Amorphos, I am totally aware of the (your) of suPposed half states. Its naïve to think of something either /or existing or not, however the confusion arises, when we try to analyse in terms-of one into the other.(((Existence in terms of non existence and inversely)
There are 2 things I have been thinking of, that may relate your problem, and one is logic, and the other, referientiality systems of semantic difficulties as ascribed by the scope of referientiality. But please scratch the above as purely a solopsism exploration.
As regards your OP, the confusion of solving and either/or type or reduction, involves the very basic logical process in selection of characteristics, with which to identify so called "factual" evaluations. These may include the supposed facts of religious belief, such as Christ's miracles, the great Schisms of the Church (catholic), martin Luther's source of motivation to break away from said Church, etc.
The identification and categorisation of the certainty of these facts, are subscribed to by an initial acceptance/rejection of alternative certainly held views at the time. These early views, were held in strict logical certainty of the type, which excluded any other view, by virtues of their definitional belief. For instance, the church’s schisms was a direct result of the breaking away of events, dogma which have been rejected out of hand. The greatest schisms the church literally ascribed to was the one having as a consequence two simultaneous popes, one in rome and one in Constantinople. These were logically consistent facts. Luther was inwardly broken, and his case, was the consequence of inner events of self certainty mirrored through his belief of the Soul, as the final arbiter of “Truth”.
But the point being, is that although both pointed to a way to identify the “what caused this to occur and therefore why?”, the mistake is to try directly answer the why? Before the what?
Before we can "know"(identify) the what? (As a discriminate among possibilities, we start the process by excluding possibilities. We exclude them for various reasons, attributes, qualities, thus narrowing the range(scope) of possibilities. This is how we arrive at what it is, it's identity, this is how we identify, and learn what it is.
After we can identify, learn what it “is”, then we can evaluate it in terms of “truth function”. If, the evaluation does not lead to a satisfactory conclusion, then we go back to qualifying by exclusion.
These two processes are seemingly anomalous for most, thereby hindering logical train of identification. We may misidentify truth values,or, semantically misnamed them, giving false truth values and consequent misuse of them.
From here referientiality may shift, away from the process of quantification—(representation). Toward the primary qualifier—the cogito-in-itself.
(God presenting Himself like in burning bush)
When this happens, science and religion part company, since their relation has to be based on a relationship between absolute and representational Truth, on a logical level. Science tends to “identify” by use of variables, using those variables as standard (fixed). On the other hand, religion, based on ontology, identifies “truth value” by presentation of singular facts, and disqualifying ones that which are not" truth" related. So “existence” is an attribute of God, because God exists. Because God exists, “god does not (not) exist”. Because a non existent God has no truth value.
With science, to say “God exists” is not to qualify or disqualify on basis of truth, but only state a neutral non factual statement, with a potential to evaluate. Science does not operate on the level of qualification truth, (presenting), but representing the presumption of both assertions. The existence of God will not be disqualified on basis logical certainty (eliminating all possible cases of non-existence, but by identifying “God” as the totality which needs to be represented in all of it’s aspects. Since this can not be done “God” as a concept cannot substantially be self referential. It will depend on representations, which can only be defined in reference to other representations. Trying by eliminating by reference to the singularity All (the Almighty God)This will become impossible, since that singularity is self identifying(I am who I am)
In the early days of Descartes, self certainty was a given, within the certainty of assigned social roles, and the erosion of Faith, was a patent view, shown to be latent later on, by Luther, Nietzsche and others.
Forgive the length of this, and hey, don’t’ feel obliged not to read between the lines for a general drift.