Each of the following three propositions strikes me as very reasonably maintained. But they cannot all be true.
A. Worship Entails Reference: If S worships x, then S refers to x.
B. Reference Entails Existence: If S refers to x, then x exists.
C. Worship Does Not Entail Existence: It is not the case that if S worships x, then x exists.
It is easy to see that the triad is inconsistent. The conjunction of any two limbs entails the negation of the remaining one. For example, (A) and (B), taken in conjunction, entail the negation of (C).
What makes the triad a very interesting philosophical problem, however, is the fact that each of the constituent propositions issues a very strong claim on our acceptance. I am inclined to say that each is true. But of course they cannot all be true if they are logically inconsistent, which they obviously are.
Why think that each limb is true?
Ad (A): While there is much more to worship than reference, and while reference to a god or God can take place without worship, it is surely the case that whatever one worships one refers to, whether publicly or privately, whether in overt speech or in wordless thought.
Ad (B): Unless we make a move into Meinong's jungle, it would seem that reference is reference to what exists. There are different ways for reference to fail, but one way is if the referent does not exist. Suppose I think Scollay Square still exists. Trying to say something true, I say, 'Scollay Square is in Boston.' Well, I fail to say something true because of the failure of reference of 'Scollay Square.' My sentence is either false or lacks a truth-value. Now if one way for a reference to fail is when the referent does not exist, then reference entails existence.
Here is a second consideration. Philosophers often speak of reference as a word-world relation. Better: it is a relation between a word of phrase thoughtfully deployed by a person and something that exists extralinguistically. But surely if a genuine relation R holds, then each of R's relata exists. In the dyadic case, if x stands in R to y, then both x and y exist. A weaker principle is that of existence-symmetry: if x stands in R to y, then either both relata exist or neither exists. Both principles rule out the situation in which one relatum of the reference relation exists and the other doesn't.
So if reference is a genuine relation, and a person uses a word or phrase to refer to something, then the thing in question, the referent, exists. So again it seems that (B) is true and that reference entails existence. If the referent does not exist, then the reference relation does not hold in this case and there is no reference in this case. No referent, no reference. If reference, then referent.
Ad (C): Some say that the Christian God and the Muslim God are the same. But no one this side of the lunatic asylum says that all gods are the same. So at least one of these gods does not exist. But presumably all gods have been worshipped by someone; ergo, being worshipped does not entail existence.
So how do we solve this aporetic bad boy? We have three very plausible propositions that cannot all be true. So it seems we must reject one of them. But which one?
(A) is above reproach. Surely one cannot worship anything without referring to it. And I should think that (C) is obviously true. The idolater worships a false god, something that does not exist. As Peter Geach points out, the idolater does not worship a hunk of gold, say, but a hunk of gold as God, or God as a hunk of gold. But then he worships something that does not exist and indeed cannot exist. The only hope for solving the triad is by rejecting (B). For (B) does not share in the obviousness of (A) and (C). (B) is very plausible but not as plausible as the other two limbs.
London Ed will presumably endorse (B)-rejection as the solution since he is already on record as saying that one can successfully refer to purely fictional (and thus nonexistent) individuals and that one also be confident that it is numerically the same fictional individual to which different people are referring in different ways. Thus if London Ed brings up in conversation the fictional detective who lives on Baker Street, has an assistant named 'Watson,' etc. , then I know he is referring to Sherlock Holmes. And referring successfully. We are talking about one and the same individual. Successful reference thus seems not to require the existence of the referent.
But notice. If there is successful reference to nonexistent individuals, then it would seem that reference is an intentional state just like worshiping is. Or to put the point in formal mode: it would seem that 'refers' is an intentional verb just like 'worship' is. What one worships may or may not exist without prejudice to one's being in a state of worship. On (B)-rejection, what one refers to may or may not exist without prejudice to one's being in the state of referring.
By the way, it is not words that refer, but people using words. Of course, one can say that 'cat' in English refers to furry, four-legged mammals, but that is elliptical for saying that competent English speakers who are using 'cat' in a standard, non-metaphorical, way refer by the use of this word to furry, four-legged mammals. Linguistic reference is grounded in and parasitic upon thinking reference, intentional reference. And not the other way around. Not everyone agrees, of course. (Chisholm and Sellars famously disagreed about this.) This is yet another bone of contention at the base of the Same God? controversy. And one more reason why it is not easily resolved.
Well, suppose that linguistic reference is like mental reference (intentionality) in this respect: just as the intentio is what it is whether or not the intentum exists, the reference is what it is whether or not the referent exists. This makes sense and it solves the above aporetic triad. We simply reject (B).
Now where does my solution to the above triad leave us with respect to the question, Does the Christian and the Muslim worship the same God? My solution implies that they do not worship the same God. For it implies that reference to an individual or particular is not direct but mediated by properties. Let's consider private, unverbalized worship in the form of discursive prayer. Suppose I pray the Jesus Prayer, or some such prayer as 'Lord, grant me light in my moral and intellectual darkness.' Such prayer is on the discursive plane. It is not a matter of infused contemplation or any state of mystical intuition or mystical union. On the discursive plane I have no knowledge of God by acquaintance, and certainly not by sensory acquaintance. My knowledge, if knowledge it is, is by description. I refer to God mentally via properties as that which satisfies, uniquely, a certain identifying description. Obviously, I cannot have God before my mind as a pure, unpropertied particular; I can have God before my mind only as 'clothed' in certain properties, only as an instantiation of those properties.
Now if the properties in terms of which I prayerfully think of God include the property of being triune, and the properties in terms of which a Muslim thinks of God include the property of not being triune, then no one thing can be our common mental referent. For in reality outside the mind nothing can be both triune and not triune.
If you object that there is a common God but that the Muslim has false beliefs about it, then I say you are either begging the question or assuming a causal theory of reference. It is certainly true that different people can have contradictory beliefs about one and the same thing. But if you say that this is the case with respect to the Muslim and Christian Gods, then you assume that there is one God about whom there are contradictory beliefs -- and that is precisely to beg the question. This is the very mistake that Beckwith and Tuggy and others make.
If, on the other hand, you are assuming a casual theory of reference, then how will you solve my triad above? Besides, you take on board all the problems of the casual theory. The notion that reference can be explained by causation is a very questionable one, about which I will have more to say later.