The buzz on the interwebs these days amongst lay people in religion forums where theists and atheists clash is what many people are calling "The Ontological Argument" which is in fact 'The Cosmological Argument.' It states that creation exists and therefore something caused it to exist, that 'cause' would be reasonably defined as God, i.e. an uncreated creator who is not temporally or spatially conditioned, and who is all powerful over creation (omnipotent and omnipresent). They are right to call this an ontological argument because, it deals with the existence of creation and God; and ontology is the study of being.
The great irony here is that the theist is taking up the side of rationalism and the atheist is taking up the side of empiricism. That's ironic, of course, because the claim leveled against theists by atheists is that they are irrational. The atheist is denying the existence of 'The Cause' because there is no empirical evidence of that 'Cause,' whereas the theist approaches the issue rationally like an algebraic equation where P= 1. The atheist's view states that all knowledge must come from experiencing what is, and the theist's view is quite the opposite and states that it isn't necessary to import any information about the universe in order to know something. For instance, if we say that 1=1 we know it to be true, and if we say 1<1 we know it to be false because it must be itself. But if we say 1<?, then we know that the latter two propositions cannot be the case and we know that any number less that 1 cannot be the case, and so by making an assumption, proving a contradiction, and ejecting it we know that there is such a number that is at least greater than one: 1<2. This is how we know that there are an infinite amount of numbers without having counted them all, because we can assume, show a contradiction and eject using the rational approach which doesn't import any premise found in the empirical universe. And further proof of that is, we can conceive of a number that is larger than any amount of anything in the universe, which exceeds tangible proofs.
However, the ontological argument that stands out in philosophical circles is St. Anselm's Ontological Argument for the existence of God, or 'The Perfect.' Instead of using something which may be reasonably perceived as caused (creation itself) as a proof for God's existence, it offers a rational proof for the existence of God after the same manner of mathematics, and it goes like this (df means same as):
1.) The Perfect = df Something other than which nothing greater can be conceived.
2.) The Perfect = The Perfect = df (X=X)
/.: 3.) The Perfect cannot be conceived not to be.
Now, the average person will say," That is a load of crap. I could replace God or 'The Perfect' with a Unicorn and prove the existence of unicorns, square circles, a number which is both greater and less than one, and I can prove the existence of men who are women." Not so. This is because 'The Perfect' necessarily exists according to the definition of 'The Perfect' and is therefore a necessary being, whereas unicorns and the other things are contingent. I'll show you what I mean.
The above argument, the three premises, are predicated by the description of 'The Perfect' in St. Anselm's 'Proslogion II." It states that:
1.) 'The Perfect' has all positive properties. (This is because evil is a lack of something and not the presence of anything. Therefore, to have negative qualities would delimit anything perfect, even in a mathematical sense, but to be sure, also in an ethical, moral, and substantial sense. Thus, 'The Perfect' would not be perfect if it had negative qualities. So it's necessary for 'The Perfect' to have all positive qualities.)
2.) Existence is one such property.
/.: 3.) 'The Perfect' exists.
We cannot conceive of a thing such as 'The Perfect' that does not exist, because existence itself is necessary to formulating the concept of 'The Perfect.' Such a necessary being might represent X. Now, if we conceive of the selfsame being that is contingent, and say it is also X, then we have a contradiction, and the conception is necessarily false, because a thing cannot exist as a necessary being and a contingent being at once. This is because a contingent being can fail to exist, but a necessary being cannot fail to exist. It must be one or the other.
So, we can certainly conceive of such a unicorn that exists and we can conceive one that does not exist, because it is not necessary that unicorns exist for us to conceive of them accurately. But in order to accurately conceive of 'The Perfect' it is necessary to conceive of it existing, otherwise it is not itself. This is because 'The Perfect' is something other than which none greater can be conceived, and that being the case if we conceived of something other than which none greater can be conceived that did not exist, it would be less than something other than which none greater can be conceived that does exist. So, it is impossible to conceive of God not existing and have an accurate conception of Him because (X =X). That is not the case with unicorns, men who are women, square circles or the like.
Human beings are rational creatures, and one of the things that predicates reason in a being is its ability to distinguish between true statements and contradictions. Every person knows that (p=/=p) is a contradiction precisely because they have reason. However, the atheist thinks that he can conceive of 'The Perfect' not existing, which is a contradiction and necessarily false; it's unintelligible to even say. It only becomes intelligible if his conception is not identical to 'The Perfect,' in which case he still hasn't dismissed God but a non-God, and therefore the assertion is still nonsense and unintelligible. Again, this is because a being that must exist is greater than a being that can exist and not exist.
The most immediate and common atheistic reply to this argument comes from 'Positivism' which is basically empiricism. The atheist would reply," Very clever, but it's an empty concept. You have no empirical evidence of such a being and even if you could make contact with such a being you would have no way to prove it to be what it is because it is infinite, and likewise we atheists would have no way of disproving it because it is immeasurable."
However, this approach is problematic, because of two little words: good and bad. If you take this approach that states 'only that which is empirical has meaning', it follows necessarily that good and bad are also rejected, or at least diminished to a merely emotional value.
At that point the whole subject of ethics disappears. Saying that rape, murder, or genocide are bad, or that philanthropy, volunteering, and nurture are good becomes a mere expression of emotions, with absolutely no substance. Subjects aren't good or bad, they don't have positive or negative properties, you are merely projecting your emotions (which mean nothing) onto things which themselves have no intrinsic value (everything is worthless). So, ethics and morals become meaningless subjective nonsense under the lens of 'Positivism,' because 'Positivism' is empirical and excludes reason; and a 'do what thou whilt' attitude sets in. Rationalism is diametrically opposed to 'Positivism' because, rationalism states that sentient beings do have intrinsic value, and that because of this there are concrete morals and ethics, and an attitude of 'lawfulness' takes root.
So, the atheist empiricist comes off rather badly from this argument, because he is a fool for thinking he can conceive of what cannot be conceived and insists on a contradiction that is necessarily false, while admitting that he does not believe in morals or ethics, and that he believes nothing has any meaning and everything is worthless. On the other hand, the theist rationalist comes off rather well. He asserts what is necessarily so, gives assent to ethics and morals, and states that sentient beings do have intrinsic value.
This argument really pulls the atheist's pants down, and shows him to be in fact the opposite of what he wants to seem. He desires to seem a courageous, hyper-rational stoic who is brave enough to face the nothing that the theist is so afraid of he goes and makes 'an imaginary friend in the sky'. Because of this he would have people think that he is the moral and intellectual superior of the theist, because he makes himself seem braver and more rational. When in fact the atheist doesn't believe in any kind of real courage, because he doesn't believe in virtues, ethics or morals; and beyond this, he isn't the intellectual superior in any case because he gives assent to that which cannot be logically admitted... which of course makes him seem rather stupid.
Anyway, that's St. Anselm's Ontological Argument.
"Every art and every inquiry, and similarly every action and choice, is thought to aim at some good; and for this reason the good has rightly been declared to be that at which all things aim." ~Aristotle~