Dear Ms Stoica,
"The highest levels appear from the lowest level by ignoring details, resulting in a coarse graining of the state space." You identify it is as a process of abstraction. In a long time, I find a person that agrees on this. Thank you. Yet, its potential is far greater.
You take this example to defend the emergence of indeterministic statistical laws from deterministic processes at the most fundamental level. I cannot agree with this entirely. By asking to ignore the details at the lower level, what you allow is that many microscopic states map to one macrostate, and at macroscopic level, there is a many to one mapping. At the microscopic level though, evolution proceeds as one to one mapping between cause and effect, which in turn causes unique thread of macroscopic evolution, regardless of what it may appear at coarser level of macroscopic details. In fact, even if we consider many to one mapping at microscopic level, still we do not escape the unique trajectory in phase space. That is, the past of the universe may have many descriptions, but the future is unique since you do not allow one to many mapping. This logic could be applied to the earliest possible epoch, and then we could say that one is tracing a single thread of outcomes making the universe entirely deterministic. Therefore, indeterminism may arise only if at the fundamental level also many to one, and one to many mapping occur in the state space. Otherwise, statistical significance would vanish with sufficiently powerful computing technology.
In sections |9> to |11>, you have touched upon so many ideas and notions that overlap with elements of my own, that if I try to discuss and compare them all, it would be as much as the essay itself. Yet, let me take a few.
All of our thoughts have informational basis, all descriptions are informative, all communications are exchange of information. And here I do not mean quantity of information (as per Shannon), but the semantics (meaning) of information. All information is relational. Does information have a reality of its own? Information does not have to be digital or discrete at all. Due to our ability to draw inferences from observation of states of matter we tend to accept that association of information with states results from an act of modeling, without realizing that unless the system like brain has the ability to store, process, and transmit information by natural means, no information may ever come to reality. Therefore, either information has a reality of its own in the function of the universe, or it can never come about. In fact, if we associate information with states of matter, then the states must naturally bear correlation with that information. Moreover, with each interaction then information processing takes place.
Panpsyschism does not have to be right. Goals / aims are abstract information of expressions of 'need or want' that can emerge from specific structured information processing in a reproducing systems, as I have attempted to work out in my essay. That is, goal is not fundamental, information is.
"Is this impossibility to give an objective definition of subjectivity a proof that the hard `problem doesn't exist? ... A subjective science can't be objective ..."
Hard problem may dissolve if we find objective process of building abstraction. The process of abstraction that you mentioned is the potent mechanism to give rise to irreducible symbolism -- you may refer to my submission. Yes, you are right in saying, "Maybe subjective experience emerges from the organization of matter, or as a property of information.", It is not as much as the organization of matter as it is for the organization of information processing.
"This leads us straight to Tegmark's mathematical universe hypothesis, which posits that physical existence equals mathematical existence."
1) There are other mathematical structures that are not applicable to physical world as we see it. And there cannot be a limit on number of mathematical structures.
2) Mathematics as we construct and apply are deterministic, it cannot deal with indeterminism. Laying down the probabilities is not a description of the physical function.
3) If a priori truth of mathematics is equivalent to physical universe, then description of the universe had the reality of eternity beyond time; there could not be anything that has not happened, and there could not be anything that is not happening at each moment of time. Indeterminism comes to rescue here again to save the universe from the eternity of the mathematical laws. Prof Max Tegmark is off the mark maximally.
By the way, I apply the following statement of yours, "because there are structures that can't not exist - mathematical structures", in a slightly different way. An universe has no existence if there is no pattern, no constancy in the function of its elements, but then given any correlation or constancy of relation, it cannot avoid exemplifying a mathematical structure.
As an aside, it appears that you have practiced Vipassana technique of meditation, it is not possible to be so accurate in articulating without having gone through the experience.
Rajiv