Francis Beckwith and Dale Tuggy, two philosophers I respect, answer in the affirmative in recent articles. While neither are obviously wrong, neither are obviously right either, and neither seem to appreciate the depth and difficulty of the question. In all fairness, though, the two articles in question were written for popular consumption.
Beckwith begins with an obvious point: from a difference in names one cannot validly infer a difference in nominata. 'Muhammad Ali' and 'Cassius Clay,' though different names, refer to the same person. The same goes for 'George Orwell' and 'Eric Blair.' They refer to the same writer. So from the difference of 'Yahweh' and 'Allah' one cannot infer that Yahweh and Allah are numerically different Gods. Similarly, with 'God' and 'Allah.' Difference in names is consistent with sameness of referent. But difference in names is also consistent with difference of referents, a point that Beckwith does not make. 'Trump' and 'Obama' are different names and they refer to different people. 'Trump' and 'Zeus' are different names but only one of them refers, which implies that they do not have the same referent. It may be that 'God' and 'Allah' are like 'Trump' and 'Zeus' or like 'Trump' and 'Pegasus.'
Another obvious point Beckwith makes is that if some people have true beliefs about x, and other people have false beliefs about x, it does not follow that there is no one x that these people have true and false beliefs about. Suppose Sam believes (falsely) that Karl Marx is a Russian while Dave believes (truly) that he is a German. That is consistent with there being one and same philosopher that they have beliefs about and are referring to. Now suppose God is triune. Then (normative) Christians have the true belief that God is triune while (normative) Muslims have the false belief that God is not triune. This seems consistent with there being one God about whom they have different beliefs but to whom they both refer and worship. But it is also consistent with a difference in referent. It could be that when a Christian uses 'God' he refers to something while a Muslim refers to nothing when he uses 'Allah.'
Of course, both Christian and Muslim intend to refer to something real with their uses of 'God' and 'Allah.' But the question is whether they both succeed in referring to something real and whether that thing is the same thing. It could be that one succeeds while the other fails. And it could be that both succeed but succeed in referring to different items.
Consider God and Zeus. Will you say that the Christian and the ancient Greek polytheist worship the same God except that the Greek has false beliefs about their common object of worship, believing as he does that Zeus is a superman who lives on a mountain top, literally hurls thunderbolts, etc.? Or will you say that there is no one God that they worship, that the Christian worships a being that exists while the Greek worships a nonexistent object? And if you say the latter, why not also say the same about God and Allah, namely, that there is no one being that they both worship, that the Christian worships the true God, the God that really exists, whereas Muslims worship a God that does not exist?
And then there is the God of the orthodox Christian and the Deus sive Natura of Spinoza. Would it make sense to say that the orthodox Christian and the Spinozist worship the same God? Would it make sense for the orthodox Christian to give this little speech:
We and the Spinozists worship the same God, the one and only God, but we have different beliefs about this same God. We Christians believe (truly) that God is a transcendent being who could exist without having created anything, whereas Spinozists believe (falsely) that God is immanent and could not have existed without having created anything. Still and all, we and the Spinozists are referring to and worshiping exactly the same God.
Are the Christians and the Spinozists referring to one and the same being and differing merely about its attributes? I say No! The conceptions of deity are so radically different that there cannot be one and the same item to which they both refer when they say 'God' or Deus. (Deus is Latin for 'God.')
This is blindingly obvious in the case of the orthodox Christian versus the Feuerbachian. They both talk and write about God. Do they refer to one and same being with 'God' or 'Gott' and differ merely on his attributes? This is impossible. For the Feuerbachian, God is an unconsciously projected anthropomorphic projection. For the orthodox Christian, God is no such thing: he exists in reality beyond all human thoughts, desires, projections. It's the other way around: Man is a theomorphic projection. The characteristic Feuerbachian thesis, although it appears by its surface structure to be a predication ascribing a property to God, namely, the property of being an unconsciously projected anthropomorphic projection, is really a negative existential proposition equivalent to 'God does not exist.' Compare: 'Sherlock Holmes is a purely fictional item.' Is this at logical bottom a predication? Pace Meinong, it is not: in its depth structure it is a negative existential equivalent to 'Sherlock Holmes does not exist.' To be precise, it entails the latter. For it also conveys that the character Holmes figures in an extant piece of fiction which of course does exist.
To sum up the main point: there are concepts so radically different that they cannot be concepts of one and the same thing. Some people say that thoughts, i.e., acts or episodes of thinking, are brain states. Others object: "Thoughts are intentional or object-directed, whereas no physical state is object-directed; hence, no thought is a brain state." This is equivalent to maintaining that the concept intentional state and the concept physical state cannot be instantiated by one and the same item. So it cannot be the case that the mind-brain identity theorist and I are referring to the same item when I refer to my occurrent desiring of a double espresso.
Dale Tuggy writes,
Christians and Muslims disagree about whether God has a Son, right? Then, they’re talking about the same (alleged) being. They may disagree about “who God is” in the sense of what he’s done, what attributes he has, how many “Persons” are in him, and whether Muhammad was really his Messenger, etc. But disagreement assumes one subject-matter – here, one god.
I think Tuggy is making a mistake here. Surely disagreement about the properties of a putatively self-same x does not entail that there is in reality one and the same x under discussion, although it is logically consistent with it.
A dispute between me and Ed Feser, say, about whether our mutual acquaintance Tuggy has a son no doubt presupposes, and thus entails, that there is one and the same man whom we are talking about. It would be absurd to maintain that there are two Tuggys, my Tuggy and Ed's where mine has a son and Ed's does not. It would be absurd for me to say, "I'm talking about the true Tuggy while you, Ed, are talking about a different Tuggy, one that doesn't exist. You are referencing, if not worshipping, a false Tuggy." Why is this absurd? Because we are both acquainted with the man ('in the flesh,' by sense-perception) and we are arguing merely over the properties of the one and the same man with whom we are both acquainted. There is simply no question but that he exists and that we are both referring to him. The dispute concerns his attributes.
But of course the situation is different with God. We are not acquainted with God: God, unlike Tuggy, is not given to the senses. Mystical intuition and revelation aside, we are thrown back upon our concepts of God. And so it may be that the dispute over whether God is triune or not is not a dispute that presupposes that there is one subject-matter, but rather a dispute over whether the Christian concept of God (which includes the sub-concept triune) is instantiated or whether the Muslim concept (which does not include the subconcept triune) is instantiated. Note that they cannot both be instantiated by the same item similarly as the concept object-directed state and the concept physical state cannot be instantiated by one and the same item such as my desiring an espresso.
The point I am making against both Beckwith and Tuggy is that it is not at all obvious which of the following views is correct:
V1: Christian and Muslim can worship the same God, even though one of them must have a false belief about God, whether it be the belief that God is unitarian or the belief that God is trinitarian.
V2: Christian and Muslim must worship different Gods precisely because they have mutually exclusive conceptions of God. So it is not that one of them has a false belief about the one God they both worship; it is rather that one of them does not worship the true God at all.
There is no easy way to decide rationally between these two views. We have to delve into the philosophy of language and ask how reference is achieved. How do linguistic expressions attach or apply to extralinguistic entities? How do words grab onto the (extralinguistic) world? In particular, how do nominal expressions work? What makes my utterance of 'Socrates' denote Socrates rather than someone or something else? What makes my use of 'God' (i) have a referent at all and (ii) have the precise referent it has?
It is reasonable to hold, with Frege, Russell, Searle, and many others, that reference is routed through, and determined by, sense: an expression picks out its object in virtue of the latter's unique satisfaction of a description associated with the referring expression, a description that unpacks the expression's sense. If we think of reference in this way, then 'God' refers to whatever entity, if any, that satisfies the definite description encapsulated in 'God' as this term is used in a given linguistic community.
Given that God is not an actual or possible object of (sense) experience, this seems like a reasonable approach to take. The idea is that 'God' is a definite description in disguise so that 'God' refers to whichever entity satisfies the description associated with 'God.' The reference relation is then one of satisfaction. A grammatically singular term t refers to x if and only if x exists and x satisfies the description associated with t. Now consider two candidate definite descriptions, the first corresponding to the Muslim conception, the second corresponding to the Christian.
D1: 'the unique x such that x is omnipotent, omniscient, omnibenevolent, created the world ex nihilo and is unitarian'
D2: 'the unique x such that x is omnipotent, omniscient, omnibenevolent, created the world ex nihilo, and is triune.'
Suppose that reference is not direct, but routed through sense, or mediated by a description, in the manner explained above. It is easy to see that no one entity can satisfy both (D1) and (D2). For while the descriptions overlap, nothing can be both unitarian and triune. So if reference is routed through sense, then Christian and Muslim cannot be referring to the same being. Indeed, one of them is not succeeding in referring at all. For if God is triune, nothing in reality answers to the Muslim's conception of God. And if God is unitarian, then nothing in reality answers to the Christian conception.
And so, contrary to what Miroslav Volf maintains, the four points of commonality in the Christian and Muslim conceptions do NOT "establish the claim that in their worship of God, Muslims and Christians refer to the same object." (Allah: A Christian Response, HarperCollins 2011, p. 110.) The four points are:
a. There is exactly one God.
b. God is the creator of everything distinct from himself.
c. God is transcendent: he is radically different from everything distinct from himself.
d. God is good.
For if reference to God is mediated by a conception which includes the subconcept triune or else the subconcept unitarian, then the reference cannot be to the same entity. And this despite the conceptual overlap represented by (a)-(d).
A mundane example (adapted from Saul Kripke) will make this more clear. Sally sees a handsome man at a party standing in the corner drinking a clear bubbly liquid from a cocktail glass. She turns to her companion Nancy and says, "The man standing in the corner drinking champagne is handsome!" Suppose the man is not drinking champagne, but mineral water instead. Has Sally succeeded in referring to the man or not?
Argumentative Nancy, who knows that no alcohol is being served at the party, and who also finds the man handsome, says, "You are not referring to anything: there is no man in the corner drinking champagne. The man is drinking mineral water or some other bubbly clear beverage. Nothing satisfies your definite description. There is no one man we both admire. Your handsome man does not exist, but mine does."
Now in this example what we would intuitively say is that Sally did succeed in referring to someone using a definite description even though the object she succeeded in referring to does not satisfy the description. Intuitively, we would say that Sally simply has a false belief about the object to which she is successfully referring, and that Sally and Nancy are referring to and admiring the very same man.
But note how this case differs from the God case. Both women see the man in the corner. But God is not an object of possible (sense) experience. We don't see God in this life. Hence the reference of 'God' cannot be nailed down perceptually. A burning bush is an object of possible sense experience, and God may manifest himself in a burning bush; but God is not a burning bush, and the referent of 'God' cannot be a burning bush. The man in the corner that the women sees and admire is not a manifestation of a man, but a man himself.
Given that God is not literally seen or otherwise sense-perceived in this life, then, apart from mystical experience and revelation, the only way to get at God is via concepts and descriptions. And so it seems that in the God case what we succeed in referring to is whatever satisfies the definite description that unpacks our conception of God.
My tentative conclusion, then, is that (i) if we accept a description theory of names, the Christian and Muslim do not refer to the same being when they use 'God' or 'Allah' and (ii) that a description theory of names is what we must invoke given the non-perceivability of God. Christian and Muslim do not refer to the same being because no one being can satisfy both (D1) and (D2) above: nothing can be both triune and not triune any more than one man can both be drinking champagne and not drinking champagne at the same time.
If, on the other hand, 'God' is a logically proper name whose reference is direct and not routed through sense or mediated by a definite description, then what would make 'God' or a particular use of 'God' refer to God? If names are Millian tags, we surely cannot 'tag' God in the way I could tag a stray cat with the name 'Mungo.'
One might propose a causal theory of names.
The causal theory of names of Saul Kripke et al. requires that there be an initial baptism of the target of reference, a baptism at which the name is first introduced. This can come about by ostension: Pointing to a newly acquired kitten, I bestow upon it the moniker, 'Mungojerrie.' Or it can come about by the use of a reference-fixing definite description: Let 'Neptune' denote the celestial object responsible for the perturbation of the orbit of Uranus. In the second case, it may be that the object whose name is being introduced is not itself present at the baptismal ceremony. What is present, or observable, are certain effects of the object hypothesized. (See Saul Kripke Naming and Necessity, Harvard 1980 p. 79, n. 33 and p. 96, n. 42.)
As I understand it, a necessary condition for successful reference on the causal theory is that a speaker's use of a name be causally connected (either directly or indirectly via a causal chain) with the object referred to. We can refer to objects only if we stand in some causal relation to them (direct or indirect). So my use of 'God' refers to God not because there is something that satisfies the definite description or Searlean disjunction of definite descriptions that unpack the sense of 'God' as I use the term, but because my use of 'God' can be traced back though a long causal chain to an initial baptism, as it were, of God by, say, Moses on Mt. Sinai.
A particular use of a name is presumably caused by an earlier use. But eventually there must be an initial use. Imagine Moses on Mt. Sinai. He has a profound mystical experience of a being who conveys to his mind such exogenic locutions as "I am the Lord thy God; thou shalt not have false gods before me." Moses applies 'God' or 'YHWH' to the being he believes is addressing him in the experience. But what makes the name the name of the being? One may say: the being or an effect of the being is simply labelled or tagged with the name in an initial 'baptism.'
But a certain indeterminacy seems to creep in if we think of the semantic relation of referring as explicable in terms of tagging and causation (as opposed to in terms of the non-causal relation of satisfaction of a definite description encapsulated in a grammatically proper name). For is it the (mystical) experience of God that causes the use of 'God'? Or is it God himself who causes the use of 'God'? If the former, then 'God' refers to an experience had by Moses and not to God. Surely God is not an experience. But if God is the cause of Moses' use of 'God,' then the mystical experience must be veridical. (Cf. Richard M. Gale, On the Nature and Existence of God, Cambridge UP, 1991, p. 11.)
So if we set aside mystical experience and the question of its veridicality, it seems we ought to adopt a description theory of the divine names with the consequences mentioned in (i) above. If, on the other hand, a causal theory of divine names names is tenable, and if the causal chain extends from Moses down to Christians and (later) to Muslims, then a case could be made that Jews, Christians, and Muslims are all referring to the same God when they use 'God' and such equivalents as 'Yahweh' and 'Allah.'
So it looks like there is no easy answer to the title question. It depends on the resolution of intricate questions in the philosophy of language.