There is. It's called quantum field theory. QFT has the peculiar property that the interactions between elementary particles in it are symmetric in space and time. What that means, is that if an exotic particle is capable of interacting with some of the commonly known everyday particles, which we know the brain is made of, we are also capable of producing that exotic particle using our common, everyday particles. That means that if exotic particles exist, they interact with the everyday particles very weakly - otherwise we would've already produced them in the LHC.
That means that even if exotic particles existed, they wouldn't have a practical effect on everyday matter, and thus, to our brain.
This all, of course, lies on the assumption that the symmetry property of QFT is correct. It's very likely to be (at least in everyday conditions, such as in a slab of fat in 37 C heat bath) – after all, QFT is the most experimentally precise scientific theory ever discovered in the history of science.
They are an example or P that doesn't belong to P', using your terms. Check this talk of the cosmologist Sean Carroll's, he adressess this problem and claims that the underlying physics of our everyday reality are completely known: https://youtu.be/xv0mKsO2goA
Is there any reason for the operations of brain to be limited to those involving P' only?