ABSTRACT
The business of pinning numbers on things has become a pandemic activity in modern science and human affairs. An analogous story can be told of measurement. The fact that numerals can be assigned under different rules leads to different kinds of scales and different kinds of measurement, not all of equal power and usefulness. The final divorcement between the formal, abstract, analytic system and the empirical questions that originally sparked its development has clarified the relation between mathematics and measurement. Both fundamental measurement and derived measurement usually result in ratio scales, which are invariant under multiplication by a constant. The fourfold classification of scales of measurement provides a convenient framework on which to display some of the common statistical measures. One interesting possibility would be to base a scale of measurement on the three empirical operations: determination of equality, determination of greater or less, and determination of equal ratios.
