The Methodological Arguments of Mach’s Economy of Science

Lydia Patton

Virginia Tech

In the chapter “The Economy of Science” of Ernst Mach’s 1883 The Science of Mechanics, Mach defends a “biological-economical”, naturalist account of scientific knowledge. According to this account, the aim of science is “to replace” or “save” experiences by the use of memory and anticipation. Science allows humans to orient themselves to experience in as economical a manner as possible. Along these lines, Mach rejects the argument that laws of nature are or depict real relations. According to Mach, “There is no law of refraction in nature, only different cases of refraction”; the law is a rule for organizing our experience using memory, not the basis of a description of reality or of nature. One might object that using science to orient oneself to future experience requires at least tacit acceptance of the view that the relationship represented by a law or principle picks up on a real regularity or uniformity in nature. Otherwise, why would an economical theory work as a way to orient oneself in nature, and to the future? Mach gives at least two arguments in the chapter that would reply to this objection. The first has to do with the epistemological and ontological character of mathematics, as a means of codifying regularities and relationships. “Numerical operations,” Mach argues, are “independent of the objects operated on,” and so a law, like the law of refraction, that is essentially a mathematical equation is an economical principle in Mach’s sense, and is independent of the character of the objects or elements of experience it organizes. The second argument is the main focus of this talk: a methodological argument, according to which the principles and laws of science are heuristic guides to experimental inquiry into nature, not descriptions of the characteristics of nature itself. This methodological role for principles and laws is a stimulus for Mach’s rejection of the claim that laws and principles reflect or depict real relationships in nature. Mach’s methodological argument has at least two facets. One is practical, having to do with the role of posited mathematical and lawlike relationships, or “conceptions,” in setting up experiments. The other is theoretical, having to do with the independence of hypotheses about new phenomena from the properties of the phenomena themselves. Mach’s view of theory change and discovery informs his account of theory assessment: for Mach, scientific principles and laws are used as heuristic “conceptions,” not to describe nature’s independent properties. His argument in the chapter constitutes a skeptical objection to accounts according to which the progressive unification, simplification, or mathematization of science is an indication of its tendency to depict real relationships in nature. I weigh the strength of Mach’s objection against accounts by his approximate contemporaries, Heinrich Hertz and Auguste Comte. Finally, I (very briefly) indicate the relevance of Mach’s work in this direction to the development of early philosophical interpretations of the theory of relativity.