20th WCP: Music, Science, and Analogies: Teaching the Philosophy of Science with Non-Scientific Examples

Without a doubt, one of the most difficult tasks in teaching undergraduate philosophy courses is motivating the students to take an active interest in the abstract and complex issues normally presented. One obvious method of overcoming this dilemma is to provide numerous historical examples and analogies of the relevant philosophical problem, since concrete instances are frequently less complicated than general descriptions, articulate the main points more clearly, and have the added bonus of being more "personal" and relatable. Thus, if one were presenting, say, Imre Lakatos theory of scientific research programs, describing the conflict between the Ptolemaic and Copernican views would serve as an excellent backdrop for the introduction of Lakatos' ideas. Nevertheless, if the students are unfamiliar and/or bored by the kinds of examples employed, the strategy will, of course, spark little enthusiasm from the class. This is a problem particularly acute in teaching the philosophy of science, moreover, since the average college student's generally low levels of instruction in science, let alone the history of science, will render the majority of real-life scientific examples as opaque as the philosophical issues they were supposed to make clear!

In this essay, one possible strategy for overcoming this obstacle, which has been culled from personal experience, will be recommended by way of demonstration. In short, the suggestion is to devise examples and analogies from outside the realm of science and its history, but which can serve to both highlight and augment the actual scientific cases typically offered, as well as provide an interesting test-bed for the exploration of philosophical concepts. If these examples are tailored to reflect the interests of the students, most notably by drawing upon the humanities and popular culture, then a marked increase in class enthusiasm and participation will be the likely result. In short, these non-scientific analogies can help explain the nature and purpose of a philosophical/scientific concept. In what follows, consequently, we will develop a lengthy example which will demonstrate this very strategy: the philosophical concept will be Thomas Kuhn's notion of a scientific "paradigm", the key element in his theory of scientific revolutions; and the non-scientific topic adapted to explain this theory will be the history of musical styles and the structure of musical compositions.

The concept of a "paradigm" is the key component in Kuhn's philosophy of science. (1) Briefly, a paradigm is a guiding framework of theories or ideas which shapes and determines our understanding of the world. Newtonian mechanics, Darwinian evolution, Freudian psychology, are a few instances of a paradigm according to Kuhn. For example, an evolutionist will likely interpret the data accumulated from molecular biology as confirmation of their view that species have evolved over millions of years according to a mechanistic process of genetic variation and natural selection; while a creationist will regard the same data as vindicating their theory that God simultaneously formed distinct species a mere 6,000 years ago. In short, the paradigm you hold largely determines the nature of your scientific "facts", since the ambiguity and vagueness inherent in the majority of scientific experiments and observations routinely admits numerous conflicting theoretical interpretations--and it is this conjunction of observations and theoretical interpretations which constitutes our scientific "facts". The separate functions of a paradigm are as follows: the paradigm describes the entities of the particular science (planets, atoms, etc.), how these entities behave, the questions that can be legitimately asked concerning them, the techniques used to answer these questions, and the criterion of success and failure of the various answers.

Classical sonata form, as practiced by Haydn and Mozart, admirably demonstrates the point that many non-scientific subjects which are particularly amenable to a paradigm interpretation. Introduced in the middle of the eighteenth century, sonata form gave composers a solid framework on which to construct and arrange their musical ideas. Basically, it is a mold into which composers pour their thoughts. Sonata form incorporates a definite pattern: a short introduction, the exposition (which presents the main "subjects", melodies, and themes of the piece), the development (which explores these ideas, often in dramatic fashion), the recapitulation (a repeat of the exposition), and a short concluding coda. Classical sonata form also involves the use of a certain key relationship (not to mention the fact that the work is built on the diatonic scale). Usually the first, and most important, movement of a multi-movement work (symphony, string quartet, solo sonata, etc.) employed sonata form during the Classical period in music (1750-1820).

As is evident, sonata form (in its classical incarnation) was a perfect vehicle for the organization and structuring of musical ideas. It served many of the same functions as a paradigm (as above). First of all, sonata form furnished and described the entities with which the composer worked (first subject, second subject, exposition, development, etc.), as well as the ways in which those entities behave (if the movement's main key is minor, for example, the first subject will likely be traumatic or tragic in mood). Likewise, sonata form provided the questions that could be legitimately asked, such as, "Can we introduce a new theme into the development?"; as well as the techniques and standards of evaluation for answering such questions; "Yes, you can introduce a new theme, but only as long as it doesn't undermine the recapitulation or upset the balance of the movement as a whole." Overall, just as in the analogous case of science, a musical paradigm thereby largely determines and controls the musical thoughts and experiences of the composer.

Classical music is not the only source of musical paradigms, moreover. Most popular musical forms possess their own equivalent of sonata structure, although this aspect of contemporary music is rarely acknowledged. In rock-'n'-roll songs, for instance, one can detect a similar set of stock "entities"; such as, themes, melodies, riffs, etc.. The function of these musical ideas, as well as the standards of acceptable composition, are no less circumscribed or enforced in rock music than in classical. Our common experience of songs, and possibly entire records, that "didn't work" or "didn't sound right" is strong testimony to the latent power of musical paradigms to shape and determine our musical expectations, and more generally, our musical experiences. Indeed, popular music may exhibit the paradigm concept even more successfully than classical, since even most classical connoisseurs are only exposed to the great masterpieces of the classical "repertoire", and not the many mediocre and poor compositions which constitute the vast majority of classical works. In contrast, our common experience of much mediocre contemporary music is a constant reminder of the enormous difficulties that face successful rock composition, both in matters of structural form and inspired content.

Nevertheless, returning to our classical music analogy, sonata form also resembles Kuhnian paradigms in the manner of training. Like scientists, composers perfect their trade under the tutelage of accomplished masters, often in an apprenticeship lasting many years. The teachers of classical sonata form handed down this style, and all the entities and standards it entails, to their pupils in the same fashion that it had been handed down to them (or as they had developed it). For example, Haydn, who helped to invent sonata form, handed down this technique to his greatest student, Beethoven. These apprentices soon learned to channel their musical thoughts through this form, much like scientists learn to construct their hypotheses within the framework of sanctioned methodologies and other well-confirmed theories. The classical music teachers, furthermore, offered many musical "exemplars" (which is a specific example of, say, a sonata form piece) that they expected their students to study and emulate in their own practice compositions. In the end, the teachers hoped that their students would go out into the musical world and extend the scope and domain of the styles they had taught them--but, of course, within the paradigm of classical sonata form, or classical style as a whole. So, students should help refine and extend the paradigm, but not reject it; which Kuhn regards as the identical goal of advanced instruction in the sciences.

Another way in which musical structures resemble Kuhn's paradigm theory is with respect to the concept of meaning dependence or "incommensurability". According to Kuhn, the meaning of a term is determined by the paradigm as a whole; so that the term "mass", for example, has a quite different meaning in Newtonian mechanics than it does in Relativistic mechanics (due to the different structures of these respective theories). Likewise, such musical terms as "theme" or "chord" receive their precise meaning from the entire classical sonata form paradigm. As is the case with physical theories, you have to know the relevant theory, here, classical sonata form, to know what these words stand for in the context of that paradigm. In fact, "theme" or "chord" can take a very different sort of meaning in the context of one musical paradigm, say, romantic opera, than it does in another, such as baroque concerto form. More often than not, the style and usage of the "things" that the term refers to has changed drastically. Therefore, Kuhn draws the lesson that a strict or exact comparison of similar terms from different paradigms is, in principle, an impossible task (which he dubs "incommensurability").

In addition, Kuhn's ideas about scientific "revolutions" can be adapted to the study of musical history. In scientific revolutions, an old paradigm is replaced by the adoption of a new one; but the switch is really only a matter of choice (or so at least some passages in Kuhn seem to read; 1970, p. 150-151). Kuhn believes that no scientific paradigm can lay claim to the "truth" in an absolute sense, since all paradigms have their own unique evolution and meaning dependence of terms (as above). Despite the existence of some general "rules of thumb" for comparing the relative merits of paradigms, such as, simplicity, consistency, quantitative precision, etc., these cross-paradigm criteria are not fixed and inviolable. Rather, any method for comparing paradigms can be revised or rejected in the course of practice. This incommensurability of entire scientific paradigms, as opposed to the incommensurability of identical terms from different paradigms (as discussed above), appears to have an analogue in classical music, as well. We cannot compare the music of the baroque period, a distinct paradigm, with the music of this century, another paradigm, to discover which one is "better". The entire core of techniques and values within these paradigms are largely different, sometimes radically so. For these reasons, we cannot compare, for instance, a sonata form movement of Mozart with one from Bartok. We have no basis for the comparison; therefore neither one can be said to be better.

At this point, the students will most likely want to reject the analogy being drawn between musical and physical theories. Their reasoning will probably run along the following lines: while science is concerned with trying to understand the ultimate "reality" underlying our experiences, music only aims at the production and study of aesthetically appealing musical experiences. In other words, science deals with facts and "truths" about our world, whereas music only involves, at best, someone's idea of what constitutes "good" music. In opposition, a hard-core relativist, who accepts a radical interpretation of Kuhnian philosophy, would likely retort that the acceptance of a scientific theory is as equally a matter of aesthetics or personal taste as, say, choosing your favorite rock band. Since all theories are underdetermined by empirical evidence, they argue, there must be either personal or social factors responsible for the choice of a scientific theory. (2) The realists in the classroom (of which I include myself), will find these relativist assertions perplexing, if not downright false--and the instructor should play the "devil's advocate" to the hilt if no one defends the relativist's position. The teacher can instigate a fruitful discussion of this issue by presenting "what is at stake" through the use of short, direct questions: Was the choice of the Copernican over the Ptolemaic theory merely a matter of taste? Does the same hold for creationism versus evolutionism? Overall, the students may decide that the incommensurability of musical paradigms actually fits Kuhn's thesis better than the scientific paradigms for which it was designed. They may reason that, whereas personal (or social) opinion seems a perfectly legitimate explanation of musical revolutions, mere opinion does not accurately reflect all the factors involved in the choice of competing scientific paradigms. (Ultimately, the class may argue, one of the scientific paradigms will fit the evidence better than the other!)

If the concept of a revolution seems to work better in the case of music than science, there are other aspects of Kuhn's thesis that do not translate well into our musical analogy. The main problem centers upon the concept of an "anomaly", which is an observation or experiment that conflicts with the prevailing paradigm. According to Kuhn, anomalies are one of the primary causal agents that precipitate scientific revolutions. If enough anomalies accrue to a paradigm which it is unable to resolve, a revolution usually entails. Unfortunately, there is no musical equivalent of a scientific anomaly in the case of our musical paradigms, or at least none in the way that anomalies function in science. On the whole, experimental evidence does not appear to play a large role in music: it is quite difficult to come up with an historical case where observations or experimental evidence led to a musical revolution. If there is a manner in which a rough anologue of Kuhn's anomalies can be read into musical history, it would appear to resemble more an internal development than an external conflict of evidence and theory. That is, a Kuhnian revolution of scientific paradigms is rather Hegelian: a thesis (our paradigm) encounters an anti-thesis (the "conflicting" experimental evidence) which leads to a synthesis (a new paradigm which account for the problem). But with musical revolutions, the transformation of paradigms is more an evolution from within (Darwinian, or better yet, Lamarckian) than the synthesizing of an opposing, external factor. Because there are no external, empirical anomalies, what apparently happens in music is that composers feel the need to express themselves in a different, more unique fashion. This process thus constitutes a somewhat different type of revolution, for the composers appear to be generating their own anomalies, rather than waiting for "nature" to present them.

Interestingly, some of the difficulties with Kuhn's theory of scientific revolutions are also reflected in our musical paradigm analogy. Kuhn seemed to suggest that revolutions come in complete steps, with abrupt transitions between world views; as in the transition from Newtonian to Einsteinian mechanics. Many critics have alleged that this view of scientific revolutions is not supported by the historical record, or, at the least, is not typical of most theoretical transitions in the sciences. (3) Musical paradigms can successfully convey the critics' argument: musical revolutions do not occur all at once, in complete steps; rather, they evolve over long periods of time in short, careful steps. Even the most revolutionary works of such composers as Beethoven or Stravinsky were foreshadowed and based upon either their own earlier, less-radical works, or the more conventional works of other composers. In many ways, it is impossible to establish a strict dividing line between musical paradigms (or periods). Contrary to Kuhn's belief, the same is largely true of scientific revolutions. Copernicus is often credited with overthrowing Ptolemaic astronomy, but his use of the perfect circular orbits of that earlier tradition has often led to his being branded "the last of the Ptolemaic astronomers". (4) One might try to salvage Kuhn's thesis by declaring that all scientists, or composers, who "stretch" the rules of their paradigm are, in fact, creating a new paradigm. Yet, if this doctrine were accepted, then every scientist or composer in history would possess, by default, their own unique paradigm; and, consequently, the concept of a revolution would no longer appear to be even applicable. Likewise, Kuhn's notion of the incommensurability of scientific terms is not exempt from criticism. Just as a scientist can understand and relate the different meanings of "mass" in Newtonian as well as relativistic theory, so can a composer understand the meaning of "chord" in romantic and baroque music. Therefore, a radical interpretation of Kuhn's doctrine of incommensurability (where the meaning of a term is completely different in a rival paradigm) is not supported by the historical evidence (as Kuhn would agree; 1970, p. 202)

To summarize some of the main themes discussed, we have provided an outline of the preceding analogies in an appendix, which may also be of assistance in the classroom. Needless to say, many of the entries in the outline are open to dispute. In fact, the instructor may devise such a list in the classroom, or ask the students to come up with one of their own, thus providing an additional means of promoting discussion.

In conclusion, there are many benefits to be gained by the use of non-scientific examples and analogies in teaching philosophy of science courses, or general introductory courses. These examples serve two general, and difficult, needs which most instructors face, especially when teaching lower-level courses: first, they assist in motivating the students to take an active interest in the material, since the examples concern more familiar aspects of the culture in which they have a predisposed interest; and second, the examples will express difficult material against the backdrop of a familiar, non-threatening domain of common experiences--and this process will make the material seem less forbidding and alien. The more advanced the course becomes, obviously, the less need there will be for such tactics; yet, even graduate students will find such examples instructive. At the very least, the utilization of non-scientific examples can assist in breaking the "barrier of silence" that all too often rises up between instructor and student --and any means of initiating fruitful conversation and dialogue within the classroom is to everybody's benefit.

Notes

(1) The work in which Kuhn first presents his theory is, of course, The Structure of Scientific Revolutions, 2nd. ed., Chicago: University of Chicago Press, 1970. The book first appeared in 1962, but the second edition includes a postscript wherein he attempts to answer the critics of his paradigm concept. Much of the material discussed below is contained in the first few chapters of Kuhn (1970), and the postscript.

(2) The social constructivist school, in the branch of philosophy known as the sociology of scientific knowledge, attempts to reduce many disputes and conflicts in the history of science to socio-political factors in the larger culture of the time. See, for example, H. M. Collins, Changing Order: Replication and Induction in Scientific Practice, London: Sage, 1985.

(3) For a lengthy discussion of this topic, and many more, see; I. Scheffler, Science and Subjectivity, 2nd ed., Indianapolis: Hacket, 1982.

(4) Ironically, Kuhn's early work on the Copernican revolution seems to corroborate this view; i.e., that the demarcation of paradigms and revolutions is somewhat arbitrary. See, T. Kuhn, The Copernican Revolution, Cambrdige, Mass.: Harvard University Press, 1957.

Appendix

Scientific Paradigms: Evolution // Creationism

1) Entities: (evol.) species, animals, plants, genes, etc. // (creat.) same entities, but with an original supernatural designer (God).

2) Behavior of entities: (evol.) genetic variation, natural selection, plus possible other unknown natural mechanisms // (creat.) God's initial creative act, and very limited genetic variation and natural selection.

3) Legitimate questions: (evol.) How did this species evolve from this earlier species? // (creat.) Why did God create this particular species?

4) Techniques for answering questions (and standards of success): (evol.) Are there relevant structural, genetic, anatomical, spatial (location), temporal (in geological strata), etc., similarities between the species? // (creat.) What use is this species to humans or environment (which is possibly not answerable by humans)?

5) Exemplars (successful previous application of theory): (evol.) observed genetic variation and natural selection in living species (fleas, moths, etc.), anatomical and genetic similarities in species, and fossil records // (creat.) fossil records and/or other evidence that allegedly disproves evolution.

6) Incommensurability: 'human' in evolutionary theory means an animal species that has evolved over time through a natural process of genetic variation and natural selection (not specifically designed) // 'human' in creationism means a species of being specifically designed by God to be masters of the planet earth.

Musical Paradigms: classical sonata form // rock-n'-roll song

1) Entities: (class.) theme, chord, development, exposition, etc. // (rock) theme, chord, riff, guitar solo, etc.

2) Behavior of entities: (class.) first theme in exposition is in main key // (rock) guitar solo is in middle of song after presentation on main melodies.

3) Legitimate questions: (class.) Can a new theme be introduced in the development section? // (rock) Can the song last for more than three minutes?

4) Techniques for answering questions (and standards of success): (class.) Yes, but as long as it doesn't undermine the recapitulation. // Yes, but don't expect much radio air play, or video exposure.

5) Exemplars (successful previous application of theory): (class.) a sonata form movement by one of the acknowledged master, such as Haydn, Mozart, etc. // a hit song by one of the great rock bands, such as Beatles, Rolling Stones, etc.

6) Incommensurability: 'theme' in classical sonata form is designed for maximum development capacity, and is (usually) in either tonic or dominant key // 'theme' in rock music is usually designed for maximum melodic capacity, must allow lyrics to be set to the theme, and may not strictly follow the tonic-dominant tonal scheme.