Depends on whether you consider facts or theory. Facts don't prevent logical arguments from seeming to work, but lack of free will is theory. When theory doesn't match facts, theory is wrong.

We have built systems that don’t have free will and respond to logical arguments, so no theory is required here.

Random processes can’t use logic.

Fuzzy logic deals with truth values between 0 and 1. You can for example map water temperatures in such systems without having arbitrarily important cutoff points.

Such system often deal with uncertainty quite well including random noise on their inputs. The output ends up a function of both logic and randomness, but can still be useful.

Agreed, I don’t believe a system like that can access the platonic realm of mathematical truths. It’s clear that an electron doesn’t carry the laws of physics with it as it travels.

Why not? The human brain is hardly a perfect system of logic but can emulate such.

Something is orchestrating the decisions that the brain executes in the conscious realm though. (As opposed to or in contrast to the mathematical realm and the realm of the physical laws). We are clearly surrounded by invisible realms, unless you believe electrons are carrying lookup tables of how to respond to invisible electric fields.