Meinong’s jungle
Nonexistents and indeterminates
Nonexistent entities are particulars that don’t exist, or lack being. This concept arises naturally when considering some ordinary assertions: if I say that there is no current king of France (negative existential statement), that James Bond is a spy (claim about fiction), or that the first female president will have executive experience (statement about future events), to what extent am I conjuring these "persons" into some form of being?
Alexius Meinong, who pioneered the type of approach we will describe, thought that such objects carried considerable explanatory force, and deplored his fellow philosophers’ prejudice in favor of the actual. For instance, to a Russellian about names, one cannot make any true statement about objects that lack existence (Russell denied they are anything else than disguised descriptions). The consequences can be counter-intuitive: a statement like "the current king of France is a king" would be false.
Following this introduction, it may seem I’m just retracing my steps here: aren’t non-actual possible objects and impossible objects archetypes of these nonexistent entities? Indeed they are. But in (im)possible-worlds modal metaphysics, the worlds are members of our ontology, and the objects their denizens. There is no such intermediation in traditional versions of Meinongianism. Meinong introduced more precisely incomplete objects, as we’ll see, whose modal nature is essentially indeterminate.
But let’s come back to our first point: how committed shall our ontology be to objects we’ve defined as nonexistent? Meinong denies there is a contradiction: everything is an object, even though some of these objects lack any form of being. This is formalised with the concept of so-being (Sosein): the various ways that an object can be. Meinong’s key principle is that of indifference: an object is characterized by its so-being (we might say, its properties, its essence...) and its being or non-being is indifferent to that nature. The Sosein of the square rectangle is being a rectangle with the property of being square; that of the square cirle is being a circle with the property of being square. We know that the former exists (has being) while the latter doesn’t (has non-being); yet to Meinong the Sosein is not affected by the Sein — they are independent. Unlike Russell, Meinong is able to state that the square circle is square, or that the current king of France is a king.
His typology actually goes deeper than a simple binary:
Real objects are defined as having existence and thus also being. Meinong includes physical and psychological objects there, so we might say that conrresponds to our first and second realms.
Ideal objects lack existence but they subsist and according to Meinong also have being. That would include for instance numbers, true propositions or states of affairs that obtain. Many objects from our third realm of abstract entities would thus be in that category.
Non-being objects are neither real nor ideal: they do not exist, nor do they subsist. They include what Meinong called "non-contradictory" objects (the golden mountain, Pegasus...) and "contradictory" ones (the round square, the largest prime number...). With hindsight we might prefer to use "possible" and "impossible" to reap the benefits of modal notions.
Indeterminate objects do not have being, but they also don’t have non-being. This category essentially matches the class of incomplete objects. An object with only one property, like that of being blue, cannot exist nor subsist. Meinongians insist that incomplete objects are distinct from properties: the object that is only blue (which is blue) is not the same as blueness (which is not blue). Meinong also includes here objects like a triangle. An indeterminate triangle is not an ideal object, since it is incomplete. It could be a complete ideal object if we knew its three angles and the length of one side.
In my view, the main flaw in Meinong’s original typology is the lack of clarity as to what separates ideal objects from the non-being realm. Even Russell showed signs of the utmost confusion on these matters, in a harmful fashion for Meinong’s legacy. At times he seemed to believe the golden mountain or false propositions to be subsistent entities. To be fair, the distinction between susbsistence and "non-being" does seem fairly nebulous to the modern Meinong reader.
It is best to consider Meinong’s ideas, not as a consistent body of ontological doctrine (which would "explain" being), but rather as the origin of an influential principle: that it is possible to de-ontologize large swathes of things whilst still referring to, quantifying over, or thinking about them. Alongside that founding principle, neo-Meinongians, starting with his student Mally, have proposed different ways to fine-tune the resulting metaphysical positions and dispel paradoxes. The first one, possibilism reverts to a possible/impossible-worlds model in an attempt to port the Meinongian nomenclature there. The second one, the dual-property strategy, distinguishes between nuclear and extra-nuclear properties. Extra-nuclear attributes can be ontological ("is existent"), modal ("is possible"), intentional ("is believed by me") or technical ("is complete").
Lastly, veering away even further from Meinongian orthodoxy is the dual-copula strategy. According to proponents like Edward Zalta, properties can be exemplified, but also encoded. For instance, a real dog in my street can exemplify the property "being a dog". But White Fang only encodes the property "being a dog", as well as "being a wolfdog", "being born wild", etc. But White Fang exemplifies many others: "being a fictional character", "having been created by Jack London", "being famous", "being nonexistent", etc. Similarly, the round square encodes exactly two properties ("being round" and "being square") but "is" not round nor square (if we assign that English-language copula to exemplification). The round square, however, is impossible, nonexistent, non-subsistent... Objects can thus be seen as correlates of sets of properties.
Fictions
Our discourse is saturdated with a type of entities whose existence is questionable: fictional ones. They can be literary characters like Rastignac, the ambitious young man from la Comédie humaine, mythical figures like Pegasus, the flying horse, places like Rivendell, the refuge of Elves in the Tolkienian Third Age, institutions like the Ministry of Magic from J.K. Rowling’s lore, and much more. Such entities have sometimes appeared in sections above as examples of possible, impossible, or inexistent objects. Indeed, should one entertain a realist position about such ficta, it is tempting to simply consider them a subclass of those broader categories, according to one’s preferred modal doctrine. I’ll take the opportunity to recapitulate those: first, possibilist approaches including Lewisian modal realism and diverse forms of ersatzism (chiefly, propositionalism and combinatorialism); second, Meinongian theories, either orthodox or reconstructed (with dual properties or dual copula).
What all these models cannot account for, though, is the act of creation. They all tend to build a Platonic-style picture of objects not located in time and independent from everything but their constituents (e.g. their properties). But it’s a platitude to say that fictional objects were created when the fictional work they belong to was first recited, written, sung...The contention that fictions are "seized" or "discovered" rather than created or imagined is a hard one to accept. Hence the appearance of a new class of realist models, called creationism or artefactualism, which aim to describe fictional objects with a beginning in time, as well as an explicit dependence upon a creator. We may note this approach’s defects are complementary to those of possibilism and Meinongianism. These traditional stances offer clear identity criteria for fictional objects but ignore their origin in the human mind, while creationism accounts for this fact, but struggles to provide clear identity criteria.
On the other hand, traditional antirealist approaches such as Russellianism quickly get into trouble with fictional entities. The fact they don’t refer to anything real leads to a statement like "Rastignac is French" to be prima facie false, which is impractical. It’s always possible to use a definite description, but even outside of fictional contexts, descriptions of proper names have suffered significant blows. One significant development is called fictionalism. It essentially introduces a fictional operator that allows to distinguish between internal and external metafictional sentences. "According to J.R.R. Tolkien’s legendarium, Gandalf is a wizard" is an internal sentence, that can be true because according to these works of fiction, the name "Gandalf" refers. "Gandalf is an icon in fantasy literature" is however an external sentence, and brings us back to square one: Russellians think that in our world, Gandalf does not refer. Various strategies have been devised, including one that construe realist positions as fictional universes, interpreting external sentences as: "According to fictional realists, Gandalf is an iconic character" (that seems slightly contrived to me). Lastly, one may note the additional difficulty of sentences that seemingly mix both modes, like "the Flash runs faster than Usain Bolt" or "Sherlock Holmes is smarter than any actual detective".
Developments about fictional entities specifically are justifiable by the importance of fiction in our culture. In addition, it’s interesting to note how the dedicated approaches described above have outgrown their intial scope. Artefactualism has been applied beyond its creationist origins (focusing on individual creations of fiction at a single point in time) to all types of human-originated references (institutions, laws, nations...). Meanwhile fictionalist conceits have been generalized to apply to all sort of entities, including, fruitfully, mathematical objects. Purported truths about apparently abstract entities can then be deemed true in the modal context of useful discourse (equivalent to a fictional context). Therefore, "4 is even" would be false but "according to mathematical discourse, 4 is even" would be true. This line of thinking has also allowed to set up the foundations of modal fictionalism, an anti-realist take on possible worlds.