Abstract

One can conclude then that in some instances theories are invoked in introducing quantitative concepts into science, even when the concept is treated as though it had been introduced by fundamental measurement. On the other hand, one sees in Maxwell an instance of fundamental measurement that does not invoke theory. It is not the case either that all our metric concepts are theory-laden or that they are theory-free. We must look to individual cases to discover how measurement functions in science. ;I have looked at two examples of the measurement of electric charge, one quantity thought to be measurable fundamentally. Charles Augustin Coulomb is often credited with having quantified the notion of electric charge in the course of determining the force law for electrified bodies. This quantification, however, was established not by fundamental measurement, but by an application to charged bodies of Newton's theoretical arguments concerning mass and gravitational forces. Coulomb treats charge as though it had been measured fundamentally. His quantitative concept of charge is thus theoretical. James Clerk Maxwell , in the course of setting out a theory of electricity and magnetism, present several experiments that constitute a fundamental measurement of charge. Although this concept is presented in the context of a theory, it does not appear to be theoretical. ;Classical physics presents some theories and concepts whose development is recent enough and well enough within our view that we can hope to understand the relations between them. The development of the science of electromagnetism from the initial work of William Gilbert has taken place within the past four hundred years. In philosophical accounts of measurement, it is often noted that there are a number of electrical quantities that might be measured by fundamental measurement, but the quantities actually considered are usually mass, length and, occasionally, time, quantities whose historical development is much more remote from us. ;The first account of fundamental measurement, given by Norman Campbell, sets out four principal features of this way of devising measurement scales: that, by experiment, first, bodies can be placed in a quasi-serial order with respect to the property, and secondly they can be combined to yield other bodies having that property; thirdly, that numbers can be assigned by using the correspondence of the combination operation to the arithmetic operation of addition; and fourthly, that this measurement procedure does not require the measurement of other properties. These features are thought to have the result that such a quantitative concept can take at least the rational numbers as values, and that it can be mathematically developed in science. ;The problem considered in this paper is: Is fundamental measurement as independent of scientific theory as the account, given above, presumes? My aim is to explore whether theories are invoked by the procedures for fundamental measurement. My aim is also to explore the nature of the connection of scientific theories to fundamental measurement, for it has been argued against Campbell that all the important quantitative concepts, for example, length and mass, are theory-laden or devised along with theories. I have examined the plausibility of these arguments as well as two particular cases of measurement from the history of physics. ;Fundamental measurement is presumed, in a number of philosophical discussion of measurement, to present two indispensable cornerstones for mathematical physics. It is understood to ground the representation of properties by numbers and thereby their mathematical development in science, first, by its direct application, and, secondly, by its indirect use in defining other properites. It appears then that without fundamental measurement there would be no mathematical physics