Extrapolating these principles, the Hylomorphist concludes that always and everywhere, form (a term that can generally be understood as a property) : matter :: act : potency, and it is on this proportion that all of Aristotelian and Thomistic metaphysics are based. Prime matter, is the first material principle, or a principle that has no existence in itself and is in potency to every form capable of existing in matter.
Take Aquinas's third way as an example.* In a nutshell, this argument says that we know that some things come to be and pass away, so they are able to exist while it is not necessary that they exist. This cannot be true for everything, or nothing would exist, so there must be at least one extant thing which cannot not exist. If there are necessary things that are not necessary of themselves but receive their necessity from another necessary being, then there must be a first necessary being that is necessary of itself and does not receive its necessity from anything. This first necessary being, all men call god.
There are several ways of responding to this argument, but one refutation that is often overlooked is to grant the whole argument while denying only the last premise: Say it is true that there must be a first necessary being, we have no reason to think that this first necessary being would be god.
For a Thomist, this premise is the most obvious part of the argument because of the observations that this post opens with. A necessary being will be the thing that has the most existence, which means that it will be the most perfect, which means that it has all of the perfections of everything else more perfectly than everything else has their perfections.** How could this most perfect thing not be god?
The answer: Because you relied on a refuted assumptions to get to the conclusion that a first necessary thing would be a most perfect thing.
Fill a balloon with hydrogen and light it on fire. The hydrogen and oxygen will combine and become water. The water that results has different properties from any of the three things that went into the change (fire, oxygen and hydrogen), so where did these properties come from? Since it is the fire that puts the change into motion, it would be the agent, and the new properties in the term of the change are supposed to pre-exist in the agent, so fire should have all of the properties of water that are not found in either hydrogen or oxygen.
Another way of looking at this issue is by asking the question, "Why does the water exist?" If hylomorphism were a universally true system of thought, the answer would be "because the form of fire (the agent) was imposed on the matter (hydrogen and oxygen) so that the matter gained the sort of existence the fire (agent) already had.
On the contrary, any new properties that water has, distinct from those properties that hydrogen or oxygen already had, arise on account of the proportions and arrangement of the parts (electrons, protons and neutrons), and those properties, proportions, and arrangements, together with the water itself, all exist because those parts exist. In turn, electrons, protons and neutrons have the properties that they have on account of the proportions and arrangements of their parts, and so forth. Why does a plant do plant things? Because of the proportions and arrangements of its parts, and because its parts exist. Why does an animal do animal things? Because of the proportions and arrangements of its parts, and because its parts exist. Why does a man do man things? Because of the proportions and arrangements of its parts, and because its parts exist.
This all means that in fact, parts are more necessary than the wholes from which they are composed. The wholes come to be and cease to be because the parts arranged in a certain way or left that arrangement. The existence of a whole comes from the existence of its parts.
Now plug this into the third way.
Some things come to be and pass away, so there must be some necessary thing. We should expect that this necessary thing is the most undetermined material principle of anything's existence. If there are several fundamental parts of material things that do not come to be and pass away, and if there is a first among them, this first is totally unformed and never exists on its own. This first necessary being would be prime matter.
Hylomorphism is a hierarchical system, but modern science has turned that hierarchy on its head. God was at the actual/formal beginning of the hierarchy, so now it is at the potential/material, beginning of the hierarchy. As Aquinas says, it is very stupid to call god prime matter. I agree. That's why I'm an atheist.
* The full third way, as found in the Summa Theologica:
The third way is taken from possibility and necessity and runs thus: We find in nature things that are possible to be and not to be, since they are found to be generated and to corrupt, and consequently, they are possible to be and not to be. But it is impossible for these always to exist and not to exist, for that which is possible not to be at some time is not. Therefore, if everything is possible not to be, then at one time there could have been nothing in existence. Now if this were true, even now there would be nothing in existence, because that which does not exist only begins to exist by something already existing. Therefore, if at one time nothing was in existence, it would have been impossible for anything to have begun to exist; and thus even now nothing would be in existence - which is absurd. Therefore, not all beings are merely possible, but there must exist something the existence of which is necessary. But every necessary thing either has its necessity caused by another, or not. Now it is impossible to go on to infinity in necessary things which have their necessity caused by another, as has been already proved in regard to efficient causes. Therefore we cannot but postulate the existence of some being having of itself its own necessity, and not receiving it from another, ut rather causing in others their necessity. This all men speak of as God.
** The "four causes" are to be understood with reference to the three principles of change:
The material cause is the underlying (1)
The formal cause is the property received property (2)
The agent cause (that from which the motion begins) is the thing that has in itself and gives to the underlying (1) the property it gains (2)
The final cause (that for the sake of which the change occurs) is the good that moves the agent to impost the property (2) on the underlying (1) and that results from the underlying (1) being joined to the property (2)
Aquinas argued specifically to god being one in question 3 and perfect in question 4 of the first part of the Summa, though if you do much reading, you'll see that he draws these conclusions pretty directly from these understandings of these "four causes".