Rowan Williams responded to the Common Word letter from several dozen Muslim scholars, and there is a very nice section in his response about the Trinity, which follows:
Because God exists in this threefold pattern of interdependent action, the relationship between Father, Son and Holy Spirit is one in which there is always a ‘giving place’ to each other, each standing back so that the other may act. The only human language we have for this is love: the three dimensions of divine life relate to each other in self-sacrifice or self-giving. The doctrine of the Trinity is a way of explaining why we say that God is love, not only that he shows love.
That having been said, need I mention that inter-religious dialogue only happens in places where Muslims are a minority? Islam, in the end I suspect, has no use for such dialogue.
I have written about this topic in Islam and the Other Religions.
