It occurs to me I ought to share a few more excerpts from Athel Cornish-Bowden's article to underscore the difference. Rosen's book makes the point exquisitely by mathematics, it cannot be escaped. But Athel's brief description here may be kinder to the reader:
Yet that is what a living organism does. Not only does it make itself (something no existing machine can do), but it also monitors the working state of all of its parts, and replaces those that need replacing, all of this being done from within. As we know, in good conditions a human being typically lives for about 70 years (even without the intervention of modern medicine, which is, of course, external), while containing necessary components with lifetimes in the range of minutes. This is a discrepancy of well over six orders of magnitude in the lifetime of the organism compared with that of its parts. Proteins vary considerably in their lability, and in many cases they are degraded as a result of specific catalyzed processes and not just by being worn out, but, even if this is ignored, none survive completely unchanged for decades. Some proteins, such as the crystallins of the vertebrate eye, are never replaced, and remain in use for 90 years or more, but this does not mean that they remain in perfect condition and suffer no damage. On the contrary, cataract is just the most obvious indication that crystallins do not survive unchanged for decades. The difference for crystallins is that the organism can survive without repairing the damage, whereas the overwhelmingly more usual case is that damage needs to be repaired at a rate essentially the same as the rate at which it occurs.
Understanding how this maintenance is achieved is a huge problem, and even if we restrict attention to the purely chemical part of what it means to be alive, that is to say to metabolism, it is still a huge problem. The chemical reactions that constitute metabolism require enzymes to catalyze them, and these enzymes survive for periods that are several orders of magnitude shorter than the period in which the metabolism continues to function normally. They therefore need to be replaced. (Rosen referred to "repair" rather than replacement, but that was an unfortunate choice of term, especially now that we know of many examples of genuine repair of nucleic acids, and a few examples of repair of proteins.) The enzymes themselves must therefore be regarded as metabolites, i.e. products of metabolism, and other enzymes are needed to catalyze the replacement process. However, these other enzymes also have finite lifetimes, and also need to be replaced, in processes catalyzed by yet other enzymes, which also need to be replaced, and so on for ever unless there is a way to close the circle. We therefore need a way of conceiving that the organization of metabolism is circular, so that at no point do we need to rely on any external help.
For almost all modern organisms a small amount of external help does exist, in the sense that apart from strict chemotrophs we are all parasites, as we need some of the products left by other organisms in order to survive. However, this dependence on other organisms solves only a tiny part of the problem, even for the most thoroughly parasitic of organisms, and it cannot even have solved a tiny part for the first organisms, which needed to survive in a world with no others to parasitize. Even the first organisms, of course, required some inorganic nutrients, just as all modern organisms do, so of course no organism is closed to material causation (and Rosen did not suggest that they were). This statement of the problem is probably clearer and easier to understand than the proposal of circular organization as a solution to it.
Or to put it another way, under the mechanistic, reductionist, contemporary view everything physical is a machine and can be analyzed and synthesized. That is the Newtonian paradigm. But it cannot admit that which has not yet occurred, i.e. final cause, the reason for which a thing is.
The one exception to this in the mechanistic paradigm is when the future is expressed in the present, such as in the Fibonacci series. But Rosen closes the causation by his circular model which entails much more and features encoding and decoding in the "chasing" (read Shannon here.)
In sum, biology is seen as a "special case" within the mechanistic worldview. And is generally ignored under the presumption that it must also be mechanistic because the paradigm works so well for physics, chemistry, etc.
But in reality, biological systems actually anticipate and thus Rosen steps away from the mechanism and instead models the organization without appeal to any outside causation. And thus the time issue disappears.
And yet the Newtonian Paradigm proffers no help whatsoever in the small matter of "closing the circle." Yet "strong Newtonians" will demonize you as some kind of deranged mystic for even noticing the problem. Notwithstanding, it is STILL THERE: If you can't "close the circle," you cannot avoid the perils of the problem of infinite regress. Nothing infinitely regressive can ever mean anything.
On the other hand, one cannot "close the circle" absent the idea of final cause.
How can such a trusty old friend as Newtonian mechanics be so silent on the question, What is life? As Robert Rosen suggests, it lacks the universality it claims because of the constraints of its own self-imposed formalism. This formalism requires us to view Nature as a syntactical system.
To put "syntactical system" into context: Under the auspices of Natural Law, we are entitled to "deconstruct" any natural language into two separable components, semantics and syntax.
Very crudely put, semantics pertains to meaning — it associates a word directly with an external referrent (something in Nature that we try to establish cognitively by defining it, in communicable terms to others who speak/read the Natural Language). Once this association is established, the meaning of the word is established.
Syntax, on the other hand, is directly associated with the idea of grammar in a natural language: The "rules of the road" that specify how the parts of natural speech (e.g., nouns, verbs, adjectives, adverbs, pronouns, articles, prepositions, et al.) can be fittingly combined so to effectively convey semantic meaning in the given Natural Language. This is, in fact, a pretty "universal idea" — provided it can be isolated from the context of Nature altogether (i.e., from the context of meaning). Which is done implicitly by "pulling Nature itself" into the formalism. Nature then becomes, not a system containing inorganic and organic objects, but a set of syntactical rules.
When we speak of a "syntactical" approach or formalized model of Nature — as Newton evidently was glad to do (he said he was only interested in "descriptions" anyway) — we are already dealing with a world of total abstraction from Nature. We have withdrawn into the mental world of the formal construction, because we clearly understood that, if you want to have a "universal" law, it must be independent of any of its particular realizations. Only then can we say an observation is perfectly "objective" — because all the "baggage" of subjective engagement of questions precisely about meaning have been forbidden. The price one pays for this "objectivity" is: the abolition of all "external referents" by which "meaning" can be "entailed!" But we do get our "universality" that way.
As an observer from the semantic universe, I see how all this fails. The semantic aspect of meaning is never reducible to syntax. Therefore, I would expect all syntactical formalizations seeking to give a "universal" answer to the question, What is Life?, to fail against the tests of Nature.
Somehow Nature is meaningful. Natural Law already states this.
Rosen has certainly raised some interesting problems for me, dearest sister in Christ! And you also it appears! Thank you so very much for the excerpt from Athel Cornish-Bowden. He does manage to take away the "sting" of the seemingly relentless math of Rosen's reasoning, boiling it down to more intuitive concepts. Still, I believe Rosen ultimately must speak for himself, and in the terms he has chosen.
I'm no great mathematical genius myself when you come right down to it. Rosen relies heavily on set theory and (above all) Category Theory — pretty "high-level maths" for your average bear. But I could follow him throughout. He made sure of it — what with his graphs and his relational diagrams, married to excellent communication skills. :^)
In closing, just a remarkably astute comment from the sainted Einstein on this very point: "One can best feel in dealing with living things how primitive physics still is."
To God be the Glory!