This really is the branch of philosophy that tends to make my head hurt. It is hard to focus and to discuss in an orderly way what we mean by "being", by the verb "is" when it is not used as a copula, by "existence". And I guess I have to concede it is even a question whether one can talk about "being itself" and say anything worth saying.
Here is the kind of mental and intellectual self-torture which leads to saying "God does not exist." A useful beginning would be to wonder if, say, justice "exists" or "is" in the same way as the chair you're sitting on exists. Or we could wonder how the statement,"It is true that Albany is the capital city of New York" differs from "The Pythagorean Theorem is true," and whether they both differ meaningfully from, "It is true that 'truth is beauty.'"
What kind of existence or being does the truth of those statements have? Does Truth "exist"? Does "existence itself" exist? Or, even worse, "Is there "being itself" and if there is what does "is" mean in that sentence?
Or we could ask why do we even have the word "existence" with its etymological suggestion of "Standing out"? Is there a difference between saying "Justice is," and "Justice exists"?
How (if at all) does the the word "exists" vary in meaning in the statements "Forest Keeper exists" and "The chair he's sitting on exists" and "Justice exists" and "God exists"?
And to get closer to why we say God does not exist, "What, if anything, does God share with Forest Keeper, his chair, and Justice?"
It is the "stand out from" suggestion of the word "exist" that pushes some of us to say that God does not exists. There is nothing for Him to stand out from. He is that from which created things, by His act, stand out. He, as it were, provides the matrix of existence in which created things stand out from one another and from Him.
Why, when God gives his name, does He choose Hebrew to do it, of all languages? Maybe because, in His providence, Hebrew is a language in which it is impossible to say clearly, unequivocally, and unmysteriously "I am that I am," since the tenses in Hebrew seem to be able to mean whatever the speaker wants, (well, almost).
Tillich is not my favorite thinker, but he is not so bad when He suggests that God doesn't so much "be" as "let be" (NOT in the colloquial sense of "leave alone" but in the sense, more or less, of "make it possible for existent things to exist."
It is the rank uncreated differentness of God that requires us to talk about Him using analogies, that makes everything we say about Him (but note, NOT everything we say about TALKING about Him) an analogy.
So to say that God "exists" and to think we mean the same thing as we mean when we say "FK exists," or "FK's chair exists," seems to posit something like a "thing" called existence in which these three "existents" share. That in turn seems to call into question the root of monotheism, by giving us something like, 'Before the beginning there was existence and God,' While we want to say "Before there beginning there 'was — so to speak and whatever that means' only God."
So saying God does not exist seems to the theists who say it, the necessary consequence of monotheism.
It may be relevant to insert here that the only Mormon "thinker" I've ever read completely disavows this entire enterprise and its conclusion.
I would say that justice is an "attribute" (some people use that word differently) of God, so it must exist just as the chair does. It just has different properties, such as not having atoms. Our evidence for its existence is inferential, but nonetheless real.
Or we could wonder how the statement,"It is true that Albany is the capital city of New York" differs from "The Pythagorean Theorem is true," and whether they both differ meaningfully from, "It is true that 'truth is beauty.'"
I would say the first is true by arbitrary definition. The second is true by theory and practice. The third is just an opinion and is only true subjectively to the individual.
What kind of existence or being does the truth of those statements have? Does Truth "exist"? Does "existence itself" exist? Or, even worse, "Is there "being itself" and if there is what does "is" mean in that sentence?
"Yes" to all (yes-no questions). We can ONLY know all of these things if we start with an infinite-personal God, and know that He created us in His image. Once we accept that God is personal, and that therefore we are personal, then the existence questions fall neatly into place. If we KNOW that God is there, the real God, and that He is personal, then there should be no metaphysical problems concerning existence. That simple statement is what has confounded philosophers for centuries, all the way until this day.
ONLY a personal-infinite God can answer the needs of unity and diversity simultaneously, i.e. in the Trinity.
How (if at all) does the the word "exists" vary in meaning in the statements "Forest Keeper exists" and "The chair he's sitting on exists" and "Justice exists" and "God exists"?
Perhaps human ideas "exist" in a different sense, but all of the things you listed exist because we know for sure that God is "there". That is the crucial presupposition.
And to get closer to why we say God does not exist, "What, if anything, does God share with Forest Keeper, his chair, and Justice?"
Justice we throw out because that is already "OF" God. In terms of God being infinite, Forest Keeper and the chair are the same. In terms of God being personal, Forest Keeper was created in God's image and separated from the chair (and everything else not human). They are all the same and lower than FK, and still lower than God.
It is the "stand out from" suggestion of the word "exist" that pushes some of us to say that God does not exists. There is nothing for Him to stand out from. He is that from which created things, by His act, stand out. He, as it were, provides the matrix of existence in which created things stand out from one another and from Him.
I suppose that definition seems a little artificial to me. It is relational and perhaps helpful in all cases, EXCEPT for God. Could we say that God's existence stands out from His lack of existence? :)
Why, when God gives his name, does He choose Hebrew to do it, of all languages? Maybe because, in His providence, Hebrew is a language in which it is impossible to say clearly, unequivocally, and unmysteriously "I am that I am," since the tenses in Hebrew seem to be able to mean whatever the speaker wants, (well, almost).
I would doubt that God created and then used a specific language for the purpose of being evasive. :)
As I've said before, First we say, "God is Father, and I have some clue about that because I am a father." Then, and I'm not sure this can happen in the individual without grace and prayer, we come to realize that God is THE Father and that my relationship with my daughter is a pale and smudged imitation of real fatherhood - and that I can learn more about being a father by having frequent recourse to The Father in prayer.
I'm with you here. :) God is personal and we are personal.