On the theory of uniqueness in measurement

This paper describes problems in the theory of uniqueness which occur when there are two different measurement homomorphisms f and g with g not attainable from f by a transformation on the range of f. In this case, the theories of scale type and of meaningfulness of statements using scales are in trouble. It is shown that unless extreme care is taken in the definitions, it is possible for two measurement homomorphisms of the same fixed relational system to have different scale type and it is possible for seemingly meaningless statements to be judged meaningful.