Mutually-independent opposites ([self - other] [fate - freedom] [existence - nonexistence] [meaning - meaninglessness] ect) exists only conceptually and follow these rules.
Another example is a coin. There is either heads, or tails. You cannot have both, but at the same time, you cannot have one without the other. The appearance of heads both negates AND is dependent on tails. This apparent contradiction lies in the nature of the coin itself. Again, this structure is both heads, tails, and neither heads nor tails. In it's truth as a coin, it contains them all.
A lack of conceptual or linguistic tools to describe God means we can, at best, point towards him/it rather than capture God in language. So - a metaphor:
On the existence of God - first we must ask: what is existence? What is it's nature?
You cannot consider existence without considering non-existence. Upon close enough examination, I submit that one will find that these two opposites relate in the same way as my examples above. If existence itself is like heads, then non-existence is like tails - so what is the coin? This is where God can be found, imo.
Now, so what does this mean about simple statements of God's existence?
Does I believe "God" exists? - no
However this statement only works with the understanding of existence described above, so that one can still have a relationship with God or experience God, without having to put God into a box, either of Existence or Non-existence, which are concepts that are really dependent on our own minds.