The Principled-Constructive theory distinction

A few possible sources for Einstein's distinction between theories and some of the implications drawn.

Reading a post on a tangentially related matter I was reminded of a taxonomic idea about scientific theories and made some comments about it. My story begins when Einstein wrote a piece in the Times of London offering a brief explanation of his theories of relativity. This was in 1919 shortly after Eddington’s famous eclipse expeditions. The eclipse expeditions had offered some dramatic confirming evidence for Einstein’s General Theory of Relativity in the deflection of light by the Sun’s gravity and generated great interest in the idea.

Before discussing relativity Einstein begins by distinguishing two types of scientific theories. Constructive theories and theories of principle:

“Most of them are constructive. These attempt to build a picture of complex phenomena out of some relatively simple proposition. The kinetic theory of gases, for instance, attempts to refer to molecular movement the mechanical thermal, and diffusional properties of gases. When we say that we understand a group of natural phenomena, we mean that we have found a constructive theory which embraces them.

But in addition to this most weighty group of theories, there is another group consisting of what I call theories of principle. These employ the analytic, not the synthetic method. Their starting-point and foundation are not hypothetical constituents, but empirically observed general properties of phenomena, principles from which mathematical formula are deduced of such a kind that they apply to every case which presents itself. Thermodynamics, for instance, starting from the fact that perpetual motion never occurs in ordinary experience, attempts to deduce from this, by analytic processes, a theory which will apply in every case. The merit of constructive theories is their comprehensiveness, adaptability, and clarity, that of the theories of principle, their logical perfection, and the security of their foundation.” (Einstein 1919)

He then explains relativity is a theory of principle and attempts a short survey of those principles and compares them to Newtonian mechanics. Einstein’s emphasis on principle makes sense given the importance just such abstract principles play in relativity. The special theory of relativity is explicable by two short postulates (and the implicit structure of physics). The emphasis on abstract logical form allows him to connect relativity to Newtonian mechanics and suggest how his own work has strong continuity with and dependency on those earlier theories.

The distinction is also pregnant with various issues in physics and science more generally. The importance of understanding or explanation as a merit of scientific theorizing. The question of the strength and enduring nature of evidential support (the security of foundation) of some theories over others. It also hints at a major scientific change and debate of the 19th and early 20th century, the development of thermodynamics and how statistical mechanics (consisting of theories such as the kinetic theory of gases) arose to elucidate mechanisms for thermodynamics that were resisted (such as the existence of atoms). Einstein was involved in these developments in his 1905 paper deriving properties of molecules such as size from features of Brownian motion.

It is probably in part because of this that Einstein’s 1919 paper has become, in my estimation, a common reading in history of science courses and collections of essays about Einstein, relativity and science. I have known several philosophers who found the distinction interesting and suggestive. The Stanford Encyclopaedia article by Don A. Howard and Marco Giovanelli on Einstein’s philosophy of science for example says “Einstein’s most original contribution to twentieth-century philosophy of science lies elsewhere, in his distinction between what he termed “principle theories” and “constructive theories.”” (Howard & Giovanelli 2025)

I and every person I ever remember talking about this distinction with took the distinction as original to Einstein (although Einstein does not himself make that claim). As I will now relate I think the distinction is much older. I don’t want to make too much of this. I don’t think the sources I’m going to now cite are particularly obscure, many others may unbeknownst to me made the same distinction. Howard and Giovanelli’s Stanford Encyclopedia article suggests some influences and precursors. However this also includes this thought that I think definitely requires some correction “What is puzzling, and even a bit sad, is that this most original methodological insight of Einstein’s had comparatively little impact on later philosophy of science or practice in physics. Only in recent decades, Einstein constructive-principle distinction has attracted interest in the philosophical literature, originating a still living philosophical debate on the foundation of spacetime theories.” (Howard & Giovanelli 2025) Let me now detail some things Howard and Giovanelli at least overlooks.

Back in May of 2020, I was for some reason skimming bits of a 1934 book on logic and scientific method co-authored by Ernest Nagel (who is my favourite 20th century philosophical Nagel) and Morris Cohen (I’ve never heard of Cohen so I put Nagel 1st but Cohen has top billing on the title page). I can not remember why exactly. Perhaps I was looking for responses to John Stuart Mill’s Logic or perhaps I just wanted to see what Nagel had to say about philosophy of science in 1934. It was the height of the pandemic, and I was reading a little more then, but I spend a lot of time reading odd things here and there. Whatever the reason I was struck by this passage:

“There is however, another interesting distinction between theories. Some theories appeal to an easily imagined hidden mechanism which will explain the observable phenomena; other theories eschew all reference to such hidden mechanisms, and make use of relations abstracted from the phenomena actually observable. The former are called physical theories; the latter are called mathematical or abstractive theories.” (An Introduction to Logic and Scientific Method, 1934, M. R. Cohen and Ernest Nagel, p. 397)

Here was Einstein’s distinction between constructive and principled theories with the slight change of labels. A constructive theory became a physical theory, a theory of principle becomes a mathematical or abstractive theory. They rehearse some examples and the classification matches Einstein, the kinetic theory of gases is a physical theory, the theory of relativity an abstractive theory. Although the basic distinction is the same Cohen and Nagel do not give it the same significance or implications that Einstein does. They see the two types of theories as indicative of the idiosyncrasies of scientists and the trends of the time.

“As we suggested, it is useless to quarrel as to which type of theory is the more fundamental and which type should be universally adopted. Both kinds of theories have been successful in coordinating vast domains of phenomena, and fertile in making discoveries of the most important kind. At some periods in the history of a science, there is a tendency to mechanical models and atomicity; at others, to general principles connecting characteristics abstracted from directly observable phenomena; at still others, to a fusion or synthesis of these two points of view. Some scientists, like Kelvin, Faraday, Lodge, Maxwell, show an exclusive preference for “model” theories; other scientists, like Rankine, Ostwald, Duhem, can work best with the abstractive theories; and still others, like Einstein, have the unusual gift of being equally at home with both kinds.” (Cohen and Nagel, p. 399)

So unlike Einstein they see no special virtues (such as clarity or logical rigour) in the two types of theories. Also although they reference Einstein as a scientist here they make no reference to his use of the same distinction (and may well have been unaware of it). They do however reference an 1855 paper by Scottish physicist William John Macquorn Rankine and give a long quote of his distinction between the two types of theories. Rankine’s 1855 Outlines of the Science of Energetics is the earliest source I have found making the distinction. I have not really looked for any earlier instances. Still it is worthwhile to see how and what Rankine makes of the distinction.

The paper is mostly an attempt to outline what will become standard thermodynamic concepts and link them to existing ideas in physics. Such as defining kinetic and potential energy in Newtonian mechanics. However the paper begins by outlining how theories are derived form observation. He then continues:

“Two methods of framing a physical theory may be distinguished, characterized chiefly by the manner in which classes of phenomena are defined. They may be termed respectively the ABSTRACTIVE and the HYPOTHETICAL methods.

According to the ABSTRACTIVE method, a class of objects or phenomena is defined by describing, or otherwise making to be understood, and assigning a name or symbol to, that assemblage of properties which is common to all the objects or phenomena composing the class, as perceived by the senses, without introducing anything hypothetical.

According to the HYPOTHETICAL method, a class of objects or phenomena is defined according to a conjectural conception of their nature, as being constituted in a manner not apparent to the senses, by a modification of some other class of objects or phenomena whose laws are already known. Should the consequences of such a hypothetical definition be found to be in accordance with the results of observation and experiment, it serves as the means of deducing the laws of one class of objects or phenomena from those of another.

The conjectural conceptions involved in the hypothetical method may be distinguished into two classes, according as they are adopted as a probable representation of a state of things which may really exist, though imperceptible to the senses, or merely as a convenient means of expressing the laws of phenomena; two kinds of hypotheses, of which the former may be called objective, and the latter subjective. As examples of objective hypotheses may be taken, that of vibrations or oscillations in the theory of light, and that of atoms in chemistry; as an example of a subjective hypothesis, that of magnetic fluids.” (Rankine 1855)

So we see that Rankine’s terminology differs slightly again from Cohen and Morris. Instead of physical theories Rankine talks of hypothetical theories. Also he distinguishes between objective and subjective hypothetical theories. Rankine differs also in that he takes it that there is a significant difference in the implications of being one or the other. He defines mechanics (Newtonian mechanics) as the exemplar of the abstractive method and the only complete physical theory.

He discusses the efficacy of hypothetical theories in allowing diverse phenomena to be explained by a few simple rules, but cautions:

“Such are the results to be expected from well-framed hypotheses in every branch of physics, when used with judgment, and especially with that caution which arises from the consideration, that even those hypotheses whose consequences are most fully confirmed by experiment, never can by any amount of evidence attain that degree of certainty which belongs to observed facts.”

[...]

“The neglect of the caution already referred to, however, has caused some hypotheses to assume, in the minds of the public generally, as well as in those of many scientific men, that authority which belongs to facts alone, and a tendency has consequently often evinced itself to explain away, or set aside, facts inconsistent with these hypotheses, which facts, rightly appreciated, would have formed the basis of true theories; thus the fact of the production of heat by friction, the basis of the true theory of heat, was long neglected, because inconsistent with the hypothesis of caloric;” (Rankine 1855)

Like Einstein Rankine thinks that abstractive (principled) theories have a more secure evidential base than hypothetical (constructive) theories. However Rankine takes it further and emphasizes an absolute distinction in the evidential basis for the matter. As mentioned Cohen and Nagel deny any substantive distinction between the value and reliability of the theory.

Rankine discusses how extension of mechanics to science (such as kinetic molecular theories of heat) has been successful) and may come to encompass all of science, which is a kind of combined method of occult molecular or atomic hypothesis combined with observed abstractive laws of motion. What we might now thing of as a single unified theory of physics. He offers an alternative path in extending abstractive method as follows:

“Instead of supposing the various classes of physical phenomena to be constituted in an occult way of modifications of motion and force, let us distinguish the properties which those classes possess in common with each other, and so define more extensive classes denoted by suitable terms. For axioms, to express the laws of those more extensive classes of phenomena, let us frame propositions comprehending as particular cases, the laws of the particular classes of phenomena comprehended under the more extensive classes. So shall we arrive at a body of principles, applicable to physical phenomena in general, and which being framed by induction from facts alone, will be free from the uncertainty which must always attach even to those mechanical hypotheses whose consequences are most fully confirmed by experiment. This extension of the abstractive process is not proposed in order to supersede the hypothetical method of theorizing; for in almost every branch of molecular physics it may be held, that a hypothetical theory is necessary as a preliminary step to reduce the expression of the phenomena to simplicity and order, before it is possible to make any progress in framing an abstractive theory.” (Rankine 1855)

This sort of thinking illustrates how differently Rankine understood the distinction than Cohen and Nagel or Einstein. Abstractive methods for Rankine are more evidentially secure and there is no sense hypotheses are needed for understanding as Einstein seems to suggest. For Rankine hypothesis is necessary at the beginning of investigation to identify what properties and relations to abstract.

I feel as though it is clear that Einstein’s basic distinction between constructive and principled theories must be the same distinction as Rankine’s (Cohen and Nagel cite Rankine so the pedigree of their distinction is clear). This is not certain since two people considering the same physics might arrive at a similar taxonomy due to similarity of subject matter, but I this seems unlikely to me. If I am right how then did Einstein learn of the distinction. One possibility is that Einstein read Rankine’s 1855 paper. Einstein did work on thermodynamic and energetic subjects. Again, the possibility can not be ruled out, but it struck me that Einstein was known to have read Duhem and Duhem wrote histories of physics and so might well have come across Rankine.

Sure enough in Chapter 3 of 1906 La théorie physique, son objet, sa structure (The Aim and Structure of Physical Theory), Duhem extensively quotes Rankine, introducing him with this paragraph:

“The first contributions of Macquorn Rankine to the progress of the mechanical theory of heat had been attempts at explanation; but his ideas soon evolved and, in a short paper of his, too little known, he traced very clearly the characteristics which distinguish a representative theory — called by him “abstractive theory” — from an explanatory theory — designated by the name “hypothetical theory.” (p, 52 English translation by Philip P. Wiener)¹

Again we find different labels representative theory (théorie représentative) for the abstractive (principled) theory and explanatory theory (théorie explicative) for the hypothetical (constructive) theory. Also the implications that are drawn are different again. For Duhem explanatory theories and explanation are always of quite limited power, more explanations or hypotheses can be put forward by the physicist and never penetrate to the ultimate nature (the metaphysical nature) of the underlying reality. Thus for Duhem science is always ends in a representative theory, a simplified and orderly representation of phenomena. Chapter 3 where Rankine is quoted is “Representative Theories and the History of Physics”². This is not necessarily that at odds with Einstein’s understanding since a metaphysical understanding may be a more rarified thing than Einstein was thinking of when he considered constructive theories to allow understanding. Indeed skimming Howard and Giovanelli I see that Einstein rejected talk of the hypotheses of physics being real. I have not actually read Duhem thoroughly. Again skimming the Stanford Encyclopedia article on Einstein I see that Duhem’s holistic concept of science probably militates against his view that hypothesis and explanation are easy. Under Duhem’s holism individual elements can not be evaluated and so treating individual hypotheses as loose or interchangeable is militated against. Still I feel as though Einstein is giving more credit to the value of explanation that Duhem does in the passages I’ve read.

As Howard and Giovanelli chronicles it seems likely Einstein read Duhem in 1909 when he was neighbours with the German translator of La théorie physique (1908). This would suggest a vector by which Einstein could have learned the distinction between types of theories.

Not only the labels but also the implications change greatly between the different people who make the distinction. For Cohen and Nagel (whose book continued to be reissued into the 1960s) the distinction was more a mark of the style of certain physicists and times. In defense of this one can point out that it is not merely hypothetical entities but indeed the posited relations between observables that are different in different theories. As relativity shows, the relationships of space, time and motion are subject to revision and phenomena like time dilation can be received with the same incomprehension or incredulity as notions like unseen atoms. However this might not be enough to refute Rankine’s sense that abstractions from phenomena are more reliably known than hypothesized elements or Einstein’s sense that the foundations of principled theories were more secure. Duhem’s skepticism of explanation in science and so of hypothetical methods seems stronger than any reservations Einstein or Rankine had.

Another aspect interesting to me is the way this distinction seems emblematic of thermodynamics and statistical physics. The examples in that field seem most suggestive. There are also aspects of the famous doctrine of Newton not to propose a hypothesis about the mechanism of gravity that is often taken as a general maxim for science. The depreciation by Rankine and Duhem especially of hypothetical methods suggests it. There is clearly much more to be uncovered here, but I have been sitting on this for 6 years and thought it worth getting out.

Bibliography

Cohen, Morris R. and Ernest Nagel, An Introduction to Logic and Scientific Method, Routledge and Kegan Paul Ltd., 1934.

Duhem, Pierre, La théorie physique, son objet, sa structure, Chevalier & Riviére, 1906.

Duhem, Pierre, The Aim and Structure of Physical Theory, trans. Philip P. Wiener, Princeton University Press, 1954.

Einstein, Albert, “Time, Space, and Gravitation”, in Science, 51 (No. 1305); January 2, 1920; pp. 8-10, originally published: London Times; November 28, 1919.

Howard, Don A. and Marco Giovanelli “Einstein’s Philosophy of Science” in The Stanford Encyclopedia of Philosophy, 2025.

Rankine, William John Macquorn, “Outlines of the Science of Energetics” in Proceedings of the Royal Philosophical Society of Glasgow, Volume 3, by Royal Philosophical Society of Glasgow, 1855. pp.381-399.

1. Les premières contributions de Macquorn Rankine aux progrès de la théorie mécanique de la chaleur avaient été des essais d`explication; mais bientôt ses idées évoluèrent et, dans un petit écrit trop peu connu, il traça avec une admirable netteté les caractères qui distinguent la théorie représentative — nommée par lui théorie abstraite — de la théorie explicative — désignée sous le nom de théorie hypothétique. (p. 80, 1906 edition of Duhem)

2. Les théories représentatives et l`histoire de la physique