The problem arises when we try to represent natural-language sentences in the predicate calculus. If “Some A’s are B” is translated to “there are A’s that are B”, and hence if it is represented as ∃x(A(x)∧B(x)), then this sentence indeed states non-emptiness of some set, namely the intersection of A and B and thus it sates thatthere are some objects. It was Hume who said that there is no difference between existent objects and just objects, and hence that to be an object is to be an existent object. If so, then by saying that “Some A’s are B”, we are stating also that some objects exist.
One could, however, claim that to be an object and to be an existent object is not the same: that there are non-existent objects as well as existent. Within such an approach “there are A’s” is usually considered not equivalent to “A’s exist” and existence is claimed to be a normal first-order predicate like any other term naming a property, like “red”, “material”, “round”, etc. Then, the sentence “A’s exists” would be represented not as ∃xA(x) (which would represent rather a sentence “there are A’s”) but with the use of a first-order “existence predicate” (Ex) and hence as: ∃x(A(x)∧Ex(x)).
In modern philosophy the possibility that existence could be a first-order pred- icate is usually rejected. The Kantian argument against “existence predicate” is invoked together with the famous quotation: “A hundred real thalers do not con- tain the least coin more than a hundred possible thalers.” (Kant, 2006) The idea of the argument is that if we have a full and adequate description of an object, we do not need to add existence as one of the object’s properties. Our descrip- tion is already complete and stating existence will not give any new information. Thus, existence is different from normal first-order predicates. It is claimed to play a similar role to the truth-predicate, and hence is rather considered to be a second-order predicate. In those logics that stand in the Frege-Quine tradition, it is sustained that both “there is” and “exists” are expressed by means of the ex- istential quantifier (∃), which is, consequently, interpreted as having “ontological import”.
The view that granting existence to an object does not add anything to the description of this object is probably one of the greatest philosophical prejudices. Certainly adding to a description of an object P that P exists (or not) changes essentially our knowledge about this object. I can describe P and P may turn out to be my hallucination. If this fact is unknown to me and also to my inter- locutor, then if she concludes that P exists – only becauseP has some properties which usually belong to existent objects – then her conclusion is false. Thus the information that P is not real, and so does not exist, is an essential completion to the description of P. In fact the qualitative descriptions of many fictitious objects, e.g. characters from “James Bond”, will not be much different from de-
4.2. How to separate existence from the existential quantifier 105 scriptions of real characters, even if evil characters from James Bond are much less dangerous to us than real bandits. Real and merely possible golden thalers in my pocket differ essentially, in that the latter are of no use.
At this point the defender of the view that existence is not a part of a de- scription of an object might say that of course existent objects are different from non-existent ones and that she is not claiming anything opposite. Her point is that descriptions of those objects do not differ, since the information whether a description refers to an existent or a non-existent object is not a part of this de- scription. These are properties used in the description that enable us to check if a described object exists, and using a property “existent” for determining whether it is really existent would be like reading the same newspaper twice to make sure that it is telling the truth (to use a popular philosophical metaphor). In other words, the information that an object exists does not change the conditions under which sentence asserting the existence of this object are true, and is not used in the procedure of verification. In this way objects are like sentences. True and false sentences differ a lot, but sentences “it is true thatp” and “p” do not differ with respect to the truth conditions they have to fulfill to be true and the pro- cedure of checking their truth-value is exactly the same. Moreover, saying that
p is true will not make p true and similarly saying that P exists will not make
P exist. The last argument appears to be a weak sophism in this respect that it works similarly with other properties: saying thatP is red, will not make P red, since P is either red or not and, exactly the same way, P either exists or not.
Even if we find the above arguments weak, there is much more to say against the first-order “existence predicate”. One of the strongest argument consists in showing how the assumption that existence is a (first-order) predicate allows con- structing so-called ontological proof. We will not reconstruct this argument here (as it is well-known in philosophy and not relevant for our further investigations), but focus rather on so-called meinongean paradoxes of non-existent objects. If existence is a predicate which can be assigned to some objects or not, and thus we have both existent and non-existent objects, we need to answer the question “what does it mean to be an object”.
In the most classical theory of non-existent objects, given by Meinong, to every single property and to every set of properties, there is a corresponding object, either an existent or a non-existent one. Thus, there is, for instance, an object that has the property of being blue as its sole property, one might call it “the object blue”, or simply “blue”. There is aslo an object that has the property of being round and the property of being blue, and no other properties (the object “round and blue”). And so forth. But “an object blue” cannot exist since it is impossible to have blue as a sole property. Certainly, “an object blue” is not identical with the property “blue”, and it seems that every colored object needs to have also e.g. shape and size. Such an object (“blue”) must be incomplete and indeed Meinong admits that such objects cannot exist, they are not only non- existent but even necessarily non-existent objects (Reicher,2008). Furthermore,
according to this theory, there can be also an object which is round and square (or even, to make it explicit, round and not round), which breaks the law of contradiction. Again, Meinong replies that the law of contradiction applies only to the existent objects and “round square” is a necessarily non-existent object. But this is not the end of problems. If “blue” is an object that has “blue” as its sole property, it has also a property “of having only one property”, but then it has at least two properties, so we again get a contradiction.
Because of the above difficulties, non-existent objects together with exis- tence predicate were not liked by many logicians and philosophers, although neo-meinongean theories, trying to find ways out of the aporias while preserv- ing non-existent objects, also grew in large numbers. Later on we will refer to one of the most interesting, developed by Graham Priest, which uses a possible worlds semantics for this purpose. The reason why we do not want just to give up on these problematic non-existent objects is that identifying existence with the existential quantifier, or – using Quine’s words – claiming that “to exist is to be a value of a bound variable”, is not in the least deprived of weaknesses. Since we quantify in natural language over both real and merely possible objects, e.g. objects from fictional discourse, we are back to the problem of logical form and truth-value of sentences that use terms referring to such objects.