By Gregory E. Ganssle, Ph.D. (Taken from http://www.everystudent.com/wires/prove.html)
Ever since Immanuel Kant wrote his Critique of Pure Reason, it has been common for thinking people to insist that it is impossible to prove the existence of God. In fact this claim has been elevated to the level of dogma in American intellectual culture. The reason I know this is considered unquestionable dogma is the reaction I get when I call it into question. When someone says "You cannot prove the existence of God," I want to ask, "How do you know? You just met me! How do you know what I can do?"
What do most people mean when they recite this claim? Most people mean that I cannot provide a philosophical argument for the existence of God which will convince all thinking people. It is impossible, so the story goes, to provide an argument which will compel assent. If my argument will not convince the most ardent atheist, they say, I have not proven God's existence. Since I cannot convince such an atheist to believe, my arguments do not count as proof in their eyes. If they do not count as proof, what good are they?
I agree that I cannot provide an argument that will convince all thinking people. But what does this tell me? Does this tell me anything about God? No. This tells me more about the nature of proof than it does about whether God exists. I cannot provide an argument which will convince everyone, without a possibility of doubt, that God exists. That is no problem. You see, I cannot provide an argument for any interesting philosophical conclusion which will be accepted by everyone without possibility of doubt.
I cannot prove beyond the possibility of doubt -- in a way that will convince all philosophers -- that the Rocky Mountains are really here as a mind-independent object. I cannot prove that the entire universe did not pop into existence five minutes ago and that all of our apparent memories are not illusions. I cannot prove that the other people you see on campus have minds. Perhaps they are very clever robots.
There is no interesting philosophical conclusion that can be proven beyond the possibility of doubt. So the fact that arguments for the existence of God do not produce mathematical certainty does not by itself weaken the case for God's existence. It simply places the question of God's existence in the same category as other questions such as that of the existence of the external, mind-independent world and the question of how we know other people have minds.
Does this mean that arguments for the existence of God are useless? Not at all. Sure, I cannot provide an argument which will convince all thinking people but this does not mean I don't have good reason to believe in God. In fact some of my reasons for believing in God may be persuasive to you. Even if you aren't persuaded to believe that God exists, my arguments may not be useless. It is reasonable to believe that the mountains are real and our memories are generally reliable and that other minds exist. It is reasonable to believe these things even though they cannot be proven. Maybe some argument for God's existence will persuade you that belief in God is reasonable.
So how can we know that God exists? Instead of looking for undoubtable conclusions, we weigh evidence and consider alternatives. Which alternative best fits the evidence?If you'd like to see some reasons which support God's existence, see the article Is There a God?