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My responses aren't in chronological order.
1.They hold that God is truth, among other things, and if truth is the result(i.e. the end) of reasoning, then so is God. This was included not to reason for the existence of God, but to answer the original question in part.
2.Concerning my bringing up of Shrodinger's Cat: I used the idea derived from it, that by observing something one affects the outcome. Should we then assume that this claim is false? It is an unfalsifiable proposal.
3.Catholics believe that God is omnipresent , and thus would be an unobservable affect. Your reasoning also begs the question if everything is nothing.
This is last and most important because it is the tool you have used to disprove the existence of the spiritual:
4.The burden of proof has no place here. Where does it lie and how can this be determined when arguing philosophy? What makes the claim no existence of God any more or less ordinary than the claim of the existence of God? So in the arguments of philosophy where the argumentum ad ignorantiam is so common in philosophy. Nothing can be assumed here, as opposed to arguments of law, so the claim of spiritual being can neither be proven nor denied.