Perhaps the single best-known phrase emanating from Rosen’s work is “closed to efficient causation”. Unfortunately, this is perhaps also one of the most commonly misunderstood phrases from his works. Below, I attempt to describe the meaning of this phrase.
The origin of the phrase
The phrase “closed to efficient causation” originates in Rosen’s book Life Itself, p. 244:
The reader who as come this far may recall that, at the very beginning, we started with a question. The question was: “What is life?” We have discussed many things between then and now, things that often seem to ramify off in many directions unconnected with this question. But in fact, everything we have discussed in these pages is there only because it plays its role in allowing us at last to propose an answer.
The answer we propose is now this: a material system is an organism if, and only if, it is closed to efficient causation. That is, if f is any component of such a system, the question “why f?” has an answer within the system, which corresponds to the category of efficient cause of f.”
The above passage is in the context of Rosen’s conclusion after many chapters that include discussion of Aristotelian causality in simple system (i.e., mechanisms and machines). The upshot of those discussions is that mechanisms and machines have a paucity of entailment structure: most everything about them in terms of efficient cause must be entailed from outside of them. When we ask “why f?” about a component in such a system, and look for an answer in terms of efficient cause, it can ultimately only come from outside the system itself. The drawback to such systems is that if we wish to entail those efficient causes, we must do so by adding yet another component to entail it. But, of course, now the newly-added component is unentailed, and an incipient infinite regress follows.
Rosen’s contention is that biological organisms – by contrast to mechanisms and machines – entail most everything about their functional organization within themselves. As a result, biological organisms can answer “why?” questions about components of their functional organization in terms of efficient cause from within this organization. However, the notion that such entailment occurs has tremendous implications for biology, physics and science in general. At the very least, such a requirement means that organisms have models (such as the metabolism-repair system model) which describe impredicative loops of causation. These kinds of models are thus noncomputable: they cannot be turned into algorithms for computational processing.  Further, state-based descriptions, upon which all of physics rests (including quantum mechanics) are unable to describe systems possessing these models. The result is that the limits of description imposed by the approaches of computational modelling and by state-based physics are entirely artefactual, and do not represent fundamental limits of the material world. With regard to biology, those approaches are incapable of answering fundamental questions about organisms, such as “what is life?”, because they are unable to represent the relevant features of the material systems we call “organisms” within their formalisms.
Brief Overview of the Metabolism-Repair Model
Looking at the diagram of the metabolism-repair system (also called an “(M,R)-system”) model  above, we are viewing a diagram of sets and mappings, related by arrows of efficient and material cause. Briefly, the diagram shows three functions (f, b, F), which together comprise a minimal model of functional organization in an organism. [Without going into the technical details, b is defined as being derived from an element of the set B. ]
The function f represents metabolism:
Raw materials (elements of A) are processed into (elements of B). As mentioned above, b is derived from an element of B, so f can be thought of as also a function for generating new copies of b.
The function F represents repair:
Repairs the metabolism function. The output of F is H(A, B), which means “a set of mappings from A to B“. The elements of H(A, B) include the mapping f. Hence, F can be thought of as a function for creating new copies of f.
The function b represents replication:
Replicates the repair components. Just as the output of F includes new copies of f, so too the output of b includes new copies of F. IMPORTANT: It is crucial to keep in mind that “replication” here refers to replication of the repair components (F); it does not refer to reproduction of the organism!!
As Rosen says, “It is not too misleading to think of f as a kind of abstract enzyme, which converts substrate a ® A into products f(a) ® B, and to think of F as a process that converts these products into new copies of such an abstract enzyme”. 
So…what is “closed”?
We can see that each function (f, b, F) is entailed from within the diagram by another function. Specifically, each function is entailed in terms of efficient cause by another function. Chasing the red arrows through the diagram: f entails b (by producing elements of B), b entails F (by producing elements of H(B, H(A, B))), and F entails f (by producing elements of H(A, B)).
We therefore have a loop of entailments of efficient causes of functional components. So, my summary is as follows:
“Closed to efficient causation” refers only to the existence of a loop of efficient causes in the entailment structure of the functional components in the (M,R)-system model.
A helpful way to think about this is to consider the opposite case: what would the entailment structure be like if the (M,R)-system were open to efficient cause instead of closed? In that case, the functions would have to be entailed from outside the diagram. In other words, in order for a function such as metabolism, for example, to occur in an material system open to efficient cause, there would have to be some external efficient cause – some external entity – that would act as the processor that generates the processor f in the metabolism function. Similarly for repair and replication.
However, this is not how organisms work: organisms contain their own processors, their own efficient causes of at least these basic functions. Organisms, then, are a material realization of an invariant pattern of organization of these functional components and their efficient (and formal) causes. 
So…what is not closed?
As we have seen, “closed to efficient causation” refers to the loop of entailment of efficient cause within a single living organism’s functional organization. The use of the word ‘closed’ regrettably often brings to mind in some people very different notions of ‘closed’ or ‘closure’ other than “loop of entailment”. It is typically the erroneous substitution of these other notions of ‘closed’ that is the source of the misunderstandings.
“Closed to efficient causation” does not refer to, or imply, “a closed system”, in the usual sense. Indeed, an organism is a paradigmatic example of an open system.
“Closed to efficient causation” does not refer to, or imply, an organism is thermodynamically closed. An organism is obviously thermodynamically open.
“Closed to efficient causation” does not refer to, or imply, an organism is materially closed. (Note that node A in the (M,R)-system is explicitly unentailed: the source of raw materials for an organism comes from its environment.)
“Closed to efficient causation” does not refer to, or imply, that an organism is structurally closed. Metabolism, repair and replication are functions that are spread across physical structures in an organism. In other words, functional organization does not coincide 1-to-1 with the organism’s structural organization. So, attempts to purport to show that “closed to efficient causation” is false by use of gedanken experiments involving replacing organs, excising tissue, and other structural alterations which leave the organism alive, are misguided.
“Closed to efficient causation” does not refer to, or imply, that an organism is closed with respect to its offspring or it’s progenitors. The loop of entailment at issue occurs within the functional organization of the individual organism. Progenitors and offspring are other distinct and separate individuals. (Perhaps the misunderstanding that “closed to efficient causation” relates to offspring or progenitors derives from a misinterpretation of the function of replication (b) as erroneously meaning “reproduction of the organism” rather than “replication of repair components (F)”.)
“Closed to efficient causation” does not refer to, or imply, that an organism’s metabolism, repair or replication cannot be affected by other influences. This would be a misconstrual of “closed” as “closed off”. However, Rosen does not indicate the latter connotation anywhere.
“Closed to efficient causation” does not refer to, or imply, that an organism is functionally closed (i.e., cannot have other functional relationships aside from metabolism, repair and replication). The (M,R)-system model is only a minimal model: an organism is at least a realization of an (M,R)-system, but it may (and most likely does) have additional functions.
In the formulation in Life Itself, Rosen asserts that “closed to efficient causation” was both a necessary and a sufficient condition to call a system a living organism, as can be seen in the quote shown in the origin section, above.
In the posthumously published Essays on Life Itself, Rosen appears to have reconsidered this assertion. Specifically, he appears to consider “closed to efficient causation to be only a necessary condition:
“To be sure, what I have been describing [e.g., “invariant graphical patterns of formal and efficient causation” – TG] are necessary conditions, not sufficient ones, for a material system to be an organism. That is, they really pertain to what is not an organism, to what life is not. Sufficient conditions are much harder; indeed, perhaps there are none. If so, biology itself is more comprehensive that we presently know.” 
However, as pointed out by Aloisius Louie, this is not at variance with the previous assertion:
Let’s backtrack a bit, and list three quotes from Bob:
Quote 1. A material system is an organism if, and only if, it is closed to
efficient causation. (p.244 of “Life Itself”, Section 10A. The Answer)
Quote 2. To be sure, what I have been describing are necessary conditions, not sufficient ones, for a material system to be an organism. That is, they really pertain to what is not an organism, to what life is not. Sufficient conditions are harder; indeed, perhaps there are none. If so, biology itself is more comprehensive than we presently know. (p.28 of “Essays on Life Itself”, Section on What Is Life?)
Quote 3. A cell is (at least) a material structure that realizes an (M,R)-system. (p.263 of “Essays on Life Itself”, Section on The (M,R)-Systems)
Q1 is a statement of both necessity (the “only if” part) and sufficiency (the “if” part). Q2 is self-explanatory. Q3 is a statement on necessity (the “at least” part is an emphasis on this “necessary-but-not-sufficient” condition).
In my retort of the Landauer-Bellman paper (that I sent you a few months ago), I wrote “Landauer and Bellman are confused between necessity and sufficiency. The Rosennean statement is that “a cell is a material structure that realizes an (M,R)-system”. This is a statement of necessity. It means that if C is a cell, then THERE EXISTS an (M,R)-system S such that C realizes S. It does NOT mean that if one comes up with an arbitrary (M,R)-system (or worse, something that only vaguely resembles an (M,R)-system), there has to be a cell that realizes it. “If C, then S” (S is necessary for C), is not “if S, then C” (S is sufficient for C).” I was, of course, using Q3 there.
I have not kept up with the literature and debates on the subject, so I wouldn’t know what the “five authors, Landauer, Goertzel, Casti, Wolkenhauer, and McMullin” did. Well, the last four anyway, if this “Landauer” is the same one as in the Landauer-Bellman paper. I don’t know what [this person] meant by “completely characterizes the M-R process”; but as I said, “It does NOT mean that if one comes up with an arbitrary (M,R)-system (or worse, something that only vaguely resembles an (M,R)-system), there has to be a cell that realizes it.”
Note that even if Q3 were stated in the necessary-and-sufficient form:
Q3′. A material structure is a cell (i.e. alive) if and only if it realizes an (M,R)-system. my argument would still hold. This is because of the indefinite article “an” that Bob used. This statement of Q3′ would still mean that if C is a cell, then THERE EXISTS an (M,R)-system S such that C realizes S. And if THERE EXISTS an (M,R)-system S such that C realizes S, then C is a cell. It STILL does NOT mean that if one comes up with an arbitrary (M,R)-system, there has to be a cell that realizes it. See how crafty Bob was in his use of the language!
So it would not “collapse” Bob’s theory even if somebody comes up with an (M,R)-system that no cell can realize.
The nature of a “necessity statement” is that the better the necessary condition (in characterizing a property, in this case “life”), the smaller the complementary set (i.e. things that do not have the property, in this case “not life”); in other words, the closer the condition to being sufficient. I felt that the condition “closed to efficient causation” is so close the being sufficient that one may as well ACCEPT, or BELIEVE, that it is so. Or, MAKE IT SO (quoting Jean-Luc Picard), as it were. I believe that was what Bob did in Q1.
One must also understand that the “if, and only if” phrase is what mathematicians use when they DEFINE something. So we can take that Q1 is Bob’s DEFINITION OF LIFE. The “only if” part provides what is needed, and the “if” part tightens the complementary set.
Q2, then, is not so much a retraction, as it is an explanation. It is Bob’s Godelian suggestions that perhaps the sufficient conditions for life are undecidable.
Immediately following Q3, we have this sentence:
Q4. Conversely, I see no grounds for refusing to call such a realization an autonomous life from, whatever its material basis may be. (p.263 of “Essays on Life Itself”, Section on The (M,R)-Systems)
This is the sufficiency part of Q3. But note that Bob used “I see no grounds for refusing”. This is not a mathematical proof. This is a statement of BELIEF (dare I say FAITH). This is a “Make it so!”
References & Footnotes
AS: Rosen, R. 1985. Anticipatory Systems. Pergamon Press
EL: Rosen, R. 1998. Essays on Life Itself. Columbia University Press
FM: Rosen, R. 1978. Fundamentals of Measurement and Representation of Natural Systems. Elsevier Science
LI: Rosen, R. 1991. Life Itself. Columbia University Press
Rosen, R. (ed). 1985. Theoretical Biology and Complexity. Academic Press
Rosen, R. (ed). 1972. Foundations of Mathematical Biology, Vol 2. Academic Press
 Note that ‘model’ and ‘simulation’ are quite different creatures in Rosennean terminology. Models maintain a congruence of entailment structure in a Modeling Relation with the object system. Simulations have no such requirement, and are often geared toward mimicking behavior, rather than modeling causal structure. As such, simulations are often equivocations on the very notion of modelling. There are additional issues regarding simulations that require that they be carefully distinguished from models. The interested reader might review LI ch. 7, EL p. 40-43, and Theoretical Biology and Complexity, pp 190-191.
 LI ch. 4
 The (M,R)-system is described by Rosen most deeply in Foundations of Mathematical Biology, vol 2, ch. 4. Additional discussions are in LI ch. 10 and EL ch. 17, as well as some earlier papers.
 Rosen sometimes describes the (M,R)-system as a cell model (i.e., 1972, EL p. 261), but also uses it as a model of organisms in general (EL p. 263).
 See Rosen 1972, LI p. 251, or EL p. 262.
 EL p. 261
 EL p. 28
 EL p. 28