Here is a plausible principle: if n items stand in an n-adic relation, then all of them exist. And necessarily so. If Miami is between Superior and Globe, then all three towns exist. Combine this principle about relations with the plausible idea that the intentional nexus is a dyadic relation that relates a thinker (or a mental act of a thinker) to an object of thought. So far, so good. But what if the object of thought does not exist? Then what we have is a relation that relates an existent thinker to a nonexistent object in violation of the plausible principle about relations. The puzzle can be cast in the mold of an aporetic triad:
1. We sometimes think about the nonexistent.
2. Intentionality is a relation that ties a thinker to an object of thought.
3. Every relation is such that, if it holds, then all its relata exist.
The limbs are individually plausible but jointly inconsistent.
Some will be tempted at this point to distinguish between two modes of being, a strong mode and a weak mode if you will, call them existence and subsistence. The relations principle could then be reformulated to say that if a relation R holds, then all of R's relata have being (either exist or subsist). This seems to allow a solution of our problem. When Tom thinks about a nonexistent item such as a mermaid, he does indeed stand in a relation to something, it's just that the item in question subsists rather than exists. The object of thought has being but does not exist.
Now I don't think this solution is a good one even if there are different modes of being, but at least it illustrates how one might be tempted to embrace a doctrine of modes of being. And I agree with Reinhardt Grossmann that the above is not a good argument for modes of being. But he seems to think that there are no good arguments for modes of being, and indeed that the very idea is fallacious. Grossmann writes,
Are there any other arguments for the existence of modes of being?
It seems to me that all the rest of such arguments are of the following form. One first points out that two kinds of thing are fundamentally different, that they differ 'categorially', so to speak. Then one asserts that such a tremendous difference must be a difference in their modes of being. While one kind of thing, say exists, the other kind merely subsists. [. ..]
This type of argument is obviously fallacious. From the fact that two kinds of things differ fundamentally in their properties, it simply does not follow that they must have different modes of being. Of course, they may exist in different modes, but that they do so exist cannot be shown in that way. (The Existence of the World: An Introduction to Ontology, Routledge 1992, pp. 95-96)
Grossman is making two claims here. One is about the invalidity of a form of argument whereby one infers a difference in mode of being from the fact that two kinds of thing are very different. Grossmann is right that this is a non sequitur. The other claim is that all arguments for modes of being have this fallacious form.
But this second claim is false. Earlier I argued that if there are substances and if there are accidents, then substances and accidents differ in their mode of being. My argument was not that substances and accidents are so radically different in their natures that this difference in nature entails a difference in mode of being. My argument hinged on the relation between substances and accidents. Suppose Socrates is a substance and his being sunburned is an accident inhering in him. The substance and the accident both exist and they differ in nature. But then how do we account for the fact that an accident cannot exist except as inhering in the substance whose accident it is? We cannot account for this characteristic feature of accidents by saying that both exist or that they differ in nature. We have to say that accidents and substances exist in different ways. Accidents exist in an existentially dependent way whereas substances exist in an existentially independent way.
Clearly, we have to introduce a distinction between different modes of being if we are to explain how substances and accidents are related. Now this argument I just gave does not commit the fallacy that Grossmann mentions. It does not infer a difference in mode of being from a difference in nature. So Grossmann's second claim is mistaken.