known as The History of Mechanics. This book went through nine editions both in German and in English, seven of which were published in Mach’s lifetime. The physicists whose works Mach examined were not phenomenalists, and he set out to write a critical history of mechanics from the perspective of his own phenomenalist philosophy of science. As he stated in the introduction to the first edition, the book’s purpose is to clarify ideas, reveal the real significance of the matter, and to purge physics of its metaphysics. For Mach this agenda amounted to purging physics of theory. With this aim in mind he critiqued the contributors of the past as he salvaged and reconstructed what he found in their works to be of lasting value. Even the achievements of the great Isaac Newton did not escape his phenomenalist criticism unscathed. Mach criticized Newton’s principle of reaction, his concept of mass, and his concepts of absolute space and absolute time. Starting from his own view that all phenomena are related, Mach concluded contrary to Newton that all masses, all velocities, and all forces are relative, a thesis known as Mach’s phenomenalistic relativity. And he proposes his own set of definitions and empirical propositions to replace Newton’s. The outcome of this criticism was to have a large impact on the histories of both philosophy of science and physics.
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 measurement the dictionary that enables the physicist to make this translation.
For any practical
