I agree that the mind seems to operate as a formal system, though this may be difficult/impossible to see on the lowest levels (i.e. machine language). However, it is also not a closed system in itself. The formal system of the mind is truly formal, but not consistently in effect. A misplaced neutron from an outside or inside particle could break a single atom/molecule/protein, and the rules may change to some extent. The mind is only a truly formal system when scope is limited and events are restricted. Basically, all minds and all matter are just bits of one formal system, and while levels above that of quantum physics (i.e. a mind) mimic the same formal system within themselves and abide by its laws completely, they are not truly formal in the end, because they are not in themselves closed systems from other influences.So yeah, a mind operates formally, but in practice, this never really happens, except on levels that would not distinguish a "mind" as an independent object in the first place. I would say that calling the mind a formal system is the same as calling the process of evolution a formal system. Perhaps legitimate, but, like quantum physics, statistics is probably the best or only kind of tool available for making valid predictions.In sum, the mind as an independent object is a formal system with some informal rules for changing based on lower-level events. Sort of a crappy chaos-theory-spectrum qualifier, but "in practice" is what is always going to be observed, so I consider it crucial to a scientific understanding. A perfect mind, I think I concede, is formal.
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