Abstract

An intuitive idea concerning degrees of precision is widely accepted, and it is that we increase precision of theories by paying attention to ever decreasing orders of magnitude of measurements which we incorporate in these theories. We increase precision of measuring or of predicting measurement of length, for instance, if we pay attention not only to centimeters but also to millimeters, microns, angstroms, and so on. And our theories are precise to centimeters, then to millimeters, and so on respectively. The idea is that increased precision is the process of capturing a point within nested intervals, and that this is reflected both in experimental and in theoretical progress. An intuitive analogy may be drawn with series of photos made by a camera which approaches the moon's surface. A corollary from this intuitive idea which has been stated by a number of writers is that observation reports and theories are not overthrown even when superseded by more accurate observation because within the limits of their own precision-range they are still valid. When a law in physics is stated, it is stated usually without such qualifications; but this is a mere matter of convenience, we are told. The idea is that a tacit proviso is understood and the law should be understood to be not the statement “such and such is the case” but the statement “within this and that limit of accuracy such and such is the case”; in such a formulation, the law, once verified, remains unshaken regardless of further progress in the field.