Causal theories of reference strike me as hopeless. Let's see how they fare with the problem of negative existentials.
There are clear cases in which 'exist(s)' functions as a second-level predicate, a predicate of properties or concepts or propositional functions or cognate items, and not as a predicate of individuals. The affirmative general existential 'Horses exist,' for example, can be understood as making an instantiation claim: 'The concept horse is instantiated.' Accordingly, the sentence does not predicate existence of individual horses; it predicates instantiation of the concept horse.
This sort of analysis is well-nigh mandatory in the case of negative general existentials such as 'Flying horses do not exist.' Here we have a true sentence that cannot possibly be about flying horses for the simple reason that there aren't any. (One can make a move into Meinong's jungle here, but there are good reasons for not going there.) On a reasonable parsing it is about the concept flying horse, and says of this concept that it has no instances.
The same analysis works for negative singular existentials like 'Pegasus does not exist.' Pace Meinong, everything exists. So, given the truth of 'Pegasus does not exist,' 'Pegasus' cannot be taken as naming Pegasus. Since 'Pegasus' has meaning, contributing as it does to the meaning of the true sentence, 'Pegasus does not exist,' and since 'Pegasus' lacks a referent, a natural conclusion to draw is that the meaning of 'Pegasus' is not exhausted by its reference: it has a sense whether or not it has a referent. So, along Russellian lines, we may analyze 'Pegasus does not exist' as, 'It is not the case that there exists an x such that x is the winged horse of Greek mythology.' Or we can take a page from Quine and say that nothing pegasizes. What we have done in effect is to treat the singular term 'Pegasus' as a predicate and read the sentence as a denial that this predicate applies to anything.
In this way the paradox attaching to singular negative existentials is removed. But the Russell-Quine analysis is based on the assumption that names are definite descriptions in disguise (Russell) or else transformable into predicates (Quine). But how does one deal with the problem of negative existentials if one denies the Russell-Quine approach to proper names, holding instead that they refer directly to their nominata, and not via the sense of a definite description or Searlean disjunction of definite descriptions?
Keith Donnellan tackles this problem in "Speaking of Nothing" (reprinted in S. P. Schwarz, ed., Naming, Necessity, and Natural Kinds, Cornell UP, 1977, pp. 216-244).
Consider 'Santa Claus does not exist.' What does a child come to learn when he learns this truth? He does not learn, as a Russellian would have it, that nothing in reality answers to (satisfies) a certain
description; what he learns is that the historical chain leading back from his use of 'Santa Claus' ends in a 'block':
When the historical explanation of the use of a name (with the
intention to refer) ends in this way with events that preclude any
referent being identified, I will call it a "block" in the history.
In this [Santa Claus] example, the block is the introduction of the
name into the child's speech via a fiction told to him as reality
by his parents. (237)
Having defined 'block,' Donnellan supplies a rule for negative existence statements, a rule which he says does not purport to supply the meaning of negative existentials but their truth-conditions:
If N is a proper name that has been used in predicative statements
with the intention to refer to some individual, then 'N does not
exist' is true if and only if the history of those uses ends in a
block. (239)
'God' would appear to satisfy the antecedent of this conditional, so Donnellan's theory implies that 'God does not exist' is true if and only if the history of the uses of 'God' ends in a block.
There is something wrong with this theory. If 'God does not exist' is true, then we may ask: what makes it true? What is the truthmaker of this truth? The most natural answer is that extralinguistic reality makes it true, more precisely, the fact that reality contains nothing that could be referred to as God. There is nothing linguistic about this truthmaker. Of course, if 'God does not exist' is true, then 'God' does not refer to anything, and if 'God' does not refer to anything then the sentence 'God does not exist' is true. But the wholly nonlinguistic fact of God's nonexistence is not identical to the partially linguistic fact of 'God''s not referring to anything. Why not? Consider the following modal argument:
1. God's nonexistence, if it obtains, obtains in every possible world.
2. The fact of 'God''s not referring to anything obtains in only some
possible worlds. (Because the English language exists in only some
worlds.)
Therefore
3. The two facts are distinct.
The argument just given assumes in its initial premise Anselm's Insight: if God exists, then he necessarily exists, and if he does not, then he is impossible. But I don't need this assumption. I can
argue as follows:
5. God's nonexistence, if it obtains, obtains in some possible worlds.
6. Among these possible worlds, some are worlds in which English does
not exist.
Therefore
7. There is at least one world in which neither God nor the English
language exists, which implies that God's nonexistence in that world
cannot have as truthmaker any fact involving the name 'God.'
Let me put it another way. If 'God does not exist' is true, then the same fact can be expressed in German: 'Gott existiert nicht.' This is one fact expressible in two different languages. But the fact of
'God''s not referring to anything is a different fact from the fact of 'Gott''s not referring to anything. The facts are different because they involve different word-types. Therefore, neither fact can be
identical to the fact of God's nonexistence.
Since the two facts are different, the wholly nonlinguistic fact of God's nonexistence cannot have as a truth-condition the partially linguistic fact of the history of uses of 'God' ending in a block, contrary to what Donnellan says. If one assertively utters 'God does not exist,' and if what one says is true, then extralingustic reality must be a certain way: it must be godless. This godlessness of reality, if it indeed obtains, cannot be tied to the existence of any contingent language like English.
Note that the descriptivist need not fall into Donnellan's trap. When he assertively utters 'God does not exist' he says in effect that all or most of the properties associated with the use of 'God' — such
properties as omniscience, etc. — are not instantiated: nothing in extralinguistic reality has them. Since these properties can be viewed as having an objective, extralinguistic existence, the descriptivist needn't tie the existence/nonexistence of God to the existence of any contingent language.
What is (linguistic) reference? Is it a relation? Edward the Ockhamist assumes that it is and issues the following request: "To clarify, could I ask both you and Bill whether you think the reference relation is ‘internal’ or ‘external’?"
Here is an inconsistent tetrad:
1. 'Frodo' refers to Frodo
2. 'Frodo' exists while Frodo does not.
3. Reference is a relation.
4. Relations are existence-symmetrical: the terms (relata) of a relation are such that either all exist or none exist.
Since the members of this quartet cannot all be true, which one will Edward reject? Given what he has said already, he must reject (4). But (4) is exceedingly plausible, more plausible by my lights than (1). I myself would reject (1) by maintaining that there is no linguistic reference to the nonexistent. It is not there to be referred to!
For me, reference is a relation. Is it internal or external? Being the same color as is an example of an internal relation. If a and b are both red, then that logically suffices for a and b to stand in the same color as relation. Suppose I paint ball a red and then paint ball b (the same shade of) red; I don't have to do anything else to bring them into the aforementioned relation. You could say that an internal relation supervenes upon the intrinsic properties of its relata.
But to bring the two balls into the relation of being two feet from each other, I will most likely have to do more than alter their intrinsic properties. So being two feet from is an external relation. If the balls fall out of that relation they needn't change in any intrinsic respect. But if the balls cease to stand in the same color as relation, then they must alter in some intrinsic respect.
In sum, internal relations supervene on the intrinsic properties of their relata while external relations do not.
Suppose 'Max' is the name of my cat. Then 'Max' as I use it has a definite meaning. The sound I make when I say 'Max' and the cat are both physical items. Surely they do not stand in a semantic relation. No physical item by itself means anything. So the semantic relation must connect a meaningful word (a physical item such as a sound or marks on paper 'animated' by a meaning) with the physical referent, the cat in our example. Suppose the meaning (sense, connotation) of 'Max' is given by a definite description: the only black male feline that enjoys linguine in clam sauce. Then the relation between the meaningful word 'Max' and the cat will be external since that meaning (sense, connotation) is what it is whether or not the cat exists.
If, on the other hand, the meaning of 'Max' = Max, then the semantic relation of reference is internal. For then the relation is identity, and identity is an internal relation.
So it seems that whether reference is external or internal depends on whether reference is routed through sense or is direct. I incline toward the view that reference, since routed through sense, is an external relation.