Here’s a view about propositions:
A proposition P is a set of ordered pairs <A,G> where the first object is an individual and the second a property. These propositions are generally expressed by declarative statements such as my utterance of the sentence `Alvin is Green’. Call this `Structured Propositions’.
Here’s an argument against this view of propositions.
P1) If propositions are structured then one must either: a) become Meinongian, or b) accept gappy propositions.
P2) According to Russell, Meinongianism entails contradictions, so it’s unacceptable.
P3) Gappy propositions cannot explain informative speech acts where true negative existential are asserted. Such speech acts cannot express gappy propositions. So, gappy propositions are unacceptable.
P4) From P2 and P3, it follows that we should neither be Meinongian nor gappy proposition theorists.
C) Propositions are not structured.
Here’s an argument for P1.
Suppose that the name `Alvin’ is referenceless. I go on and utter the sentence `Alvin is Green’. Which proposition did I assert? If propositions are structured, then what I asserted looks either like this ‹A, G› or like this ‹ , G›. The first one requires you to believe that Alvin, who does not exist, IS in fact some kind of object: a non-existent, or subsistent one. That’s Meinongianism. The second option requires you to believe that there are gappy propositions: propositions with unfilled spots in their structure.
For Russell’s argument for P2, read his “On Denoting’’.
As for P3, here’s an argument. Suppose you reply to my assertion by uttering the sentence `Alvin does not exist’, which happens to be true. Which proposition did you assert? Assuming that you cannot be Meinongian, the proposition looks something like this: NEG‹A, E›, where `NEG’ stands for negation and `E’ stands for the property of existence. The proposition is, clearly, a gappy one. The problem is that it should not be.
Here’s why. We need evidence to show that a particular speech act ends up having a propositional gap. More often than not, this is signaled by a presupposition failure. The traditional example is Russell’s King of France: `The present King of France is bald’ presupposes that there is some such thing as a present King of France. Since this presupposition is not fulfilled then the utterance does not express a full-blown, truth-evaluable proposition. Suppose, for argument’s sake, that that’s a good paradigm of propositional gaps. Does that happen with true negative existentials?
The answer is no. In general no existential claim carries existence presupposition. If they had then they would all be useless: i.e., they would all be asserting what they are presupposing. Your reply, for example, would like these:
Let us suppose that Alvin exists. By the way, Alvin does not exist.
Or, think of the more problematic, affirmative existential claim:
Let us suppose that Alvin exists. Now let me tell you something about Alvin. Alvin exists.
The absurdity of these speech acts goes to show that existential claims in general do not carry existence presuppositions. If you want, you can run the usual “hey, wait a minute’’ tests and see this for yourself. The main point here is that existential claims in general do not carry existence presuppositions.
How does this help? Well, if they don’t carry existence presuppositions, then your utterance of the true sentence `Alvin does not exist’ doesn’t carry an existence presupposition. If so, then the fact that `Alvin’ is referenceless does not affect the presuppositions of your speech act. In particular it does not make it so that there is some presupposition failure involved in it. And this is important because if there is no presupposition failure then there is no reason to think that what you uttered has any propositional or truth-value gap whatsoever.
It follows then that whenever someone utters a true negative existential claim they manage to convey a full-blown proposition. But non-meinongian fans of structured propositions are forced to say that these speech acts express a gappy proposition. Which is simply false. True negative existentials cannot express gappy propositions.
Structured proposition theorists are forced to be Meinongians. I referred to Russell’s argument against this view. But here’s a brief, sketch of it. What would happen if you become Meinongian in order to save the day for Structured Propositions? Well, you would end up having something like this: NEG ‹A, E› which literally says that there IS an object that does not exist. Of course, Meinongians would like to distinguish between ways of existing. What the proposition really says is that there IS a Subsistent object that does not exist. But Meinongians should also accept that there is an important set of things that REALLY do not exist: like the square circle. Otherwise you run into contradictions. So they have to distinguish between objects like Alvin and the square circle, they all have different ways of not existing. And all that just seems ridiculous.