Existence and Non-Existence
We have puzzled over the nature of existence and the nature of non-existence, but we don’t ask how these two categories relate to each other. Does one entail the other? Not in the sense that if something exists then it doesn’t exist, and vice versa, but in the sense that if one thing exists then other things must not exist, and vice versa. If certain things exist in a possible world, must there also be other things that don’t exist in that world? And if certain things don’t exist in a possible world, must there also be things that do exist in that world? Could there be a world of pure existence (no non-existence), and could there be a world of pure non-existence (no existence)? For example, is there a world which contains the usual existent planets but no non-existent planets like Vulcan, and is there a world which contains all the Greek gods but no existing human beings or other entities? I think these alleged possibilities ought to strike us as peculiar, conceptually problematic. There is the feeling that existence and non-existence are parasitic on each other—not identical, to be sure, but mutually dependent. Why might this be?
Two ideas suggest themselves. The first is that these are contrastive concepts: non-existence is by definition the absence of existence, and existence is by definition the absence of non-existence. Thus, the concepts lose their grip in alleged cases of one applying without the other; we would have no use for either concept if its complement concept had no application. To say that Mars exists is to say that it is not like Vulcan being-wise, and to say that Vulcan does not exist is to say that it is not like Mars being-wise. This is suggestive: we do tend to think of each category as the opposite of the other, choosing certain paradigms of each, and we are hard put to come up with anything more substantial than that. The terms have no meaning outside the “language game” of attributions of existence and non-existence (that is their actual use). Isn’t this contrast really what we are thinking when we employ the notions of existence and non-existence? If so, it will not be possible to separate the two concepts: we need instances of both in order to make sense of either. A pure existence world and a pure non-existence world put too much pressure on these concepts as they are ordinarily employed. So, existence always occurs side by side with non-existence, and non-existence always presupposes existence: necessarily, if one, then the other. In fact, we might want to say that in a world consisting of a number of existing objects there must be hugely many non-existent objects—all the objects in other possible worlds that don’t exist in that world. And non-existent objects always imply existing objects: it could not be that the universe contained all the non-existent objects we normally talk about but no existing objects. The world of fiction is surely parasitic on the world of fact.
The second idea is that fictional objects are products of the human mind, so they require the existence of such minds. Unicorns need unicorn thoughts, and thoughts occur in minds, so unicorns require existing minds. To say that there are unicorns but no existing minds is therefore contradictory. So, a world containing fictional objects must contain non-fictional minds: we can deduce existing minds from non-existing unicorns. This gives us an inverted form of the ontological argument: given that God does not exist, we can infer that something else exists, viz. the mind or minds that thought the idea of God up. If I came up with the idea, then I can state, “God does not exist, therefore I do exist”. We can’t perform this kind of inference using a true existential statement as the premise. Thus, existence is implicit in non-existence: in a world containing non-existence there must be existent minds. We can’t seal the concept of non-existence off from the concept of existence: where one is instantiated so must the other be—not in the non-existent object, to be sure, but beside it.
Here is an analogy: the concepts of necessity and contingency are similarly intermingled. In our world we have both necessary and contingent truths, but could there be a world containing only necessary truths or only contingent truths? Again, the idea seems outlandish: don’t the two concepts feed off each other? We can produce examples of both that can be used to ground the contrast, but absent these we lose our grip on the concepts of necessity and contingency. A modally homogeneous world is not really an intelligible world. If everything is necessary, then nothing is; and similarly for contingency. What is necessary is what is notcontingent (and now we give examples), and what is contingent is what is not necessary (more examples). Without the contrast class we are left with the notion of mere non-modal truth (compare generous and miserly). Every possible world must consist partly of necessary truths and partly of contingent truths. Similarly, there can be no possible world consisting only of the future, or only of the past; each presupposes the other. Truth and falsehood are the same: where there is a true proposition there has to be a false one, and vice versa. Or identity and distinctness. Or good and evil. These concepts come in pairs not singly. Presence presupposes absence and absence presupposes presence—which is another way of saying that existence and non-existence necessarily go together. We shouldn’t compartmentalize these categories, as if each member of the pair had an independent identity. Existence and non-existence are really parts of the same package—semantically and metaphysically indissoluble.
 I discuss this in Logical Properties (2000), chapter 2. The topic of existence is extremely confusing and I slide over potential pitfalls in this short paper, but be assured that I am well aware of the dangers. In particular, we have to be careful about the interpretation of quantifiers.