Matthew Stevens, writing on The Secular Web, doesn't know if God exists or not, but is sure God is limited (so, therefore, not what most people mean by God). He says:
The traditional view of God holds that he is both omniscient and omnipotent, that God created the universe and has taken a keen interest ever since. But how can we actually know this for sure? How can we, with science--civilisation's finest intellectual achievement--test and probe, and so establish that God is both? In short, we can't. Physics describes the universe. God, by definition, exists somehow "outside" the universe. Therefore physics, and science more-broadly, cannot describe God. The existence of God is a matter of faith, and faith is the antithesis of science, which is characterised by enquiry and testable theories. (Put simply, science is knowledge through evidence. Faith is belief in the absence of evidence.) We can never prove or disprove the existence of God.There is a good deal more, which you are invited to read via the link, and some of it has to do with aspects of physics that I understand no more than my cat does. But the paragraph above probably summarizes Stevens's essential thesis, as well as those of many scientific-minded skeptics and agnostics.
I would in no wise try to deny Stevens his right to his conclusions, nor do I think there is usually much point in debating questions relating to anything spiritual. But it is worthwhile to point out from time to time, in connection with articles like Stevens's, that however rational they are (and I have no particular quarrel with his reasoning), they are still based on assumptions. And those assumptions can be questioned: not by me (who cares?), but by the experience of the human race.
"How can we, with science--civilisation's finest intellectual achievement--test and probe, and so establish that God is both?" he asks. "In short, we can't." Well, it depends on what kind of instrument you use for your probe. Every scientific instrument Stevens reckons with is designed to measure matter or energy (which we are told are the same thing in different states), even if the matter consists of subatomic particles that behave very strangely indeed. He presumes that God must be some kind of matter or energy, he looks around and sees no matter or energy that corresponds with his concept of God, and declares God a no-show.
But what if God is not matter or energy in any mechanistic sense? (I think most people who believe in some kind of God would agree that he/it is not, although of course Stevens is not obliged to agree.) And what if God is not "outside" the universe, but exists within it but in a non-material form that doesn't register on science's instruments?
That God is both within the universe and within each individual is a prime teaching of Vedanta (roughly: the core of Hinduism without its culture-specific attributes), which seems to me the most profound spiritual psychology ever devised by the mind of man. It is full of enquiries and testable theories.
Even some Christian thologians have tried to find a way to express this mystery of a God who is in the world but not of it — for instance, Paul Tillich's phrase, "Ground of Being."
The obvious retort is, if we can't see or measure this God within or Ground of Being, aren't we back where we started, with an unknowable that is no more than a faith?
But there are different instruments for different purposes. Patanjali's Yoga Sutras are as pragmatic as can be, an instruction manual for spiritual development. Do this, this, and this (many things, almost all of them taking immense effort and moral self-reconstruction), he says, and you'll know God. The sages of Vedanta (and in their very different terms, Buddhism) assure you that when you know God you will have your proof.
For perceiving God, the instruments are the heart and the mind. Not the heart of sticky sentiment, but of fierce yearning to find perfection. Not the mind of engineering or physics, but the mind that is capable (with enough time and discipline, or with that gift known as Grace) of letting go of sense data and intellectual categories, and shifting its consciousness to perceive other realms — realms that we can only describe, in the impoverished language of everyday life, as "higher" or "spiritual."
Faith is not to be understood rightly in the childish sense Stevens uses — "belief in the absence of evidence." St. Paul expressed it in words that can seem paradoxical, because he was expressing a truth that is paradoxical in ordinary intellectual terms, when he called it "the evidence of things not seen." There is an evidence of consciousness: things not seen but experienced.
Update (October 28): Someone who knows much more about Biblical scholarship than I do tells me that St. Paul's Letter to the Hebrews, from which the quotation is taken, is not considered by modern scholars to have actually been written by Paul. Rather it's thought to be by one of his followers, probably someone familiar with the actual Pauline letters. My interpretation remains, however.