It doesn’t actually matter, for the sake of this argument, whether the “cause” in the cause-effect relationship is entirely within our brain chemistry, or from external (material) forces. It’s the deterministic, or non-freely-chosen nature of thought in a purely material context that’s the problem.
If a conscious agent is to construct a logical argument, they must be able to freely choose the links in that argument, otherwise there is no effective difference between “logical” thought and “random thoughts about subject X”. And the very idea of actual free will (as opposed to the mere appearence of it) seems to be incompatible with the idea that the material world is all there is, and that every state in the physical world is caused by a previous existing state. So in a purely material world you can never tell whether an argument is logical (rather than merely the result of aberrant brain chemistry) - including any argument proving that the material world is all there is
“notice the effects of” might have been a better term to use, regarding the non-physical world.
If we’re going to be debating whether any sort of non-material world exists, it’s helpful to figure out what the characteristics of any such construct would be if it existed. If we don’t know what it is, it makes it a lot harder to decide if it is, if you see what I mean. So in my points a - d, you can add the phrase “any such non-material world must have the characteristic” to the front of all of them, if it makes things any clearer.
Point (a) is simply “the particular non-material world whose existance or otherwise is one which has (or “would have”) regular interactions with the material world”. I take it that both sides in this debate would have to agree to that, otherwise the debate might veer off into discussion of miracles and other one-off events which would (if proven to have happened) refute the OP’s position. I take it that this is not the sort of thing under discussion, we’re just talking about regular every-day thought, existence etc as experienced by everybody.
The position of a particle by itself is not an “event”. An event is an interaction between at least two objects, so in order to measure it accurately you need to know accurately the position and velocity of two different objects. That cannot be done (for appropriate values of “accurately”).
Furthermore, you cannot measure an event without changing that event. Bounce a photon off a pair of particles to check where they’re hitting each other and you’ll shift their position.
So given that level of uncertainty in the actual fabric of the universe, how could you ever tell if there was “something” influincing the material world which was not part of it?