ERNST MACH AND PIERRE DUHEM ON PHYSICAL THEORY
BOOK II - Page 3
Duhem's Philosophy of Science
The Aim of Science
Duhem’s statement of the aim of science is similar to Mach`s:
the aim of science is economy of thought. Like Mach, Duhem
believes that experimental laws contribute an intellectual
economy, because they summarize a large number of individual
facts including data measurements. But unlike Mach, Duhem
furthermore says that theories also contribute to the
realization of the aim of science. The economy achieved by the
substitution of a law for individual facts is redoubled for the
mind, when the mind substitutes theories for the numerous
mathematically expressed experimental laws. A theory is a system
of mathematical propositions mathematically derived from a small
number of principles, which aim to represent as simply, as
completely, and as exactly as possible, a set of experimental
laws. Its aim in other words is economy of thought by
schematically representing and logically organizing experimental
Duhem developed a sophisticated theory of scientific criticism, and it is central to his philosophy of science. He is very emphatic in defending the autonomy of empirical science from any encroachment by metaphysics or natural philosophy. Metaphysics pertains to realities that underlie the phenomenal appearances hidden by the phenomena, while science pertains only to these appearances. Consequently whatever may be the criteria and procedures for criticizing a metaphysical thesis, they are not relevant to empirical science. In empirical sciences that are nonmathematical, the generalizations such as “Every man is mortal” may be accepted or rejected as simply true or false. But in mathematical physics the equations both of the empirical laws and of the hypothetical theories are not simply regarded as true or false, but are approximate. The amount of underdetermination due to the approximate nature of the values of the variables in these equations will be reduced as experimental and measurement techniques improve. And because measurement instruments depend on physical theory, the improvement in instruments occurs due to the improvement in theory. As the range of this indeterminacy becomes smaller, the equations of either the empirical laws or the hypothetical theories that represent the laws may no longer be able to predict values for their variables that fall within the smaller range of measurement error. When this happens, the equations are no longer satisfactory. Duhem maintains that the only criterion that may validly operate in scientific criticism is the ability of the law or theory to make accurate predictions. This exclusion of all prior ontological or metaphysical criteria from scientific criticism has been carried forward into the contemporary pragmatist philosophy of science. It shows up for example as Quine’s rejection of all “first philosophy.”
In his theory of scientific criticism Duhem rejected the use of so-called crucial experiments as a means of establishing the validity of a theory. His thesis is that if the physicist is confronted with several alternative theories, the rejection of all but one cannot imply the establishment of the remaining one. As an example he cites the two alternative theories of light: one theory is the hypothesis that light is a stream of high speed projectiles, and the other is the hypothesis that light consists of vibrations whose waves are propagated in ether. This is not an anticipation of the Copenhagen duality thesis; Duhem is thinking of the wave and particle theories as alternative theories. His position is that the choice is not mutually exclusive, because no one can ever enumerate completely all of the various hypotheses, which may pertain to a group of phenomena. He thus maintains that several alternative theories may fall within the range of indeterminacy of the measurement data and experimental laws, so that more than one theory may be satisfactory. This represents a pluralistic thesis about science, and in the crucial experiment discussion, it means that even if all hypotheses could somehow be enumerated, elimination could not leave but one to be considered as established. This pluralism is another aspect of his philosophy of physical theory that has been carried forward into the contemporary pragmatist philosophy of science.
His theory of scientific criticism also reflects his wholistic view of theories. This wholistic view not only makes the meanings of the mathematical symbols mutually determined by the context consisting of the equations of the theory, it also necessitates testing the theory as a whole together with all the hypotheses used in the experiment including assumptions about the measuring instruments. Thus if the prediction in the test is wrong, not only may the proposition being tested be at fault, but also the whole theoretical scaffolding used by the physicist. The physicist can never subject an isolated hypothesis to experimental test, but only a whole group of hypotheses. The only thing that the experiment reveals is that among all the theoretical propositions used to predict the phenomenon, there is at least one error. Thus the failure of the prediction does not inform the physicist where the error lies or reveal which hypothesis should be modified.
In Duhem’s view physics is not like a machine which lets itself
be disassembled; the physicist cannot test each piece in
isolation and then make adjustments to the isolated part found
wanting. Duhem compares physics to an organism in which one part
cannot be made to function except when the parts that are most
remote from it are called into play. When there is a malfunction
felt in the organism, the physician must ferret out through its
effects on the entire system, the organ that needs to be
remedied or modified without the possibility of isolating the
organ and examining it apart. Duhem says that the physicist
confronted with a failed prediction is more like a physician
than a watchmaker.
Duhem also has a philosophy of scientific discovery. Unlike Mach’s view on discovery and invention in science, Duhem’s is not principally a theory of perception and empirical generalizations. He anticipates later philosophers including the logical positivists with his emphasis on the language of science. For him scientific discovery is not reduced to noticing what had previ¬ously been overlooked in perception; for him discovery is also the construction of hypothetical theories.
The construction of a theory involves four successive
operations: Firstly certain physical properties are taken as
simple, so that other things are combinations of these simple
properties. These properties are not simple in any absolute
sense like Mach’s elements, but are taken as simple only for
purposes of the theory. The simple properties are measured, and
the magnitudes are assigned to symbolic variables. Secondly the
magnitudes are connected by propositions, i.e.,
equations that are hypotheses, and that serve as postulates of
the deductive system. Thirdly the postulates are not realistic
or phenomen¬alist, but are freely created; using them requires
only that the logic of algebra be correctly applied for making
deductions. Fourthly the conclusions drawn from the postulates
are compared with the experimental laws that the theory is
intended to represent and organize.
If the conclusions agree with the laws within the degree of approximation corresponding to the measurements taken in the experiments, then the theory is said to be an acceptable theory. Such acceptable theory may in turn be used for the further development of measuring instruments used in experiments, as well as constituting the final product of the scientific endeavor with its maximum economy. Improved theory produces improved instruments, which in turn produce better measurements. These better measurements reduce the range of the indeterminacy in the numerical data, which may cause the theories to fail in their predictions. Such failure will occasion two types of responses. The initial response is to modify the theory with corrections, which will enable the predictions made with the theory to fall within the smaller range of indeterminacy produced with improved measurements. But these corrections also complicate the theory, and in due course “good sense” may lead some physi¬cists to decide to refrain from adding more complicating corrections, and instead attempt to revise the hypothetical postulates of the symbolic schema, i.e., of the whole theory itself. The accomplishment of such a revision is the work of the genius.
But Duhem does not subscribe to the heroic concept of invention; history creates the genius as much as the genius creates history. The physicist does not choose the hypotheses on which he will build a new theory; the theory germinates within him. This germination is not sufficiently explained by the contemplation of the experimental laws that the theory must represent. It is a larger cultural development. In due course when the cultural process that he calls universal science has prepared minds sufficiently to receive a new theory, it arises in a nearly inevitable manner. Often physicists who do not know one another and who are working great distances from one another, generate the same theory at the same time. In the course of his studies the historian of science according to Duhem often observes this simultaneous emergence of the same theory in countries far from one another.
On Duhem’s philosophy theories do not explain the laws nor do the laws explain the facts. Explanation is proper only to metaphysics and not to science. In the opening sentence of the introduction to his Aim and Structure of Physical Theory, Duhem says that he offers a simple logical analysis of the method by which physical science makes progress. While affirming the autonomy of physics with his thesis that agreement with experiment is the sole criterion of truth for a physical theory, Duhem has a distinctive concept of scientific progress, which he elaborates in the appendices to the book.
He says that there are two types of development in physics that are occurring simultaneously. One is what today would be called the revolutionary type of development consisting of a succession of alternative theories, in which one theory arises, dominates the scene for the moment, and then collapses to be replaced by another theory. The other is an evolutionary progress in which more ample and more precise mathematical representation of the phenomenal world is constantly disclosed by experiment. When the progress of experimental science goes counter to a theory and compels the theory to be modified or transformed, the purely representative part enters nearly whole into the new theory, bringing to it the inheritance of all the valuable possessions of the old theory, while the hypothetical part falls away in order to give way to another theory. The first type is identified with the mechanistic physical systems including Newtonian physics as well as Cartesian and atomic physics. The second type is identified with general thermodynamics, which Duhem believes will lead physical theory toward its goal.
Duhem believes that the goal of physics is the convergence toward an analogy with Aristotle’s physics. He concludes in his discussion of the value of theory, that the physicist is compelled to recognize that it would be unreasonable to work for the progress of physical theory, if theory were not the increasingly better defined and more precise reflection of a metaphysics. He thus concludes his book with the thesis that belief in an order transcending physics is the ultimate metaphysical justification of physical theory.
Duhem's History of Physics
Just as Mach had written a history of physics viewed through the lenses of his philosophy of science, so too did Duhem. However, Duhem's effort was relatively monumental; it is a work originally intended to be twelve volumes of which ten were actually written before its author's death in September 1916. This magnum opus was his System of the World: A History of Cosmological Doctrines from Plato to Copernicus. The central thesis of this work is summarized in a much smaller book begun earlier, To Save the Phenomena: An Essay on the Idea of Physical Theory from Plato to Galileo (1908). The thesis is that the hypotheses of physics and especially the heliocentric hypothesis in astronomy are mere mathematical contrivances for the purpose of saving the phenomena.
Pope Urban VIII condemned Galileo in 1633 for maintaining that Copernicus’ heliocentric theory is not merely a mathematical contrivance, but is rather a description of the real world. Formerly known as Cardinal Bellarmine, this Pope maintained that regardless of how numerous and exact may be the confirmations of a theory by experience, these confirmations can never transform a hypothesis into a certain truth that can be taken realistically, since this transformation would require that the experimental facts should contradict any other hypotheses that might be conceived, a requirement that cannot logically be satisfied. Galileo, on the other hand, maintained that because Copernicus’s theory saved the phenomena more adequately than any alternative hypothesis, the Copernican theory had to be a realistic one.
Contemporary pragmatists agree with Duhem’s rejection of any prior ontological criteria for the criticism of scientific theory, but contrary to Duhem they furthermore agree with Galileo’s practice of ontological relativity, i.e., scientific realism. Contemporary pragmatists are realists, who let the most empirically adequate theory decide the ontology. Galileo’s argument for realism is the same as Quine’s doctrine of ontological relativity, and Feyerabend calls it the Galileo-Einstein tradition of realism. And Heisenberg invoked this tradition, when he referenced Einstein’s realistic interpretation of relativistic time in the relativity theory, and then used it as a precedent for his own realistic interpretation of the quantum theory’s duality thesis, notwithstanding Bohr’s instrumentalist complementarity principle. Duhem, however, denied that theory is realistic, and he construed Galileo’s argument as a case of the fallacy of the crucial experiment; he argued that it is impossible to enunciate all the possible hypotheses, and establish the truth of one by elimination of all others. The accomplishment that Duhem credits to Kepler and Galileo is the rejection of Aristotle’s view that celestial and terrestrial physics are fundamentally different, and that hypotheses of physics must save all the phenomena of the inanimate world.