The Qur’an claims that God is non-triune and non-incarnated, doesn’t that make their God fundamentally different than the God of Christianity?
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YHVH in the Jewish tradition is non-triune and non-incarnated (the expected Jewish Messiah was ‘anointed’ of YHVH, not conceived by YHVH). These are the exact properties which Leithart uses to claim that the ‘Muslim God’ is fundamentally different from the ‘Christian God’, and therefore does not exist.
So, if the ‘Muslim God’ does not exist because of these attributes, then the ‘Jewish God’ does not exist because of these attributes. Which means that YHVH (being non-existent) could not have incarnated, nor inspired any of the Judeo-Christian Scriptures. Which means that Christianity is false. It also gives us a bit of trouble with the Incarnated Christ being a practicing Jewish rabbi.
If we give Jews a pass and state that their understanding of God is incomplete because they do not understand the nature of God as revealed through the incarnation of the Logos as the Christ, then we must give the same pass to the Muslims, who understand the same attributes of God as the Jews.
Finally, there is the simple fact that there CANNOT be more than one God. God is not ‘a god’, some supernatural anthropomorphism among many. God is the metaphysical First Cause of reality. If Christianity is the perfect revelation of God’s nature, that does not mean that Brahman, Allah, or the Dao are ‘false Gods’; they are simply the attempt of other human beings–made in the image of and with the longing for God–to understand God without that perfect revelation. In many cases, they are very sophisticated and worth the study.
Where we find ‘false God’ is when people use God as ‘a god’–just a super-powerful person, who happened to make the universe. Because when this happens, people start to think that God WANTS things (which disqualifies their idea as God, since God is perfect and by definition wants nothing). And what they think God wants, always looks an awful lot like what THEY want.
Which is how we have Baptist preachers telling people that the Christ turned water into “red wine vinegar” at that wedding, because Christians shouldn’t drink. And how we have Muslims slaughtering their way around the world, because God “wants them to.” It is the same error, the same pride. The Muslims have just taken it to the furthest extreme.