As Quine puts it: "Non-being must in some sense be, otherwise what is it that there is not?" In asserting, for instance, "Pegasus does not exist", I appear to commit myself to the existence, or to the being, of Pegasus. What is it that I'm saying doesn't exist? If Pegasus is nothing, then when we use the word "Pegasus", we're not talking about anything, which would render any statements containing the word nonsensical. "Pegasus does not exist" would amount to "_ does not exist". So, Pegasus, along with other nonexistent things, must have being of some sort, in order to account for the intelligibility of our discourse about nonexistents.
We might formalize the argument like so:
(P1) If "Pegasus" names nothing, then statements about Pegasus are nonsensical.
(P2) Statements about Pegasus are not nonsensical.
(C) So, "Pegasus" must name something.
Another way to see the problem is that it would appear that, if "Pegasus" and "Santa Claus" name nothing, than "Pegasus does not exist" and "Santa Claus does not exist" are each saying exactly the same thing. In each case, we're referring to nothing, and saying it doesn't exist.
(P3) If "Pegasus" names nothing and "Santa Claus" names nothing, then "Pegasus does not exist" and "Santa Claus does not exist" both say the same thing.
(P4) "Pegasus does not exist" and "Santa Claus does not exist" do not say the same thing.
(C) "Pegasus" and "Santa Claus" must each name something.
"Pegasus" names something, but what? One option is to hold that Pegasus has a kind of being as an unactualized possible object (Quine attributes this view to a character called "Wyman"). Reality consists of existent, actual objects; and also various nonexistent, merely possible objects.
Quine's objections to unactualized possibilia
1. First, how do we individuate such entities? What are their conditions of identity? The moment we try to analyze possible objects in any detail, we find that we can't answer simple questions about them:
Take, for instance, the possible fat man in that doorway, and, again, the possible bald man in that doorway. Are they the same possible man, or two possible men? How do we decide? How many possible men are there in that doorway? Are there more possible thin ones than fat ones? How many of them are alike? Or would their being alike make them one? Are no two possible things alike? Is this is the same as saying that it is impossible for two things to be alike? Or, finally, is the concept of identity simply inapplicable to unactualized possibles? But what sense can be found in talking of entities which cannot meaningfully be said to be identical with themselves and distinct from one another?2. A second objection, related to the first, not explicitly stated by Quine but I think implicit in his paper, is that due to the problem of individuating possible objects, postulating possible objects doesn't actually solve the problem of referring to non-existent things. For if we can't individuate possible objects, we can't ever know what is being referred to when people use the term "Pegasus".
I don't think Wyman should be too troubled by these first two objections. In the first place, over the last few decades very detailed theories of modal metaphysics have been worked out that make answering questions such as these perfectly straightforward. Consider, for instance, Lewis's modal realism. Lewis would deny that there is a possible fat man in that doorway. Rather, at some possible world, a fat man is standing in the counterpart of that doorway. At some other possible world, a bald man is standing in the counterpart of that doorway. At some other world, a fat, bald man is standing in the counterpart of that doorway; at some other world, two fat, bald men are standing in the counterpart of that doorway; etc. Re whether any two possible men are alike, we evaluate the similarity of different possible objects in just the same way we evaluate the similarity of actual objects. Re identity, again, this is essentially just the same as for actual objects. (This is not to suggest that Lewis's theory, or any other realist theory of possibilia, is particularly plausible. But I think that Wyman could appeal to such developments to defuse Quine's objection.)
Second, as Richard Routley argues in his paper "On What There Isn't", precisely the same sort of difficulties arise for existing objects. Routley parodies the passage from Quine:
Take, for instance, the cloud in the sky above; and again, the adjacent cloud in the sky. Are they the same cloud or two clouds? How are we to decide? How many clouds are there in the sky? Are there more cumulus than nimbus? How many of them are alike? Or would their being alike make them one? ... is the concept of identity simply inapplicable to clouds? But what sense can be found in talking of entities which cannot meaningfully be said to be identical with themselves and distinct from one another?Perhaps Routley isn't entirely fair here - surely there must be more difficulties with possible objects, if only because possible objects are so much more extensive, and include many stranger things, than actual ones - but the basic point is, I think, correct: just because it turns out to be difficult to answer seemingly simple questions about a certain class of objects, it hardly follows that we have reason to believe that there are no such objects. Reality is full of strange, difficult things. It's also full of perfectly straightforward things that turn out to be puzzling when subjected to certain questions, as when we try to come up with clear criteria for individuating clouds.
3. The notion of a possible object rests on a confusion. Modality, Quine suggests, applies to whole sentences, not to particular things. "It is possible there is a man in the doorway" is perfectly acceptable, the possibility in this case attaching to the sentence "there is a fat man in the doorway"; but it's illegitimate to infer from this to "there is a possible man in the doorway", with the possibility attaching to an entity, the fat man. (Quine doesn't present his reasoning for this in this paper. His arguments here are complex and I won't go into them here. I did start a video series on this, which I never got around to finishing. Michael Morris's An Introduction to Philosophy of Language also covers it.)
Quine suggests that the main motive for expanding possibility from sentences to objects is to deal with the riddle of nonbeing. I'm not convinced. I suspect that the main motive is the problem of explaining what the truthmakers of modal sentences are. The Nazis could have won WWII, I could have become a research chemist, nothing can exceed the speed of light, Frank couldn't have done any better in the exam, etc - in virtue of what, exactly, are such sentences true? Positing possible worlds is one way to deal with this.
4. Even putting aside the above problems, Wyman's account is simply incomplete. The postulation of unactualized possible objects doesn't help at all when we consider terms that apparently refer to impossible objects, such as "the round square cupola on Berkeley college". Quine suggests that one option for Wyman would be to hold that such terms are meaningless. So, regarding our riddle of nonbeing:
(P1) If "round square" names nothing, then statements about round squares are nonsensical.
(P2) Statements about round squares are not nonsensical.
(C) So, "round squares" must name something.
Wyman could reject (P2), accepting that "round square" names nothing and hence that statements about round squares are meaningless. Quine has two objections to this move. First, he argues, the claim that statements about round squares are meaningless "has no intrinsic appeal"; i.e. it's an unattractive and ad hoc hypothesis proposed simply to save the theory. Now, I'm not sure I agree with Quine here. To me, at any rate, "round square" does indeed seem to be meaningless, in some important sense. Of course, I can use the phrase "round square"; and I know what round things are and I know what square things are, so I might think that I'm able to make some inferences about what properties we might attribute to a round square. On the other hand, when I try to think about it in any detail, it slips out of my grasp. Can I really make inferences about it? Here's an easy one: it's a square, and square things have four sides, so it must have four sides. But this just ignores that we're talking about a round square. Round things don't have any sides.
It may be objected that "round square" is obviously contradictory, and this is why we struggle to assign any meaning to it. Sometimes however contradictions are disguised. Only on analysis do we realize that a proposed object is contradictory. Consider the suggestion that God, at least as conceived in Western monotheistic traditions, is contradictory, re arguments that properties such as omnipotence and omniscience lead to irresolvable paradoxes. Even if the atheist is correct about this, it's still the case that people have been able to talk about God in detail, and structure their lives around their belief in God, and even believe that they can have a personal relationship with God. Surely then we can't insist that the concept of God is simply meaningless.
There are two ways Wyman might deal with this. First, he could simply bite the bullet. Any concept that can be shown to entail contradictions is thereby meaningless. This is not such a radical position. The logical positivists held that a statement is meaningful only if it's analytically true or empirically verifiable; with this criterion they attempted to show that a whole host of apparently meaningful statements aren't meaningful after all, including statements about God (see e.g. Ayer's Language, Truth and Logic, chapter 6). Our ability to talk about God, to hold detailed religious beliefs, etc, can be explained by appealing to meaning in a weaker sense, e.g. emotional or poetic meaning. "Colourless green ideas sleep furiously" has no literal meaning, but we might say that it's meaningful in some extended, metaphorical sense.
Second, Wyman could reduce the force of the problem by suggesting that some contradictions are possible. Consider contradictory objects like the Penrose triangle or Penrose stairs.
Are these impossible? Round squares are simply inconceivable and can't be intelligibly talked about, but staircases that keep going up without ever getting higher can actually be visualized. By allowing that some contradictions are possible, Wyman significantly reduces the number of apparently meaningful statements he has to consign to meaninglessness. Of course, this option genuinely would be radical, but the ground has been prepared by dialetheism and paraconsistent logics.
Quine's second objection to the suggestion that statements apparently about impossible objects are meaningless is that this "makes it impossible, in principle, ever to devise an effective test of what is meaningful and what is not." Quine says: "it follows from a discovery in mathematical logic, due to Church, that there can be no generally applicable test of contradictoriness." I assume that what Quine actually has in mind is Gödel's second incompleteness theorem, which demonstrates, essentially, that any consistent formal system cannot prove its own consistency. So put simply: if contradictory objects are impossible, and statements about impossible objects are meaningless, then since there's no test for determining contradictoriness, there's no test for determining meaninglessness.
I have two comments about Quine's objection: (a) Why exactly do we need a strict, systematic way of determining what's meaningful? Why wouldn't it be good enough just to have a few basic rules of thumb? (It's not as though Quine is any stranger to indeterminacy of meaning!) (b) Again, Quine's criticism evaporates if Wyman severes the link between possibility and consistency, and holds that contradictory objects can be possible. Then he doesn't need to say that all contradictory statements are meaningless. In which case, it doesn't follow from the fact that there can be no effective test of what's contradictory that there can be no effective test of what's meaningful.
Ultimately then, it seems to me that rejecting (P2) is a much more plausible move than Quine suggests. Let me make one final comment here. Another obvious option for Wyman is simply to accept both (P1) and (P2), and draw the conclusion that there are unactualized impossibles, in just the same way as there are unactualized possibles. Quine objects to this move that if Wyman admits unactualized impossibles, then he will be trapped in contradictions. But why would this trouble Wyman? After all, he's openly admitting impossibles. Why wouldn't he also admit that some of those impossibles are contradictory?
5. Fifth, Quine suggests that the puzzle of nonbeing rests on a confusion between meaning and naming. Consider again (P1) and (P3):
(P1) If "Pegasus" names nothing, then statements about Pegasus are nonsensical.
(P3) If "Pegasus" names nothing and "Santa Claus" names nothing, then "Pegasus does not exist" and "Santa Claus does not exist" both say the same thing.
These claims seem to rest on the assumption that the meaning of a name is simply is referent (called direct reference theory or Millianism). If names have meanings above and beyond their referents, then "Pegasus" can be perfectly meaningful despite failing to refer to anything (and "Santa Claus" can also be perfectly meaningful, and can mean something different from "Pegasus", despite failing to refer). But Millianism has been subjected to a number of serious objections. Quine appeals to the famous problem of "Frege's Puzzle". Consider the following propositions:
(1) The Morning Star is the Morning Star.
(2) The Morning Star is the Evening Star.
"The Morning Star" and "the Evening Star" both refer to the same object, namely Venus, which on Millianism seems to entail that the phrases have exactly the same meaning. Now, if "the Morning Star" and "the Evening Star" have the same meaning, then we should be able to substitute one for the other in a sentence without changing the meaning of the sentence, which entails that (1) and (2) have the same meaning. But surely this isn't right: (1) is simply trivial, whereas (2) is interesting and informative; (1) is a tautology, whereas (2) tells us something important about the world; (1) is knowable a priori, whereas it takes hands-on empirical investigation to confirm the truth of (2).
I don't have anything to say about this point. I agree with Quine that Millianism isn't adequate, and that if Millianism goes, the justification for (P1) and (P3) is undermined.
6. Finally, Quine appeals to Occam's Razor. Admitting unactualized possible objects massively expands our ontology without good reason. Quine thinks there's an alternative, more ontologically parsimonious solution to the riddle, which appeals to Russell's theory of descriptions. I won't discuss Quine's own solution here. I only note here that the view that there exist, or there are are in some sense unactualized possibilia, has a variety of motivations (cf. Lewis again). Quine's appeal to Occam's Razor is rather less convincing if we have to accept possibilia anyway for other reasons.
