I missed an excellent post by our friend the Maverick Philosopher back in January:
…if the proper parts of a cat can be feline in the very same sense in which the cat is feline, without themselves being cats, then we have an analogy that renders intelligible the claim that the Persons of the Trinity are divine without being Gods. The picture is this: God or the Godhead or the Trinity is a whole the proper parts of which are exactly the Father, the Son, and the Holy Spirit. The Persons are distinct among themselves, but each is divine in virtue of being a proper part of God. There is one God in three divine Persons. The mereological model allows us to avoid tritheism and to affirm that God is one and three without contradiction.
Bill doesn’t think it works… read on. Don’t forget that the Maverick often philosophizes about the Trinity. And the Maverick is always worth hearing out.
Here’s an old trinities post on what Bill’s talking about above – the rational reconstruction of Trinity formulas by Moreland and Craig.
We could add that if one wants to be a classical trinitarian, as some but by no means all trinitarians want to be, then one must reject this approach. The ancient version of trinitarian affirms divine simplicity – that in God there are no multiple anythings, including any parts. Bill has an excellent free piece on that too.