ERNST MACH AND PIERRE DUHEM ON PHYSICAL THEORY

BOOK II - Page 2

 Duhem on Physical Theory and Metaphysics

Pierre Duhem (1861-1916), another important early positivist, studied physics at the Ecole Normale in Paris, where he received a doctorate in physics, and was a professor of physics at the University of Bordeaux for most of his career. His principal interest was physical chemistry, where he aspired to recast the theoretical foundations of chemical processes on the basis of a generalized thermodynamics. Unlike Mach, Duhem accepted the Aristotelian metaphysics, which he viewed as separate from positivist physics, and believed that progress in physical theory asymptotically approaches a “natural classification”, which he equated to the cosmology of Aristotle. Duhem’s philosophy differed from Mach’s philosophy by the former’s acceptance of physical theory as integral to physics, and by his development of a semantical metatheory to locate theory in positivist physics. The contemporary pragmatist philosopher Willard van Quine elaborated Duhem’s semantical metatheory for mathematical physics into a general philosophy of language, and retrospection reveals that it has been Duhem’s more lasting philosophical contribution.

Mach influenced Duhem who in turn also called his own philosophy of science positivist. But there were other intellectual influences in Duhem’s thought, and as a result Duhem differed from Mach in at lease two important respects: firstly Duhem accepted scientific theory as a valid and integral part of science, and secondly he reserved a place in human knowledge for metaphysics. Mach’s philosophy is often called “scientistic”, by which is meant that only science offers valid knowledge and that no nonphenomenalist discourse, which is summarily called “metaphysical”, is valid. While Mach was a physicist, philosopher, historian of science, and atheist, Duhem was a physicist, philosopher, historian of science and believing Roman Catholic. Like Mach, Duhem rejected the mechanistic, atomistic physics although for very different reasons than Mach. Unlike Mach, Duhem wished to retain the natural philosophy and cosmology of the Aristotelian and Scholastic philosophies upon which had been built the theology of his religion since Thomas Aquinas.

The outcome of these differences between Mach and Duhem is a complex philosophy of science that affirms and protects the autonomy of physics from any encroachment by metaphysics, while conversely affirming and protecting the autonomy of metaphysics from any encroachment by physics.  This mutual isolation of physics and metaphysics is due to Duhem’s view that on the one hand metaphysics, natural philosophy, and cosmology pertain to realities that are hidden and that underlie the phenomenal appearances accessible by the senses, while on the other hand physics pertains only to observed phenomena.  Furthermore and contrary to Mach, Duhem maintained that theories are integral to physics and are valid science.  The only cri­terion for scientific criticism of a theory, unlike a phenomenal description, is the theory’s ability to make predictions that are correct with a sufficient degree of approximation, i.e., correct within the range of indeterminacy produced by a degree of measurement error that always exists in experimental data.  Thus when Duhem rejected mechanism, one reason that he gave is that no mechanical atomic theory has been found to be sufficiently accurate, when judged by his purely scientific criterion for the criticism of theories.

But his principal reason for saying that the autonomy of physical theory is protected from the metaphysical thesis that physics must be mechanistic, is that physical theory has a special semantics that forbids interpreting the hypothetical postulates realistically, even if a proposed mechanistic hypothesis were scientifically adequate. Physical theory in Duhem’s view can never have a realistic semantics. No metaphysical or cosmological philosophy may be called upon to supply theoretical physics with its axioms. For this reason Duhem denies that physical theory has any explanatory function in science; only metaphysics is able to “explain”, and metaphysics has no place in physics. The distinctive semantics of physical theory is a very strategic part of Duhem’s philosophy of science. His religious and other intellectual influences may have operated in his developing this distinctive philosophy of science, but his stratifying the semantics of the language of science into the realistic and the nonrealist has as its basis, reasons that are entirely integral to his concept of empirical science itself. These reasons are semantical, and must be examined before attempting an exposition of his philosophy of science.

Duhem's Stratified Semantics for Physics

As mentioned above, the second respect in which Duhem differs from Mach is the former’s views on physical theory, and the difference is the most distinctive and lasting aspect of Duhem’s philosophy of science. Mach had rejected theory as “metaphysical”, meaning nonphenomenalist, and he maintained that ultimately in the ideal state of science all theory would be eliminated from science. Duhem’s alternative view is set forth in his Aim and Structure of Physical Theory (1906). In this work as well in other works he not only recognized a valid metaphysics distinct from science, but also considered theory to be characteristic of science in its highest state of development. Over and above the economy that Mach saw in the empirical laws of science, Duhem furthermore saw an additional economy offered by theory. Physical theory is a hypothetical axiomatized system of equations that orders the multiplicity of experimental laws by means of a symbolic structure, which is not identical with the empirical laws but which “represents” them in a parallel language.

This symbolic structure consisting of the axiomatized mathematical system, which constitutes the theory, is a distinctive language in science. It is different from all other language of science including the realistic semantics of common discourse, the nonmathematical generalizations of descriptive sciences such as physiology, and the phenomenalist semantics of mathematically expressed empirical laws of science such as Kepler’s laws. The language of theory is distinctive from nontheory language, because the nontheory language has a semantics that describes either the phenomenal or real world, while the language of theory does not have these semantics. Instead the semantics of theory language is called “symbolic”, which means that its meaning is a sign of the meanings of the nontheory language. Thus the semantics of science in Duhem’s philosophy is stratified into two levels, in which one represents the other.

The basis for Duhem’s distinguishing the semantics of theory language from that of all other language is the existence of a numerical indeterminacy caused by the fact that measurements, which may occur in the equations of theory, are always approximate. There are two reasons for the indeterminacy between the equations of theory and the nontheoretical language. The first reason is simply the approximate character of all measurements. When measurements are made, a “translation” must also be made from what Duhem called a “practical” fact to a “theoretical” fact. The practical fact describes the observed phenomena and circumstances of the experiment; the theoretical fact is the set of mathematical data that replaces the practical fact in the equations of the theory. Duhem calls the method of measure¬ment the dictionary that enables the physicist to make this translation.

For any practical fact there is always an infinity of potential theoretical facts, even when the degree of inde¬terminacy is reduced with improved instruments and measure¬ment procedures. So long as the one or several equations of a theory are correct, the numbers that are the solution set for the equations will fall within the range of measurement indeterminacy. Duhem illustrates the semantical duality caused by this numeric indeterminacy in his discussion of the different meanings of the phrase “free fall.” One meaning is contained in a phenomenal description given by any person who knows nothing about physical theory. And a second meaning occurs in the physical theory that includes the idea of uniform acceleration. These are two distinct meanings; the former may be either a realist or phenomenalist meaning, while the latter is called the symbolic meaning. The latter is a sign of the former, so long as the theory is accurate enough to be accepted as true.

However, the numerical indeterminacy that occasions the semantical distinction between practical facts and theoretical facts is not unique to the variables occurring in the equations of theories, the equations that are the conclusions drawn from the hypotheses which are the postulates of the theory. It also occurs in the variables occurring in the equations of empirical laws, the equations that are developed by experimental or other observational judgments. This creates another occasion for numerical indeterminacy, one which exists between the values of the variables in the equations of theory and the values of the corresponding variables in the equations of the empirical laws that a theory orders. Duhem discusses this numerical indeterminacy and the semantical duality to which it gives rise, when he criticizes Newton’s claim that his theory of gravitation is not based on hypotheses.

The basic question is whether or not Newton’s theory was or could be developed empirically by generalizing from Kepler’s laws. Duhem argues that Newton had actually created hypotheses, because the mathematical deduction from these hypotheses produces conclusions that formally contradict Kepler’s observational laws. In other words the solution sets for the empirical law and for the theory are not the same. Kepler’s laws are approximate, and therefore admit to an infinity of small deviations. The measurements by Tycho Brahe permit the theorist to choose a variation of Kepler’s laws, which is also produced by deduction from Newton’s theory. Just as there must be a translation from practical facts to theoretical facts resolving the indeterminacy in measurements, so too there must be a translation from empirical laws such as Kepler’s laws to “symbolic” laws such as Newton’s dynamics. Here again the numeric indeterminacy causes a semantic dualism, and a translation is made in which the new symbolic formulas derived from Newton’s hypotheses, are substituted for the old phenomenalistic formulas, which are Kepler’s observational laws.

Having shown that there are different semantics for theory and nontheory language in science, Duhem then gives two ways in which the meanings of the symbols in theory language differ from the meanings in all the other language of science. The first way, which is most important to him, is that the semantics of theory language is neither realistic nor phenomenalist; it does not describe the world of phenomena as does the semantics of empirical laws like Kepler’s laws, nor does it describe the real world as does the semantics of common-sense discourse. When Duhem states, therefore, that theories represent laws, he means to be taken literally; he means that theories do not represent the world but instead represent the empirical statements, which in turn represent the phenomenal world. Thus he cannot be called an instrumentalist in the sense that he denies that theory language has any semantics. He has stratified the semantics of science such that theory has its own higher level semantics.

He also states that when a theory agrees with experimental laws to the degree of approximation enabled by the measuring procedures employed, and furthermore when the theory correctly predicts the outcome of an experiment before the outcome has occurred, then there is reason to believe that the theory is not merely an economical representation of the experimental laws. Such a theory is also a “natural classification” of these laws in which the logical order in which the theory organizes the experimental laws is a reflection of the metaphysician’s ontological order that underlies the physicist’s phenomenal order. However, professionally the physicist cannot pass judgment on this analogical apprehension of the underlying ontological order, because this order is the proper subject only of metaphysics or natural philosophy.

The second way in which the meanings of the symbols in theory language differ from those in the other language of science is that the meanings of theory are determined by their context, by the statements that constitute the theory itself. Therefore, according to whether the physicist adopts one or another theory, the variables in the symbolic law change their meaning, so that the law may be accepted by one physicist who admits one theory while it may be rejected by another physicist who admits an alternative theory. Duhem illustrates this contextual determination of meaning in theory language in his discussion of Kepler’s observational laws and the symbolic laws of Newton’s theory. The formulas that constitute Kepler’s laws refer to orbits, but when they are replaced by the symbolic formulas that are deduced from Newton’s dynamics, the symbolic law contains variables referring to forces and masses also. The translation from Kepler’s laws into symbolic laws presupposes the physicist’s prior adherence to the hypotheses of the theory. The contextual determination of the meanings of theories is Duhem’s wholistic concept of theory, a concept that is strategic to his views about scientific criticism of theories. With his wholistic view he says theoretical physics is not like a machine but is more like an organism.

Finally it should be noted that although the higher level semantics of theory language is relatively remote from the phenomena described by the semantics of the nontheory language, nevertheless theory is not remote from the experimental situation. He states that an experiment in physics is not simply the observation of a phenomenon, but is furthermore the theoretical interpretation of it. And this theoretical interpretation is not just a technical language, but one that makes possible the use of instruments.

He illustrates this distinction between observation and interpretation in physical experiment by offering two descriptions of an experimental apparatus in a laboratory. One description is given in the vocabulary of the physicist who understands the theory of electricity, and the other description is given in the observational language of the observer innocent of such theoretical understanding. The experimenting physicist actually has two distinct representations of the instrument in his mind. One is the phenomenal image of the concrete instrument that he manipulates in reality. The other is a schematic model of the same instrument constructed mentally with the aid of the symbols from the theories that the physicist accepts. Without knowing the theories that the physicist regards as established and that he uses for interpreting the facts he observes, it is impossible for anyone to understand the meaning he gives to his statements. And when a physicist discusses his experiments with another physicist, who accepts an alternative theory, it is necessary for the two physicists to seek to establish a correspondence between their different ideas and then to reinterpret the experiment.

Twenty years before the development of the quantum theory Duhem cited as an example the two alternative theories of light: Newton’s emission theory and Frensel’s wave theory. He maintained that the observations and experiments interpreted in the concepts of one theory could be translated into the concepts of the other theory. In his philosophy this is possible, not because he anticipated quantum theory, but because he was a positivist, who believed that the two theories could be related to a common theory-neutral phenomenalist semantics.

Duhem’s stratification of the semantics of the language of theoretical science is central and strategic to his phil¬osophy of science. It is not surprising that he stated that the approximate fit between measurements and theory creates a semantical difference. Haavelmo did the same thing for his theory of econometrics forty years later. But it might seem more correct were he to have said that the resolution of the indetermi¬nacy in measurement by the calculated value for a variable in a theory actually resolves a semantic vagueness instead of saying, as he does, that it creates two distinct meanings. But it is surprising to find him concluding that the distinct meaning of the symbol in the theory is a “sign” of the phenomenal meaning defined by the experimental measurement method. It is this latter position that stratifies the semantics of science, so that theory cannot be given a realistic or phenomenalistic interpretation.

Nonetheless Duhem has a reason for taking this position. In his “The Physics of a Believer”, an appendix to Aim and Structure of Physical Theory, he reports that earlier in his career he attempted unsuccessfully to conform to Newton’s methods set forth in Newton’s “General Scholium”. He concluded that physical theory is neither a metaphysical explanation nor a set of general laws, whose validity is established, but rather that theory is an artificial construction manufactured with the aid of mathematical magnitudes. Thus the relation of the magnitudes to the abstract notion emergent from experiment is that of sign to thing signified. The key concept seems to be the idea of artificial construction. The artificial nature of theory gives it an artificial semantics, and this artificial semantics is of a different kind than the natural semantics of language that describes the phenomenal world.

Throughout most of the history of philosophy, philosophers believed that while the multiplicity of languages argues for the existence of a conventional aspect in human language, still, as Aristotle said, while men speak different languages, they have the same cognitive experiences. This is the thesis of a naturalistic semantics; all men have the same cognitive experience when in the presence of the same reality, because there is a natural relation between knowledge and reality. Mach’s theory of sensations and of their identification with elements of the phenomenal world is a contorted variation of this thesis. But Duhem could not fit this thesis to the language of physical theory, even while he, like Mach, maintained it for the language of observation. He viewed physical theory as so artifactual that its meanings could not be natural but had to be artificial. Thus physical theory does not describe either the real or the phenomenal world of nature; it only describes symbols. But he was not led to conclude that theory is meaningless. His reconciliation strategy was to make the artificial semantics of theory describe the language of science, in effect a metalanguage.

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