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.His examples bring out, in my view, the problem with description theories of singular reference. Suppose that, according to religion A1, there is one god who satisfies the uniquely applying description F1. And suppose that, according to religion A2, there is one god who satisfies the uniquely applying description F2. And suppose, for sake of argument, that F1 and F2 are contraries. Nothing can be both F1 and F2 (Bill's example is 'unitarian' and 'triune'. Then if religion A1 is correct, there is exactly one F1 and (from the logical properties of F1) there can be no being that satisfies F2. Conversely, if religion A2 is correct, there is exactly one F2, and there can be no being that is F1. According to a description theory, neither god can be identical with the other, if either exists.
But now suppose that both religions have the same ‘core’ holy book B, which refers to one god by name G, but which gives no uniquely defining property for that god. However, at some point in the past there was a disagreement over some heresy, and each religion now has a different supplementary holy book – B1 in the case of religion A1, and B2 in the case of religion A2. It is from these supplementary texts that the disagreement over the uniquely defining properties F1 and F2 arises. But both texts refer to god using the same name G as the core book B. Thus the intended or purported reference of G is the same for both competing religions. The disagreement is not about the identity of the purported referents of G – for these have to be one and the same being – but rather the properties F1 and F2. Both religions agree they are worshipping one and the same god, but they disagree about whether he has the uniquely defining F1 (in the case of A1) or the uniquely defining F2 (in the case of A2).
Something like this clearly holds for Judaism and Christianity. The purported referent of ‘YHWH’ is the same for both Christians and Jews. That is a logical conclusion from the semantics of the Old and New Testament names. You will not understand the New Testament unless you understand that the names 'God' and 'Lord' are meant to refer to the intended referent of 'YHWH' in the Old Testament. But the properties are different. Christians hold that YHWH had a son, who is one and the same god as YHWH, but a different person. Jews do not hold this belief. So a description theory has the god of the Jews and the god of the Christians as being numerically different. But a reference theory (which holds that identity is determined by intended identity or intended referent) has them as being the same.
I do not know much about Islam, but I believe that the Islamic holy books are the records which Muslims believe were dictated by God to various Islamic prophets throughout the history of mankind. I.e. Moses (according to Muslims) was an Islamic prophet. Since Christians, Jews and Muslims agree that YHWH gave the laws to Moses, the intended reference of ‘YHWH’ is the same for all. I.e. if YHWH exists, all three religions are referring to him, even though they disagree fundamentally, and bitterly, about his properties. E.g. Christians believe YHWH he has a son in Jesus. Muslims believe he has a prophet in Jesus, Jews disagree with both of these things, believing Jesus to have been a heretic and a blasphemer, for which reason he was executed.