Suppes’s outlines of an empirical measurement theory

According to Suppes, measurement theory, like any scientific theory, should consist of two parts, a set-theoretical defined structure and the empirical interpretation of that structure. An empirical interpretation means the specification – ‘coordinating definitions’ – of a ‘hierarchy of models’ between the theory and the experimental results. But in the case of measurement theory, he defined the relationship between numerical structure and the empirical structure specifically in terms of homomorphism. This is rather a highly restrictive relation between models, and therefore he never succeeded in giving his measurement theory empirical content. This paper discusses what an empirical measurement theory will look like if we would use less restrictive ‘coordinating definitions’ to specify the relationships between the various models.