(1) If there is a God, he is perfectly loving.
(2) If a perfectly loving God exists, reasonable nonbelief does not occur.
(3) Reasonable nonbelief occurs.
--(3) and (2) gets us:
(4) No perfectly loving God exists.
--(4) and (1) it follows that:
(5) There is no God.
This argument is valid and commits no error of logic, given (1), (2), and (3), we may validly conclude (5).
So, putting this as near to standard form as possible, we have:
If there is a God, he is perfectly loving.
If a perfectly loving God exists, reasonable nonbelief does not occur.
Reasonable nonbelief occurs.
Therefore, there is no God.
Now, this would appear to be, far from a valid deductive argument, a situation in which the conclusion of the argument doesn't follow necessarily from the premises at all. There is no apparent logical connection between the existence of "reasonable" non-belief (a mental state and body of belief about God), and the non-existence of God
qua non-existence, which would be an existential reality that could only be known by direct apprehension of that non-existence (one would have to
know God did not exist the way one
knows unicorns do not exist, and unicorns are "hidden" and non-existent in a very different manner than God is considered "hidden, and within a vastly different context). To move from reasonable unbelief (arguments, premises, evidence thought to count as being against God's existence etc.) to a "therefore" claim about God's existence, one would require a clear logical connection between premises and conclusion here that has not been provided.
Part of the problem clearly inheres in the second premise, that "If a perfectly loving God exists, reasonable nonbelief does not occur." The reason this premise should be assumed to be true such that it can function as a legitimate premise from which the conclusion could be derived is not at all clear. In the first instance, it is not at all clear what God's perfect lovingness has to do with the manner or means by which he reveals himself to human beings, or
if he does so, and upon what conditions.
A hidden assumption also appears to be present in that, if God existed, and if he was all-loving, then it is thought for some reason to follow that he would in some sense be empirically present or the created world would make his existence logically self evident in an obvious way, among humans on earth (otherwise, how could it be the case that, if God is all loving, non-belief is impossible?) The reason for this assumption is also not at all clear.
If reasonable non-belief occurs, then it must be because there is no all-loving God since his hiddeness has been made contingent on his attribute of being all-loving. His all-lovingness, in other words, would appear to condition his conduct toward humans such that, were he all-loving, he would by necessity be non-hidden - unambiguously present.
The basis for the second premise is deeply hazy, at this point, and needs to be made explicit.
The only thing left for the Mormon to do is try to deny one of those three premises, but where do they begin?
I think (1) and (3) can be strongly supported, so the weakest point open for attack would be (2). What would it take for a Mormon to show that the denial of (2) is plausible?
I see you were already aware of its problems and what the first line of attack would be.
I suggest that (2) is false if and only if there is a state of affairs in the actual world which it would be logically impossible for God to bring about without permitting the occurrence of at least one instance of reasonable nonbelief. That is to say, it must be a state of affairs whose existence logically necessitates the permission of reasonable nonbelief, otherwise an omnipotent and perfectly loving God would bring it about without permitting the occurrence of reasonable nonbelief.
If one were to take this as definitive, then literally everything that exists in the natural world, as they can be explained at various levels of analysis without referring directly to God, is evidence for non-belief, and premise (2) must be correct. The problem - and a severe one - lies in the implicit assumption (again) that if God existed, he would make his existence conspicuously obvious by creating a world in which nothing that existed could be thought of as evidence against his existence.
Given what LDS theology teaches regarding the "plan of salvation" and the character and attributes of God, there is no reason to believe that God would "operate" in this manner regarding the question of how human beings are to be made aware, or if specific persons are to be made aware, of his existence, regardless of his attribute of all-lovingness (which, for LDS, could not utterly dominate and overwhelm his other attributes, such as his absolute respect of human free agency, and his perfect knowledge of the requirements of the plan of salvation relative to the capacities and needs of his children).
A further problem lies in another implicit assumption that would place upon God the sole responsibility for making his existence known. The fundamental basis of gospel teaching, however, is that only as we "knock" is the door opened, and only as we ask, is it given. A
relationship between man and God regarding the manner, conditions, and timing of the revelation of God's existence to a particular human being is present in the actual teaching of the gospel (and Christianity generally) that is completely washed out of stak's argument.
God's existence is made known to individuals, individual by individual, predicated upon the conditions and requirements governing the reception of that kind of knowledge, and not in a general empirical way or logically required way, because, again, of
the requirements of the plan of salvation relative to us and our needs as mortals undergoing a "probation." in the "telestial" world. His personal attributes do not exist in isolation from eternal law and his relationship to us as, not just God, but as our
Father in Heaven following the necessities of the plan through which we can return to him and become like him (deification).
Part of that plan, indeed, a requirement of it, as understood in LDS theology, is the existence of a world that can be interpreted in a variety of ways, even though the same phenomena are at issue.
Does the LDS Faith have an answer to this? I would say that it does not and therefore can be rejected.
You are far from making that case, and I don't think a strict adherence to formalistic deductive logic is going to get you very far along the way unless it is combined with other means of critical reasoning.