The Thematic Component

by Gerald Holton

While the existence of presuppositions in S1 cannot be denied—indeed, some of their aspects have been central preoccupations of philosophers for more than three centuries—they make it puzzling how scientific work can succeed at all. Would such preconceptions not hobble one in the search for the objective state of affairs? How can science change directions, and yet also preserve continuities? How has the scientific profession managed to construct a corpus that is largely so successful and so beautiful, despite this and other limitations on the individual scientific contributor?

Portions of the essays discussing a particular type of preconception which I have called thematic have been mentioned above. But since the concept of thematic analysis will perhaps be the least familiar and the one most easily confused with other current conceptions, we shall here go into a little more detail on the role themata play in scientific work. This may also help the reader by providing the outlines of the theoretical framework within which the material here being surveyed can be more readily accommodated.

All philosophies of science agree on the meaningfulness of two types of scientific statements, namely, propositions concerning empirical matters of fact (which ultimately boil down to meter readings) and propositions concerning logic and mathematics (which ultimately boil down to tautologies). To be sure, observation is now often carried on at the output end of a complex of devices. The observation that counts in, say, an experiment such as the first "observation" of the antiproton seems completely buried under both the total output of data obtainable from the mountain of special equipment and the mass of sophisticated technological knowledge and physical theory without which one neither could set up the conditions for the observation in the first place, nor would know what one is looking for, nor should be able to interpret the thin trace on an oscilloscope or in a photographic emulsion under the microscope by which one finally "sees" the action of the antiproton. But "propositions concerning empirical matters of fact" can be interpreted to be propositions concerning this final stage, protocol sentences in common language that command the general assent (i.e., assent in S2) by specialists concerned with this type of "empirical matter of fact"; and this is what makes them "meaningful."

The propositions concerning logic and mathematics are analytical propositions. They are meaningful insofar as they are consistent within the system of accepted axioms, though they may or may not turn out to be more widely useful. Thus the algebra of ordinary commutative groups suffices for Newtonian mechanics, but not for quantum mechanics.

These two types of meaningful propositions may be called phenomenic and analytic and by way of analogy one may imagine them roughly as corresponding to a set of orthogonal x‑ and y‑axes that represent the dimensions of the plane of usual scientific discourse.

One may name the x‑y plane the contingent plane. The word contingent has been used [3] in a sense that is supposed to be more subtle than the term empirical: a contingent proposition is one "to whose truth or falsity experience is relevant"�as against "logically necessary." [4] But this is not the sense in which I intend "contingent" to be used; for, on the one hand, it unnecessarily introduces by the back door arguments concerning the nature and warrant of truth; and, on the other hand, a proposition can be contingent not only on empirical evidence but also on analytical evidence. The concept of the electron as part of the nucleus was discarded not on empirical grounds (on the contrary, electrons appear to "come out" of decaying nuclei all too conspicuously), but rather because it was thought wiser to retain the then new formal system of quantum‑mechanical analysis, according to which an electron bound in the nucleus could be calculated to require utterly unreasonably large energies.

I therefore define the contingent plane as the plane in which a scientific concept or a scientific proposition has both empirical and analytical relevance. Contingency analysis is the study of the relevance of concepts and propositions in the x‑ and y‑dimensions. It is a term equivalent to operational analysis in its widest sense.

All concepts and propositions can in general be subjected to contingency analysis. And we can reformulate the claim of the modern philosophies of science that are rooted in empiricism or positivism that those concepts or propositions are "meaningless" which have zero or nearly zero components in the x‑ or y‑dimension (or in both x‑ and y‑dimensions), that all meaningful science therefore happens in the x‑y plane. This, in brief, was the content of Newton's public pronouncements against the postulation of innate properties and occult principles. It also lies behind Hume's exhortation, the persistent attacks of Comte and Mach and their followers, and, outside science itself, the fury of Locke against the doctrine of innate principles, the suspiciousness of J. S. Mill against the intuitionism of the Scottish school, the reduced role that Ayer assigns to philosophy when he writes that the function of philosophy is "to clarify the propositions of science by exhibiting their logical relationships, and by defining the symbols which occur in them," and the fear of many modem scientists that going outside the contingent plane necessarily means opening the gates to a flood of obscurantism.

It is indeed one of the great advantages of the scheme that in the x‑y plane many questions (e.g., concerning the reality of scientific knowledge) cannot be asked. The existence of such questions is not denied; but they do not have to be admitted into scientific discussions, since the possible answers are not verifiable or falsifiable, having no component that can be projected on the phenomenic dimension of empirical (observational) fact, and obeying no established logical calculus (beyond that of grammar) in which the analytic projection of the statement can be examined for consistency.

In fact, this attitude is one reason why science has grown so rapidly since the early part of the seventeenth century; keeping the discourse consciously in the contingent plane means keeping it in the arena of S2, where statements can be shared and publicly verified or falsified. This habit has minimized prolonged disagreement or ambiguity or the mere authority of personal taste. It has helped expel certain metaphysical propositions which were masquerading as empirical or analytical ones. And in these ways, it has also helped forge a strong and wonderfully successful profession.

These successes do not, however, hide the puzzling fact that contingency analysis excludes an active and necessary component that is effective in scientific work, both on the personal and on the institutional level; that is, it neglects the existence of preconceptions that appear to be unavoidable for scientific thought, but are themselves not verifiable or falsifiable. Their existence has long been commented upon, and some of their properties have been examined from different points of view; [5] but much more can be said on this subject. Related to the first is a second puzzle, namely, why contingency analysis helps us to understand neither how the individual scientific mind arrives at the products that later can be fitted into the contingent plane, nor how science as an historical en�terprise grows and changes. Thus in his influential book, Scientific Explanation, the philosopher R. B. Braithwaite offers the rather typical confession that an explanation of such matters is beyond the realm not only of the scientist but also of the philosopher:

The history of a science is the history of the development of scientific systems from those containing . . . few generalizations . . . into imposing structures with a hierarchy of hypotheses. . . . The problems raised by this development are of many different kinds. These are historical problems, both as to what causes the individual scientist to discover a new idea, and as to what causes the general acceptance of scientific ideas. The solution of these historical problems involves the individual psychology of thinking and the sociology of thought. None of these questions are our business here. [6]

If, however, we want to make them our business, it is at this point—to return to our analogy—that we define a third, or z‑axis, perpendicular to the x‑ and y‑axes of the contingent plane. It is the dimension of themata, of those fundamental preconceptions of a stable and widely diffused kind that are not resolvable into or derivable from observation and analytic ratiocination. They are often found in the initial or continuing motivation of the scientist's actual work, and also in the end product to which his work reaches out. Thus, while the two‑dimensional x‑y plane may suffice for most discourse within science in the sense of S2, it is in the three‑dimensional, x‑y‑z space within which a more complete analysis—whether historical, philosophical or psychological—of scientific statements and processes should proceed. For example, the study of the rise or fall of a thematic preoccupation is among the most interesting problems for the historian. Some themata grow slowly, as the result of a sequence of local successes, e.g., the thema of strict conservation, as embodied in the laws of conservation of mass and of energy, explained chemical reactions (such as the formation of HCl) better than the earlier use of material "principles" (such as the acidifying principles). The chemical ideas of material change became by and by so successful that whereas in Newton's time chemical reactions were understood in terms of organic digestive processes, a century and a half later the arrow of explanation had turned around and organic digestive processes were explained in terms of chemical reactions. [7] Some thematic concepts found their place more rapidly, perhaps as a result of stunning virtuoso demonstrations (e.g., the concept of a causal, mechanistic universe which was at least the external result of Newton's system of the world). Other themata have atrophied or are now discredited as explanatory devices—ideas such as macrocosmic‑microcosmic correspondence, inherent principles, teleological drives, action at a distance, space filling media, organismic interpretations, hidden mechanisms, or absolutes of time, space, and simultaneity. [8]

Yet other themes are long lived and apparently stable. To find examples, we need only glance at some reports of current research in the physical sciences and related areas, selected almost at random and quoted or paraphrased from recent issues of research reports in the journals of the profession.

At the top of the pile of journals on my desk at the moment is a report of deep inelastic scattering of nuclear particles observed at the Stanford University linear accelerator, which has drawn comment from theorists. The problem is: what is the structure of the proton�which to an historian of science sounds like a contradiction in terms. The current candidates are pointlike hypothetical constituents, be they quarks, dions, partons, or stratons. One thing is clear: the antiquity of this quest for an elementary—although perhaps protean—constituent of all matter, a quest that has made sense to scientists all the way back to Thales. It is nothing less than an a priori commitment that deserves to be called thematic.

Almost invariably, for every thematically informed theory used in any science, there may also be found a theory using the opposite thema, or antithema. (Sometimes we find not merely opposing (θ‑[anti]θ) dyads, but even triads.) Thus opposition exists to current theories that believe all hadrons to be dynamical constructs, satisfying self‑consistency conditions. There are publications insisting, for example, that nature exists in an infinite number of strata with different qualities, each stratum being governed by its own laws of physics and each always in the midst of creation and annihilation. Still another view of the matter is hinted at in work such as that of G. F. Chew, who has speculated that the way to enlarge current ideas in elementary particle physics is to break out in entirely new directions: "Such a future step would be immensely more profound than anything comprising the hadron bootstrap [approach]; we would be obliged to confront the elusive concept of observation and, possibly, even that of consciousness. Our current struggle . . . may thus be only a foretaste of a completely new form of human intellectual endeavor, one that will not only lie outside physics but will not even be describable as 'scientific.'"

What seems certain is that regardless of temporary victories for one side or another, the dialectic process of this sort between a thema and its anti‑thema, and hence between the adherents of two or more theories embodying them respectively, is almost inevitable, and is perhaps among the most powerful energizers of research. If the past is a guide, this process will last as long as there are scientists interested in putting questions to nature and to one another.

Next I find a report of a conference of physicists on fundamental interactions at high energy. P. A. M. Dirac opened the conference with the question, "Can equations of motion be used?" Although agreeing that Heisenberg's 1925 view can be a good guiding principle (e.g., that only observable quantities should be used in formulating a physical theory), he felt it nevertheless unlikely that the analytic S‑matrix description would be the final answer in high‑energy physics. Some day, according to Dirac, we would be discussing equations of motion of entities only remotely related to experimental quantities. He thought this prophecy would come to pass because of his "feeling for the unity of physics" and because of the important role played by equations of motion in all other branches of physics. This confidence, somewhat in the face of current fashion and experimental evidence, led Dirac to say, "a theory that has some mathematical beauty is more likely to be correct than an ugly one that gives a detailed fit to some experiments."

Such a quasi‑aesthetic judgment is a form of thematic commitment with deep psychological roots. It is frequently the basis for choices made in actual scientific work (for example, when one ad hoc hypothesis is accepted and another is rejected, or when a whole approach to a scientific field is adopted or dismissed), though it is not common to see this confessed in public print. Thus, in 1926, Heisenberg wrote to Pauli, "The more I ponder the physical part of Schrödinger's theory, the more disgusting it appears to me." At about the same time, Schrödinger in his turn wrote about Heisenberg's approach: "I was frightened away [by it], if not repelled." And Fermi wrote to Enrico Persico in the same vein about what he called "the formal results in the zoology of spectroscopic terms achieved by Heisenberg. For my taste, they have begun to exaggerate their tendency to give up understanding things." At least since Copernicus defended his theory as "pleasing to the mind," it has been an everyday fact in the life of scientists that some of the terms and attributes they use have for them great motivating power, but cannot be subjected to contingency analysis.

Further on in a recent issue of Physics Today, I find the report of a delicate analysis made on a meteorite that fell on Australia. A team assembled from several institutions reports finding 16 amino acids, at least five of which are common in living systems: these five would constitute an essential part of any chain in the chemical evolution toward living forms. In a sense, this is merely another report in a recent series that suddenly has shown the "dead interstellar spaces" to be populated with more and more complex materials, from hydroxyl radicals to formaldehyde. But what now excites the interest of the scientists most is the evidence of equal quantities of laevogyrate (left‑handed) and dextrogyrate (right‑handed) amino acids in the samples. The fact that the chirality in these samples is of both kinds increases by far the likelihood that these amino acids are not merely contaminations from handling; for reasons that are still entirely mysterious, the amino acids in living things on earth are almost all left‑handed. Now it has become quite likely that the ideas of chemical basis of evolution are entering a new phase of elaboration: a search for clouds of amino acids in space becomes sensible. Chemistry, biology, geology, physics, and astronomy are being brought together in a remarkable interdisciplinary attempt to understand the historic, and perhaps continuing, evolution of life.

Triggered in part by this finding and this way of thinking is another review, Chirality, Broken Symmetry, and the Origin of Life. The title itself alerts us to the whole set of thematic elements that are basic in major areas of research today, as they were in other areas in the past: the efficacy of geometry as an explanatory tool; the conscious and unconscious preoccupation with symmetries; the use of the themata of evolution and devolution that might have been taken from the ordinary life cycle but that have become, in any case, fundamental tools of scientific thought (as much in psychological and sociological research as in genetics and astrophysics). It is the interdisciplinary spread or sharing of such fundamental themata that has produced something like a scientific imagination shared by all scientists, forming one of the bonds among them, and making possible the interdisciplinary approach that characterizes so many of the new developments.

Though certain themata are developed in detail in some of the essays that follow, it will be fruitful here to make distinctions between three different uses of the concept of themata:

(1) A thematic concept is analogous to a line element in space which has a significant projection on the z‑ or thematic dimension. Purely thematic concepts seem to be rare in established science. What is more significant is the thematic component of concepts such as force or inertia, which have strong x and y components also. Therefore, when we speak of force or inertia as a thematic concept we mean the thematic component of this concept.

(2) A thematic position or methodological thema is a guiding theme in the pursuit of scientific work, such as the preference for seeking to express the laws of physics whenever possible in terms of constancies, or extrema, (maxima or minima), or impotency ("It is impossible that . . .").

(3) Between these two is the thematic proposition or thematic hypothesis, e.g., a statement or hypothesis with predominant thematic content, or the thematic component of a statement or hypothesis. A thematic proposition contains one or more thematic concepts, and may be a product of a methodological thema. Thus, the principle of constancy of the velocity of light in relativity theory is a thematic proposition, and it also expresses the constancy‑seeking methodological thema.

Without preempting the discussion in the essays that follow, it will be useful here to touch briefly on a few other properties of themata. One is the question concerning their source. They are certainly not unapproachably synthetic a priori, in the eighteenth‑century sense; nor is it necessary to associate them with Platonic, Keplerian, or Jungian archetypes, or with images, or with myths (in the nonderogatory sense, so rarely used in the English language), or with irreducibly intuitive apprehensions. [9]

It is likely that the origin of themata will be best approached through studies concerned with the nature of perception, and particularly of the psychological development of concepts in young children. Another direction that seems to have promise is the work building on Kurt Lewin's dynamic theory of personality. But, pending reliable results, [10] the most fruitful stance to take for the moment seems to me akin to that of a folklorist or anthropologist, namely, to look for and identify recurring general themes in the preoccupation of individual scientists and of the profession as a whole, and to identify their role in the development of science.

Another point concerns the antiquity and paucity of themes—the remarkable fact that the range and scale of recent theory, experience, and experimental means have multiplied vastly over the centuries while the number and kind of chief thematic elements have changed little. Since Parmenides and Heraclitus, the members of the thematic dyad of constancy and change have vied for loyalty, and so have, ever since Pythagoras and Thales, the efficacy of mathematics versus the efficacy of materialistic or mechanistic models. The (usually unacknowledged) presuppositions pervading the work of scientists have long included also the thematic couples of experience and symbolic formalism, complexity and simplicity, reductionism and holism, discontinuity and the continuum, hierarchical structure and unity, the use of mechanisms versus teleological or anthropomorphic modes of approach.

These, together with others further discussed in the essays and perhaps a few more—a total of fewer than 50 couples or triads—seem historically to have sufficed for negotiating the great variety of discoveries. Both nature and our pool of imaginative tools are characterized by a remarkable parsimony at the fundamental level, joined by fruitfulness and flexibility in actual practice. Only occasionally (as in the case of Niels Bohr) does it seem necessary to introduce a qualitatively new theme into science.


3. E.g., by R. B. Braithwaite, Scientific Explanation (Cambridge: Cambridge University Press, 1953), p. 22. [—> main text]

4. Ibid., p. 107. [—> main text]

5. E.g., Ludwig Wittgenstein, Tractatus Logico‑Philosophicus (London: Routledge & Kegan Paul, 1961), 6.3211, 6.33, 6.34, 6.35; or Stephen Toulmin, Foresight and Understanding (Bloomington, Indiana: Indiana University Press, 1961), p. 100. [—> main text]

6. Braithwaite, op. cit., pp. 20‑21; italics added. [—> main text]

7. See Toulmin, op. cit., p. 69. [—> main text]

8. Of course, not all themata are meritorious. As Bacon warned in discussing the four Idols that can trap the scientific mind, some have turned out to divert or slow the growth of science.

Nor do all sciences have to benefit equally; the holistic viewpoint introduced at the start of the nineteenth century may have had benefits in physics but was on the whole a handicap for biology. Nor is there any necessity that the allegiance by a given scientist to a given thema must be unshakable. Scientists can and occasionally do change loyalties to a thema, as is demonstrated in the discussion of the philosophical development of Einstein in the eighth essay. [—> main text]

9. Similarly, it should not be necessary to stress that thematic analysis is not an ideology, a school of metaphysics, a plea for irrationality, an attack on the undoubted effectiveness of empirical data and experimentation, or, a desire to teach scientists how to do their job better. Nor is it a theoretical framework for accommodating such notions as paradigms or research programs. [—> main text]

10. These may first be merely the establishment of typology. Just as Ostwald had discerned a dichotomy between classical and romantic styles within science (which Albert Szent‑Gyorgyi recently renamed systematic and intuitive, or Apollonian and Dionysian), Lewin distinguished between the Aristotelian and Galilean modes of thought, and showed their persistence in contemporary scientific work. [—> main text]

SOURCE: Holton, Gerald. Thematic Origins of Scientific Thought: Kepler to Einstein. Cambridge, MA: Harvard University Press, 1973. Introduction, pp. 11-44; section: "The Thematic Component," pp. 21-29; notes, pp. 43-44.


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by Gerald Holton
(book freely downloadable)

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