Dear Larissa,
I carefully read your essay. Your approach and mine are radically different, but this precisely could be a sufficient reason to have a good discussion.
Your essay has a great merit. You honestly describe the constraints a given system has to master so that we can ascribe to the system in question. " A system can only 'process' information to the extent that it has mechanisms to do so." And "The cause-effect structure of a system in a state specifies the information intrinsic to the system, as opposed to correlations between internal and external variables. If the goals that we ascribe to a system are indeed meaningful from the intrinsic perspective of the system, they must be intrinsic information, contained in the system's cause-effect structure (if there is no mechanism for it, it does not matter to the system)." Finally "Yet, the system itself does not 'have' this intrinsic information. Just by 'processing' information, a system cannot evaluate its own constraints. This is simply because a system cannot, at the same time, have information about itself in its current state and also other possible states."
Shortly speaking, for the concept "goal" related to any system to have a meaning, the system in question must be equipped by a a lot of natural or artificial devices, whereas the set of the latter is supposed to be configured in an exactly determined way.
Suggesting that the forgoing is easy to say, but much less easy to realize, and even to model, you are absolutely right.
Well, but do you not agree that the problem is much more fundamental?
To specify the information intrinsic to any system, the required internal causal structure of this system must be "able to specify" information, and this "ability" presupposes other "abilities" like the "ability" to recognize information before and after being specified. So, the more fundamental question is: where do these "abilities" come from?
Yes, "by 'processing' information, a system cannot evaluate its own constraints", but the very fact of evoking systems "'processing' information" already implies the presence of "information processors" within these systems, and once again, we have to ask the more fundamental question is: where do these "information processors" come from?
And so on.
These "more fundamental" questions which until further notice have no answers converge to the problem of generalized irreversibility. In a classical manner going back to Clausius, generalized irreversibility can be formulated as follows: For any system S apparently violating irreversibility, there is a "wider" system S' "comprising" S, so that at the level of S', irreversibility is reestablished. In the classical formulation, notions like "wider systems" or "systems 'comprising' other systems" are rather vague, and so not really appropriated for taking into account intrinsic information or integrated information you are focusing on.
Now, in order to touch the essential without too formal developments, let us consider the good old Maxwell's Demon operating on its Boltzmannian gas. In your eyes, Maxwell's Demon perhaps belongs to ancient history, whereas most authors, for diverging motivations going from Landauer's "principle" to whatever it may be, believe that the Demon is not able to accomplish its mission. But on the other hand, the Demon represents an intuitive mean to grasp the more fundamental problem being behind all superstructure problems concerning integrated information. So let us do as if Maxwell's Demon could do its job.
Operating in the well-known way, the Demon pushes the gas back to its ordered initial state. Under single-step selection conditions, the improbability of the transition would be tremendously high. Considered alone, the gas expresses a genuine irreversibility violation. In fact, the gas is not alone, because of the Demon's presence. Here the "wider system" reestablishing irreversibility is to be interpreted as a system with integrated information, and so all the questions arising with regard to information integration arise again. It is easy to "imagine" - like Maxwell - the existence of the Demon. By contrast, it would be hard - infinitely hard - to equip a mesoscopic, perhaps I should say microscopic device so that it is able to detect instantaneously the motion state - velocity, acceleration, direction - of each molecule present in the neighborhood of the gate, knowing that in the sole neighborhood of the gate you find an unimaginable number of molecules. Further, the microscopic Demon has to be able to take instantaneously the good decision. And then, the Demon must be conditioned to be a serious, conscious scientist respectively meticulously the experimental protocol, and not a trouble-maker misusing its quasi-infinite intelligence to make bad jokes or something else, and this point presupposes moral qualities. And so on. Yet, the foregoing is not a bit easy caricature. A task like re-ordering a disordered gas - a simple task in comparison with other tasks implying aims and/or intentions - needs information integration we cannot master, neither technologically, nor intellectually. I think, you agree.
But now we arrive to the essential: Beyond integration problems, there remains the more fundamental problem of generalized irreversibility. Even if the Demon, against Landauer, Szilard, Brillouin, Costa de Beauregard ..., actually managed to "generate work by entropy reduction", generalized irreversibility would not violated: the transition of the gas from maximal disorder to initial order under single-step selection conditions is tremendously improbable, yes, but the "emergence" of the Demon under the same single-step selection conditions is infinitely more improbable. So, as well as within any case of generalized irreversibility, the apparent irreversibility violation by the gas is "paid" by a given higher improbability at the level of the "wider" system consisting of the gas and the Demon.
As long as the devices required by information integration are given, information integration is hard to formalize, hard to realize, but at least we can conceive it to some extent.
By contrast, in a context like evolution where the devices required by information integration are not given, we have to ask where they come from, and at this level of analysis we merely are lost.
So, in my own paper Daring Group-theoretic Foundations of Biological Evolution despite Group Theory I try to tackle the problem at source, at the fundamental level concerning irreversibility.
Just because of the differences between your really interesting paper and mine, a discussion about both papers would be a pleasure for me.
All the best; good luck
Peter