The question of whether Christians and Muslims worship the same God .
keep in mind the Fregean point that a difference in sense does not entail a difference in reference.
Second, even a speaker’s erroneous beliefs don’t entail that he is not referring to the same thing that speakers with correct beliefs are referring to.
That the errors are “important” or “crucial” is not by itself sufficient to prevent successful reference.
Having said that, it is also true that not anything goes. As I noted some time back in a post about Peter Geach’s essay “On Worshipping the Right God,” it is possible for someone’s body of beliefs about some thing to be so thoroughly disconnected from reality that he cannot plausibly be said successfully to refer to that thing.
Even errors concerning God’s Trinitarian nature are not per se sufficient to prevent successful reference.
The Mormon conception of deity, then, makes of God something essentially creaturelyand finite, something which lacks the absolute metaphysical ultimacy that is definitive of God in Catholic theology and in classical theism more generally. They can plausibly be held not really to be referring to the same thing as the latter, and thus not worshipping the same God as the latter.
Now, say what you will about Islam, it does notmake of God something essentially creaturely. That God is absolutely metaphysically ultimate.
What all this shows is that we need to distinguish between how God has to be and how we have to conceptualize God. What the doctrine of the Trinity entails is that God could not possibly be other than three divine Persons in one substance. But it does not entail that we cannot conceptualize God other than as three divine Persons in one substance.
Hence it is evident that a Catholic saying that an idol is not God contradicts the pagan asserting that it is God.
The idea here is that it is precisely becausethe pagan in question, no less than the Catholic, can understand that “God” signifies that which is the cause of the world, etc. that the Catholic and pagan can genuinely disagree about whether a certain idol is God.
What I have said in this post applies to Christianity and Islam in the abstract and to Christians and Muslims in general. But it is nevertheless still possible that there are particular individualChristians and particular individualMuslims whose personal conceptions of God differ in such a way that they do not plausibly worship the same God