Hotting up this week. A more contentious argument! St Thomas knows this and builds slowly. So shall we, by breaking up the chapter over two weeks.
Chapter 42 That God is One
 From what has been shown it is evident that God is one.
 For it is not possible that there be two highest goods, since that which is said by superabundance is found in only one being. But God, as we have shown, is the highest good. God is, therefore, one.
 Again, it has been shown that God is absolutely perfect, lacking no perfection. If, then, there are many gods, there must be many such perfect beings. But this is impossible. For, if none of these perfect beings lacks some perfection, and does not have any admixture of imperfection, which is demanded for an absolutely perfect being, nothing will be given in which to distinguish the perfect beings from one another. It is impossible, therefore, that there be many gods.
Notes Argument  is delightful. And it shows, albeit indirectly, that all those religious systems peopled with multitudes of gods must (as they of course do) acknowledge their gods fall short of perfection, and that even this demi-dieties must look to something higher than themselves. And this higher thing can only be God.
 Again, that which is accomplished adequately through one supposition is better done through one than through many. But the order of things is the best it can be, since the power of the first cause does not fail the potency in things for perfection. Now, all things are sufficiently fulfilled by a reduction to one first principle. There is, therefore, no need to posit many principles.
Notes I’ve lost the link to an article which shows that Ockham is not the originator of his razor. If I rediscover it, I’ll put it here.
 Moreover, it is impossible that there be one continuous and regular motion from many movers. For, if they move together, none of them is a perfect mover, but all together rather take the place of one perfect mover. This is not befitting in the first mover, for the perfect is prior to the imperfect. If, however, they do not move together, each of them at times moves and at times does not. It follows from this that motion is neither continuous nor regular. For a motion that is continuous and one is from one mover. Furthermore, a mover that is not always moving is found to move irregularly, as is evident among lesser movers among whom a violent motion is stronger in the beginning and weaker at the end, whereas a natural motion proceeds conversely. But, as the philosophers have proved, the first motion is one and continuous. Therefore, its first mover must be one.
 Furthermore, a corporeal substance is ordered to a spiritual substance as to its good. For there is in the spiritual substance a fuller goodness to which the corporeal substance seeks to liken itself, since whatever exists desires the best so far as this is possible. But all the motions of the corporeal creature are seen to be reduced to one first motion, beyond which there is no other first motion that is not in some way reduced to it. Therefore, outside the spiritual substance that is the end of the first motion, there is none that is not reduced to it. But this is what we understand by the name of God. Hence, there is only one God.
Notes Once more, I beg you will review Chapter 13. Motion means change, and the start of every here-and-now change must have an impetus. This is God. Thomas emphasizes that they’re cannot be two or more first causes. Since there can only be one, it must be God, who is one.
 Among all the things that are ordered to one another, furthermore, their order to one another is for the sake of their order to something one; just as the order of the parts of an army among themselves is for the sake of the order of the whole army to its general. For that some diverse things should be united by some relationship cannot come about from their own natures as diverse things, since on this basis they would rather be distinguished from one another. Nor can this unity come from diverse ordering causes, because they could not possibly intend one order in so far as among themselves they are diverse. Thus, either the order of many to one another is accidental, or we must reduce it to some one first ordering cause that orders all other things to the end it intends. Now, we find that all the parts of this world are ordered to one another according as some things help some other things. Thus, lower bodies are moved by higher bodies, and these by incorporeal substances, as appears from what was said above. Nor is this something accidental, since it takes place always or for the most part. Therefore, this whole world has only one ordering cause and governor. But there is no other world beyond this one. Hence, there is only one governor for all things, whom we call God.
Notes Take time to digest this. It doesn’t quite stand on its own but is a sort of corollary to the prime mover argument (Chapter 13 again). It still holds if we are part of a “multiverse” or whatever. Something has to be at the base of all. That is, if there is an ordering, there must be a hierarchy which is objective. That hierarchy must have an end and (to make it short) this is God.
 Then, too, if there are two beings of which both are necessary beings, they must agree in the notion of the necessity of being. Hence, they must be distinguished by something added either to one of them only, or to both. This means that one or both of them must be composite. Now, as we have shown, no composite being is through itself a necessary being. It is impossible therefore that there be many beings of which each is a necessary being. Hence, neither can there be many gods.
Notes Simple! But what about this whole Trinity (get it? get it?) thing? We come to it, but a way down the road.