ERNST MACH AND PIERRE DUHEM ON PHYSICAL THEORY
BOOK II - Page 1
This BOOK examines two variations on positivism formulated by two turn-of-the-twentieth-century physicists, Ernst Mach and Pierre Duhem. And it previews the story of positivism’s rejection by the physicists who made the two great scientific revolutions in twentieth-century physics, Einstein and Heisenberg.
Ernst Mach (1838-1916) is a representative figure of the early positivist philosophy of science in physics at the turn of the twentieth century. He earned a doctorate in physics from the University of Vienna in 1860, taught experimental physics for most of his career at the University of Prague (1867-1895), and then held the chair of Inductive Philosophy at the University of Vienna (1895-1901). He was several times nominated for the Nobel Prize. He set himself the philosophical task of implementing the phenomenalist philosophy of David Hume in physics while Newtonian mechanics still prevailed in physics.
Prior to contemporary pragmatism philosophers based their philosophies of science on one or another metaphysical viewpoint. Though positivists philosophers including Mach were explicitly “antimetaphysical” (Mach even denied that he was a philosopher), they were actually advocating their own metaphysics while labeling the views they opposed as “metaphysical”, and used the term pejoratively. Positivism is a philosophy that evolved in reaction against the various romantic philosophies, and what the positivists meant by “metaphysics” was the metaphysics of the romantics. Just as the views of the romantics evolved from the philosophical tradition of the rationalists, similarly those of the positivists evolved from the tradition of the empiricists. Thus Mach’s epistemology is very similar to the views of the empiricists Berkeley and Hume, and he explicitly expressed indebtedness to them in his works.
Mach’s principal work setting forth his phenomenalist philosophy is his Analysis of Sensations (1885), which went through five editions in both German and English, although Mach also discussed his epistemological views in many of his other works. His epistemology postulates “elements” such as individual sounds, temperatures, pressures, spaces, times, and colors. When these elements are considered in relation to one another, they are studied by the physical sciences, and when they are considered in relation to the human mind or rather the nervous system of the human body, they are called “sensations” and are studied by psychology.
One of the central theses of Mach’s Analysis of Sensations is that the only difference between elements and sensations is the aspect under which they are viewed, and that physics and psychology therefore have the same subject matter. The distinction between the physical and the psychical is entirely a matter of convenience or practicality, because everything is merely a function of these elements. Everything other than these elements is a mental construct consisting of complexes of sensations. All material things including our own bodies and even the ego are nothing but complexes of elements that are constructs made by the human mind and that have some fixedness or constancy in sense experience.
A fundamental thesis of Mach’s philosophy is that material bodies do not produce sensations, but rather complexes of sensations are associated together by the human mind to produce material bodies. Ultimately all that is valuable in science is the discovery of functional relations of dependency of sensations upon one another. The constancies that enable our mental construction of physical bodies have no privileged reality status. This is even more so with such mental constructs as the physicists’ molecules and atoms, which are mental constructs that unlike those of physical bodies are not found in experience. The positivist phenomenalist philosophy is a nonrealist metaphysics, and if it is generously said to have an ontology, the ontology consists merely of the phenomenal elements/sensations.
Mach's Philosophy of Science
Aim of Science
Mach’s philosophy of science is rich enough that it addresses
all the four basic topics conventionally considered in a
philosophy of science: the aim of science, discovery, criticism
and explanation. He offers several statements of the aim of
science. One sets forth the “biological task of science”, which
is to provide the fully developed human individual with as
perfect a means of orienting himself as possible. In a second
statement he says that the aim of all science is the
representation of facts in thought either for practical purposes
or for removing intellectual discomfort, since every practical
and intellectual need is satisfied when our thoughts can
represent the facts of the senses completely. He adds that our
knowledge of a phenomenon of nature is as complete as possible,
when thoughts are set before the mind’s eye such that all the
relevant sensible facts can be regarded as a substitute for the
phenomenon itself. Then the facts appear to be familiar and are
not able to occasion any surprise. In a third statement he says
that the goal of science is the simplest and most economical
abstract expression of facts. The noted economy of science
involves uncompleted facts, judgments or laws. The last two
statements of the aim of science are contained in Mach’s
philosophy of scientific explanation.
Mach set forth his theory of scientific explanation in many places including his Analysis of Sensations, his “The Economical Nature of Physical Inquiry” (1882) and “On the Principle of Comparison in Physics” (1894) reprinted in his Popular Scientific Lectures (1898). He says that explanation is the economical description of experience in terms of elements. When we examine facts for the first time they appear confusing. In time we discover simple stable elements out of which we can mentally construct the entire factual domain, and when we have reached the point where everywhere we can discuss the same facts with other persons, then we no longer feel lost and the phenomenon is explained. The explanation offers a survey of a given domain of facts with the least expenditure of thought. The representation of all the facts of a domain by one single mental process is economical. He adds that the greatest perfection in mental economy occurs when science uses mathematics.
Not all descriptions are explanations; only direct descriptions
can be explanations, while theories on the other hand are
indirect descriptions and are not explanations. Direct
descriptions may be either complete or incomplete. Description
of what is presently observed is a complete description.
Incomplete description refers to what is presently unobserved
but observable and what is associated by a law, as for example
the movement of a comet that is presently unobserved or the body
of a man who disappears behind a pillar. The incomplete
description can be completed by the human mind by means of the
associations made by a scientific law. A direct description is
one in which a single feature of resemblance among facts is
called from memory, while a theory such as the description of
light as a wave motion is an appeal to another description that
had previ¬ously been made elsewhere. A theoretical idea offers
more than what we actually observe in a new fact. It can be used
to extend a fact and enrich it with features, which we are
firstly induced to seek from its suggestions and, which are
often actually found. A theory may lead to discoveries, but the
adoption of a theory always carries a danger: even the most
fruitful theory may be an obstacle to inquiry. By way of example
Mach says the theory that light is an undifferentiated straight
line of particles impeded the discovery of the periodicity of
light. The ideal of a given domain of facts is direct
description; such description accomplishes all that the
scientific investigator could wish.
In the Analysis of Sensations Mach states that he has taken Hume as his starting point, and this starting point is reflected in his views on scientific criticism. The scientist like everyone else knows the elements with complete certainty as sensations. But scientists and other persons also make judgments that are laws or generalizations. Since the aim of science is the adaptation of thoughts to facts, a new fact may require a new adaptation, which finds its expression in the operation of judgment. A judgment is the supplementing of a sensational presentation, in order to repre¬sent more completely a sensational fact. In the adaptation of thoughts to facts the adaptation can be made only to what is constant in the facts. Only the mental construction of constant elements can yield economy. But our confidence in the constancy in our judgments or generalizations rests entirely on the supposition, which in a given case has been substantiated by numerous trials, that our mental adaptation is sufficient. And we must be prepared to find this supposition contradicted at any moment.
Therefore empirical laws as well as theories are provisional in
Mach’s view, but for different reasons. The empirical
generalizations are provisional, because they impute constancies
to an infinite number of individual occurrences of sensations
while only a limited number have actually been experienced. On
the other hand theories postulate things that have never been
experienced; no one for example has ever (in Mach’s time)
actually seen atoms or molecules nor has anyone ever experienced
Newtonian absolute space or absolute time. Mach did not seem to
find the provisional status of empirical laws to be very
disturbing and in fact he considered laws to be necessary for
science to have its economy. But he considered the provisional
status of theories to be an unsatisfactory expediency for
science. His philosophy of scientific criticism includes a
phenomenalist criterion that rejects theories. Initially the
logical positivists who followed Mach were reluctant to accept
Hume’s skeptical views on scientific criticism, and instead
accepted the idea of “verification”, the view that scientific
laws or empirical generalizations can be established in some
permanent sense, an idea that historically had been definitive
of truly scientific knowledge. But Carnap and the logical
positivists moved toward Mach’s acceptance of scientific laws as
provisionally true instead of permanently true, even as they
moved away from his phenomenalism.
Unlike most other philosophers, Mach’s concept of scientific discovery does not involve the idea of theory development. In his “The Part Played by Accident in Invention and Discovery” (1895) in his Popular Scientific Lectures Mach notes the importance of accident in invention and discovery, but maintains that the inventor is not passive. In fact Mach compares the discoverer to the artist. He says that no man should consider attempting to solve a great problem unless he has thoroughly saturated his mind with the subject, so that everything else recedes into relative insignificance. Then the discoverer can detect the uncommon features in an accidental occurrence and their determining conditions. Mach believed that it is the idea that dominates the thinking of the inquirer and not vice versa. The movement of thought obeys the laws of association, and in a mind rich with experience every sensation is connected with so many others that the course of thought is easily influenced by apparently insignificant circumstances, the accidental occurrence of which turn out to be decisive.
Therefore there is a process of discovery, and Mach considered how this process could be guided. He explicitly rejected any combinatorial approach as too laborious and extensive. The man of genius in Mach’s view consciously or unconsciously pursues systematic methods, and in his deliberate presentiment he omits many alternatives and abandons others after hasty trial, alternatives on which less endowed minds would squander their energies. From the abundance of fancies that a free and active imagination produces, there emerges one particular configuration, which fits perfectly with a basic design or idea. Mach does not elaborate further upon this process; and while he believes that it may be guided, he does not propose any consciously repeatable procedure. Perhaps he could go no further in this investigation, because he also believed in gestalt qualities and accepted a wholistic view of complexes of sense impressions. In any event his belief that the process can be guided leads him to conclude that genius may be regarded as only a small deviation from the average mental endowment. He states that the way to discovery must be prepared long beforehand, and that in due course the truth will make its appearance inexorable as if by divine necessity. Apparently therefore he rejected the heroic theory of invention.
Mach's History of Mechanics
Mach’s most popular work was his Science of Mechanics: A Critical and Historical Account of Its Development (1883) also 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.