First solution to the paradox of "believing all things"

I realized last night that the practice of "believing all things" logically calls on a person to believe¹, for example, both that God exists and that God doesn't exist, or, equivalently, both to believe that God exists and to disbelieve it (which is ironic, given that believing all things seems such a positive moral and spiritual act).

Of course, "God exists" is logically incompatible with "God doesn't exist." They are mutually exclusive, they can't both be true—logically speaking. Note that miracles are literally logical contradictions. By definition, they violate "the Laws of Nature." But miracles are God things, right? Weird things can happen when it comes to God. The miracle of the universe itself (even if no other miracle occurred after the universe came into existence) introduces a sense of the uncanny: the mystery of being, the spine-tingle when you try to wrap your mind around the question: Why is there something rather than nothing?

If believing and disbelieving the same thing is a logical contradiction, then (according to Bertrand Russell, for example) anything whatsoever follows from it. That sounds like a disastrous situation, one that destroys our entire enterprise. Personally, however,I prefer to dare to go ahead and see whether anything insightful or interesting turns up.

In the first place, is "I believe that God exists" as incompatible with "I believe that God doesn't exist" as "God exists" is incompatible with "God doesn't exist"? Or does "believing that" add a new dimension? In any case, it seems a paradox. How could it be possible to believe two diametrically opposed things? In other words, what is the solution to the paradox of "believing (and disbelieving) all things"?

The first possible solution that comes to mind is that I may believe and disbelieve at different times, alternating from one to the other. Actually, this is not that unusual. A young man seriously infatuated with a girl can believe from a smile one moment that "she loves me," then from a frown the next that "she loves me not." I have experienced this. Perhaps you have too. And I have also experienced awakening with praise welling up from my body and spirit, and rising to meet the day believing that God exists and I'm in contact with Him, then, on another day—maybe after reading a book by Sam Harris, Richard Dawkins, or Daniel Dennett?—becoming cold-eyedly "rational" and beginning to doubt it or outright disbelieve it, and maybe even concluding that my birth, life, and eventual death are "just Nature."

This reminds me of my wife's needlepoint:

Who plants a seed
beneath the sod
and waits to see
believes in DNA.

[My next post will examine another possible way to solve the paradox of "believing (and disbelieving) all things."]
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1. Remember, I'm investigating "belief" in the sense that we can't believe a thing that we know to be true, which is not so obvious as that we can't believe what we know to be false.