And you're bad at this.
> If Charlie holds to different laws of logic than Bill...whose brain is right?
If they're using different forms of logic, then they're both right according to the form they're using, but they can't be compared to each other unless they're using the same kind of logic.
> Your view is that laws are just conventions of thought. Those aren't laws, then.
It's not my view, it's simply the way it is. Different rules of logic exist [1]; such systems are axiomatic and obey their own rules. There is no one "correct" system of logic, there are many competing systems. The term law is meaningless, logic isn't a law in the sense you seem to think, it is merely a system of formalized thinking according to rules.
> I again assert: rationality is impossible without laws of logic. With conventions of logic, you just have strong opinions.
Logic is merely a branch of philosophy concerned with valid reasoning. Reasoning is not in opposition to materialism. Materialists do not argue that thoughts don't exist and logic is merely a formal method of thinking. You're objecting to materialism when it's quite clear you don't understand what it is.