Metrology in general and measurement theory in particular, have grown from various roots into fields of great diversity in the natural and social sciences, engineering, commerce, and medicine. Informally, and in its widest empirical sense, a measurement of a property, exhibited by stereotype objects in variable degrees or amounts, is an objective process of assigning numbers to the objects in such a way that the order-structure of the numbers faithfully reflects that of degrees or amounts of the measured property. Measuring instruments with pointers and calibrated scales for reading are the basic empirical means by which numerical assignments are realized. Abstractly, a particular way of assigning numbers as measures of extents of a property in objects is called a quantity scale. In the natural sciences, the results of measurement on a quantity scale are expressed in the form of denominate numbers, each...