You're confusing two different kinds of relation. Logical relations are timeless, connecting essences or characters. Causal relations are temporal, and connect events. Hence in reasoning, logic is not the cause of the outcome. Logic is not a series of causes and effects, whether physiological or psychological.
Logic is simply the fact of the consistency of one statement with another. It's the knowledge of these consistencies and inconsistencies which is to some slight extent the cause. Causality links events and the events in the case being considered are first my acceptance of the conclusion, then my apprehension that the premises entail the conclusion, and my acceptance of that conclusion.
It is between these events, or psychical facts, that the causality holds, and it's as meaningless to say that one such event entails another as it is to say the premises cause the conclusion.
An attractive view, for the moment. You're trying to draw a line horizontally through a train of events, and say that above that line are the characters or universals of logic, and below that line are the existences or occurrences of causality.
But that kind of line can't be drawn. Even if it could, causality would have no necessity or meaning. The characters dealt with by logic do enter into the causal process. An event without characters is no event at all.
If what happens is nothing, then nothing happens.
When a hammer drives a nail, the cause in part is the motion of a certain mass at a certain velocity. These characters are an integral part of the cause. It's because of their presence that this effect rather than some other is produced, and no statement of what caused the effect could disregard them.
In the same way, the psychical event called the occurrence of a judgment in a mind is not a naked act or event. It's always a presentation of this rather than that.
And the character of this content enters vitally into the causation.
Now if the contents or characters of the events enter into the process, we can't say that the relations between these characters are irrelevant to it. Maybe no one would deny that there is a fact such as association by similarity. And however difficult it may be to construe the mechanism at work, it would be futile to deny that the similarity of content sometimes has something with the appearance of an associate. That relations within the content play a part in causation is even clearer when the relation is logical necessity.
In explicit inference we have a process in which we can directly see not only that one event succeeds another, but in large measure why one event succeeds another. It would be absurd if after the presence in our minds of the judgments, 'the squire was the abbe's first penitent' and 'that first penitent was a murderer', and the conclusion, 'the squire is a murderer', that we said we didn't have the slightest notion of why this conclusion emerged rather than a judgment about Florida grapefruit.
The fact that this was the logical conclusion to draw is relevant to its appearance as an event. And this does not commit us to say that necessary relations, connecting the content now before us with something else that is not before us, have something to do with the development of this content in one direction rather than another, that necessities within the subject-matter lay under some degree of compulsion the temporal path of thought. You may not accept the metaphysical theory I offered earlier to explain this compulsion, but the compulsion is an undeniable fact.