Footnotes to Science as Paradigmatic complexity
 

 Paul Feyerabend, when he was criticizing Imre Lakatos, brought up something that seems; apropos here; "The excellence of science is assumed, it is not argued for. The same is true of the standards proposed by the methodology of research Programmes. These standard; are obtained by an analysis of modern science. Their excellence is; therefore again assumed, it is not argued for. There is not a single argument to show that they are better than the standards that underlie the practice of magic"

Forewarned, then, even though I don't necessarily agree with Feyerabend, I proceed with my thesis with the express understanding that normative evaluations are not of concern to it. The science I am discussing is not presented as something better than magic, metaphysics, or pseudo-science, it Is just something that is different, and in some way separated from them.

 Popper separated the definition of Demarcationism and its importance. He defined it in these terms. "The problem of demarcation is to find a criterion that permits us to distinguish between statements that belong to the empirical sciences (theories, hypotheses) and other statements; but also mathematical and logical statements. the problem of demarcation is to be distinguished from the far more important problem of truth: theories which have been shown to be false--as for example the radiation formula of Rayleigh-Jeans and of Wien, Bohr's atom model of 1913--can nevertheless retain their character of empirical, scientific hypotheses

At the same time, regarding its importance, he said; "There cannot be any sharp demarcation between science and metaphysics; and the significance of demarcation, if any, should not be overrated. In spite of this, I contend the problem of demarcation is highly significant. It is so not because there is any intrinsic merit in classifying theories, but because a number of genuine and important problems are clearly linked with it; in fact, all the main problems of the logic of science." It is with this spirit that I advance this thesis.

 Nevertheless each tried to see the others in their own eyes. Paul Feyerabend, Lakatos' ideal sceptic, dedicated his book, "Against Method" to "Imre Lakatos, a fellow anarchist", and Stephen Toulmin, his archetypal elitist was miffed because Lakatos compared him with Thomas Kuhn, and not himself.
 Joseph Agassi offers this; version of the sceptic code taken from Michael Polanyi. The argument has been very forcefully presented by Michael Polanyi; I think ln his "Logic of Liberty" and elsewhere. Some people believe in science, some people believe in the bible, he said. It all depends on your starting point, which is arbitrary and idiosyncratic; it depends on the tradition you align yourself with. In science, there is. no objective standard of rationality, taste, style, idiom, and the like, matter as much in science as in the arts, or in religion. Commitment is arbitrary; and where you Stand is a matter of initial commitments.
 Feyerabend expresses the skeptical sentiment in these terms. We find, then, that there is not a single rule, however plausible, and however firmly grounded in epistemology, that is not violated at some time or other. lt becomes evident that such violations are not accidental events, they are not the results of insufficient knowledge or of inattention which might have been avoided. On the contrary, we see that they are necessary for progress.
 Popper's own words best illustrate his attitude. "Even those who, like myself, cannot follow Kant all the way can accept his view that the experimenter must not wait till it pleases nature to reveal its secrets, but that he must question her. He must cross-examine nature in the light of his doubts, his conjectures, his ideas, and his inspirations." (Popper 1968)
  Lakatos said that the first modern elitists were Bacon and Descartes. Bacon thought that the scientific mind was one purged of "prejudices," Descartes thought it was one which had been through the torment of skeptical doubt. The Nazi's held that Aryan science was superior to Jewish science. Other elitists appraise communities for "scientificness" rather than individuals. For some pseudo-Marxists, the quality of science depends on the structure of the society which produced it: feudal science is better than ancient slave science, and the proletarian science is true.
 Toulmin said, If all men's concepts, interpretations, and rational standards--in morals or in practical life--are historical and cultural variables, so that our habitual modes of thought are as much reflections of our particular time and place as our habitual modes of social behavior, then the same fundamental problem arises in each case. what solid claims can any concepts and modes of thought have on our intellectual allegiance?
 Close historical investigation of a given specialty at a given time discloses a set of recurrent and quasi-standard illustrations of various theories in their conceptual, observational, and instrumental applications. These are the communities paradigms, revealed in its textbooks, lectures, and laboratory exercises. By studying them and by practicing with them, the members of the corresponding community learn their trade. the historian, of course, will discover in addition, a penumbral area occupied by achievements whose status is still in doubt, but the core of solved problems and techniques will usually be clear. Despite occasional ambiguities, the paradigms of a mature scientific community can be determined with relative ease. (Kuhn )
 Scientists work from models acquired through education and through subsequent exposure to literature often without quite knowing or needing to know what characteristics have given these models the status of community paradigms. And, because they do so, they need no full set of rules. the coherence displayed by the research tradition may not even imply the existence of an underlying body of rules and assumptions that additional historical or philosophical investigation might uncover. . (Kuhn )
 Clifford Grobstein described the elements of a complex hierarchical system using the following equation: S=[A,B,C...N]R S is a component of a complex hierarchical set. A,B,C, and N also are comparable sets, and R is the relationship that binds them into a set.
 Herbert Simon who. with his article "The Architecture of Complexity" began the study of complex hierarchies, described complex: hierarchies as special kinds of Chinese boxes. A set of Chinese boxes usually consists of a box enclosing a second box, which, in turn encloses a third--the incursion lastinq as. lonq as the patience of the craftsman holds out. The Chinese boxes called "Hierarchical" are a variation on that pattern. Opening any given box in a hierarchy discloses not just one, but a wholesimall set of boxes; and opening any one of these component boxes discloses a new set ln turn.)
 Hierarchical control programs were developed originally as a mechanism for describing the complex- interactions in biological organisms. Biologist James. Bonner described their action in biological organisms in these terms. "We know. for example, that in humans we have two genes for making the two protean chains oh hemoglobin. We know that these two genes; are turned on for transcription of the messenger RNA for making hemoglobin in certain body cells, those of the bone marrow, which give rise to the reticulites. and thence to the erythrocytes. Also we know that these same genes. do not make the messenger RNA for making hemoglobin in other cells of the adult organism. Clearly the genes for making hemoglobin are turned on in one kind of cell and make their appropriate messenger RNA, but in other kinds of body cells they are turned off and do not make their messenger RNA. We can think- of many cases which show that particular elements of the genetic material are turned on only in particular places.
 Joseph Agassi noted that in the case of Michael Faraday, for example, Newtonian dogmatism obscured ideas that were later found to be important. "The historical case of Michael Faraday is tragicomic. Even recognizing Faraday's ideas as interesting was. a heresy, since! these ideas contradicted the well-established cannons of Newtonian science. A man like Faraday could do nothing, then, except lecture and write almost exclusively about his. own ideas."
  Agassi provided this observation that. we might consider here. "There is; one idea I have learned from my -schooling by Popper, or perhaps. it is an observation he made which has impressed me so. The school which tends to keep -vigilantly the purity of the doctrine, Popper observes, keeps changing its doctrines. all the time.
  Popper, in his, postscript to his logic of scientific discovery described the three worlds ln these terms. "By 'World 1' I mean what is usually called the world of physics: of rocks and trees, and physical fields of forces. :I also mean to include here the worlds of chemistry and biology. By 'World 2' I mean the psychological world. It is studied by -students of the human mind. but also of the minds. of animals. :It is; the world of feelings of fear and of hope, and of dispositions to act, and of all kinds of subjective experience, including subconscious. and unconscious experiences. Thus the terms 'World-1' and "World-2' area both easily explained. By 'World 3' I mean the world of products of the~ human mind. Although I include works of- art in world 3 and also ethical values. and social institutions and thus, one might say, societies, I shall confine myself to scientific problems, and to theories, including mistaken theories.
  Popper's explanation of the reality of the autonomous third-world is shown in this quote. "My next point is that this autonomous part of world 3 is; 'real' in the sense that it can interact with world 2 and also, via world 2, with world 1. If -some men or many men seek for a solution of an as. yet unsolved problem, then they are all, possibly in many different ways, influenced by this problem. The success of their attempt. to solve it will depend, at least partially, on the existence or non-existence, in world-3, of a solution to their problem, and partly on whether or not they are led by their thought processes to objectively- true thought contents
 Popper shuned strict definitions, but he offered this view of verisimilitude'. "What, then, is the object of our 'rational belief? It is, I submit, not the truth, but what we may call the truth likeness (or verisimilitude) of the theories of science so far as they have stood up to severe criticism, including tests. What we believe (rightly or wrongly) is. not that Newton's theory or Einstein"s theory is true, but that they are good approximations to the truth, though capable of being superseded by better ones.
Popper defended this in these terms. "For in this case we should be faced with the problem of explaining not only the new observed regularities, but also the old ones. Our problem would be (a) to construct a theory from which the old theory could be obtained, under certain conditions as a good approximation, and (b) to show what circumstances (initial conditions) brought about the change. This approach, which ensures the survival of the superseded theory as an approximation, is demanded by realism and the method of science. Simply to submit to the fact that the change has happened, and to record it, would he tantamount to the acceptance of miracles, to the abandonment of the quest for rational explanation, and thus of the task of science--of rationality.
"Confronted with anomaly or crisis, scientists take a different attitude toward existing paradigms, and the nature of their research changes accordingly. The proliferation of competing articulations, the willingness to try anything, the expression of explicit discontent, the recourse to philosophy and to debate over fundamentals, all these are symptoms. of a transition from normal to extraordinary research. (Kuhn)
The renormalization group is. not a descriptive theory of nature but a general method for constructing theories. It can be applied not only to a fluid at the critical point but also to a ferromagnetic material at the temperature where magnetism spontaneously first sets in, or to a mixture of liquids at the temperature where they become fully miscible, or to an alloy at the temperature where two kinds of metal atoms take on an orderly distribution. Other problems that have a suitable form include turbulent flow, the onset of superconductivity and of superfluidity, the conformation of polymers and the binding together of the elementary particles; called quarks. A remarkable hypotheses that seems to be confirmed by work with the renormalization group is that some of these phenomena, which superficially seem quite distinct, are identicle at a deeper level.
Colin Renfrew made these interesting observation~ about Thoms' catastrophe theory. "The beauty of this description is that it analyzes. how ~sudden changes in the local behavior of the system can be Produced by altogether gradual and continuous. changes in the control variables. We see how discontinuities within the system, abrupt changes of behavior, arise without any sudden changes; in the forces acting upon it.