So far, Ed Feser's is perhaps the best of the Internet discussions of this hot-button question, a question recently re-ignited by the Wheaton dust-up, to mix some metaphors. Herewith, some notes on Feser's long entry. I am not nearly as philosophically self-confident as Ed or Lydia McGrew, so I will mainly just be trying to understand the issue for my own edification. But I am sure of one thing: the question is difficult and has no easy solution. If you think it does, then I humbly suggest you are not thinking very hard, indeed, you are hardly thinking.
1. Feser rightly points out that a difference in (Fregean) sense does not entail a difference in (Fregean) reference. So the difference in sense as between 'God of the Christians' and 'God of the Muslims' does not entail that these expressions differ in reference. Quite so. But I would add that on a descriptivist semantics reference is routed through, and determined by, sense: an expression picks out its object in virtue of the latter's unique satisfaction of an identifying 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 whichever entity, if any, that satisfies the definite description encapsulated in 'God' as this term is used in a given linguistic community. So while difference in sense does not by itself entail difference in reference, difference in sense is consistent with difference in reference, so that in a particular case it may be that the difference in sense is sufficiently great to entail a difference in reference. Suppose that in one linguistic community a person understands by 'God' the unique contingent being who created the universe but was himself created, while in another a person understands by 'God' the unique necessary uncreated being who created the universe. In this case I think it is clear that the difference in sense entails a difference in reference. Both uses of 'God' may fail of reference, or one might succeed. But they cannot both succeed. For nothing can be both necessary and contingent.
From what has been said so far, 'God' (used by a Christian) and 'Allah' (used by a Muslim) may have the same reference or may have a different reference. The issue cannot be decided by merely pointing out that a difference in sense does not entail a difference in reference.
2. Feser makes a point about beliefs that is surely correct. You and I can have conflicting beliefs about a common object of successful reference without prejudice to its being precisely a common object of successful reference. For example, we both see a sharp-dressed man across the room drinking from a Martini glass. Suppose I erroneously believe that he is drinking a Martini while you correctly believe that he is drinking water. That difference in belief is obviously consistent with one and the same man's being our common object of perceptual and linguistic reference. "Similarly, the fact that Muslims have what Christians regard as a number of erroneous beliefs about God does not by itself entail that Muslims and Christians are not referring to the same thing when they use the expression 'God.'" (Emphasis added.)
True, but it could also be that conflicting beliefs make it impossible that there be a common object of successful reference. It will depend on what those beliefs are and whether they are incorporated into the respective senses of 'God' as used by Muslims and Christians. I will also depend on one's theory of reference, whether descriptivist, causal, hybrid, or something else.
It should also be observed that in perceptual cases such as the Martini case there is no question but that we are referentially glomming onto one and the same object. The existence and identity of the sharp-dressed drinker are given to the senses. Since we know by direct sensory acquaintance that it is the same man both of us see, the conflicting beliefs have no tendency to show otherwise. But God is not an object of perception via the outer senses. So one can question how much weight we should assign to the perceptual analogies, and indeed to any analogy that makes mention of a physical thing. At best, these analogies show that, in general, contradictory beliefs about a putatively self-same x are consistent with there being in reality one and the same subject of these beliefs. But they are also consistent with there not being in reality one and the same subject of the contradictory beliefs.
But not only is God not an object of sensory acquaintance, he is also arguably not an object among objects or a being among beings. Suppose God is ipsum esse subsistens as Aquinas held. It will then be serious question whether a theory of reference that caters to ordinary references to intramundane people and things, beings, can be extended to accommodate reference to self-subsistent Being. Not clear! But I raise this hairy issue only to set it aside for the space of this entry. I will assume for now that God is a being among beings. I bring this issue up only to get people to appreciate how difficult and involved this 'same God?' issue is. Do not comment on this paragraph; it is off-topic for present purposes. See here for one of the posts in which I disagree with Dale Tuggy on this issue.
3. Now consider these conflicting beliefs: God is triune; God is not triune. Please note that it would be question-begging to announce that the fact of this dispute entails that the object of the dispute is one and the same. For that is exactly what is at issue. The following would be a question-begging little speech:
Look man, we are disputing whether God is triune or not triune; we are therefore presupposing that there is one and the same thing, God, about whose properties we are disputing! The disagreement entails sameness of object! Same God!
This is question-begging because it may be that the tokens of 'God' in "God is triune; God is not triune" differ in sense so radically that they also differ in reference. In other words, the mere fact that one and the same word-type 'God' is tokened twice does not show that there is one and the same object about whose properties we are disputing.
4. Feser writes,
Even errors concerning God’s Trinitarian nature are not per se sufficient to prevent successful reference. Abraham and Moses were not Trinitarians, but no Christian can deny that they referred to, and worshiped, the same God Christians do.
[. . .]
But shouldn’t a Christian hold that some reference to the Trinity or to the divinity of Jesus is also at least necessary, even if not sufficient, for successful reference to the true God? Doesn’t that follow from the fact that being Trinitarian is, from a Christian point of view, also essential to God? No, that doesn’t follow at all, and any Christian who says otherwise will, if he stops and thinks carefully about it, see that he doesn’t really believe that it follows. Again, Christians don’t deny that Abraham and Moses, or modern Jews, or Arians and other heretics, refer to and worship the same God as orthodox Christians, despite the fact that these people do not affirm the Trinity or the divinity of Jesus.
There is a modal fudge across these two passages that I don't think it is mere pedantry on my part to point out. In the first passage Feser claims in effect that
A. No Christian CAN deny that Abraham and Moses worshiped the same God that Christians do
while in the second Feser claims in effect that
B. No Christian DOES deny that Abraham and Moses worshiped the same God that Christians do.
If we charitably substitute 'hardly any' for 'no' in (B) then we get a statement that I am willing to concede is true. (A), however, strikes me as false. I myself am strongly tempted to deny that Jews and Christians worship the same God -- assuming that the Jewish God is non-triune and explicitly determined to be such by Jews -- and what I am strongly tempted to do strikes me as entirely possible and rationally justifiable. Why can't someone reasonably deny that Jews and Christians worship the same God?
Feser thinks he has cited some incontrovertible fact that decides the issue, the fact being that everyone or almost everyone claims that Jews and Christians worship the same God. I concede the fact. What I don't concede is that it decides the issue. My claim against Feser on the present occasion is not that he is wrong to maintain that (normative) Jews, Christians, and Muslims all worship the same God, but that he is not obviously right, his confident asseverations in the passages lately quoted notwithstanding. I am saying to Feser what I said to Beckwith and Tuggy: you gentlemen think this issue easily resolved. But it isn't, in large part because its resolution depends on the solution of hitherto unsolved problems in the philosophy of language.
Here are two questions we ought to distinguish:
Q1. Do Christians use 'God' and equivalents with the intention of referring to the same being that Jews refer to or think they are referring to with 'God' and equivalents?
Q2. Do Christians and Jews succeed in refer to the same being?
An affirmative answer to the first question is consistent with a negative answer to the second question. I agree with an affirmative answer to (Q1). But this affirmative answer does not entail an affirmative answer to (Q2). Moreover, it is reasonable to return a negative answer to (Q2). I will now try to explain how it is reasonable to answer (Q2) in the negative.
5. The crux of the matter is the nature of reference. How exactly is successful reference achieved? And what exactly is reference? And how is worship related to reference?
First off,the causal theory of Kripke, Donnellan, et al. is reasonably rejected and I reject it . It is rife with difficulties. (See e.g., John Searle, Intentionality, Cambridge UP, 1983, ch. 9) Connected with this is my subscription to the broadly logical primacy of the intentional over the linguistic. Part of what this means is that words don't refer, people refer using words, and they don't need to use words to refer. All reference, at bottom, is thinking reference or mental reference. Reference at bottom is intentionality. To refer to something, then, whether with words or without words, is to intend it or think of it. This is to be understood as implying that words, phrases, and the like, considered in their physical being as marks on paper or sounds in the air or carvings in stone (etc.) are entirely lacking in any intrinsic referential, representative, semantic, or intentional character. They are not intrinsically object-directed. There is no object-directedness in nature apart from mind. (Though it may be that dispositionality is an analog of it. See here.) This is equivalent to saying that there is no objective reference without mind. A word acquires reference only when it is thoughtfully used.
Reference to particulars in the sense of 'refer' just explained is always and indeed necessarily reference to propertied particulars. This is because reference to a particular 'picks it out' from all else, singles it out, designates it to the exclusion of everything else. Particulars taken in abstraction from their properties cannot be singled out to the exclusion of all else. To think of a thing or person is to think of it as an instance of certain properties and indeed in such a way as to distinguish it from all else. So, to think of, and thus refer to, a particular is to think of it as an instance of a set of properties that jointly individuate it.
To refer to God, then, is to think of God as an instance of certain properties. I cannot think of God directly as just a particular, and then as instantiating certain properties. This ought to be quite clear from the fact that in this life our (natural) knowledge of God is not by acquaintance but by description. I don't literally see God when I look upwards at "the starry skies above me" or gaze inward at "the moral law within me" to borrow a couple of signature phrases from Immanuel Kant. Our only access to God here below is indirect via his properties, as an instance of those properties. Here below we approach God from the side of his properties as we understand them. The existence and identity of my table is known directly by acquaintance. Not so in the case of God. The existence of God is not given to sense perception but has to be understood as the being-instantiated of certain properties. The God I know by description is God qua uniquely satisfying my understanding of 'God.'
Someone could object: What about mystical experience? Is it not possible in this life to enjoy mystical knowledge by acquaintance of God? This is a very large, and I think separate topic. To the extent that mystical experience leads to mystical union it tends to collapse the I-Thou and man-God duality that is part of the framework of worship as we are discussing it in this context. See my Buber on Buddhism and Other Forms of Mysticism. It also tends to explode the framework in which questions about reference are posed . I mean the framework in which: here is a minded organism with linguistic capacity who thoughtfully utters certain words and phrases while out there are various things to which the organism is trying to refer and often succeeding.
There is also the question of the veridicality of mystical experience. How do I know that an experience of mine is revelatory of something real? How do I know that successive experiences of mine are revelatory of the same thing? How do I know that the mystical experiences of different people are veridically of the same thing? So I suggest we bracket the question of mystical experience.
Any natural knowledge of God in this life, then, is by description. Reference to God is indirect and via the understanding of 'God' within a given religion. Now the orthodox Christian understanding of 'God' is that God sent his only begotten Son, begotten not made, into our predicament to teach us and show us the Way (via, veritas, vita) and to suffer and die for our sins. Together with this contingent Sending goes the triunity of God as the necessary condition of its possibility. This is part of what an orthodox Christian means by 'God,' although I reckon few Christians would put it the way I just did. It is part of the sense of 'God' for an orthodox Christian. But this is not part of the sense of 'God' for the orthodox Muslim who denies the Trinity, the Incarnation, and the soteriology connected with both.
So do Christians and Muslims succeed in referring to the same being? No. Successful reference on a descriptivist semantics requires the cooperation of Mind and World. Successful reference, whether with words or without words, requires that there exist outside the mind something that satisfies the conditions set within the mind. (Remember: it is not primarily words that refer, but minds via words and mental states.) Now suppose there exists exactly one God and that that God is a Trinity. Then the Christian's understanding of 'God' will be satisfied, and his reference to God will be successful. But the Muslim's reference will fail. The reason for this is that there is nothing outside the mind that satisfies his characteristic understanding of 'God.'
Of course, the Muslim could put it the other way around. Either way, my point goes through: Muslim and Christian cannot be referring to the one and the same God.
You say the Christian and Muslim understandings of 'God' overlap? You are right! But this overlap is but an abstraction insufficient to determine an identifying reference to a concrete, wholly determinate, particular. In reality, God is completely determinate. As such, he cannot be neither triune nor not triune, neither incarnated nor not incarnated, etc. in the way the overlapping conception is. So if the triune God exists, then the non-triune God does not exist. Of course, we can say that the Christian and the Muslim are 'driving in the same direction.' Heading West on Interstate 10, I am driving toward the greater Los Angeles area, and thus I am driving toward both Watts and Laguna Niguel. But there is a big difference, and perhaps one pertaining unto my 'salvation,' whether I arrive in Watts or in Laguna Niguel. What's more, I cannot terminate my drive in some indeterminate location. The successful termination of my peregrination must occur at some wholly definite place. So too with successful reference to a concrete particular: it must terminate with a completely determinate referent.
Here is another related objection. "If the Christian God exists, then both Christian and Muslim succeed in referring to the same God -- it is just that this same God is the Christian God, i.e., God as understood in the characteristically Christian way. The existence of the Christian God suffices to satisfy the common Christian-Muslim underdstanding of 'God.'"
In reply I repeat that both mind and world must cooperate for successful reference on a descriptivist semantics. So it is not enough that God exists and that there be exactly one God. Nor is it enough that the one God satisfy the common Christian-Muslim conception; for the Muslim God to be an object of successful reference it must both exist and satisfy the characteristic Muslim understanding of 'God.'
My thesis is a rather modest one. To repeat what I said above:
My claim against Feser on the present occasion is not that he is wrong to maintain that (normative) Jews, Christians, and Muslims all worship the same God, but that he is not obviously right, his confident asseverations in the passages lately quoted notwithstanding. I am saying to Feser what I said to Beckwith and Tuggy: you gentlemen think this issue easily resolved. But it isn't, in large part because its resolution depends on the solution of hitherto unsolved problems in the philosophy of language.