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In the chapter in Summa Theologica on the simplicity of God, Aquinas says the following in arguing that God is not composite:
... in every composite there must be potentiality and actuality; but this does not apply to God; for either one of the parts actuates each other, or at least all of the parts are potential to the whole.
What does he mean by this, and why does he say it?
See the first of the 24 Thomistic Theses:
Potentia et actus ita dividunt ens, ut quidquid est, vel sit actus purus, vel ex potentia et actu tamquam primis atque intrinsecis principiis necessario coalescat.
Potency and Act so divide being that whatsoever exists either is a Pure Act, or is necessarily composed of Potency and Act, as to its primordial and intrinsic principles.
Commentary by Pedro Lumbreras, O.P.:
Every actual subsisting being—inanimate bodies and animals, men and angels, creatures and Creator—must be either Pure Act—a perfection which is neither the complement of Potency, nor the Potency which lacks further complement—or Potency mixed with Act—something capable of perfection and some perfection fulfilling this capacity. This statement is true both in the existential and in the essential order. In each of these orders the composition of Act and Potency is that of two real, really distinct principles, as Being itself; intrinsic to the existing being or to its essence; into which, finally, all other principles can be resolved, while they cannot be resolved into any other. [Summa Theologiae, Iª q. 77 a. 1; Sententia Metaphysicae, lib. 7 l. 1 et lib. 9 l. 1 et l. 9]
cf. also Edouard Hugon, O.P.'s commentary: Les vingt-quatre theses thomistes or Garrigou-Lagrange, O.P.'s short The Essence & Topicality of Thomism.
There are a lot of historical perspectives already given. But setting aside the history, this still makes sense outside the context of Aristotle.
From a sort of mathematical view, a composite entity has a set of parts that could have been the parts of a different configuration had things gone differently.
When they are taken as parts, with other options for deployment, they only potentially make up the composite that they happen to make up. They are potentially also parts of something else.
And yet they are actually parts of what they happen to constitute.
But if God is inevitable, or if he existed before time created alternative possibilities, or if any of a range of other assertions about him that the Catholic theology in which Aquinas is embedded asserts are true, then the things that make Him up could not possibly have come together in any other way. His parts do not have a potentiality to have been otherwise, there is only actuality involved.
In every composite there must be actuality and potentiality; but this does not apply to God
Aquinas is commentating on Christian theology following Aristotles theory of change, elaborated in his Physics; so it might help elucidating Aquinas by looking at Aristotle first.
Now A says that for something to change, it must have parts, and so it must be a composite; change also occurs through potentiality and actuality (this is A's solution to the paradox of Parmenides/Zeno. This might sound bizarre from the perspective of todays physics but note that for motion to occur in a gravitational or electromagnetic field, potential energy is converted to kinetic energy; or more fundamentally, in QM, the wave function (potentiality) is collapsed into actuality (measurement)).
However, God does not change being perfect; and so none of this applies to Him.
I haven't read the book, but I believe what he says is that the 'trinity' is not a composite - i.e. you don't need the Holy Spirit, Jesus AND God (father) to become God - i.e. Jesus is God, Holy Spirit is God and God is God - God has manifested himself in these three forms.
I base this on the composite VIDEO signal:
TV was first black and white. So, TV stations only had to transmit the levels of white (black is zero - for arguments sake -some signals were inverse, i.e. white was zero).
Anyway, when Colour was introduced there had to be a way to transmit color as well as be compatible with back and white TVs (people would not watch colour if they had to throw away their B&W TVs, right?).
So, the method was to send the normal black and white signal (called luminance) and send the colour information (called chrominance) 'separately' so that black and white TVs would understand the luminance but colour TVs aware of the crominance would 'look' for it and process it. If a chrominance signal was not availabe the colour TV would run in B&W mode. The 3rd part of the signal is the sound.
So, in composites, the colour signal alone is useless, the B&W signal alone is useless and the sound signal alone is useless (i.e. you don't get the full picture).
But with God, each of the holy trinity are independent but are also one. You get the total 'picture' either independently or as a trinity.
I am not saying St. Thomas Aquinas is right (I believe his analysis is meritorious), what I am trying to do is breakdown the explanation of (possibly) what he meant or to give you a better understanding...
Trust this helps.
