I think that sometimes science misunderstands the subjective perspective an therefore misses much of what is important to us as humans. Many scientists only accept as "evidence" that which can be verified objectively by others, and dismiss personal experience as "subjective" and therefore, unreliable.
God cannot possibly exist because he is not casually observable by a crowd looking into the sky and saying "There he is!"
If that is all you are going to count as "evidence" then of course there is no "evidence" for him. You are presuming the answer in the way you ask the question.
"Look- up in the sky- it's a bird! It's a plane! It's God!"
We think in linguistic models-and many philosophers and scientists are beginning to understand that better. Thomas Kuhn, who understood the nature of scientific models is one such writer.
But every thought anyone ever expresses is expressed in language, and language itself can be seen as a "model" of what we call "reality". So science itself is nothing more or less than a lingusitic model for reality which changes from time to time. And yes, that was an intentional ambiguity in that last sentence.
We have also come up with models for God and the best yet devised, in my opinion, is the Mormon model which says that God IS indeed himself a Man who organizes reality the way men do.
Some see the conflict as being between faith and science. I think that is incorrect because indeed scientists themselves use faith in their personal lives all the time- for example they have faith that if they do an experiment today, and do the same one tomorrow, the results will be the same and that there is constancy in the universe. That is a presumption they take on faith. They assume that indeed there is a natural order to the way things operate, and that supernatural things do not exist.
They exercise personal faith a million times a day, believing that when they want to move their arm, that it will move; that their plans for getting that grant, for their next vacation and what they will do on the weekend will indeed come to pass. They exercise faith that their car will start when they turn the key, they exercise faith that when they stop off for a gallon of milk, that the store will not have run out of it.
But we know that thousands daily find that they cannot move their arms or legs or find their lives cut short through circumstances they could have never forseen. The universe is indeed a surprising place and we are forced to exercise alternative plans on virtually a daily basis. We trip over things. We run out of eggs. The pot boils over. Our faith in the way things will go is continually stymied.
In fact, as organisms reacting and responding in our environments, surprise is more the rule than regularity, but that is another subject.
Is it unreasonable to exercise faith that you will live to see tomorrow? Chances are for most of us, it is a good bet. But the point is, it IS a bet. None of us know what tomorrow will bring.
The classic arguments against God in most cases do not apply to the Mormon model of God and I think it is important that we think these things through.
A God who is transcendent, aloof, a "Trinity" of "essences" and outside of time is indeed a God which can only be understood as a mystery.
But that is not our Mormon God. Our God is Man. He is The Man of Holiness. Arguments against his existence are arguments against the existence of humankind.
He is the "Ideal Man" and arguing against his existence is like arguing that we cannot conceive of what an "ideal man", or an "ideal father" would be. Yet of course we can conceive of such an entity. And like us, the model says He exists in time. The model says He is immanent, not transcendent. The model says he interacts with his children as a Father would. The model suggest possibly that indeed He himself had a Father.
We model him as our Father. To me, pragmatically, that is identical to saying "He is our Father". In cases like this, as also in science, there is no difference THAT WE CAN SPEAK OF between saying that "He is our Father" and saying that "We model him as our Father" because no one indeed can know the difference.
Models only exist until we know that something in the "data" is different than the model, and then the model must be changed. That happened of course with the Ptolemaic model of the universe, and the paradigm needed to be changed and it was, and it was supplanted by the Copernican model of the universe.
The idea of a transcendent unchanging God who is of a different "essence" than man ceased to be a useful model around, actually, the time that Joseph restored the gospel. Around the same time that Brigham Young was leading the Mormons westward, a man named Nietzsche, in Europe, proclaimed that man was god and that God was dead. In fact, though he perhaps misunderstood it himself, ironically, he was exactly right. The sectarian god, the transcendent Platonic god indeed WAS dead! And despite his misunderstanding that what he was presenting philosophically was indeed a new model for God, Nietzsche in his own way was proclaiming much of what Joseph Smith saw in his visions and revelations.
A God who matters to humans must be human. Man is god, but one in embryo who must be spiritually nourished and grow.
Let me give you two different lingusitic models for what I take to be substantially the same understanding of the nature of God.
The first is the Mormon model:
The God of the Restoration, as the Man of Holiness organizes worlds as we know them through the power of his Word, his Messenger, who is also our Savior. Through his Word, he has organized or defines all that man, as gods in embryo, can know.
Now the humanistic model:
Man, who has taken the place of the transcendent Neoplatonic god, defines reality through linguistic models, comprised of words, into different scientific "paradigms" as Kuhn has shown, thereby defining all that man can know.
Can you see that these two different models for the way reality is organized are just that? That their difference is just words? Two different linguisitic models- amounting to virtually the same insight- nothing more, nothing less?
But I can hear you asking- "But does that mean that God is not 'real'- that he exists only in the minds of believers"?
No, in fact it would be more accurate to say that he exists in their "hearts". But does that mean he is not "real"? Of course it does not mean that.
Everything that our atheistic scientist (let's call him Bob) knows about "reality" is in Bob's mind- his brain, his heart, "wherever" it is! All that he knows and believes are just that: What Bob knows and believes. They are the models of reality as Bob understands it, including his (let us assume) his rejection of what he understands as "faith" for what he understands as "science" or "evidence".
We are all products to a large degree of our environment and our culture.
So is that God in our minds and hearts "real"? Of course he is just as real as anything important to us- he is as real as the love we have for our spouses and children, he is as real as the feeling of choice we have in every choice we make in our lives, as real as knowing right from wrong, as real as the confirmation we receive of the "still small voice". He is as real as our conception of everything that is good and true and beautiful and ideal. He IS in some sense those Platonic forms after all, but now he dwells in our hearts and is no longer the abstract and undefinable First Cause, which hasn't "existed" since Hume demolished that model in the 17th Century.
But is he "really out there"??
What would it take to show that? Sending a rocket into space and taking his picture? We all know that is not going to happen.
The best we can hope for is a kind of Alma 32 (in the Book of Mormon) experimentation on the "data" found in our hearts when we try those beliefs.
After all, turning those feelings in our hearts into understanding him as "real" takes faith which is after all a "hope for things NOT seen, but true".