Abstract

The distinction itself is best explained as follows. At the empirical level (at the bottom), there are curves, or functions, or laws, such as PV = constant the Boyle’s example, or a = M/r 2 in Newton’s example. The first point is that such formulae are actually ambiguous as to the hypotheses they represent. They can be understood in two ways. In order to make this point clear, let me first introduce a terminological distinction between variables and parameters. Acceleration and distance (a and r) are variables in Newton’s formula because they represent quantities that are more or less directly measured. The distinction between what is directly measured and what it is not is to be understood relative the context. All I mean is that values of acceleration and distance are determined independently of the hypothesis, or theory, under consideration. I do not mean that their determination involves no kind of inference at all. For instance, acceleration is the instantaneous change in velocity per unit time, and this is not something that is directly determined from raw data that records the position of the moon at consecutive points in time. It is consistent with that raw data that the motion of the moon is actually discontinuous, so that the moon has no acceleration. So, there are definitely theoretical assumptions make about the moon’s motion that are used to estimate the moon’s acceleration at a particular time. But these assumptions are not unique to Newton’s theory. The same assumptions are also made by the rival hypotheses under consideration. In fact, the existence of quantities such as instantaneous acceleration is only called into question by the far more recent theory of quantum mechanics. Likewise, in the case of Boyle’s law, there is no controversy in viewing the volume of the trapped air as being determined in a way that does not make use of the theory that Boyle is introducing.