Thomas Aquinas provides five proofs for God's existence; actually there are four proofs because two fold into each other.
The four proofs:
1 and 2. Cause and Motion
3. Contingency and Necessity
4. Degrees of Perfection
5. Teleology
1 and 2. Cause and Motion
First it is important to understand that Aquinas' proofs were not composed in an age of doubt or disinterest. When Aquinas rote virtually everyone believed in God and was Catholic (or Jewish or Moslem, depending on what part of the Western world you lived in.
Believing in God then was different from what it is now. God as everywhere; there were typically 100 religious holidays a year, and people lived in an atmosphere of images of saints and Mary and Jesus.
Proofs of God were hardly relevant to most people, most of whom were illiterate in any event. So, why did Aquinas bother to do this and what did he mean by it?
Aquinas was both a priest and an intellectual, a member of a university faculty. Priests are people who have been given the power to perform sacraments, that is to connect 'civilians' with God through enacting certain rituals. They are already God's agents, or service reps or officers, so to speak, so proving that their boss exists is something that would never occur to most of them.
What then is up? Aquinas, I think, resembles a Silicon Valley techie in the early days of computer and internet development. He has this very cool tool -- human reason, logic, argument, definitions - and he ants to test it, to see how far he can get using it. This was an age of faith and tradition. People for the most part did not travel. They were born, lived and died in the same place doing the same things and they lived and died in the religion of their ancestors and lived according to village rules and traditions.
Aquinas however lived in am ore cosmopolitan world, that of the university, where educated clerics spoke and wrote in a common, highly valued language, Latin, the language of civilization and the past. The five proofs, and all philosophical writing, was done in Latin until at least the seventeenth century.
The Proofs:
Aquinas picks out features of the world that any educated person might notice. These features tend to be universal - they occur everywhere and everywhen - and they are features that seem necessary for their to be a world at all. So the features are universal and necessary.
He uses these features to make an argument that asks how these features could possibly be features of the world unless there were some further feature to account for them. The proof strategy is to say: 'We always have this; but if we always have this, must we not also always have this other? Example: if you lift weights regularly your muscle strength will increase and you will look more toned. The lifting causes the toning and the strength to increase. Conversely if you stop lifting and do nothing to compensate you lose tone and strength.
Here is what Aquinas does: he says that every event that has ever occurred has to have some cause or other. He means that things don't just happen. People don't just get more toned or stronger for no reason. We don't all of a sudden know how to play a mean lead guitar; that requires practice. And so forth.
So, if every event has a cause, and if we trace events back, looking for the cause of each cause, we will eventually get back to the very first event in a series of causes. (Think of Adam and Eve, the first human parents. There had to be a first set of identifiably human parents, and when we get to them we ask, what caused them?)
At some point, says Aquinas, we need to stop seeking earlier causes for things unless we want to say that events go back and back and never have a starting point. Did the universe, for example, have to be caused or has it always been there? And even if it has, did it just spring into existence by itself?
Aquinas answers that an infinite regress of causes really does not explain anything; we still have to ask what caused the first event, for example, the universe, to be there at all.
And the only anser to this question for Aquinas is that there must be a first cause, a cause that begins the series; and that cause clearly cannot itself by caused by something other than itself. So, there must be a first, self-caused cause.
Aquinas says that we can call this first self-causing cause, God.
The proof from motion resembles the proof from causation. In the motion proof Aquinas argues that since everything that is moved must be moved by something other than itself there has to be a first, unmoved or self-moving mover to start the series of movements in the first place.
This unmoved first mover we call God.
3. Contingency and Necessity
The third proof, from contingency, operates on a different premise. Here Aquinas focuses on a feature that everything has rather than on something that happens to everything.
The feature that interests Aquinas is the fact that everything that exists can be thought of as not existing. This is a little abstract but he does have a point. He means that we cannot think of anything that exists as absolutely having to exist, including the universe itself. We can conceive - think in a purely abstract way - nothingness, the non-occurrence of the universe. Or we can think of a universe that is slightly or very different from the one in which we live.
The point is, for anything that exists we can imagine its non-existence without contradicting ourselves. But if everything that exists might not have existed, the truth is that all sorts of things, including the whole universe, do exist, and if these non-necessary things that do not have to exist do exist then there must be some necessary existence, something hose very nature it is, to exist, that exists to account for the existence of all the non-necessary things. Without the necessary existent there is no explanation for the existence of all the non-necessary existents.
4. Degrees of Perfection
The fourth proof, from degrees of perfection, again takes a common feature that all things possess and have to possess and asks where that feature comes from. In this case the feature is something we are dimly aware of but do not think about that much -- namely, a thing's perfection.
Everything, says Aquinas, has some degree of perfection, which means that it is a more-or-less good instance of what it is. Cell phones, cars, jeans all have degrees of perfection. Many things fall short, and we both know this and say it -- "This phone would be perfect if it only had turn-by-turn GPS'; of course once it comes out with that feature we say, 'This phone would be perfect if it only had a 6 megapixel camera, or HD video, or this or that." Or, rarely but not never, we might even say, 'Y'know, this phone is perfect for my purposes'. But not the qualifier: ' for my purposes'. We have an idea of what a perfect cell phone would be and sometimes there are phones that fit our requirements perfectly. But we also know that being a perfect cell phone never means that this is a perfect vehicle, or mate, or pair of shoes. Being perfect is hard, but the interesting thing is we all seem to know, most often without being able to specify, what being perfect means. And we know this because we know with utter certainty that the things we have are most often not perfect at all.
But just the fact that we all have an idea of perfection, and know that the things we have are either imperfect or perfect as a this or a that without being perfect in every way, means that all of us come already equipped with an idea of perfection, an idea that we can apply to every different kind of thing. If we have such an idea, Aquinas argues, it must be because there is an absolute perfection, something perfect in itself and in every way, that serves as a benchmark or standard for all our local and particular judgments about the perfection or imperfection of this or that thing.
The idea is, we could not make judgments about relative perfection unless we already possessed a universal standard of perfection and possessing this standard means that there must be something perfect, of hich we have an idea already, to provide the baseline for all our judgments.
Therefore there is a perfect being and we call that being God.
5. Teleology
The word 'teleology' means the study of ends, or goals, or purposes. In Aquinas' world there was a belief that everything had its own proper purpose or end built in; the 'job' that each thing had was to become what it was meant to be. For example, a flower was meant to bud and bloom, a fox to hunt, a blade of grass to grow, a stone to rest unmoved on the ground.
The Aquinian world was therefore a collection of objects each of which had a built-in end or purpose. Under this description the world as a whole also had a telos or goal, as a world. What do I mean? Aquinas believed that when we look at our world we see a myriad (lots) of things, each with its own internal structure and purpose, its way of fulfilling what it is; but we also see, remarkably, all these different things working together so that, in fulfilling their individual destinies, they are also creating an overall order for the world. The air allows us to breathe; budding grain feeds us; our organs sustain our lives; the ground holds us up. Thus, each element inb the world, in doing its own thing, also makes it easier for other things to do their thing. The world is like a carefully constructed machine or organism, and this remarkable level of order suggests strongly that there was some intelligence designing each thing, as well as the interactions of things, to produce maximum mutual support. Such harmony makes no sense as an accident.
So, the world must have an intelligent designer and we call this being, God.