...You cannot prove or demonstrate the existence of a thing by slipping it in through a philosophical back-door, because philosophy is only a self-referential logic game. You need observation...Plenty of other commentators respond with philosophical reason, but we can answer the second part of the challenge as well as refuting the premises of the first. You want observation? We've had observation. Will it prove anything to you? Not necessarily. Why? Because they are not your personal observations; because it is possible to doubt anything one is presented with, even an appearance of God himself right in front of you; because the inquiry must be an honest one, made with an open mind, before one can permit oneself to see what's right in front of them. But if you truly want to know when God or his supernatural agents have been observed, here--I give you a small smackeral:
John Wright's Conversion
The Apparitions at Fatima
The Apparitions at Kibeho
Conversion of Roy Schoeman
Conversion of Alphonse Ratisbonne
Apparitions to St. Faustina
The Christian mystical tradition
And there's lots more where that came from. But again, as C. S. Lewis portrayed with the dwarves of the Last Battle in Narnia, people could be in paradise and refuse to accept the evidence of the world around them, of God at their back and imperishable heaven at their feet. John Wright summed it up best:
...You might wonder why, if God can convince atheists to worship Him merely by dropping by for a visit, He does not do it more often. The reason is that it does not help, not at all, not a bit. When I suffer doubts, when my faith gets weak, my faith in my memory gets weak too. Faith and faithlessness have NOTHING TO DO with evidence presented to reason or senses. It has to do with a humble will and an upright heart. If God presented evidence to skeptics, all that would happen is that skeptics would doubt their evidence. If God gave a logical argument to prove His own existence, all that would happen is that skeptics would doubt the power of logic to prove anything.And finally, there's the argument laid out throughout Scripture (alongside, of course, all those accounts of people observing God):
Skepticism pretends it is all about open-mindedness and evidence. Not so. Skepticism is about suspicion and pride and self-will. It is about pretending you are smarter than people who, if you only knew, are actually wiser than you and your sneering questions and foolish word-tricks. The only place we ever see a humble skeptic is in the physical sciences, because scientists are willing to let their conclusions be ruled on by nature...
For what can be known about God is evident to them, because God made it evident to them. Ever since the creation of the world, his invisible attributes of eternal power and divinity have been able to be understood and perceived in what he has made. As a result, they have no excuse...--Romans 1:19-20The world exists--blessed be the One at the back of all things! For more, see New Proofs for the Existence of God: Contributions of Contemporary Physics and Philosophy, Modern Physics and Ancient Faith, Chance or Purpose? Creation, Evolution and a Rational Faith.