One of several arguments for the existence of God; also called "argument from design". William Paley (1743-1805) was its most famous proponent. It has been through several incarnations; one of its most recent is the so-called "argument from the fine-tuning of the cosmological constants".
<The following is a portion of Larrys Text, wikification is encouraged>
It is called "teleological" from telos, the Greek word meaning "purpose or end." As we will see, the argument refers to the purposes or ends which we see all around us in the world. It is also called "the argument from design." And it goes like this.
Look around the world, and observe how everything fits together in one enormous, beautiful system. The planets orbit the Sun, the Earth rotates on its axis, and the Moon orbits the Earth, creating regular seasons, days, and ocean tides. The continents each contain complex, rich ecosystems which are themselves marvels of organization and interdependency. And as we look at individual organisms our amazement increases: every being seems designed to carry out the functions that are natural to it. Hawks are equipped with excellent eyesight in order to catch small prey; camels are equipped with water-retaining humps for long treks through the desert; and humans are equipped with minds that allow them to think of ways to protect their relatively weak, hairless, slow bodies. When we think about the universe in this way, we are struck with how every part of it seems to be well-designed, as though there were an architect or engineer behind it. So much in the world seems to have a purpose behind it. And how can things have purposes, without an intelligence giving them those purposes? Indeed, the universe is like one giant machine. And so, just as machines have designers, the universe must have had a designer with certain purposes for its creation.
This designer must have been a mind, in order to have those purposes; but this mind would have to be infinitely intelligent, because it designed absolutely everything in the universe. And since this mind created the universe, it would also have to be infinitely powerful. Finally, this mind has adapted nature so that, if we live well, we can be happy; so this mind must be benevolent. That means then that there is a mind, infinitely intelligent, powerful, and benevolent, that designed and created the universe. And that is just what we mean by "God." Therefore, God exists.
Unlike the cosmological argument, the teleological argument allows us to infer various things about the nature of God. The cosmological argument only allows us to conclude that a "first cause" exists; but it is not clear that that "first cause" has to be a personal God, a God of a sort which we would want to praise and worship. The teleological argument, on the other hand, is supposed to tell us that God is intelligent and loving. That is one reason why a lot of Christians use design arguments to support their belief; scientifically-minded believers, especially, see evidence of design, by a caring God, all around them. So the teleological argument is supposed to give us reason to believe in the sort of God that is worth worshipping.
But let us turn to the inevitable criticisms of the argument. The first criticism should not take long to state, just because it should be familiar to almost all of you. Namely, that there was this guy named Darwin, who came up with the theory of evolution, which explains the appearance of design in the universe, but the theory of evolution does not require a designer. In other words, in showing how the biological world might have, or has, evolved from lower life forms, Darwin (and of course almost all biologists after him) showed why there appears to be design in the world; and at the same time he showed that there is no need to suppose that there was an actual designer to explain this appearance of design.
In short, the reason that Darwin and the theory of evolution is as hated as they are, by some religious people, is that they undermine support for the teleological argument. The appearance of design, say the evolutionary theorists, does not require a designer. But notice, the teleological argument is only one argument of God. So, even if the theory of evolution undercuts support for the teleological argument, that doesn't mean that there is no way to rationally justify belief in God. There are plenty of other arguments. Much less is the theory of evolution in any way, shape, or form an argument against the existence of God. At worst, from the theist's point of view, the theory of evolution makes just one argument for the existence of God less plausible.
And the theory of evolution is, I might add, totally compatible with the view that God designed and created the universe. He would simply have chosen to create the natural world gradually. Some Christians even say that God guides the process of evolution.
But critics of the teleological argument, anyway, say that the theory of evolution does show that the conclusion does not follow from the premises; the argument has been shown invalid. In other words, the premises of the teleological argument may be true, while the conclusion is false. The proposal is: there is indeed a huge lot of appearance of design; but the claim that no God exists is entirely compatible with that appearance, because the appearance of design can be explained adequately by the theory of evolution.
Here is a second criticism of the teleological argument. David Hume is famous for coming up with a series of powerful criticisms. But I am going to focus in on what I believe is Hume's most devastating criticism.
I told you that the design argument is supposed, by its defenders, to prove the existence of the sort of God that is worth worshipping, right? Well, Hume called that into question. Be forewarned, the following is rather irreverent; but that is because Hume himself was a very irreverent person.
Suppose we admit that, indeed, there had to be some intelligent design behind the existence of the universe. But notice how we came to this conclusion: it was by drawing an analogy, a comparison, between machines like auto engines and the universe and its parts. The universe and its parts are like auto engines in that both look like they have been designed. So we concluded that the mind of God must be somewhat like the human mind; simply much greater and more powerful.
But why do we say that there is just one God? If we are arguing by analogy, why don't we say that there is a committee of Gods that has designed the universe? Maybe Zeus designed space and the sky and the weather; Poseidon designed the oceans and lakes; Demeter designed the earth; and so on. What reason do we have, as far as the teleological argument goes, to think that there is just one God? No doubt some scientifically unsophisticated peoples have thought that there are many gods precisely because of something like the design argument. Sensibly, different gods are then assigned to different aspects of the universe; the division of labor makes sense. Creating a universe is a big job!
And why say that God is perfect? If the universe is like a machine, then maybe our God is really kind of a second-rate deity, who copied the plans of some more brilliant deity -- in just the way that an engineer might borrow the designs of some fellow engineer.
For that matter, why couldn't God be a child, and our world is just his first attempt at worldmaking, an attempt of which he is now embarrassed? The teleological argument tells us nothing to confirm or deny such a possibility. Or perhaps when God created the universe he was a very old deity, and was about to die, and then after creating the universe he died. The designers of machines die all the time. If all that we know about God is that God designed the universe, and so is like the designers of machines, then we have no way of knowing that God is immortal.
I think you get the idea. Suppose that we admit that God is like the designer of machines; that doesn't allow us to conclude that the Christian God exists. And I honestly do not know how the defender of the teleological argument can get around that objection.