If you take a scientific and strictly reductionist view of the mind you might have an argument that looks similar to the following: All matter in the universe is governed by the same laws, the mind is composed of matter, the particles of which have properties we know a little about. The mind is a product of these behaviors: Πgi(xj) where i and j are all possible indices of particles and something like “quantum numbers,” respectively. Supposedly, with enough particles and quantum numbers you can account for the complexity of the world, but I think that many who take this view feel that it forbids things like the “soul” or “free will.”
This is completely reductionist, that any system can be broken down into the sum of its parts and their product can account for the behavior of the whole. This is a tenet of statistical mechanics/thermodynamics and serves as check for physics in general and also chemistry and biology, the next rungs on the scientific theory scale ladder. In regards to physics in particular this line of thinking mimics the plan of attack for basic quantum mechanics – that a system can be broken down and analyzed by assuming products of functions of independent variables.
But what if there are functions that cannot be separated in such a way? What if there are properties (functions) that have two particles as a domain – f(gi(xj), gi+1(xj))? In this case, you would have to examine both of the particles in the system in order to learn conclusively of the behavior of the property – you would have to examine the entirety of the system. This, however, is not how we explain objects.
Take a cup for example. I can tell you lots of things about it – its color, weight, topological properties. I can also examine a few of its particles. But if I am to claim I know all there is to know about the cup then I must also claim that I can extend things learned about the small part of the cup to the remainder of the parts of the cup. But I cannot make claims about properties of the cup that require more particles than I can examine – I can make guesses and see how they line up with experiments about the entirety (like weight?), but I can’t deduce these properties. So either all properties of the universe can be detected through some finite number of particles or there is no limit to the size of the domain of a property. The reductionist claim sounds like all properties are properties found through a single particle, or a single particle of each type.