Someone asks how to prove Divine Simplicity without needing to defend the entire First Way.

First, some terms. The notion of a part is, I think, intuitive enough. 

A fusion or mereological sum is a whole composed of some given parts. For instance, the fusion of all Christmas cakes is a large, scattered chunk of Christmas cake that strikes fear into the hearts of children and dietitians everywhere, and nothing else.

A proper part is a part not identical to its whole. For example, a single Christmas cake is a proper part of the fusion of all Christmas cakes. In contrast, an improper part is identical to its whole. For example, the fusion of all Christmas cakes is an improper part of itself.

An entity composed from proper parts is a composite, whereas an entity with no proper parts is non-composite or simple[1].

Finally, an entity is ontologically ultimate if and only if it doesn't depend on anything else for its existence and everything else depends on it for its existence.

Now for the argument. If God has proper parts, God's proper parts are ontologically required for Him to exist. It is, however, contrary to the Nature of God as ontological ultimate for there to be anything that, on its own, isn't God, but which God requires to exist. Hence, it's contrary to God's Nature as the ontological ultimate for Him to be composed from proper parts. If God isn't composed from proper parts, then He's Simple.

There are also considerations from Perfect Being Theology, but those can wait for another time. Merry Christmas, everyone.


[1]I've assumed there's no good reason to restrict mereological notions to physical things.