Before you read the rest of this post, or at least soon after, go watch the video underneath the first point in the attached link. It is only three minutes long and presents the essence of what I want to say with far more clarity.
Augustine’s argument for the practicality of the Trinity is essentially that all Christian ethics derive from love. In John’s letter, we read that ‘God is Love’ (1 John 4:8). We can infer from this passage then that God must be triune because love itself is triune.
- a beloved,
- a lover,
- and the immaterial love that is exchanged or shared between the beloved and the lover.
I think you can correlate which of these in the Trinity we typically associate which attribute with, but I think they all probably apply equally all throughout the Trinity.
To compare, a god such as ‘Allah’ may have the potential to love, but cannot actually love until something else comes into being. You could say, “Allah can love”; but, you cannot say “Allah is love.”
There are five more points in the linked post, but in theory, all derive from the above concept.