Truth and Aesthetics in Chemistry
A s teachers we invest a large percentage of our time rehting the facts and theories of chemistry to our students. Unfortunately we spend almost no effort discussing the history and philosophy of our science. Because we overlook the humanistic half of chemistry we educate our students to have only the vaguest conception of the reasons behind their intellectual endeavors. Thus, the once fashionable cry to close the gap between the scientist and the non-scientist was not pertinent. The scientist who labors under his own misconceptions certainly cannot properly explain his task to the general public. The discussion to follow is made in the attempt to convince others to my own prejudice; an understanding of the philosophy of science is essential to a scientist's education. The particular point of discussion deals with one misconception concerning the criteria by which the scientist establishes his goals. Approach a chemistry student and ask him to explain the goal(s) of the scientist. Almost invariably he will argue that the scientist's primary aim is the discovery of truth. The more sophisticated student, when further pressed, will admit that the truths found to date must be considered conditional, but he will further maintain that the search for some type of permanent truth is nonetheless a valid goal. To reach this goal, he might argue, one first establishes models meant to resemble the truth, and then expends all energy in refining these models so that they approach ever more closely that ideal state. I should like to argue that this conception of the scientific process is most probably incorrect. I n addition it suffersby being obscure. For if we have yet to establish one permanent truth, there is no satisfactory way to define such a beast. If we should stumble on such truth, how would we recognize it? Incorrect and ill-defined concepts have little importance, provided no further interpretations and actions ensue. This particular misconception has, however, led to an attitudc among many scientists which is indefensible, and should be eliminated from our collective psychology. With the great power pro.vided by the scientific method the researcher has, within a very short time, enunciated many new concepts, and has furthermore heen the source of a vast amount of technological spin-off. Because of these conceptual and technological contributions, our civilization has been radically altered. The combination of this proven ability to so easily change our culture with the belief in the scientific "quest-for-truth," has led bo the practitioners' arrogant position, that the scientist has the valid approach to the holy grail. And while we will admit the importance of other intellectual endeavors
provocative opinion we do not consider them to have the validity of ours. This self aggrandizement is not the rare phenomenon we might a t first believe. I, and I am sure many of the readers, have heard numerous claims as to the higher morality of scientists operating as scientists, or to the unique and distinctive role the scientist should assume in the governing of our society. Surely, these statements arise out of arrogance, no matter how unconscious the arrogance might be.' One can understand a group falling under the spell of its own rhetoric, since we are all prone to self-elevation. But the belief in the superiority of the scientific approach is also abroad in the land. In many encounters with non-scientists I have been in the sad position of defending the validity of intellectual endeavors which are not scientific. Not only is our position of arrogance indefensible, i t is harmful to our discipline as well. Two examples of the deleterious consequences come immediately to mind. Since we believe that science is the truly valid approach to the study of our world, we are encouraged to insist that our students not waste valuable time on other non-essentials; consequently, we have been producing uneducated and illiterate scientists. Because of the layman's faith in our omnipotence, we have led him to the belief that the scientist can fruitfully apply himself to any problem, including the social ills of our society. With our inability to solve such problems has come public disillusionment. Further, we now see that uncontrolled technological advance has aggravated social difficulties. And so in the eyes of the younger generation science stands doubly condemned. We are accused of crimes that we have not committed, but the accusations are the direct consequence of our own humble claims of superiority. But our claims are not valid, and I shall now discuss why the basis of our arrogance, the "quest-for-truth" concept, is incorrect. To begin I should perhaps define the term truth, and then discuss why the scientific method cannot lead us to this ideal state. However, a polemic on the nature of truth is clearly out of place in this limited space. Further it would be presumptuous to claim that I could give a thorough description of the scientific method here. What I should like to do is briefly discuss what may be essential in the scientific method. With this description I hope it will be clear that truth is not a valid concept in science, no matter how one might define that term.
' As a reaction to this position Robert Hutchins has written a. piece in "Science, Scientists and Politics" (Center for the Study of Democratic Institutions, 1963) which is, to be generous, malicious. He contends in his diatribe that scientists are more immoral than the normal variety of human. Volume 46, Number 9, September 1969
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The scientific method consists of two parts: observation and the ordering of observation into an axiomatic system of logic. I shall now expand on these points. Observation, or the collection of experimental facts, needs little explanation to the chemist, since almost his entire research effort is spent in this task. But there is one point which needs emphasis. Namely, the facts we gather cannot be conceived of as absolute entities. We realize this in that we consider the reproducibility of a n observation as a most basic property. There are three reasons for the inherent shortcomings of our observation. The first is experimental or quantitative error. This type of error is well understood and, therefore, easily handled by our constant evaluation of experimental accuracy. The scientist has for a long time treated his data no better than his stated accuracy. The second error arises from the fact that the type of observation we make is dependent on the way in which we make it. This type of error, which is essentially qualitative, is not as well recognized as inaccuracy, but has been treated equally well in the concept of operationalism as first presented by Ernst Mach. By choosing a particular method of observation we will obtain a particular type of result. Operationalism compensates for this by consciously defining results in terms of methods, thereby recognizing the dependence of the observer on his techniques. I n this way, as in a consideration of accuracy, the scientist has acknowledged the limitations of his observations. There is a final limitation for which we have not yet devised a compensatory mechanism; the psychology of the observer. What we look for and how we see depend on what we believe and how we think;%two simplistic examples. We believe in the reproducibility of nature (within of course statistical limits, but chemists for the most part do not work near those limits). Therefore, we dismiss all irreproducible results irrespective of whether the world is truly reproducible. A second example, if we were living in a culture for which there were no concepts of either the future or the past, our concept of causality could not exist. Therefore, we would not try to observe the interrelationships of events in time or space. The psychological limitation to our endeavors is one for which we have not yet been able to compensate, and we generally depend on chance and intuition to overcome our psychological barriers. For the three reasons just discussed the facts we gather cannot have the absolute qualities we unconsciously give them. If our facts, one of the bases of our intellectual structure, must be handled with constant doubt, then science as a whole must be treated in the same manner. But there is more to consider. The scientific method does not consist solely of the collection of empirical fact. We are not interested in adding new trivia to an existing, ill-digested mass of knowledge. Rather we wish to systematize our observations so as to discern relationships between them. The method used for this purpose is mathematics, an axiomatic system of logic. The mathematician starts with a small set of propositions, called axioms, and attempts to derive a large number of new propositions, or theorems, by the use of previously anreed noon logical rules. The axiomatic Drocednre For a more complete discussion of this point, see Hansen Patterns of Discovery, Cambridge University Press, New York, 1958.
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and the logical rules of mathematics have been adopted by science. The scientist begins with a small set of propositions, called hypotheses, and with the logic rules of mathematics he attempts to derive new propositions, or theories. There is, however, an important difference between mathematics and science. The mathematician operates in the realm of rationality. The propositions he studies are meaningless in the sense that they represent nothing but themselves. The important criterion in mathematical derivations is self-consistency. For the scientist the task is more difficult; the propositions he deals with represent the physical world. Thus, besides self-consistency his derivations must also be consistent with his empirical observations. As an example we can point to the difference between the axiom and the hypothesis. I n mathematics i t is permissible to start with any logical set of axioms. On the contrary, the choice of hypotheses is limited for the scientist. First, the chosen assumptions cannot themselves contradict experimental fact. Second, all the theories logically derived from a set of assumptions may not contradict experimental fact. Thus, for the scientist the logical, mathematical system must show correspondence with his observations of nature. When we wish to test a new theory in the laboratory, we do not test its derivation, or the empirical facts behind it, we test for the correspondence between the two. Having discussed the empiricism and logical structure of science and the correspondence between them, let us turn to a further description of the theories. As defined above theories are propositions logically derived from a set of hypotheses. But what is the significance of these theories? Our derived propositions have the function of describing the relationships between various, apparently disparate facts. As a n example, the kinetic theory of gases is a formulation which tells us that there are relationships between Charles' law, Dalton's law of partial pressures, the magnitude of the heat capacities of monoatomic gases, etc. These relationships are shown by the fact that we can derive mathematical statements, each of which stands for a law characterizing some aspect of the behavior of gases, and that for each of these statements we use the same small set of hypotheses. The significanceof the kinetic theory of gases is that after we have transformed the various facts about gases into mathematical propositions we can show that each of these propositions is a theorem derivable from the same set of axioms. I n the above description of the scientific method no reference was made to truth. I n fact the important criterion in science is not truth, but rather validity. As we gather our facts we do not ask ourselves if they ore true, but rather are they reproducible. Neither do we judge our theories on their truthfulness, but rather on their self-consistenoy. This being the case the "quest-for-truth" concept is an inaccurate description of how we work. We can, if we wish, rework this concept into a more acceptable form. What we as scientists seek is a systematization of experimental fact, in a rationally built superstructure. This logical framework has the very special properties that i t will be constructed from only a limited number of hypotheses, and that i t will be entirely self-consistent. This description of our task would probably be acceptable to most scientists. Indeed this idea is reflected in the belief of
many that it should be theoretically possible to reduce all of the fields of science into physics, or physics and chemi~try.~However, even this more sophisticated description is incorrect. The logic of science is mathematical logic. The two properties we wish this framework to possess are completeness and consistency. Godel has shown, however, that a rational structure of the slightest complexity, which is built using the axiomatic system, is not complete, and further cannot be proven self-consistent.' Completeness means that all the consistent postulates in a particular system are derivable from one set of axioms using the proper logical procedures. Godel has proven that there are theorems (which may be obtained in other logical frameworks) which are consistent in the logical system in question, hut which cannot be derived from the set of axioms on which the system is based, i.e., the system is incomplete. It does not matter which propositions we accept as axioms; for any set there will still be some nonderivable propositions. Not only is an axiomatic system incomplete, it is not possible to show that all of the derivable theorems are self-consistent. Since scientific logic is mathematical logic, the limitations of mathematics become the limitations of science. We can only conclude, that any logic structure we care to build will be incomplete and further that we will not be able to show i t to be self-consistent. Having faced this limitation we must ask ourselves with what criteria should we approach our work. One valid approach can be labelled as existential. Namely, our goals should still be consistency and completeness no matter how vain the attempt, for the attempt itself is noble; and in practice we may never run across meaningful inconsistency or incompleteness. Psychologically this is not a difficult position to assume. Many scientists currently undertake problems whose solution is considered impossible practically, simply because the attempt is worthwhile. But if we are willing to admit that the criteria of consistency and completeness are not valid of and by themselves, then we are permitted to choose other criteria. I should like to propose that another good criterion would be aesthetic appeal. Interestingly not all physical scientists want to understand every natural phenomenon in terms of the concepts of physics and chemistry. G. S. Stent (Science, 160, 390, (1968)) hss written that his interest in molecular biology stemmed from the desire to find principles unique to living systems. 'For an explanation of GBdel's proof see NAGEL,E., AND NEWMAN, J. R. Scientzfic American, 194, (6) 71 (1956). TAYLOR, A. M., "Imagination and the Growth of Science," Schocken Books, New York, 1967. WATSON, J. D.,"The Double Helix,'' Atheneum, New York, 1968. 'This distrust can be harmful. For example, two of the most important scientific theories of our time, those of Freud and Darwin, were presented in a non-quantified farm; and chemists have, on the whole, made no attempt to recast these theories into chemical terms. We could equally well argue that an important criterion in the scientific search is otilitmianism. But this position already has had many defenders. 'One approach to this problem has been considered by R. Batino, J. CHEM.EDUC.,46,38 (1969). 'O SARTON, G., "A History of Science: Hellenistic Science and Culture in the Last Three Centuries B.C.," Cambridge Press, Cambridge, Mass., 1959. p. ix.
There are numerous examples in which the aesthetic appeal of a scientific endeavor is discussed in print. I n A. M. Taylor's book, "Imagination and the Growth of S~ience,"~ there are many quotes which invoke the beauty of science. Watson, in "The Double Helix"" mentions that the beauty of the intellectual model he and Crick were building was an important aspect of their endeavor. Biologists, in general, have not been loathe to cite the beauty of the organisms they study, and to discuss living systems in aesthetic terms. Many such examples are relatively easy to find. For the feeling that the aesthetics of science is important is not unique to a few scientists. Certainly most of the readers of this article have been struck a t least once with the beauty of a particular experiment or theory. One could probably make a case for the thesis that some of the important theories of science find ready acceptance because of their aesthetic appeal. Chemists tend to deny or ignore the importance of aesthetic value in their work. It is difficult to enumerate reasons for this reaction, which is a psychological phenomenon. One possibility is our training. The necessary stress we place on quantification and axiomatic logic encourages in us a distrust of the qualitative and illogic,? and, therefore, a distrust of beauty. Certainly the property of attractiveness is not quantitative, nor can we use an axiomatic structure to arrive a t a proposition of beauty. But any man-made construction, physical or mental, is not successful if i t is ugly. I am not arguing that we should discard the criteria of completeness and consistency, rather that we should permit our students the necessary freedom to consider the more indefinable aesthetic appeal as a n equally valid ~ r i t e r i o n . ~How do we teach of beauty in science? This question is similar to the one of how to teach consistency and cannot be answered in this a r t i ~ l e . ~Are there any advantages in the approach I advocate? There are a t least two which are obvious. The first is enthusiasm, and the second deals with our conception of our own work, the point with which I began. A historian wrote the following words for non-scientists" Humanities are inseparable from human creations, whether these he philosophic, scientific, technical, or artistic and literary. I t would be foolish to claim that a good poem or a beautiful statue is more humanistic or more inspiring than a scientific discovery; it all depends on the relation between them and yon. Some people will be more deeply moved by poetry than by astronomy; it all depends upon their own experience, mind and sensibility.
We, on the contrary, should know that it would be foolish to claim that a scientific discovery is more valid than a good poem or a beautiful statue. I n closing let me state that none of the above discussion is original; nor do I claim i t as logically complete or consistent. My goal has been to present the argument that beauty is not a ugly word in the education of chemists. By laying some stress on scientific aesthetics we can only enrich our st,udents' education.
Michael H. Klapper Ohio State University Columbus, 43201
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