Therefore, the distinction undermines an objective verification and thus has no way of being truly verified or falsified. If I understand your argument here, John, you are saying that determinism implies causation by antecedent non-personal causes and that further implies that all of our reasoning is caused that way. Who knows, you might be right, but you need an argument showing that Calvinism entails physical determinism, which I don't think it does. I don't have the reference here with me, but Van Til somewhere critiqued Buswell's critique of his apologetic system by saying that Buswell incorrectly infers that the sovereign foreordination which is part of a robust Calvinism is identical to a physicalist understanding of determinism. I'm sure that all systems claim possession of the warrant corresponding to reality, but the system which actually does cannot be determined if thought, in general, is confined to a string of causes ending with something, or somebody, pulling the strings.
Symbolic metaphor is no substitute for logical analysis.
Though if a thinker's belief is caused by an antecedent state that is not initiated by the thinker, that's determinism. Another individual comes along and asserts non-A. When the same question put to the previous individual was asked of this individual, she replied in the same manner. For example, if person S believes p, a true proposition, on the basis of her inferring p from q, another true proposition, and if the inference from p to q is rationally warranted for S, then her believeing p on the basis of q represents no cognitive malfunction. The only problem is that each individual has her own system of interpretation dependent upon the very thing in question. I sort of smell a Montgomery in the air.