the Predica-tion Principle (PP) are logical principles that hold in Quinean logics without restriction:

Are these principles acceptable for Meinongians? That depends on how the quantifiers are interpreted. If they are interpreted as ontologically neutral, all three principles are unproblematic from a Meinongian point of view. The same is true if the quantifiers are interpreted as expressing a mode of being other than existence, such that every object has this kind of being. (Cf. Subsection 3.3, on the debate about Meinong’s notion of Außersein.)

Things are different, however, if “∃x” is interpreted as expressing existence (or some other kind of being such that not every object has it). Consider EG first: If the quantifier is interpreted as “ontologically loaded”, EG contradicts one of the Meinongian core principles, namely the principle of independence (IP) (see Subsection 1.1). Remember the paradox that arises from the statement “Pegasus is a flying horse” (Subsection 1.2.3). According to EG, this implies “∃x (x is a flying horse),” which seems to be false if the quantifier is taken to express existence. Consequently, neo-Meinongians who interpret the quantifier as expressing existence have to reject EG.Footnote ⁶⁰ They can, however, accept the following revised version of EG:

Analogous reasoning holds for UI. If universal quantification is taken to be restricted to the domain of the existent, it is not acceptable for a Meinongian. Consider:

According to UI, this would imply, for instance: The Golden Mountain is completely determined. However, as we know (see Subsection 2.2), The Golden Mountain is not completely determined. Consequently, some neo-Meinongians reject UI (see Routley, Reference Routley1980: 107; Lambert, Reference Lambert1983: 106f.). They may accept, however, a restricted version of it, namely:

Now consider PP: In Quinean logic, PP is trivially true because there “∃x (x = a)” is a logical truth, just like “∀x (x = x)”. This is because Quinean logic involves an existential presupposition with respect to singular terms. That is, it is presupposed that any individual constant that is used in a formula represents a denoting singular term. There is simply no provision for nondenoting (empty) singular terms. The rejection of this existential presupposition with respect to singular terms is the core of Free Logics (see the previous subsection). Neo-Meinongians who interpret the existential quantifier as expressing existence and the universal quantifier as restricted to the domain of existents (as, for instance, the Free Logician Karel Lambert does) have to reject “∀x (x = x)”, and they can no longer take “∃x (x = a)” as a logical truth: “∃x (x = The Golden Mountain),” for instance, would be a falsehood. Consequently, neo-Meinongians who interpret the quantifier as expressing existence have to reject PP because it contradicts the principle of independence. They may only accept the following restricted version of PP:

However, neo-Meinongians who interpret the quantifier as ontologically neutral may accept PP in its original version.

Finally, consider the following rendering of PP, which is possible in logics with an existence predicate “E!”:

If the quantifier is interpreted as expressing existence, PP‘ and PP are equivalent. Consequently, PP‘ is to be rejected by neo-Meinongians of all kinds because it is in conflict with the principle of independence.

4.1 The Nuclear–Extranuclear Distinction

The distinction between nuclear and extranuclear properties first occurs in Meinong’s writings in his monograph Über Möglichkeit und Wahrscheinlichkeit (Reference Meinong1915/1972), §25. Meinong’s starting point is the observation that nonexistent objects may be (and in most cases are) indeterminate with respect to many properties (see Subsection 2.2). Consider, for instance, the object The Blue. The Blue is neither round nor square, nor elliptical, and so on. It is indeterminate with respect to its shape, among many other things. In a similar vein, The Triangle is neither right-angled nor oblique-angled, neither equilateral nor scalene. Moreover, it is indeterminate with respect to its color, size, location, and so on.

Let’s stay with the case of The Triangle: It has been observed that it is indeterminate with respect to its color. Neither the “The Triangle is blue” nor “The Triangle is red,” and so on, are true. But what about the higher-order property of being indeterminate with respect to its color? Can’t we say that The Triangle is determinate with respect to this property? After all, it seems to be an uncontested truth (within the framework of object theory) that The Triangle is indeterminate with respect to its color.

Meinong’s answer is: Yes, being indeterminate with respect to its color does indeed belong to the properties of The Triangle. However, this property is not on a par with the property of having exactly three sides and the property of having exactly three angles. While the latter are nuclear properties of The Triangle, the former belongs to its extranuclear properties.Footnote ⁶¹

Meinong gives two examples for nuclear properties (being red, being triangular) and two examples for extranuclear properties – being indeterminate with respect to this-and-this property and being simple (i.e., having exactly one nuclear property). Moreover, Meinong makes it plain that an object’s nuclear properties – and only these – constitute the object’s “nature”. It also becomes clear that the nuclear–extranuclear distinction entails an essential revision of the original version of Meinong’s object theory: the comprehension principle (CP, see Subsection 1.1) becomes restricted to nuclear properties. The restricted version (CP^R) goes as follows:

This restriction seems to set limits to what Meinong calls “freedom of assumption” (Annahmefreiheit): The principle of the unrestricted freedom of assumption is a correlate of CP. It says that we are free to assume (imagine, think of, …) any object we like, that we can “grasp”, as it were, intentional objects on the basis of arbitrary sets of intended properties (i.e., those properties that are present to the mind in a particular act of presentation of an object), such that the grasped objects have the properties in question (cf. Meinong, Reference Meinong1915/1972: §37, p. 282). According to CP^R, however, we are confined to nuclear properties for our choice of intentional objects.

It is worth noting that nonexistent objects are incomplete with respect to their nuclear properties only. With respect to their extranuclear properties, they are as complete as any existent object. Moreover, impossible nonexistent objects (like The Round Square) have incompatible nuclear properties, but never incompatible extranuclear properties. The (seeming) conflict with PEM and PNC arises with respect to nuclear properties only.Footnote ⁶²

The nuclear–extranuclear distinction provides a solution to the paradox of simplicity (see Subsection 2.4). Consider the following structured presentation of the paradox:

1. 1. The Blue has the property of being blue as its sole property. (According to CP.)

2. 2. The Blue has the property of being blue. (1)

3. 3. The Blue has the property of having exactly one property. (1)

4. 4. The Blue has the property of being blue and the property of having exactly one property. (2, 3)

5. 5. The Blue has at least two properties (namely, the property of being blue and the property of having exactly one property). (4; contradicts 3)

The contradiction can be avoided in the following way: One has to take into account that being blue is a nuclear property, while the property of having exactly one property is an extranuclear property. In light of this, the propositions of the above deduction have to be reformulated as follows:

1. 1‘. The Blue has the property of being blue as its sole nuclear property. (According to CP.)

2. 2‘. The Blue has the nuclear property of being blue. (1)

3. 3‘. The Blue has the extranuclear property of having exactly one nuclear property. (1)

4. 4‘. The Blue has the nuclear property of being blue and the extranuclear property of having exactly one nuclear property. (2‘, 3‘)

5. 5‘. The Blue has exactly one nuclear and at least one extranuclear property. (4)

5‘ is not in conflict with any of the propositions 1‘–4‘. No contradiction arises. (Cf. Meinong, (Reference Meinong1915/1972: §25), 175f.)

The nuclear–extranuclear distinction also allows for a straightforward solution to the problem of The Existent Golden Mountain and thus provides a powerful rejoinder to Russell’s most serious objection (see Subsection 2.3). Consider a structured representation of the problem:

1. 1. ¬∃x (x is golden ∧ x is a mountain ∧ x exists).

2. 2. The Existent Golden Mountain is golden and a mountain and existent. (According to CP.)

3. 3. The Existent Golden Mountain is existent. (2)

4. 4. The Existent Golden Mountain exists. (3)

5. 5. ∃x (x is golden ∧ x is a mountain ∧ x exists) (namely, the Existent Golden Mountain). (2, 4; contradicts 1)

If existence is an extranuclear property and CP is restricted to nuclear properties only, then there is no such thing as The Existent Golden Mountain, that is, no object that has being a mountain, being golden, and being existent as its nuclear properties. That is, premise 2 in the above deduction is to be rejected. Thus, 3–5 cannot be derived, and no contradiction arises.

Surprisingly, Meinong does not take this straightforward path. He does not even mention existence as an example of an extranuclear property.Footnote ⁶³ Instead, he infamously allows for the assumption of the object The Existent Golden Mountain and claims that there is a difference between existing and being existent. Meinong explains that being existent, but not existing, may belong to an object’s nature, the set of an object’s determinations. Consequently, while we cannot assume The Existing Golden Mountain, we can indeed assume The Existent Golden Mountain. This move allows for an alternative solution of the Existent-Golden-Mountain problem. Let us disambiguate propositions 1–3 of the above deduction:

1. 1‘. ¬∃x (x has the nuclear property of being golden ∧ x has the nuclear property of being a mountain ∧ x has the extranuclear property of existing).

2. 2‘. The Existent Golden Mountain has the nuclear properties of being a mountain, of being golden and of being existent. (According to CP.)

3. 3‘. The Existent Golden Mountain has the nuclear property of being existent. (2‘)

From 3‘, however, we cannot derive

1. 4‘. The Existent Golden Mountain has the extranuclear property of existing.

Consequently, it cannot be derived that

1. 5‘. ∃x (x has the nuclear property of being golden ∧ x has the nuclear property of being a mountain ∧ x has the extranuclear property of existing).

Therefore, no contradiction arises.

The crucial point is that the nuclear property of being existent does not entail the extranuclear property of existing. At first sight, it might seem (as Russell obviously suspected) that the distinction between existing and being existent is a desperate ad hoc maneuver in order to save object theory from inconsistency. But is it? After all, Meinong’s restriction of CP to nuclear properties suffices to meet Russell’s challenge (see Subsection 2.3). Either Meinong simply did not see this easy solution to the problem of The Existent Golden Mountain and therefore contrived the doctrine of nuclear counterparts of extranuclear properties, or he had an independent reason for doing so. In the following subsection, it will be argued that the latter is the case.

4.2 A Functional Explanation of the Nuclear–Extranuclear Distinction

As has been shown, the nuclear–extranuclear distinction may be a valuable tool for saving object theory from inconsistencies. Its main problem is that it is not easy to understand. It is not at all clear from the outset which properties are supposed to be nuclear and which are supposed to be extranuclear. There is no obvious criterion for sorting properties neatly into nuclear and extranuclear ones. Meinong’s explanations are sometimes more confusing than clarifying.

Since the nuclear–extranuclear distinction led to a restriction of CP, it concerns the very foundation of object theory. Not least for this reason, it would be highly desirable to have a clear conception of it. In what follows, I will propose an unorthodox explanation, suggested by Meinong himself in the following passages:

These two passages strongly suggest that the nuclear–extranuclear distinction is not an absolute distinction among properties, that is, properties are not divided into two classes – nuclear and extranuclear – such that each property falls under exactly one of the two concepts. Rather, the nuclear–extranuclear distinction is a functional distinction. Instead of saying that a given property P is nuclear (or extranuclear), it would be better to say that, in a given context, P functions as a nuclear (or extranuclear) property, respectively.

To say that, in a given context, a property functions as a nuclear one is to say that it belongs to the object’s nature, that it is used to define the object’s essential properties. The property of being indeterminate with respect to some determination B is, in most circumstances, a typical example of an extranuclear property. It is an extranuclear property of The Blue that it is indeterminate with respect to being triangular. It is an extranuclear property of The Triangle that is indeterminate with respect to being blue; and so on. However, CP allows us to assume an object like The-Triangle-that-Is-Indeterminate-with-Respect-to-Being-Blue. In this case, the indeterminacy with respect to being blue belongs to the nature of the object in question and thus functions as a nuclear property. Similarly for existence: When we say of The Golden Mountain that it does not exist, we deny an extranuclear property of The Golden Mountain. We may, however, assume The Existent Golden Mountain, and in this case, existence (or being existent) functions as a nuclear property.

Unrestricted freedom of assumption is saved in the sense that we may assume at whim, for arbitrary Fs, an existent F, a completely determined F, and so forth. However, what we cannot do is make an arbitrary F exist or being completely determined. The Existent Golden Mountain still does not exist; The Completely Determined Blue is still an incomplete object; and so forth.

Remember the psychological origin of Meinong’s object theory: the problem of intentionality (see Subsection 1.2.1). The first and foremost purpose of assuming nonexistent objects was to provide an intentional object for every mental act (imagination, thought, desire, etc.). If one takes this into account, the functional explanation of the nuclear–extranuclear distinction no longer seems ad hoc, but makes very good sense. For we may think not only of a golden mountain, but also of an existent golden mountain, not only of a triangle, but also of a completely determined triangle. That is, the content of our thoughts may contain existence and completeness along with being golden, being a mountain, and so on. However, the assumption of an existent golden mountain does not bring a golden mountain into existence. Merely adding the determination of completeness to a finite number of nuclear properties does not turn an incomplete object into a complete one (Meinong, Reference Meinong1915/1972: §37).

Thus, Meinong himself provides an explanation of the nuclear–extranuclear distinction. According to this explanation, each property that may function as an extranuclear property in one context may function as a nuclear property in another context. A property functions as a nuclear property of an object if, and only if, it is an element of the set that constitutes the object’s essence. In principle, each property may be included in such an essence-constituting set.

The nuclear–extranuclear distinction is used by a number of neo-Meinongians. Others make use of an alternative distinction (the modes-of-predication distinction) instead of the nuclear–extranuclear distinction. We will come back to both distinctions in Subsection 5.4. In Subsection 5.4.4, it will be argued that the nuclear–extranuclear distinction, rightly conceived, is functionally equivalent to the modes-of-predication distinction.

4.3 Auxiliary Objects and Implexive Being

In Über Möglichkeit und Wahrscheinlichkeit (Meinong, Reference Meinong1915/1972), Meinong introduces several related concepts that give the whole theory of objects a completely new turn: auxiliary object (Hilfsgegenstand), target object (Zielgegenstand), and implexive being (implexives Sein).

Meinong argues that incomplete objects play an important epistemic role. In ordinary circumstances, we are intentionally directed toward existent (and thus completely determined) objects. In other words, in standard circumstances, our “target objects” are complete objects. However, our limited cognitive capacities do not allow us to fully comprehend (erfassen) a completely determined object. We are not able to comprehend the totality of the infinitely many features of a completely determined object. Rather, Meinong claims, we comprehend a complete object by means of an incomplete object. For instance, we may have an existent billiard ball as our target object. We may comprehend this complete object via the auxiliary object The Ball, that is, an object that has being a ball as its only nuclear property. In this case, The Ball is our direct intentional object, though the cognitive act ultimately aims at an existent billiard ball (Meinong, Reference Meinong1915/1972: §29).

Meinong struggles with the question of how exactly target objects and auxiliary objects are related to each other. First, he considers and rejects the idea that auxiliary objects are parts of target objects (in the usual sense of “part”). He – rightly – points out that the relation of The Ball to an existent billiard ball is clearly distinct from the relation of, for instance, a knife’s handle and blade to the knife as a whole. However, Meinong considers the relation between a target object and its auxiliary objects as something analogous to the part–whole relation. In order to avoid confusion with the standard conception of a part, he introduces the term “implecting” (implektieren):

The auxiliary object The Ball has implexive being in all existent balls, including the particular billiard ball on a particular billiard table (Meinong Reference Meinong1915/1972: §29).

Meinong’s discussion of the relation between incomplete auxiliary and complete target objects is reminiscent of Plato’s struggle with the relation between (universal) “ideas” and particulars in the dialogue Parmenides. Implexive being seems to be a relation between universals and particulars, the relation between types and tokens. “The Ball is implected, among many other things, in the red billiard ball on my friend’s table” seems to be another way of saying “The type The Ball is instantiated, among many other things, in the red billiard ball on my friend’s table.”

In the light of these considerations, Meinong’s nonexistent objects seem to be abstract, ideal universal objects that can be instantiated in particulars. Thus, they would be objects that cannot have spatial properties such as being round. This would be a radical shift from the original version of object theory, according to which The Ball is a concrete object that is round, just in the same sense as the particular billiard ball on the friend’s table. Meinong was perhaps not fully aware of this shift with all its far-reaching consequences while writing Über Möglichkeit und Wahrscheinlichkeit.Footnote ⁶⁴ But there is evidence that he later became aware of it. In a sketchy note on Über Möglichkeit und Wahrscheinlichkeit, Meinong writes:

However, this has a consequence that Meinong was obviously not aware of: If incomplete objects are ideal objects, they have – according to Meinong’s original theory – a kind of being, namely subsistence (see Subsection 1.1), that is, they are not merely außerseiend. For philosophers who do not distinguish (like Meinong) between existence and subsistence, they are not nonexistent. They exist in the very same sense as numbers, properties, theories, institutions, laws, works of music and literature, and other ideal objects. Thus, according to this interpretation of the mature version of Meinong’s object theory, the category of the nonexistent is empty. There is no longer any need for Meinong’s concept of mere Außersein. It seems as if object theory was transformed from a theory of nonexistent objects into a sophisticated version of Platonism – or at least it came very close to such a transformation.

5.1 Varieties of neo-Meinongianism

One of the aims of this section is to provide an overview of varieties of Meinongianism in contemporary philosophy,Footnote ⁶⁶ a sort of roadmap that should help one orient oneself in a rather multifarious, complex, and sometimes confusing domain. This is not an easy task, for various reasons.

The first difficulty is that it is not entirely clear from the outset what belongs to the extension of the concept of neo-Meinongianism. In Subsection 1.1, I declared that I use the term “Meinongianism” for theories that include principle M, some version of CP, and IP, and that I use the term “neo-Meinongianism” in a loose sense – as a collective term for contemporary Meinongian philosophers, as well as for those who, for one reason or another, are not Meinongians in the sense explicated in this Element, but who consider themselves to be Meinongians or are usually classified as Meinongians.

The second difficulty is that neo-Meinongian theories can be compared and classified along various coordinates, some of which run diagonal to each other. One can distinguish, for instance, “concrete neo-Meinongianism” from “abstract neo-Meinongianism”, and “ontologically committing neo-Meinongianism” from “ontologically neutral neo-Meinongianism”. Both concrete neo-Meinongianism and abstract neo-Meinongianism may be either ontologically committing or ontologically neutral.

The third difficulty is due to the limitation of space. Most (if not all) of the theories considered in what follows would deserve an extensive treatment, a detailed presentation and discussion, which would require several times the length of this Element. However, the limitation of space is not necessarily a disadvantage. After all, the aim of this Element is to provide a concise and comprehensible survey of the field, not an encyclopedic resource. Simplification will be unavoidable – hopefully simplification without distortion. Those readers who would like to dig deeper into some of the issues will find ample bibliographical references.

5.2 Concrete versus Abstract neo-Meinongianism

Borrowing a term from Fred Kroon, I start by distinguishing between two rather broad categories of Meinongianism, namely “concrete neo-Meinongianism” and “abstract neo-Meinongianism”.Footnote ⁶⁷ Concrete neo-Meinongianism is the view that Meinongian objects like The Golden Mountain, The Round Square, or The Blue are concrete objects. Abstract neo-Meinongianism is the view that all Meinongian objects are abstract objects.Footnote ⁶⁸

According to concrete neo-Meinongianism, The Golden Mountain is a concrete, spatio-temporal object. It has the properties of being golden and of being a mountain, in the ordinary sense of these expressions. The Golden Mountain is a mountain in the same sense in which Mount Everest is a mountain. It is golden in the same sense in which the Winged Victory statue on the top of the Victoria Memorial in London is golden.

By contrast, according to abstract neo-Meinongianism, The Golden Mountain is neither golden nor a mountain. It cannot have these features because it is an abstract object. As such, it is not spatio-temporally extended and located, and not perceivable by the senses and accessible to empirical investigation.

As shown in the previous sections, Meinong himself started out as a concrete Meinongian and ultimately ended up as an abstract Meinongian. The very same divide runs through neo-Meinongianism. The following philosophers belong to the camp of concrete neo-Meinongianism: Roderick M. Chisholm (Reference Chisholm and Haller1972), Terence Parsons (Reference Parsons1980), Richard Routley (Reference Routley1980), Karel Lambert (Reference Lambert1983), Dale Jacquette (Reference Jacquette1996), Jacek Paśniczek (Reference Paśniczek1998), Graham Priest (Reference Priest2005), and Francesco Berto (Reference Berto2013).Footnote ⁶⁹ Abstract neo-Meinongians include Nicholas Rescher (Reference Rescher1959 and Reference Rescher and Rescher1968),Footnote ⁷⁰ Hector-Neri Castañeda (Reference Castañeda1972), Kit Fine (Reference Fine1983), Edward N. Zalta (Reference Zalta1983 and Reference Zalta1988), Kenneth J. Perszyk (Reference Perszyk1993), Alberto Voltolini (Reference Voltolini2006), and probably also William J. Rapaport (Reference Rapaport1978, Reference Rapaport1981, and Reference Rapaport1985).

The camp of abstract neo-Meinongians can be further divided into those who consider Meinongian objects as universals, more precisely as Platonic types or kinds, and those who identify them with sets of properties.Footnote ⁷¹ In what follows, I will refer to the former as “the universalists” and to the latter as “the settists”. Universalists are Zalta and Voltolini. A “settist” is Castañeda and probably Rapaport.Footnote ⁷²

A special case is Kenneth J. Perszyk. The core thesis of his book is that Meinong’s “nonexistent objects” are to be interpreted as sets of properties, a claim that is repeated over and over again. However, at some point, it turns out that Perszyk actually interprets sets of properties as universals (Perszyk, Reference Perszyk1993: 104–126 and note 22 on p. 144). So, despite his “settist” wording, he should be classified as a universalist.Footnote ⁷³

The difference between universalist and settist neo-Meinongianism can easily be overlooked because sets of properties play a crucial role in universalist neo-Meinongianism too. After all, the pivotal principle of Meinongianism, CP, says that to every set of properties, there is a corresponding object which has (in some yet to be clarified sense of “has”) the properties in the set. Nevertheless, the distinction is ontologically significant. A set of properties is something substantially different from an object that “has” the properties in the set. This is evident for concrete objects: Mount Everest is not a set of properties that includes the property of being a mountain, but it is a mountain (or exemplifies the property of being a mountain). A set of properties is an abstract object, a mountain is a concrete object.

In light of universalist neo-Meinongianism, however, Meinongian objects are just as abstract as sets. But there is a distinction. According to the universalist conception, Meinongian objects can be instantiated in concrete objects (after all, this is what makes them universals). Sets, however, are not the kind of abstract objects that can be instantiated.

One may question whether settist Meinongianism is really a variety of Meinongianism in the first place. After all, there are probably people out there who accept that there are sets of properties without thinking of themselves as Meinongians. Given that one accepts both properties and sets in one’s ontology, there is no need to assume that some sets of properties are nonexistent objects. The set that contains the properties of being a mountain and being golden seems to be no less existent than the set that contains the properties of being a mountain and being rocky. However, Hector-Neri Castañeda, the main proponent of settist Meinongianism, explicitly declares himself to be a Meinongian, and rightly so, because he considers some sets of properties as nonexistent objects (Castañeda, Reference Castañeda1972).

5.3 Committing versus Noncommitting neo-Meinongianism

In Section 3, we saw that “there is” in “There are objects that do not exist,” as well as the quantifier “∃x”, is ambiguous in the sense that it can be read in an ontologically neutral and in an ontologically committing way. Moreover, it has been pointed out that interpreters of Meinong disagree on whether Meinong intended his theory of objects as committing or noncommitting.

It is not surprising that the same kind of disagreement occurs within neo-Meinongianism.Footnote ⁷⁴ The following neo-Meinongians explicitly claim ontological neutrality for statements that seem to involve reference to nonexistent objects: Rapaport (Reference Rapaport1978): 155–158; Routley (Reference Routley1980): in particular chapter 1, §3; Fine (Reference Fine1983): 56f.; Paśniczek (Reference Paśniczek1998): section 3.6; Priest (Reference Priest2005): in particular, vii, sections 1.3 and 1.4.Footnote ⁷⁵ Others either more or less explicitly accept an ontological commitment to nonexistent objects, or at least their writings provide some evidence for the commitment view and no evidence to the contrary: Rescher (Reference Rescher1959: 171–174); Cocchiarella (Reference Cocchiarella1969): 34f.; Parsons (Reference Parsons1980); Lambert (Reference Lambert1983);Footnote ⁷⁶ Zalta (Reference Zalta1988: 102f.); Perszyk (Reference Perszyk1993: in particular, 11f.); Jacquette (Reference Jacquette1996): part one, chapter IV.

I agree with Perszyk’s comment on the neutrality view:

It has become fashionable in contemporary philosophy to make all sorts of claims and in the same breath to reject any ontological commitments that seem to be entailed by them. (Recently, this often goes under the flag of “fictionalism”.Footnote ⁷⁷) Though I do not wish to deny that this may be an adequate approach for the analysis of some kinds of discourse, it seems to me that it is now used in an inflationary way, as a one-size-fits-all solution to get rid of all sorts of ontological commitments. In philosophical discourse, in particular, one should strive to say what one means and to mean what one says. Or, to borrow a formulation from John L. Austin: “It is better, perhaps, to stick to the old saying that our word is our bond” (Austin, Reference Austin, Urmson and Warnock1979: 236).Footnote ⁷⁸

5.4 Characterizing Properties and Predicates: The Perennial Problem Reconsidered

As shown in Subsection 2.3, the original version of Meinongianism threatens to contradict the principle of noncontradiction, because it seems to entail that there is not only The Golden Mountain but also The Existent Golden Mountain, which is both existent and nonexistent. In what follows, I will refer to this as “the paradox of The Existent Golden Mountain”. However, there is another problem with the original version of Meinongianism, which has not been explicitly mentioned yet: According to the original version of Meinongianism, The Golden Mountain literally is golden and a mountain. But it seems reasonable to assume that an object that has properties like being golden and being a mountain can be perceived by the senses. In other words, properties like being golden and being a mountain (among many others) seem to be perceivability-entailing. But, as a matter of fact (a fact that is not questioned by any Meinongian), The Golden Mountain (like any other nonexistent object) cannot be perceived by the senses. Therefore, according to the original version of Meinongianism, it must be denied that there are any properties that are perceivability-entailing. This seems to be in conflict with our very understanding of properties like being golden and being a mountain. I refer to this as the problem of nonperceivability.

Any serious neo-Meinongian theory has to propose solutions both to the paradox of The Existent Golden Mountain and the problem of nonperceivability. Neo-Meinongian theories can be divided not only into concrete and abstract, or committing and noncommitting theories, but also with respect to how they try to resolve these problems.

It has been shown in Section 4 that Meinong himself proposed a solution to the paradox of The Existent Golden Mountain, namely the distinction between nuclear and extranuclear properties. Some neo-Meinongians have adopted this distinction (Parsons, Reference Parsons1980; Routley, Reference Routley1980; Lambert, Reference Lambert1983; Jacquette, Reference Jacquette1996). Others opt for an alternative solution, namely the modes-of-predication distinction (Castañeda, Reference Castañeda1972; Rapaport, Reference Rapaport1981; Zalta Reference Zalta1983 and Reference Zalta1988; Perszyk, Reference Perszyk1993). Yet another solution is suggested by so-called Modal Meinongians (Priest, Reference Priest2005 and Reference Priest2008; Berto, Reference Berto2013). I call their proposal “the other worlds strategy”. Neo-Meinongians can hence be divided into three camps: advocates of the nuclear–extranuclear distinction, advocates of the modes-of-predication distinction, and advocates of the other worlds strategy.

All of the previously mentioned abstract neo-Meinongians (both the universalist and the settist) accept some kind of modes-of-predication distinction. None of them opt for the nuclear–extranuclear distinction. This is no coincidence. If the nuclear-extranuclear distinction is understood in the familiar way, The Golden Mountain, for instance, literally is a mountain, in the usual sense. But abstract objects cannot be mountains. The nuclear–extranuclear distinction could be an option for abstract neo-Meinongians, however, if it is interpreted in the functional sense (see Subsection 4.2). However, if it is interpreted in this sense, it becomes functionally equivalent to the modes-of-predication distinction, as will be shown in Subsection 5.4.4. Concrete neo-Meinongians either opt for the nuclear–extranuclear distinction or for the other worlds strategy. In what follows, all three suggestions will be explained and discussed.

5.5 Summary and Closing Remarks

In its origins, Meinongian object theory was primarily intended as a solution for the problem of intentionality: If every intentional attitude has an object, but some intentional attitudes do not have an existent object, there must be nonexistent objects. A second important motivation for object theory was the problem of negative singular existence statements: If “The winged horse does not exist” is a true statement, the subject term “the winged horse” cannot refer to an existent object. Therefore, it must refer to a nonexistent object.

Soon after its appearance, Bertrand Russell blamed object theory for violating basic logical principles, such as the principle of excluded middle and the principle of noncontradiction. In reaction to this, Meinong made important amendments. In doing so, he at least paved the way for a consistent version of object theory. Nevertheless, Russell’s harsh verdict remained unchallenged for some decades, at least in analytic philosophy.

It was only in the 1970s that the tide turned in favor of Meinongianism. Starting with Roderick M. Chisholm, analytic philosophers rediscovered object theory and recognized its explanatory power, not only for the problems of intentionality and negative singular existence statements, but also for a larger variety of applications, including the problem of fictitious objects and the problem of past and future objects. It was shown, often by means of formal logic, that Meinongianism can be modeled as a consistent theory. No doubt Russell’s objections are refuted.

However, the question remains whether Meinongianism is really the best solution to all or some of the problems outlined in this Element (intentionality, negative singular existence statements, fictitious objects, past and future, and others). As always in philosophy, there are alternative solutions around. The debate continues.