Well, that’s my point you see. Your “argument from fact,” to determine which God Muslim’s worship based upon the “fact” that Muslims worship the God of Abraham yields inconsistent results when used about the fact that Muslims don’t worship that same God who is the God Christians call Jesus. Jesus would call himself the God of Abraham, so do the Jews worship the God of Abraham (their idea of that God) or do they NOT worship the God of Abraham (Jesus)? Your argument seems useless to definitively answer that question, because it can be used to both determine that they do and that they don’t.
Same results when we attempt to use it to determine whether, in fact, Muslims worship the God of Abraham. If the God of Abraham is Jesus, then they clearly do not. In that case, if Jesus is the God of Abraham, and Christians cannot deny that, then since Muslims do not worship Jesus they do not worship the God of Abraham (who actually is Jesus.)
Therefore, since your argument “from fact” yields conflicting results it isn’t a reliable way to determine which God is being worshiped.
The fact that neither Muslims nor Jews worship Jesus who is himself the God of Abraham means they both do and don’t worship the same exact God. So do they or do they not worship that God? It is unclear from your argument from the fact of worship. It is ineffectual as a means to determine that.
Besides, is it the ostensible or nominal “object” of worship or is it the intention of the heart (and the conception of the object of worship) from which the “worship” arises that determines what is worshiped? It would seem that merely using the same identifying name does not necessarily indicate that different worshipers have the same reality in mind as their object of worship. That would need to be accounted for before we go grounding the entire case merely upon the name that is used to refer to what is being worshiped. Merely calling things by the same name does not guarantee anything.
What Americans call “football” is not the same reality as what the Europeans or Latin Americans call “football.” Yet, according to you, merely using the same referent – the God of Abraham – is all that is required to determine that the object of that referent is the same. I don’t think so.
In any case, I am bowing out of this thread for good since I have no interest in going down another rabbit hole.