One morning an irate C-Span viewer called in to say that he prayed to the living God, not to the mythical being, Allah, to whom Muslims pray. The C-Span guest made a standard response, which is correct as far as it goes, namely, that Allah is Arabic for God, just as Gott is German for God. He suggested that adherents of the three Abrahamic religions (Judaism, Christianity, Islam) worship the same God under different names. No doubt this is a politically correct thing to say, but is it true?
Our question, then, is precisely this: Does the normative Christian and the normative Muslim worship numerically the same God, or numerically different Gods? (By 'normative Christian/Muslim' I mean an orthodox adherent of his faith who understands its content, without subtraction and without addition of private opinions.) Islam and Christianity are both monotheistic. So if Christian and Muslim worship different Gods, then one is worshipping a nonexistent God, or, if you prefer, is failing to worship the true God.
1. Let's start with the obvious: 'Allah' is Arabic for God. So if an Arabic-speaking Coptic Christian refers to God, he uses 'Allah.' And if an Arabic-speaking Muslim refers to God, he too uses 'Allah.' From the fact that both Copt and Muslim use 'Allah' it does not follow that they are referring to the same God, but it also does not follow that they are referring to numerically different Gods. So we will not make any progress with our question if we remain at the level of words. We must advance to concepts.
2. We need to distinguish between the word for God, the concept (conception) of God, and God. God is not a concept, but there are concepts of God and, apart from mystical intuition, we have no access to God except via our concepts of God. Now it is undeniable that the Christian and Muslim conceptions of God partially overlap. The following is a partial list of what is common to both conceptions:
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 everthing distinct from himself.
d. God is good.
Now if the Christian and Muslim conceptions of God were identical, then we would have no reason to think that Christian and Muslim worship different Gods. But of course the conceptions, despite partial overlap, are not identical. Christians believe in a triune God who became man in Jesus of Nazareth. Or to put it precisely, they believe in a triune God the second person of which became man in Jesus of Nazareth. This is the central and indeed crucial (from the Latin, crux, crucis, meaning cross) difference between the two faiths. The crux of the matter is the cross.
3. Now comes the hard part, which is to choose between two competing views:
V1: Christian and Muslim worship the same God, but one of them has 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 worship different Gods precisely because they have different 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?
4. It is reasonable to hold, with Frege, Russell, and many others, that reference is routed through, and determined by, sense: an expression picks out its object in virtue of the latter's 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 wth 'God.' Now consider two candidate definite descriptions, the first corresponding to the Mulsim 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). 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 tothe 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 listed above 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.) For if reference to God is mediated by a conception which includes the subconcept triune or unitarian, the reference cannot be to the same entity.
A mundane example (adapted from 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 sparkling 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 sparkling water. 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, of Kant's moegliche Erfarhung. Hence the reference of 'God' cannot be nailed down perceptually. And so it seems that what we succeed in referring to is whatever satisfies the definite description that unpacks our conception of God.
5. 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 nonperceivability of God.
If, on the other hand, 'God' is a logically proper name whose meaning is exhausted by its reference, a Kripkean rigid designator, rather than a Russellian definite description in disguise, then what would make 'God' or a particular use of 'God' refer to God?
A particular use 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 locutions as "I am the Lord thy God; thou shalt not have false gods before me." Moses applies 'God' or 'Yahweh' to the being. But what makes the name the name of the being? One may say: the fact that the being or an effect of the being causes the use of the name.
But a certain indeterminacy seems to creep in if we think of the semantic relation of referring as explicable in terms of causation. 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 how can God be the cause of Moses' use of 'God'? Causes are events, God is not an event, so God cannot be a cause.
If these difficulties could be ironed out and a causal theory of 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 opening question. It depends on the resolution of intricate questions in the philosophy of language.