Campbell, Norman Robert (1880–1949)

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CAMPBELL, NORMAN ROBERT
(1880–1949)

Norman Robert Campbell, the English physicist and philosopher of science, was educated at Eton. From Eton he went as a scholar to Trinity College, Cambridge, and became a fellow there in 1904. From 1903 to 1910 he also worked as a research assistant at the Cavendish Laboratory, whose director, the celebrated J. J. Thomson, became the most important inspiration of his scientific work. In 1913 he became an honorary fellow for research in physics at Leeds University, but he left this post after the war and from 1919 to 1944 was a member of the research staff of the General Electric Company.

The writers who seem to have influenced him most are Ernst Mach and Henri Poincaré, apart from classical authors such as William Whewell, John Stuart Mill, and W. S. Jevons. On the other hand, such philosophers as Bertrand Russell and Alfred North Whitehead came too late to have much effect on him; the main outlines of his thought developed during the first decade of the century, and there are only occasional references to their writings.

Campbell exhibited the very rare combination of competence in both physics and philosophy, but while he preferred to think of himself primarily as an experimental physicist, it is as a philosopher of science that he made his mark. This point is brought out in the writings of F. P. Ramsey, R. B. Braithwaite, and Ernest Nagel, although these concentrate largely on the formal parts of Campbell's doctrines and pay scant attention to the more valuable contributions that he made to certain methodological ideas, particularly that of analogy. These philosophical views, shaped by Campbell's actual experiences and ideas as a physicist and expositor of physical theories, were meant to be construed as answers to intellectual pressures and problems that confronted him in the years that saw the rise of the twentieth-century atomic theory on the one hand and relativity and quantum mechanics on the other. In philosophy of science, his most important contributions were in the fields of the logic of theory construction and (to a lesser extent) the principles of physical measurement.

Philosophy of Theory Construction

Campbell's views were stated in systematic form for the first time in a popular book, The Principles of Electricity. Thereafter they were developed, with minor changes of emphasis and greater attention to the nature of "mathematical theories," in Physics: The Elements. In contrast with the usual textbook approach, his views were deeply interwoven with, and at times even explicitly discussed in, his more formal scientific treatises.

concepts and ideas

Campbell distinguishes sharply between the laws and theories of a science. In the case of laws, the constituent terms (Campbell calls them concepts) designate entities whose magnitudes may be determined more or less directly by instrumental means; they are not unlike what later came to be called operational concepts. The explanatory part of theories, the hypotheses, involve terms that Campbell calls ideas. These lack the instrumental relations of concepts, for a variety of reasons that Campbell does not always clearly distinguish.

Sometimes the ideas refer to the unobservable infrastructure of a physical system, as in the case of the atoms and electrons of modern electrical theory or, more properly (as Campbell points out), to their adjectival aspects, such as their mass, velocity, and momentum. At other times, the ideas pertain to such interstructural devices as Michael Faraday's lines of force, or the carriers of the transfer of electrical and optical phenomena, such as light waves, light corpuscles (photons) or even the "aether," considered the substantival carrier of electromagnetic energy. (Infrastructural entities are unobservable in a sense different from interstructural ones, but the question is controversial.) A third case in which theories are said to involve unobservables is that of geological and evolutionary theories. And there is yet another case, for Campbell denominates certain notions "ideas" because they involve an amount of idealization and abstraction to which no physical entities could correspond. The most frequent and important cases are those ideas which involve infinitesimals, such as the differential coefficients in James Clerk Maxwell's equations or François Marie Charles Fourier's theory of heat.

It follows from the nature of ideas that the hypotheses in which they occur are not directly testable. Their function consists merely in systematically relating a set of corresponding laws, and, through extensions of the theory, in foreshadowing further laws and experiments. This foreshadowing is sometimes negative, for when the ideas are too narrowly framed, they demand not only extension but also the formulation of additional concepts and theories.

"dictionary" of a theory

Since the ideas of the hypotheses lack operational meaning, and since their deductive development can, in the first place, yield only statement forms containing either ideas or combinations of them, it is necessary to add certain rules (a kind of "dictionary") that will coordinate the ideas with those operational concepts which occur in the laws to be explained. Of course, not all ideas need dictionary entries. In the beta-ray theory, for instance, the velocity, v, of the hypothetical electrons means "the quantity that is defined by the relation F = e [X +(v · H )]." This expression, however, is a hypothesis in Campbell's sense because v never occurs either alone or in combination in the testable derivations at all.

"mathematical" theories

All this provided Campbell with a means of distinguishing so-called mathematical theories from nonmathematical ones. In the former, each and every idea is separately coordinated with a corresponding concept by means of a dictionary entry. It follows that whether a theory is of the mathematical type depends partly on historical accidents: Maxwell's theory became a mathematical theory only after Heinrich Rudolf Hertz's experiment had demonstrated the existence of the displacement current.

Nonetheless, ideas so far have no meaning apart from their use in hypotheses and their coordination with concepts. In the mathematical cases this is often forgotten, but in the nonmathematical cases this fact is more difficult to overlook. Because of the lack of independent significance of ideas, Campbell held that a theory is not a real explanation unless certain additional requirements are satisfied. One of his reasons for this view was that it is always possible to construct an indefinite number of hypotheses that would account for a set of laws. In the case of mathematical theories, the additional element of consolidation that Campbell suggests is the regulative feature of simplicity and aesthetic elegance—for instance, through symmetrical arrangements of the parts of a theory. (Thus, it was the introduction of Maxwell's displacement current into the original equations of André Marie Ampère and Faraday that produced a symmetrical set of equations regarding the relations between the electrical and magnetic phenomena for the case of open circuits.) Furthermore, the hypotheses are not entirely arbitrary because their ideas mirror the corresponding concepts of the laws. There is, according to Campbell, a sort of analogy between ideas and concepts (Physics: The Elements, p. 141).

analogy

Analogy plays a more central role in the case of the nonmathematical theories. As we have seen, their ideas frequently cannot be clarified at all by the concepts that occur in the laws. According to Campbell, it is an analogy of the hypotheses and their ideas with corresponding laws and concepts of some testable field of science that imparts the missing element of significance and logical strength to the theory. It follows that analogies are not merely aids to the establishment of theories; "they are an utterly essential part of theories, without which theories would be completely valueless and unworthy of the name" (ibid., p. 129).

Campbell's point is that "a theory is not a law" (ibid., p. 130); that hypotheses are, from the nature of the case, never directly testable; and, hence, that their addition to the corpus of scientific knowledge would make no difference to science at all if it were not for some additional features that make the hypotheses significant. He dismisses the fact that they supply a systematic relation between the laws of the theory on the grounds that an infinity of such hypotheses can be constructed.

Campbell's positive grounds for the necessity of analogies are of various kinds. The fundamental reason is that since hypotheses are not directly testable but are only instruments for deductive development, possessing a purely formal content, they lack the sort of meaning required for genuine explanatory power: Only analogy can supply this. Another ground of a more heuristic nature is that analogies aid in the extension of theories, especially when a new field is grafted onto the dictionary of an existing theory (as when optical conceptions were added to Maxwell's generalization of the electrical theories of Ampère and Faraday).

As mentioned, however, analogy must be supplemented by additional criteria, which are clearly needed for dealing with mathematical theories. These criteria are largely derived from Campbell's actual experience with the theories with which he had been dealing in his physical textbooks. In addition to simplicity and aesthetic elegance, there is "simplification in our physical conceptions," such as was produced by the early theories of Faraday, Thomson, and Hendrik Antoon Lorentz. Campbell insists on the importance of such regulative conceptions precisely because "scientific propositions are [not] capable of direct and irrefutable proof." An additional criterion is the "anticipative force" of a theory—for instance, the suggestiveness of Faraday's lines in the direction of the existence of electromagnetic radiation, of a motion that is displaced in time, with a given velocity, in empty space.

Finally, another regulative criterion is that of importance, or depth, of the ideas involved. This is invoked particularly in those cases where analogy is barely a relevant consideration, as in such mathematical theories as Maxwell's, or Albert Einstein's special theory of relativity.

Methodological Contributions

Campbell's clear account of the logical structure of a theory, with its hypotheses, laws, and dictionary, offers an elegant means of formalizing the place of ideas (theoretical concepts) within theories. He emphasizes also the logical gap between hypotheses and laws even in cases where its existence had previously been practically overlooked—the mathematical theories. He uses this fact to question Mach's preference for such theories (called phenomenological by Mach), on the grounds that they employ hypotheses and hypothetical ideas just like any other theory. (Whether this does sufficient justice to the difference between the two types of theories must be left an open question.) The theoretical nature of such substantival entities as atoms and electrons seems to differ from that of lines of force on the one hand and, say, from the entropy functions on the other, in deeper ways not caught by Campbell's criteria of ideas.

The fact that the systematizing power of hypotheses is an insufficient criterion of their truth or explanatory power introduces the remaining feature of Campbell's doctrine—such regulative notions as the existence of a strong analogy, of simplicity, symmetry, anticipative force, and, finally, of importance. The most interesting of these is analogy, which in the end emerges as a metaphysical device in terms of which to formulate the special aspect of those theories that involve unobservables. The "absolute necessity" for an analogy is the result of the emasculation of the semantic power of hypotheses, coupled with the consideration that this emasculation entails the introduction of a special constraint that prevents such hypotheses from being mere arbitrary formulas.

Theory of Measurement

The second part of Physics: The Elements is a detailed discussion of the principles of physical measurement; this, like most of Campbell's ideas, was already contained in embryo in The Principles of Electricity (Ch. 2). His interest in measurement is not altogether removed from his main philosophical preoccupations mentioned so far. Just as he was concerned with a clear delineation of laws from theories, he was equally firm in stating the differences as well as the relations between laws and definitions. In Measurement and Calculation Campbell defines measurement "as the assignment of numerals to present properties in accordance with … laws." Thus, every measurable property must have a definite order; the systems to be measured must be capable of "addition," but what operation is considered "addition" must be carefully specified in a given situation; and whether the resultant quantities yield consistent measurements is a matter for lawlike experience. Campbell points out that the specification in question is usually tacitly adopted ab initio and is, indeed, often suggested by theory and the relevant analogy. Hence, he believes that "no new measurable quantity has ever been introduced into physics except as the result of the suggestion of some theory" (The Principles of Electricity, p. 41).

Bibliography

Campbell's works include Modern Electrical Theory (Cambridge: Cambridge University Press, 1907; 2nd ed., 1913); The Principles of Electricity (London, 1912); Physics: The Elements (Cambridge, U.K.: Cambridge University Press, 1920), which was reprinted as Foundations of Science (New York: Dover, 1957); Measurement and Calculation (London: Longmans, Green, 1928); and Photoelectric Cells, written with Dorothy Ritchie (London: Pitman, 1929; 3rd ed., 1934).

As supplementary chapters of Modern Electrical Theory, the following monographs by Campbell were published in the Cambridge Physical Series: Series Spectra, Suppl. Ch. 15 (Cambridge, 1921); Relativity, Suppl. Ch. 16 (Cambridge, 1923); and The Structure of the Atom, Suppl. Ch. 17 (Cambridge, 1923).

For works with detailed references to Campbell, see Brian D. Ellis, Basic Concepts of Measurement (Cambridge: Cambridge University Press, 1966), Chs. 4, 5, and 8; Mary B. Hesse, Models and Analogies in Science (London, 1963), Ch. 1; and George Schlesinger, Method in the Physical Sciences (London: Routledge and Paul, 1963), Ch. 3, Sec. 5.

Gerd Buchdahl (1967)

Encyclopedia of Philosophy