Natural Law and the Rosen Modeling Relation


In Life Itself, Rosen discusses the minimal foundational premises upon which all of science rests:

1. The succession of events or phenomena that we perceive in the ambience is not entirely arbitrary or whimsical; there are relations (e.g., causal relations) manifest in the world of phenomena.

2.  The relations between phenomena that we have just posited are, at least in part, capable of being perceived and grasped by the human mind, i.e., by the cognitive self.    

Science depends in equal parts on these two separate prongs of Natural Law. The first, which says something about the ambience, asserts that it is in some sense orderly enough to manifest relations or laws. Clearly, if this is not so, there can be no science, also no natural language, and most likely, no sanity either. So it is, for most of us at any rate, not too great an exercise of faith to believe this.
     The second part of Natural Law says something about ourselves. It asserts that the orderliness of the ambience is (to some unspecified extent) discernable to, and even  more, is articulable by, the self. It asserts that the posited orderliness in the ambience can be matched by, or put into correspondence with, some equivalent orderliness within the self. [p. 58-59] 

If either or both of these premises were untrue, then science would not be possible at all. Therefore, since we take it to be true that science is possible, then these premises must be true. That is, it must be true that we can codify for ourselves those causal relations, separately and distinctly from the embodiment of those relations in the phenomena in the ambience. Further, to achieve this correspondence, it must be that such codified relations can be asserted back to the world of phenomena. 

Thus the process of science rests on: 1) the premise of phenomena and relations between phenomena in the ambience, 2) the sensing of these phenomena and the relations among phenomena, 3) the articulating or codifying those phenomena and relations abstracted from the ambience, and 4) the asserting of the codified relations and phenomena back to the ambience. 

Rosen Modeling Relation

What I have just described is the Rosen Modeling Relation. We can see that it arises directly from the fundamental premises of Natural Law, upon which science is founded. Indeed, as Rosen states, “[a] modeling relation between causal entailment in a natural system and syntactic entailment in a formal one provides a concrete embodiment of the concepts of Natural Law.” (It is only a trivial step to observe that it must immediately follow that since the entailments in a formal system are, of course, orderly and discernable, then we can therefore also use the Rosen Modeling Relation where the two systems involved are both formal systems.) 

There are few, if any, who would doubt the validity and soundness of Natural Law as Rosen states it. And accordingly, the Rosen Modeling Relation, as an embodiment of Natural Law, inherits the same validity and soundness. Such ideas are so basic to science and epistemology that they have been around for a long time. Aristotle, with whom Rosen was well acquainted, discussed the perceptibility of Nature, mathematics as arising from Nature, and of the ways in which these entailment relations occur in parallel in mathematics and Nature. Indeed, for Aristotle the understanding of Nature meant the understanding of these relations. Very briefly:

These distinctions having been drawn, we must see if we can characterize and enumerate the various sorts of causes. For since the aim of our investigation is knowledge, and we think we have knowledge of a thing only when we can answer the question about it: “On account of what?” and that is to grasp the primary cause — it is clear that we must do this over coming to be, passing away, and all natural change; so that, knowing their sources, we may try to bring all particular objects of inquiry back to them.[Physics II.3]


That there are causes, and that they are as many as we say, is clear: for that is how many things the question ‘On account of what?’ embraces. Either we bring it back at last to the question “What is it?” — that happens over unchangeable things; for instance in mathematics it comes back at last to a definition of straight or commensurable or the like. Or to that which in the first instance effects the change; thus on account of what did they go to war? Because of border raids. Or it is what the thing is for: they fought for dominion. Or, in the case of things which come to be, the matter.     Plainly, then, these are the causes, and this is how many they are. They are four, and the student of nature should know about them all, and it will be his method, when stating on account of what, to get back to them all: the matter, the form, the thing which effects change, and what the thing is for.[Physics II.7]

The point here is not to begin a lengthy comparison of Aristotle and Rosen; rather, to merely illustrate that Natural Law and the role of entailment relations underlying the Rosen Modeling Relation has a very long history, perhaps even pre-dating Aristotle. (Indeed, the feckless misnomer, “Hertz-Rosen Modeling Relation”, entirely misses the history inherent in these ideas.) 

In Rosen’s typical fashion, his study led him to fix these fundamental ideas in more precise language and in a diagrammatic formalism drawn from his knowledge of the area of mathematics known as Category Theory:

     Metaphor exists on the purely formal side [of the Modeling Relation] as well. In the Theory of Categories, for example, it manifests itself in the concept of functor. The turning of metaphor into model, in those terms, is expressed in the concept of natural transformation. The whole idea of the Theory of Categories arose initially in this way, and it is illuminating to continue to regard it in this light. [LI p. 66] 

Thus arose the Rosen Modeling Relation diagram, which clarifies and crystallizes ideas that had been in prosaic form for centuries. Once set in this form, the ramifications of Natural Law and the Modeling Relation became much more evident In a sense, Fundamentals of Measurement, Anticipatory Systems, and Life Itself are all examinations of conclusions in various areas of science which logically follow from the Modeling Relation, and thus, logically follow from Natural Law. 

It has been a great triumph for Rosen to have built so much upon so little. The extent of these logical ramifications are far-reaching for science and epistemology in general. Some of those ramifications have rankled a few in science and elsewhere who were uncomfortable with logical scrutiny of their methods or arguments. (E.g., the infamous quip on Judith Rosen’s site from an annoyed scientist to Rosen: “The trouble with you, Rosen, is you’re always trying to answer questions that nobody wants to ASK!” ). The logical nature of Rosen’s body of work inoculates it from essentially every attack, and so far only misconstruals and misinterpretations of Rosen’s work have provided any basis of published criticisms.

That the body of work is a logical structure does not make its foundation so. It is, of course, not possible to prove, in any scientific sense, an epistemology since such an effort would be entirely circular or nonsensical. No one can prove that Natural Law is correct, for example. Therefore, the entire logical edifice of Rosen’s work rests on these premises, which we must take on faith. It is entirely possible that one could propose an alternative set of premises as the basis for a different epistemology (with an accordingly different basis for science) and proceed to follow wherever the logic leads one from there. Although such an endeavor is entirely possible in principle, I find it difficult to imagine a coherent epistemology which disavows either or both parts of Natural Law.



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