We must distinguish between what is the universe is and what we think it is. I am not sure if there is any point talking about the universe as it really is since this discussion takes us into the unknowable. Therefore let's talk about the universe as we can perceive it.

If we consider ourselves to be "deterministic and finite state machines" then the universe we perceive is definitely a set since we can only perceive a limited set of mental states. If we insist that the universe that we perceive is not a set, then we must also admit that our thinking process cannot be described by deterministic and finite state machines. I believe this argument presents a problem for Bruno who relies on the machine model to describe the human mind. What is a set, and what is deterministic may depend on the observer, as strange as it may seem. For example, if my mind can be modelled by 1000,000,000 states and your mind by the same 1000,000,000 states plus 1 for a total of 1000,000,001 states then I may perceive your behavior to be sometimes indeterministic or, in human terms, incomprehensible. George Levy