Reading an article on divine production recently moved me to think that God's production of the cosmos--a world peopled by finite creatures other than God--seems perfectly intelligible. We produce things that are non-human (and other than ourselves) all the time, although these productions share in our finitude. But the following propositions are harder to accept fully:
1) God the Father is innascible (unproduced or unborn and not capable of being produced or born).
2) God the Father is the timeless origin and ground of divinity for God the Son (i.e., God eternally produces the Son).
3) God the Son has all of the properties that God the Father "has" with the exception that God the Father is innascible and Father whereas God the Son is produced (eternally generated) and filial/begotten.
4) In Latin Church thinking, God the Father and God the Son produce God the Holy Spirit (i.e., the filioque).
5) The Spirit of God--"who" is also God--is neither innascible nor generated, but spirated by the Father and the Son.
6) Hence, three relations obtain in the triune Godhead: paternity, filiation, and spiration.
7) Thomas Aquinas explains that the Persons are the Relations.
It's still dificult for me to understand how one Person of the triune Godhead produces another. Aquinas and the article I just finished reading say divine production is a mystery that baffles the intellect: it can only be known via divine revelation since it transcends reason (they say).
Even some Trinitarian theologians have questioned divine production on both scriptural and logical grounds.