Existence part I. Non-existent objects

Existence is one of the most fundamental notions of metaphysics. Hence it may be advisable to start our course with a precise definition of this term. Unfortunately this task is not so easy to complete, and some even claim that the term "exist" is primitive and cannot be defined. Others come up with fancy and long-winded definitions of existence that explain nothing. Here, instead of providing a direct definition, we will focus on the way the term "exist" functions in philosophical language and its logical connections with other, closely related terms.

Let us begin with a seemingly straightforward observation: apparently we should agree that not everything exists. We can give numerous examples of fictional objects (objects that don't exist): dwarfs, fairies, centaurs, Santa Claus. But the list is not limited to mythological creatures. In science we often discover that something does not exist, for instance aether or Vulcan (hypothetical planet located inside the orbit of Mercury). In math we can rigorously prove that the greatest prime number does not exist.

But there is a logical problem here. Let us consider the sentence "Vulcan does not exist". What is this sentence about? If, as its grammatical structure suggests, it is a sentence about Vulcan, then we have a contradiction here, because Vulcan has to exist in order for the sentence to be true. One way out of trouble is to divorce the notion of an object from the concept of existence. The initial sentence is about a particular object - Vulcan, that is - but this object does not have to exist. In fact Vulcan is a nonexistent object. We have arrived at a metaphysical conception according to which the set of all objects splits into two parts: existing and non-existing ones. The word "exist" is no longer synonymous with "there is" (there is Santa Claus, but he doesn't exist). Existence becomes a property of only some objects. The main proponent of this theory is the Austrian philosopher Alexius Meinong.

The conception of non-existent objects encounters serious difficulties. Some of them are listed below.

1. What is the extent of the domain of non-existent objects? It turns out that this domain has to be pretty large, vastly outnumbering the domain of existing things. To each description must correspond an object - in the majority of cases a non-existent one. Let's consider for instance the following description: "an x-foot high golden mountain". For each real number x there is a different non-existent object that satisfies this description, so we have easily created a continuum of non-existent objects. Morever, some of the non-existent objects are contradictory: compare a square circle. But this means that we have to accept a pair of contradictory statement: "the square circle is a circle" and "the square circle is not a circle".

2. Non-existent objects are incomplete. Vulcan can only be said to possess two properties: being a planet, and being closer to the Sun than any other planet (this is a relational property). But Vulcan is indeterminate with respect to any other properties that typically characterize planets: its mass, density, period of revolution, period of rotation, etc. Consequently, non-existent objects do not admit unambiguous criteria of identity and distinctness. It is impossible even in principle to decide whether Vulcan whose diameter equals 10000 km is identical with or distinct from the Vulcan whose period of revolution around its axis equals 20 hours.

3. Non-existent objects do not admit answers to the  "How many?" questions. How many Vulcans are there? What if we define Vulcan as the only planet that orbits the Sun closer than Mercury? Then it looks like it is a definitional property of Vulcan that there is only one Vulcan, but on the other hand we can have two incompatible descriptions "The unique Vulcan whose diameter equals 1000 km" and "The unique Vulcan whose diameter equals 2000 km". Both non-existent referents of these descriptions obviously satisfy the definition of Vulcan simpliciter. If there are two unique non-existent Vulcans, we have a contradiction.

4. In what sense do non-existent object possess their properties? Vulcan is said to be an object that possesses the property of being a planet and the (relational) property of being closer to the Sun than any other planet, including Mercury. But if Vucan is literally located inside the orbit of Mercury, then it should be possible to see it there. Moreover, it should gravitationally affect Mercury and any other planet. But this is absurd. No non-existent object can gravitationally interact with existent ones. Some reply to this objection that non-existent Vulcan possesses its properties in a different sense than existent objects. But when we defined the concept of Vulcan, we wanted it to denote an object that literally possesses its definitional properties. So non-existent Vulcan understood in that way cannot be claimed to be a referent of our description.

5. If we admit non-existent objects, all laws of nature become literally false. The statement "All metals conduct electricity" is falsified by non-existent metals that do not conduct electricity. One possible solution: to limit the quantifiers in the laws of nature to existent objects only. But in that case we lose an ability to distinguish between laws and accidental generalizations.

Required reading:
Brian Garrett, "Non-existent objects", in What is this thing called metaphysics?, pp.27-31.