Here - Paul Barrett

Theories of MeasurementWhat Stevens did was to remove the status of anumerical relation system consisting of the realnumbers as an independently existing empiricalrelation system. Up until the 1950s, numberswere considered to constitute an empiricalrelational system in their own right. The systemwas self-contained, logical, possessed therequired ordering relations that constitute bothordinal and additive operations, and, in thetheory of continuous quantity, sustained thenecessary ratios necessary for such a theory. Theories of MeasurementIn short, both in the manner that scientists usedthem, as well as in their existence as a relationalsystem, numbers were considered as empiricalfacts, not abstract entities.The existence of the empirical relations betweenmagnitudes of quantity (as in the axioms ofHölder (1901) detailed above) was presumedlogically independent of the numericalassignments made to represent them.MGMT 740 – 841th March 2006 MGMT 740 – 842th March 2006 Theories of MeasurementIn order to assign a numerical relational system toan empirical relational system, it was required thatthe empirical relations could first be identifiedwithout necessarily assigning numbers to objectswithin the system. It was a prior requirement thatwhether or not an empirical relation possessescertain properties was a matter for scientificinvestigation. As Michell (1999), p. 168 states …“Simply to presume that a consistent rule forassigning numerals to objects represents anempirical relation possessing such properties is notto discover that it does; it is the opposite”. Theories of MeasurementFor, what Stevens was really saying is that it isnot the independently existing features ofobjects (the properties or relations of objects)that are represented in measurement, but ratherit is the numerical relations imposed by aninvestigator which will then determine theempirical relations between objects. This isquite wrong.MGMT 740 – 843th March 2006 MGMT 740 – 844th March 2006