You could have stopped there. A thing that is not physical, exists. Bye bye materialism. Materialism is monism, holding that things are only made of one kind of 'stuff', specifically physical stuff. You can't get around that by saying that "you don't need to invoke anything non-material to explain" non-physical things. The mind is the non-material thing. As soon as you say it exists, you've thrown out materialism. The thing you're trying to defend is physicalism, which is an entirely different ball of wax. Physicalism is exactly the sort of 'multiplication of entities' that I was referring to in the first paragraph of my original reply.
> Entities are encoded in our brains.
That doesn't make them physical, any more than '4A' is the same thing as 'J' because that's it's ASCII representation. An encoding is not the thing. The representation in the brain is physical, the thoughts in the mind concerning them as well as the entities themselves aren't.
The mind is a description of the organization/structure/function of a chunk of matter. And the matter part completely determines the non-material part, hence materialism, no?
[citation needed]
The mind is not a physical thing, that's correct, but we need not claim the existence of anything non-material to explain the mind. The mind - or more specifically consciousness is made of information, which is 100% encoded in matter, hence materialism. (See Joscha Bach's detailed description of this.)
> But that 'pointing' isn't the actual system, it's an abstract thing that helps our minds understand the underlying system it's running on.
Yep, and that's platonism in a nutshell, but that doesn't contradict materialism either.
Entities are encoded in our brains.